%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG017^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:45:23 AM UTC 2026
% Result : Theorem 54.09s 17.40s
% Output : Refutation 121.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG017^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n004.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:31:07 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.18/0.96 % (1607940)Will run a generic schedule for satisfiability detection.
% 4.18/0.96 % (1607957)dis+10_1_sil=32000:sp=arity:random_seed=1579203503:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.18/0.96 % (1607955)% WARNING: option uhcvi not known.
% 4.18/0.96 % (1607954)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=674606471_2999 on theBenchmark for (2999ds/0Mi)
% 4.18/0.96 % (1607955)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2808328975:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.18/0.96 % (1607960)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=441901204:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.18/0.96 % (1607956)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4270851879:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.18/0.96 % (1607958)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=216781574:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.18/0.96 % (1607957)Instruction limit reached!
% 4.18/0.96 % (1607957)------------------------------
% 4.18/0.96 % (1607957)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.18/0.96 % (1607957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/0.96 % (1607957)CaDiCaL version: 2.1.3
% 4.18/0.96 % (1607957)Termination reason: Instruction limit
% 4.18/0.96 % (1607957)Termination phase: Function definition elimination
% 4.18/0.96 % (1607957)Time elapsed: 0.021 s
% 4.18/0.96 % (1607957)Peak memory usage: 10 MB
% 4.18/0.96 % (1607957)Instructions burned: 105 (million)
% 4.18/0.96 % (1607959)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2147087774:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.18/0.96 % (1607969)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3386737849:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.18/0.96 % (1607955)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.18/0.96 % Exception at run slice level
% 4.18/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.18/0.96 % (1607960)Instruction limit reached!
% 4.18/0.96 % (1607960)------------------------------
% 4.18/0.96 % (1607960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.18/0.96 % (1607960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/0.96 % (1607960)CaDiCaL version: 2.1.3
% 4.18/0.96 % (1607960)Termination reason: Instruction limit
% 4.18/0.96 % (1607960)Termination phase: Property scanning
% 4.18/0.96 % (1607960)Time elapsed: 0.058 s
% 4.18/0.96 % (1607960)Peak memory usage: 11 MB
% 4.18/0.96 % (1607960)Instructions burned: 159 (million)
% 4.18/0.96 % (1607958)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.18/0.96 % (1607955)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.18/0.96 % (1607959)Instruction limit reached!
% 4.18/0.96 % (1607959)------------------------------
% 4.18/0.96 % (1607959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.18/0.96 % (1607959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/0.96 % (1607959)CaDiCaL version: 2.1.3
% 4.18/0.96 % (1607959)Termination reason: Instruction limit
% 4.18/0.96 % (1607959)Termination phase: Property scanning
% 4.18/0.96 % (1607959)Time elapsed: 0.050 s
% 4.18/0.96 % (1607959)Peak memory usage: 10 MB
% 4.18/0.96 % (1607959)Instructions burned: 133 (million)
% 4.18/0.96 % (1607971)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3018516435:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 4.18/0.96 % Exception at run slice level
% 4.18/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.18/0.96 % (1607972)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=175503000:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 4.18/0.96 % (1607973)ott-21_1_sil=16000:fs=off:random_seed=3234350812:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 4.18/0.96 % (1607958)Instruction limit reached!
% 4.18/0.96 % (1607958)------------------------------
% 4.18/0.96 % (1607958)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.18/0.96 % (1607958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.89/2.90 % (1607958)CaDiCaL version: 2.1.3
% 17.89/2.90 % (1607958)Termination reason: Instruction limit
% 17.89/2.90 % (1607958)Termination phase: Property scanning
% 17.89/2.90 % (1607958)Time elapsed: 0.076 s
% 17.89/2.90 % (1607958)Peak memory usage: 10 MB
% 17.89/2.90 % (1607958)Instructions burned: 117 (million)
% 17.89/2.90 % (1607975)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1362472536:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 17.89/2.90 % (1607971)Instruction limit reached!
% 17.89/2.90 % (1607971)------------------------------
% 17.89/2.90 % (1607971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.89/2.90 % (1607971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.89/2.90 % (1607971)CaDiCaL version: 2.1.3
% 17.89/2.90 % (1607971)Termination reason: Instruction limit
% 17.89/2.90 % (1607971)Termination phase: Property scanning
% 17.89/2.90 % (1607971)Time elapsed: 0.026 s
% 17.89/2.90 % (1607971)Peak memory usage: 11 MB
% 17.89/2.90 % (1607971)Instructions burned: 134 (million)
% 17.89/2.90 % (1607980)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2384623162:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 17.89/2.90 % (1607978)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3382346833:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 17.89/2.90 % (1607972)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 17.89/2.90 % (1607972)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 17.89/2.90 % (1607973)Instruction limit reached!
% 17.89/2.90 % (1607973)------------------------------
% 17.89/2.90 % (1607973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.89/2.90 % (1607973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.89/2.90 % (1607973)CaDiCaL version: 2.1.3
% 17.89/2.90 % (1607973)Termination reason: Instruction limit
% 17.89/2.90 % (1607973)Termination phase: Saturation
% 17.89/2.90 % (1607973)Time elapsed: 0.068 s
% 17.89/2.90 % (1607973)Peak memory usage: 11 MB
% 17.89/2.90 % (1607973)Instructions burned: 182 (million)
% 17.89/2.90 % (1607983)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1825091468:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 17.89/2.90 % Exception at run slice level
% 17.89/2.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.89/2.90 % (1607985)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3158171271:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 17.89/2.90 % Exception at run slice level
% 17.89/2.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.89/2.90 % (1607987)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1984699933:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 17.89/2.90 % (1607987)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 17.89/2.90 % (1607985)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 17.89/2.90 % (1607975)Instruction limit reached!
% 17.89/2.90 % (1607975)------------------------------
% 17.89/2.90 % (1607975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.89/2.90 % (1607975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.89/2.90 % (1607975)CaDiCaL version: 2.1.3
% 17.89/2.90 % (1607975)Termination reason: Instruction limit
% 17.89/2.90 % (1607975)Termination phase: Saturation
% 17.89/2.90 % (1607975)Time elapsed: 0.219 s
% 17.89/2.90 % (1607975)Peak memory usage: 13 MB
% 17.89/2.90 % (1607975)Instructions burned: 479 (million)
% 17.89/2.90 % (1607989)fmb+10_1_sil=64000:random_seed=3301805541:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 17.89/2.90 % (1607972)Instruction limit reached!
% 17.89/2.90 % (1607972)------------------------------
% 17.89/2.90 % (1607972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.89/2.90 % (1607972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.89/2.90 % (1607972)CaDiCaL version: 2.1.3
% 17.89/2.90 % (1607972)Termination reason: Instruction limit
% 17.89/2.90 % (1607972)Termination phase: Saturation
% 17.89/2.90 % (1607972)Time elapsed: 0.264 s
% 17.89/2.90 % (1607972)Peak memory usage: 14 MB
% 52.05/7.69 % (1607972)Instructions burned: 684 (million)
% 52.05/7.69 % (1607980)Instruction limit reached!
% 52.05/7.69 % (1607980)------------------------------
% 52.05/7.69 % (1607980)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.05/7.69 % (1607980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.05/7.69 % (1607980)CaDiCaL version: 2.1.3
% 52.05/7.69 % (1607980)Termination reason: Instruction limit
% 52.05/7.69 % (1607980)Termination phase: Saturation
% 52.05/7.69 % (1607980)Time elapsed: 0.249 s
% 52.05/7.69 % (1607980)Peak memory usage: 21 MB
% 52.05/7.69 % (1607980)Instructions burned: 1181 (million)
% 52.05/7.69 % (1607991)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2379585100:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 52.05/7.69 % (1607992)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1001666985:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 52.05/7.69 % (1607989)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 52.05/7.69 % Exception at run slice level
% 52.05/7.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 52.05/7.69 % Exception at run slice level
% 52.05/7.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 52.05/7.69 % (1607995)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2532235621:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 52.05/7.69 % (1607996)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2002558403:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 52.05/7.69 % (1607995)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 52.05/7.69 % Exception at run slice level
% 52.05/7.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 52.05/7.69 % (1607999)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=60303911:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 52.05/7.69 % (1607996)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 52.05/7.69 % (1607996)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 52.05/7.69 % Exception at run slice level
% 52.05/7.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 52.05/7.69 % (1608001)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3965341792:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 52.05/7.69 % (1607985)Instruction limit reached!
% 52.05/7.69 % (1607985)------------------------------
% 52.05/7.69 % (1607985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.05/7.69 % (1607985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.05/7.69 % (1607985)CaDiCaL version: 2.1.3
% 52.05/7.69 % (1607985)Termination reason: Instruction limit
% 52.05/7.69 % (1607985)Termination phase: Saturation
% 52.05/7.69 % (1607985)Time elapsed: 0.355 s
% 52.05/7.69 % (1607985)Peak memory usage: 15 MB
% 52.05/7.69 % (1607985)Instructions burned: 693 (million)
% 52.05/7.69 % Exception at run slice level
% 52.05/7.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 52.05/7.69 % (1608003)ott-2_1_sil=16000:newcnf=on:random_seed=3652282495:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 52.05/7.69 % (1608004)ott+10_1_sil=32000:tgt=ground:random_seed=1748708591:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 52.05/7.69 % (1608003)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 52.05/7.69 % (1607987)Instruction limit reached!
% 52.05/7.69 % (1607987)------------------------------
% 52.05/7.69 % (1607987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.05/7.69 % (1607987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.05/7.69 % (1607987)CaDiCaL version: 2.1.3
% 52.05/7.69 % (1607987)Termination reason: Instruction limit
% 52.05/7.69 % (1607987)Termination phase: Saturation
% 52.05/7.69 % (1607987)Time elapsed: 0.401 s
% 52.05/7.69 % (1607987)Peak memory usage: 16 MB
% 52.05/7.69 % (1607987)Instructions burned: 879 (million)
% 52.05/7.69 % (1608007)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1088253027:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 54.09/17.40 % Exception at run slice level
% 54.09/17.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 54.09/17.40 % (1608009)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=332585139:i=3512:aac=none_2991 on theBenchmark for (2991ds/3512Mi)
% 54.09/17.40 % (1608009)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 54.09/17.40 % (1608003)Instruction limit reached!
% 54.09/17.40 % (1608003)------------------------------
% 54.09/17.40 % (1608003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 54.09/17.40 % (1608003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 54.09/17.40 % (1608003)CaDiCaL version: 2.1.3
% 54.09/17.40 % (1608003)Termination reason: Instruction limit
% 54.09/17.40 % (1608003)Termination phase: Saturation
% 54.09/17.40 % (1608003)Time elapsed: 0.512 s
% 54.09/17.40 % (1608003)Peak memory usage: 16 MB
% 54.09/17.40 % (1608003)Instructions burned: 877 (million)
% 54.09/17.40 % (1608013)dis+21_1_sil=32000:sas=cadical:random_seed=246763299:i=3773:amm=off_2988 on theBenchmark for (2988ds/3773Mi)
% 54.09/17.40 % (1607996)Instruction limit reached!
% 54.09/17.40 % (1607996)------------------------------
% 54.09/17.40 % (1607996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 54.09/17.40 % (1607996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 54.09/17.40 % (1607996)CaDiCaL version: 2.1.3
% 54.09/17.40 % (1607996)Termination reason: Instruction limit
% 54.09/17.40 % (1607996)Termination phase: Saturation
% 54.09/17.40 % (1607996)Time elapsed: 0.884 s
% 54.09/17.40 % (1607996)Peak memory usage: 24 MB
% 54.09/17.40 % (1607996)Instructions burned: 1472 (million)
% 54.09/17.40 % (1608015)ott+11_1_sil=16000:gs=on:random_seed=2269559478:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2986 on theBenchmark for (2986ds/2251Mi)
% 54.09/17.40 % (1608015)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 54.09/17.40 % (1607995)Instruction limit reached!
% 54.09/17.40 % (1607995)------------------------------
% 54.09/17.40 % (1607995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 54.09/17.40 % (1607995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 54.09/17.40 % (1607995)CaDiCaL version: 2.1.3
% 54.09/17.40 % (1607995)Termination reason: Instruction limit
% 54.09/17.40 % (1607995)Termination phase: Saturation
% 54.09/17.40 % (1607995)Time elapsed: 1.149 s
% 54.09/17.40 % (1607995)Peak memory usage: 22 MB
% 54.09/17.40 % (1607995)Instructions burned: 5133 (million)
% 54.09/17.40 % (1608017)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=4254637497:fmbsr=1.6:i=67534_2983 on theBenchmark for (2983ds/67534Mi)
% 54.09/17.40 % Exception at run slice level
% 54.09/17.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 54.09/17.40 % (1608019)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=4256767549:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2983 on theBenchmark for (2983ds/4591Mi)
% 54.09/17.40 % (1608015)Instruction limit reached!
% 54.09/17.40 % (1608015)------------------------------
% 54.09/17.40 % (1608015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 54.09/17.40 % (1608015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 54.09/17.40 % (1608015)CaDiCaL version: 2.1.3
% 54.09/17.40 % (1608015)Termination reason: Instruction limit
% 54.09/17.40 % (1608015)Termination phase: Saturation
% 54.09/17.40 % (1608015)Time elapsed: 0.953 s
% 54.09/17.40 % (1608015)Peak memory usage: 16 MB
% 54.09/17.40 % (1608015)Instructions burned: 2251 (million)
% 54.09/17.40 % (1608021)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=3097143899:i=29340_2976 on theBenchmark for (2976ds/29340Mi)
% 54.09/17.40 % (1608009)Instruction limit reached!
% 54.09/17.40 % (1608009)------------------------------
% 54.09/17.40 % (1608009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 54.09/17.40 % (1608009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 54.09/17.40 % (1608009)CaDiCaL version: 2.1.3
% 54.09/17.40 % (1608009)Termination reason: Instruction limit
% 54.09/17.40 % (1608009)Termination phase: Saturation
% 54.09/17.40 % (1608009)Time elapsed: 1.798 s
% 54.09/17.40 % (1608009)Peak memory usage: 21 MB
% 54.09/17.40 % (1608009)Instructions burned: 3512 (million)
% 54.09/17.40 % (1608004)Instruction limit reached!
% 54.09/17.40 % (1608004)------------------------------
% 54.09/17.40 % (1608004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 54.09/17.40 % (1608004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 54.09/17.40 % (1608004)CaDiCaL version: 2.1.3
% 54.09/17.40 % (1608004)Termination reason: Instruction limit
% 54.09/17.40 % (1608004)Termination phase: Saturation
% 54.09/17.40 % (1608004)Time elapsed: 1.999 s
% 54.09/17.40 % (1608004)Peak memory usage: 69 MB
% 54.09/17.40 % (1608004)Instructions burned: 5114 (million)
% 54.09/17.40 % (1608023)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=2055714251:i=5211_2973 on theBenchmark for (2973ds/5211Mi)
% 54.09/17.40 % (1608024)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=3446709643:i=5497:nm=2_2973 on theBenchmark for (2973ds/5497Mi)
% 54.09/17.40 % Exception at run slice level
% 54.09/17.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 54.09/17.40 % (1608034)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=3594151875:fmbsr=2:i=46332_2972 on theBenchmark for (2972ds/46332Mi)
% 54.09/17.40 % Exception at run slice level
% 54.09/17.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 54.09/17.40 % (1608036)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=894694924:i=14071_2971 on theBenchmark for (2971ds/14071Mi)
% 54.09/17.40 % Exception at run slice level
% 54.09/17.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 54.09/17.40 % (1608019)Instruction limit reached!
% 54.09/17.40 % (1608019)------------------------------
% 54.09/17.40 % (1608019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 54.09/17.40 % (1608019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 54.09/17.40 % (1608019)CaDiCaL version: 2.1.3
% 54.09/17.40 % (1608019)Termination reason: Instruction limit
% 54.09/17.40 % (1608019)Termination phase: Saturation
% 54.09/17.40 % (1608019)Time elapsed: 1.268 s
% 54.09/17.40 % (1608019)Peak memory usage: 65 MB
% 54.09/17.40 % (1608019)Instructions burned: 4595 (million)
% 54.09/17.40 % (1608038)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=187617218:i=22565:add=on:rawr=on_2970 on theBenchmark for (2970ds/22565Mi)
% 54.09/17.40 % (1608040)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=761278106:i=8173:av=off_2970 on theBenchmark for (2970ds/8173Mi)
% 54.09/17.40 % (1608013)Instruction limit reached!
% 54.09/17.40 % (1608013)------------------------------
% 54.09/17.40 % (1608013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 54.09/17.40 % (1608013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 54.09/17.40 % (1608013)CaDiCaL version: 2.1.3
% 54.09/17.40 % (1608013)Termination reason: Instruction limit
% 54.09/17.40 % (1608013)Termination phase: Saturation
% 54.09/17.40 % (1608013)Time elapsed: 2.215 s
% 54.09/17.40 % (1608013)Peak memory usage: 21 MB
% 54.09/17.40 % (1608013)Instructions burned: 3774 (million)
% 54.09/17.40 % (1608042)dis+10_16:1_sil=16000:random_seed=2358769228:i=9155:fsr=off_2965 on theBenchmark for (2965ds/9155Mi)
% 54.09/17.40 % (1608023)Instruction limit reached!
% 54.09/17.40 % (1608023)------------------------------
% 54.09/17.40 % (1608023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 54.09/17.40 % (1608023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 54.09/17.40 % (1608023)CaDiCaL version: 2.1.3
% 54.09/17.40 % (1608023)Termination reason: Instruction limit
% 54.09/17.40 % (1608023)Termination phase: Saturation
% 54.09/17.40 % (1608023)Time elapsed: 3.012 s
% 54.09/17.40 % (1608023)Peak memory usage: 31 MB
% 54.09/17.40 % (1608023)Instructions burned: 5212 (million)
% 54.09/17.40 % (1608049)ott-3_8_sil=64000:random_seed=2717280790:i=20139:bs=on_2943 on theBenchmark for (2943ds/20139Mi)
% 54.09/17.40 % (1608040)Instruction limit reached!
% 54.09/17.40 % (1608040)------------------------------
% 54.09/17.40 % (1608040)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 54.09/17.40 % (1608040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 54.09/17.40 % (1608040)CaDiCaL version: 2.1.3
% 54.09/17.40 % (1608040)Termination reason: Instruction limit
% 54.09/17.40 % (1608040)Termination phase: Saturation
% 54.09/17.40 % (1608040)Time elapsed: 4.450 s
% 54.09/17.40 % (1608040)Peak memory usage: 32 MB
% 54.09/17.40 % (1608040)Instructions burned: 8174 (million)
% 54.09/17.40 % (1608056)fmb+10_1_sil=64000:tgt=ground:sas=cadical:bce=on:fmbss=9:random_seed=3812799540:fmbsr=2:i=32576_2925 on theBenchmark for (2925ds/32576Mi)
% 54.09/17.40 % Exception at run slice level
% 54.09/17.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 54.09/17.40 % (1608058)ott+10_8:1_sil=16000:sp=arity:gs=on:random_seed=2784492302:i=11404_2924 on theBenchmark for (2924ds/11404Mi)
% 54.09/17.40 % (1608042)Instruction limit reached!
% 54.09/17.40 % (1608042)------------------------------
% 54.09/17.40 % (1608042)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 54.09/17.40 % (1608042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 54.09/17.40 % (1608042)CaDiCaL version: 2.1.3
% 54.09/17.40 % (1608042)Termination reason: Instruction limit
% 54.09/17.40 % (1608042)Termination phase: Saturation
% 54.09/17.40 % (1608042)Time elapsed: 4.653 s
% 54.09/17.40 % (1608042)Peak memory usage: 26 MB
% 54.09/17.40 % (1608042)Instructions burned: 9156 (million)
% 54.09/17.40 % (1608060)ott-11_1_sil=16000:alpa=false:sac=on:random_seed=2020938450:i=14134_2919 on theBenchmark for (2919ds/14134Mi)
% 54.09/17.40 % (1608060)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 54.09/17.40 % (1608038)Instruction limit reached!
% 54.09/17.40 % (1608038)------------------------------
% 54.09/17.40 % (1608038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 54.09/17.40 % (1608038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 54.09/17.40 % (1608038)CaDiCaL version: 2.1.3
% 54.09/17.40 % (1608038)Termination reason: Instruction limit
% 54.09/17.40 % (1608038)Termination phase: Saturation
% 54.09/17.40 % (1608038)Time elapsed: 10.051 s
% 54.09/17.40 % (1608038)Peak memory usage: 75 MB
% 54.09/17.40 % (1608038)Instructions burned: 22567 (million)
% 54.09/17.40 % (1608066)dis+33_16_sil=32000:sac=on:random_seed=3427537990:i=15851:nm=0_2869 on theBenchmark for (2869ds/15851Mi)
% 54.09/17.40 % (1608060)Instruction limit reached!
% 54.09/17.40 % (1608060)------------------------------
% 54.09/17.40 % (1608060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 54.09/17.40 % (1608060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 54.09/17.40 % (1608060)CaDiCaL version: 2.1.3
% 54.09/17.40 % (1608060)Termination reason: Instruction limit
% 54.09/17.40 % (1608060)Termination phase: Saturation
% 54.09/17.40 % (1608060)Time elapsed: 6.815 s
% 54.09/17.40 % (1608060)Peak memory usage: 38 MB
% 54.09/17.40 % (1608060)Instructions burned: 14135 (million)
% 54.09/17.40 % (1608069)dis+4_1024_sil=32000:avsql=on:sp=occurrence:gs=on:avsqc=1:random_seed=2658837184:avsq=on:i=17627:add=on:amm=off_2850 on theBenchmark for (2850ds/17627Mi)
% 54.09/17.40 % (1608058)Instruction limit reached!
% 54.09/17.40 % (1608058)------------------------------
% 54.09/17.40 % (1608058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 54.09/17.40 % (1608058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 54.09/17.40 % (1608058)CaDiCaL version: 2.1.3
% 54.09/17.40 % (1608058)Termination reason: Instruction limit
% 54.09/17.40 % (1608058)Termination phase: Saturation
% 54.09/17.40 % (1608058)Time elapsed: 7.692 s
% 54.09/17.40 % (1608058)Peak memory usage: 32 MB
% 54.09/17.40 % (1608058)Instructions burned: 11406 (million)
% 54.09/17.40 % (1608073)ott+10_64_anc=all:sil=128000:sas=cadical:bsr=unit_only:nwc=1:cn=on:random_seed=1233309121:s2a=on:i=53295_2847 on theBenchmark for (2847ds/53295Mi)
% 54.09/17.40 % (1608069) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1607940-1608069"...
% 54.09/17.40 % (1608069)...printing done.
% 54.09/17.40 % (1608069)Refutation found. Thanks to Tanya!
% 54.09/17.40 % SZS status Theorem for theBenchmark
% 54.09/17.40 % SZS output start Proof for theBenchmark
% 54.09/17.40 thf(type_def_5, type, mu: $tType).
% 54.09/17.40 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 54.09/17.40 thf(func_def_0, type, qmltpeq: (mu > mu > $i > $o)).
% 54.09/17.40 thf(func_def_1, type, meq_prop: (($i > $o) > ($i > $o) > $i > $o)).
% 54.09/17.40 thf(func_def_3, type, mnot: (($i > $o) > $i > $o)).
% 54.09/17.40 thf(func_def_4, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 54.09/17.40 thf(func_def_5, type, mbox: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 54.09/17.40 thf(func_def_6, type, mforall_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 54.09/17.40 thf(func_def_7, type, mtrue: ($i > $o)).
% 54.09/17.40 thf(func_def_8, type, mfalse: ($i > $o)).
% 54.09/17.40 thf(func_def_9, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 54.09/17.40 thf(func_def_10, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 54.09/17.40 thf(func_def_11, type, mimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 54.09/17.40 thf(func_def_12, type, mequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 54.09/17.40 thf(func_def_13, type, mxor: (($i > $o) > ($i > $o) > $i > $o)).
% 54.09/17.40 thf(func_def_14, type, mdia: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 54.09/17.40 thf(func_def_15, type, exists_in_world: (mu > $i > $o)).
% 54.09/17.40 thf(func_def_16, type, mforall_ind: ((mu > $i > $o) > $i > $o)).
% 54.09/17.40 thf(func_def_17, type, mexists_ind: ((mu > $i > $o) > $i > $o)).
% 54.09/17.40 thf(func_def_18, type, mexists_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 54.09/17.40 thf(func_def_19, type, mreflexive: (($i > $i > $o) > $o)).
% 54.09/17.40 thf(func_def_20, type, msymmetric: (($i > $i > $o) > $o)).
% 54.09/17.40 thf(func_def_21, type, mserial: (($i > $i > $o) > $o)).
% 54.09/17.40 thf(func_def_22, type, mtransitive: (($i > $i > $o) > $o)).
% 54.09/17.40 thf(func_def_23, type, meuclidean: (($i > $i > $o) > $o)).
% 54.09/17.40 thf(func_def_24, type, mpartially_functional: (($i > $i > $o) > $o)).
% 54.09/17.40 thf(func_def_25, type, mfunctional: (($i > $i > $o) > $o)).
% 54.09/17.40 thf(func_def_26, type, mweakly_dense: (($i > $i > $o) > $o)).
% 54.09/17.40 thf(func_def_27, type, mweakly_connected: (($i > $i > $o) > $o)).
% 54.09/17.40 thf(func_def_28, type, mweakly_directed: (($i > $i > $o) > $o)).
% 54.09/17.40 thf(func_def_29, type, mvalid: (($i > $o) > $o)).
% 54.09/17.40 thf(func_def_30, type, msatisfiable: (($i > $o) > $o)).
% 54.09/17.40 thf(func_def_31, type, mcountersatisfiable: (($i > $o) > $o)).
% 54.09/17.40 thf(func_def_32, type, minvalid: (($i > $o) > $o)).
% 54.09/17.40 thf(func_def_33, type, rel_s4: ($i > $i > $o)).
% 54.09/17.40 thf(func_def_34, type, mbox_s4: (($i > $o) > $i > $o)).
% 54.09/17.40 thf(func_def_35, type, mdia_s4: (($i > $o) > $i > $o)).
% 54.09/17.40 thf(func_def_36, type, unit: mu).
% 54.09/17.40 thf(func_def_37, type, inv: (mu > mu)).
% 54.09/17.40 thf(func_def_38, type, e3: mu).
% 54.09/17.40 thf(func_def_39, type, e2: mu).
% 54.09/17.40 thf(func_def_40, type, e1: mu).
% 54.09/17.40 thf(func_def_41, type, e0: mu).
% 54.09/17.40 thf(func_def_42, type, op: (mu > mu > mu)).
% 54.09/17.40 thf(func_def_43, type, db2: !>[X0: $tType]:(X0)).
% 54.09/17.40 thf(func_def_44, type, db0: !>[X0: $tType]:(X0)).
% 54.09/17.40 thf(func_def_45, type, db1: !>[X0: $tType]:(X0)).
% 54.09/17.40 thf(func_def_46, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 54.09/17.40 thf(func_def_47, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 54.09/17.40 thf(func_def_48, type, vNOT: ($o > $o)).
% 54.09/17.40 thf(func_def_49, type, vOR: ($o > $o > $o)).
% 54.09/17.40 thf(func_def_50, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 54.09/17.40 thf(func_def_51, type, db3: !>[X0: $tType]:(X0)).
% 54.09/17.40 thf(func_def_54, type, vIMP: ($o > $o > $o)).
% 54.09/17.40 thf(func_def_55, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 54.09/17.40 thf(func_def_56, type, vAND: ($o > $o > $o)).
% 54.09/17.40 thf(func_def_57, type, db4: !>[X0: $tType]:(X0)).
% 54.09/17.40 thf(func_def_58, type, sK0: ($i > mu)).
% 54.09/17.40 thf(func_def_61, type, sK3: ($i > $i)).
% 54.09/17.40 thf(func_def_62, type, sK4: ($i > $i)).
% 54.09/17.40 thf(func_def_63, type, sK5: ($i > $i)).
% 54.09/17.40 thf(func_def_64, type, sK6: ($i > $i)).
% 54.09/17.40 thf(func_def_65, type, sK7: ($i > $i)).
% 54.09/17.40 thf(func_def_66, type, sK8: ($i > $i)).
% 54.09/17.40 thf(func_def_67, type, sK9: ($i > $i)).
% 54.09/17.40 thf(func_def_68, type, sK10: ($i > $i)).
% 54.09/17.40 thf(func_def_69, type, sK11: ($i > $i)).
% 54.09/17.40 thf(func_def_70, type, sK12: ($i > $i)).
% 54.09/17.40 thf(func_def_71, type, sK13: ($i > $i)).
% 54.09/17.40 thf(func_def_72, type, sK14: ($i > $i)).
% 54.09/17.40 thf(func_def_73, type, sK15: ($i > $i)).
% 54.09/17.40 thf(func_def_74, type, sK16: ($i > $i)).
% 54.09/17.40 thf(func_def_75, type, sK17: ($i > $i)).
% 54.09/17.41 thf(func_def_76, type, sK18: ($i > $i)).
% 54.09/17.41 thf(func_def_77, type, sK19: ($i > $i)).
% 54.09/17.41 thf(func_def_78, type, sK20: ($i > $i)).
% 54.09/17.41 thf(func_def_79, type, sK21: ($i > $i)).
% 54.09/17.41 thf(func_def_80, type, sK22: ($i > $i)).
% 54.09/17.41 thf(func_def_81, type, sK23: ($i > $i)).
% 54.09/17.41 thf(func_def_82, type, sK24: ($i > $i)).
% 54.09/17.41 thf(func_def_83, type, sK25: ($i > $i)).
% 54.09/17.41 thf(func_def_84, type, sK26: ($i > $i)).
% 54.09/17.41 thf(func_def_85, type, sK27: ($i > $i)).
% 54.09/17.41 thf(func_def_86, type, sK28: ($i > $i)).
% 54.09/17.41 thf(func_def_87, type, sK29: ($i > $i)).
% 54.09/17.41 thf(func_def_88, type, sK30: ($i > $i)).
% 54.09/17.41 thf(func_def_89, type, sK31: ($i > $i)).
% 54.09/17.41 thf(func_def_90, type, sK32: ($i > $i)).
% 54.09/17.41 thf(func_def_91, type, sK33: ($i > $i)).
% 54.09/17.41 thf(func_def_92, type, sK34: ($i > $i)).
% 54.09/17.41 thf(func_def_93, type, sK35: ($i > $i)).
% 54.09/17.41 thf(func_def_94, type, sK36: ($i > $i)).
% 54.09/17.41 thf(func_def_95, type, sK37: ($i > $i)).
% 54.09/17.41 thf(func_def_96, type, sK38: ($i > $i)).
% 54.09/17.41 thf(func_def_97, type, sK39: ($i > $i)).
% 54.09/17.41 thf(func_def_98, type, sK40: ($i > $i)).
% 54.09/17.41 thf(func_def_99, type, sK41: ($i > $i)).
% 54.09/17.41 thf(func_def_100, type, sK42: ($i > $i)).
% 54.09/17.41 thf(func_def_101, type, sK43: ($i > $i)).
% 54.09/17.41 thf(func_def_102, type, sK44: ($i > $i)).
% 54.09/17.41 thf(func_def_103, type, sK45: ($i > $i)).
% 54.09/17.41 thf(func_def_104, type, sK46: ($i > $i)).
% 54.09/17.41 thf(func_def_105, type, sK47: ($i > $i)).
% 54.09/17.41 thf(func_def_106, type, sK48: ($i > $i)).
% 54.09/17.41 thf(func_def_107, type, sK49: ($i > $i)).
% 54.09/17.41 thf(func_def_108, type, sK50: ($i > $i)).
% 54.09/17.41 thf(func_def_109, type, sK51: ($i > $i)).
% 54.09/17.41 thf(func_def_110, type, sK52: ($i > $i)).
% 54.09/17.41 thf(func_def_111, type, sK53: ($i > $i)).
% 54.09/17.41 thf(func_def_112, type, sK54: ($i > $i)).
% 54.09/17.41 thf(func_def_113, type, sK55: ($i > $i)).
% 54.09/17.41 thf(func_def_114, type, sK56: ($i > $i)).
% 54.09/17.41 thf(func_def_115, type, sK57: ($i > $i)).
% 54.09/17.41 thf(func_def_116, type, sK58: ($i > $i)).
% 54.09/17.41 thf(func_def_117, type, sK59: ($i > $i)).
% 54.09/17.41 thf(func_def_118, type, sK60: ($i > $i)).
% 54.09/17.41 thf(func_def_119, type, sK61: ($i > $i)).
% 54.09/17.41 thf(func_def_120, type, sK62: ($i > $i)).
% 54.09/17.41 thf(func_def_121, type, sK63: ($i > $i)).
% 54.09/17.41 thf(func_def_122, type, sK64: ($i > $i)).
% 54.09/17.41 thf(func_def_123, type, sK65: ($i > $i)).
% 54.09/17.41 thf(func_def_124, type, sK66: ($i > $i)).
% 54.09/17.41 thf(func_def_125, type, sK67: ($i > $i)).
% 54.09/17.41 thf(func_def_126, type, sK68: ($i > $i)).
% 54.09/17.41 thf(func_def_127, type, sK69: ($i > $i)).
% 54.09/17.41 thf(func_def_128, type, sK70: ($i > $i)).
% 54.09/17.41 thf(func_def_129, type, sK71: ($i > $i)).
% 54.09/17.41 thf(func_def_130, type, sK72: ($i > $i)).
% 54.09/17.41 thf(func_def_131, type, sK73: ($i > $i)).
% 54.09/17.41 thf(func_def_132, type, sK74: ($i > $i)).
% 54.09/17.41 thf(func_def_133, type, sK75: ($i > $i)).
% 54.09/17.41 thf(func_def_134, type, sK76: ($i > $i)).
% 54.09/17.41 thf(func_def_135, type, sK77: ($i > $i)).
% 54.09/17.41 thf(func_def_136, type, sK78: ($i > $i)).
% 54.09/17.41 thf(func_def_137, type, sK79: ($i > $i)).
% 54.09/17.41 thf(func_def_138, type, sK80: ($i > $i)).
% 54.09/17.41 thf(func_def_139, type, sK81: ($i > $i)).
% 54.09/17.41 thf(func_def_140, type, sK82: ($i > $i)).
% 54.09/17.41 thf(func_def_141, type, sK83: ($i > $i)).
% 54.09/17.41 thf(func_def_142, type, sK84: ($i > $i)).
% 54.09/17.41 thf(func_def_143, type, sK85: ($i > $i)).
% 54.09/17.41 thf(func_def_144, type, sK86: ($i > $i)).
% 54.09/17.41 thf(func_def_145, type, sK87: ($i > $i)).
% 54.09/17.41 thf(func_def_146, type, sK88: ($i > $i)).
% 54.09/17.41 thf(func_def_147, type, sK89: ($i > $i)).
% 54.09/17.41 thf(func_def_148, type, sK90: ($i > $i)).
% 54.09/17.41 thf(func_def_149, type, sK91: ($i > $i)).
% 54.09/17.41 thf(func_def_150, type, sK92: ($i > $i)).
% 54.09/17.41 thf(func_def_151, type, sK93: ($i > $i)).
% 54.09/17.41 thf(func_def_152, type, sK94: ($i > $i)).
% 54.09/17.41 thf(func_def_153, type, db5: !>[X0: $tType]:(X0)).
% 54.09/17.41 thf(func_def_154, type, db6: !>[X0: $tType]:(X0)).
% 54.09/17.41 thf(func_def_155, type, db7: !>[X0: $tType]:(X0)).
% 54.09/17.41 thf(func_def_156, type, sK95: (mu > $i > mu > $i)).
% 54.09/17.41 thf(func_def_157, type, sK96: (mu > $i > mu > $i)).
% 54.09/17.41 thf(func_def_158, type, sK97: (mu > mu > $i > $i)).
% 54.09/17.41 thf(func_def_159, type, sK98: (mu > $i > mu > $i)).
% 54.09/17.41 thf(func_def_160, type, sK99: (mu > $i > mu > $i)).
% 54.09/17.41 thf(func_def_161, type, sK100: (mu > mu > $i > $i)).
% 54.09/17.41 thf(f2,axiom,(
% 54.09/17.41 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 54.09/17.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mnot)).
% 54.09/17.41 thf(f3,axiom,(
% 54.09/17.41 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 54.09/17.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mor)).
% 54.09/17.41 thf(f8,axiom,(
% 54.09/17.41 (mand = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mnot @ (mor @ (mnot @ X0) @ (mnot @ X1))))))),
% 54.09/17.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mand)).
% 54.09/17.41 thf(f18,axiom,(
% 54.09/17.41 (mreflexive = (^[X0 : ($i > $i > $o)] : (! [X1 : $i] : (X0 @ X1 @ X1))))),
% 54.09/17.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mreflexive)).
% 54.09/17.41 thf(f28,axiom,(
% 54.09/17.41 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 54.09/17.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mvalid)).
% 54.09/17.41 thf(f32,axiom,(
% 54.09/17.41 (mbox_s4 = (^[X0 : ($i > $o), X1 : $i] : (! [X2 : $i] : ((X0 @ X2) | ~(rel_s4 @ X1 @ X2)))))),
% 54.09/17.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4)).
% 54.09/17.41 thf(f34,axiom,(
% 54.09/17.41 (mreflexive @ rel_s4)),
% 54.09/17.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a1)).
% 54.09/17.41 thf(f61,conjecture,(
% 54.09/17.41 (mvalid @ (mbox_s4 @ (mnot @ (mand @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ (mbox_s4 @ (mnot @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))))))),
% 54.09/17.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1)).
% 54.09/17.41 thf(f62,negated_conjecture,(
% 54.09/17.41 ~(mvalid @ (mbox_s4 @ (mnot @ (mand @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ (mbox_s4 @ (mnot @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))))))),
% 54.09/17.41 inference(negated_conjecture,[status(cth)],[f61])).
% 54.09/17.41 thf(f64,plain,(
% 54.09/17.41 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 54.09/17.41 inference(rectify,[],[f2])).
% 54.09/17.41 thf(f65,plain,(
% 54.09/17.41 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 54.09/17.41 inference(fool_elimination,[],[f64])).
% 54.09/17.41 thf(f66,plain,(
% 54.09/17.41 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 54.09/17.41 inference(rectify,[],[f3])).
% 54.09/17.41 thf(f67,plain,(
% 54.09/17.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 54.09/17.41 inference(fool_elimination,[],[f66])).
% 54.09/17.41 thf(f73,plain,(
% 54.09/17.41 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 54.09/17.41 inference(fool_elimination,[],[f8])).
% 54.09/17.41 thf(f87,plain,(
% 54.09/17.41 (mreflexive = (^[X0 : ($i > $i > $o)] : (! [X1 : $i] : (X0 @ X1 @ X1))))),
% 54.09/17.41 inference(rectify,[],[f18])).
% 54.09/17.41 thf(f88,plain,(
% 54.09/17.41 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 54.09/17.41 inference(fool_elimination,[],[f87])).
% 54.09/17.41 thf(f107,plain,(
% 54.09/17.41 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 54.09/17.41 inference(rectify,[],[f28])).
% 54.09/17.41 thf(f108,plain,(
% 54.09/17.41 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 54.09/17.41 inference(fool_elimination,[],[f107])).
% 54.09/17.41 thf(f115,plain,(
% 54.09/17.41 (mbox_s4 = (^[X0 : ($i > $o), X1 : $i] : (! [X2 : $i] : ((X0 @ X2) | ~(rel_s4 @ X1 @ X2)))))),
% 54.09/17.41 inference(rectify,[],[f32])).
% 54.09/17.41 thf(f116,plain,(
% 54.09/17.41 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 54.09/17.41 inference(fool_elimination,[],[f115])).
% 54.09/17.41 thf(f118,plain,(
% 54.09/17.41 (mreflexive @ rel_s4)),
% 54.09/17.41 inference(rectify,[],[f34])).
% 54.09/17.41 thf(f119,plain,(
% 54.09/17.41 (((mreflexive @ rel_s4)) = $true)),
% 54.09/17.41 inference(fool_elimination,[],[f118])).
% 54.09/17.41 thf(f172,plain,(
% 54.09/17.41 ~(mvalid @ (mbox_s4 @ (mnot @ (mand @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ (mbox_s4 @ (mnot @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))))))),
% 54.09/17.41 inference(rectify,[],[f62])).
% 54.09/17.41 thf(f173,plain,(
% 54.09/17.41 ~ (((mvalid @ (mbox_s4 @ (mnot @ (mand @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ (mbox_s4 @ (mnot @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))))))) = $true)),
% 54.09/17.41 inference(fool_elimination,[],[f172])).
% 54.09/17.41 thf(f174,plain,(
% 54.09/17.41 (((mvalid @ (mbox_s4 @ (mnot @ (mand @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ (mbox_s4 @ (mnot @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))))))) != $true)),
% 54.09/17.41 inference(flattening,[],[f173])).
% 54.09/17.41 thf(f179,plain,(
% 54.09/17.41 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 54.09/17.41 inference(cnf_transformation,[],[f65])).
% 54.09/17.41 thf(f180,plain,(
% 54.09/17.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 54.09/17.41 inference(cnf_transformation,[],[f67])).
% 54.09/17.41 thf(f185,plain,(
% 54.09/17.41 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 54.09/17.41 inference(cnf_transformation,[],[f73])).
% 54.09/17.41 thf(f195,plain,(
% 54.09/17.41 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 54.09/17.41 inference(cnf_transformation,[],[f88])).
% 54.09/17.41 thf(f205,plain,(
% 54.09/17.41 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 54.09/17.41 inference(cnf_transformation,[],[f108])).
% 54.09/17.41 thf(f209,plain,(
% 54.09/17.41 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 54.09/17.41 inference(cnf_transformation,[],[f116])).
% 54.09/17.41 thf(f211,plain,(
% 54.09/17.41 (((mreflexive @ rel_s4)) = $true)),
% 54.09/17.41 inference(cnf_transformation,[],[f119])).
% 54.09/17.41 thf(f238,plain,(
% 54.09/17.41 (((mvalid @ (mbox_s4 @ (mnot @ (mand @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ (mbox_s4 @ (mnot @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))))))) != $true)),
% 54.09/17.41 inference(cnf_transformation,[],[f174])).
% 54.09/17.41 thf(f240,definition,(
% 54.09/17.41 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 54.09/17.41 introduced(theory,[fool_exhaustiveness_axiom])).
% 54.09/17.41 thf(f242,plain,(
% 54.09/17.41 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 54.09/17.41 inference(definition_unfolding,[],[f185,f179,f180,f179,f179])).
% 54.09/17.41 thf(f251,plain,(
% 54.09/17.41 ($true = (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4)))),
% 54.09/17.41 inference(definition_unfolding,[],[f211,f195])).
% 54.09/17.41 thf(f270,plain,(
% 54.09/17.41 ($true != (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! 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@ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! 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@ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))))))))),
% 54.09/17.41 inference(definition_unfolding,[],[f238,f205,f209,f179,f242,f180,f242,f209,f242,f209,f242,f209,f209,f180,f242,f209,f242,f209,f242,f209,f209,f180,f242,f209,f242,f209,f242,f209,f209,f242,f209,f242,f209,f242,f209,f209,f209,f179,f180,f242,f209,f242,f209,f242,f209,f209,f180,f242,f209,f242,f209,f242,f209,f209,f180,f242,f209,f242,f209,f242,f209,f209,f242,f209,f242,f209,f242,f209,f209])).
% 54.09/17.41 thf(f271,plain,(
% 54.09/17.41 ($true != ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (~ ((~ ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y2))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y2))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y2))))))))))))) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y2))))))))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ ((~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y3))))) | (~ (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y3))))) | (~ (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y3))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y3))))) | (~ (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y3))))) | (~ (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y3))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y3))))) | (~ (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y3))))) | (~ (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y3))))))))))))) | (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y3))))) | (~ (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y3))))) | (~ (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y3)))))))))))))))))))))))))))))))),
% 54.09/17.41 inference(beta-eta_normalization,[],[f270])).
% 54.09/17.41 thf(f272,plain,(
% 54.09/17.41 ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (~ ((~ ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y2))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y2))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y2))))))))))))) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y2))))))))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ ((~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y3))))) | (~ (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y3))))) | (~ (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y3))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y3))))) | (~ (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y3))))) | (~ (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y3))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y3))))) | (~ (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y3))))) | (~ (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y3))))))))))))) | (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y3))))) | (~ (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y3))))) | (~ (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y3)))))))))))))))))))))))))))) @ sK1)))),
% 54.09/17.41 inference(sigma_proxy_clausification,[],[f271])).
% 54.09/17.41 thf(f273,plain,(
% 54.09/17.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | (~ (~ ((~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y1))))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y1))))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y2))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y2))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y2))))))))))))) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y2)))))))))))))))))))))))))))))),
% 54.09/17.41 inference(beta-eta_normalization,[],[f272])).
% 54.09/17.41 thf(f274,plain,(
% 54.09/17.41 ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | (~ (~ ((~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y1))))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y1))))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y2))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y2))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y2))))))))))))) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y2))))) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y2)))))))))))))))))))))))))) @ sK2)))),
% 54.09/17.41 inference(sigma_proxy_clausification,[],[f273])).
% 54.09/17.41 thf(f275,plain,(
% 54.09/17.41 ($false = (((~ (rel_s4 @ sK1 @ sK2)) | (~ (~ ((~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y1))))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y1)))))))))))))))))))))))))))),
% 54.09/17.41 inference(beta-eta_normalization,[],[f274])).
% 54.09/17.41 thf(f276,plain,(
% 54.09/17.41 ($false = ((~ (~ ((~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y1))))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y1))))))))))))))))))))))))))),
% 54.09/17.41 inference(or_proxy_clausification,[],[f275])).
% 54.09/17.41 thf(f279,plain,(
% 54.09/17.41 ($true = ((~ ((~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y1))))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y1)))))))))))))))))))))))))),
% 54.09/17.41 inference(not_proxy_clausification,[],[f276])).
% 54.09/17.41 thf(f280,plain,(
% 54.09/17.41 ($false = (((~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y1))))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y1))))))))))))))))))))))))),
% 54.09/17.41 inference(not_proxy_clausification,[],[f279])).
% 54.09/17.41 thf(f281,plain,(
% 54.09/17.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y1))))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y1)))))))))))))))))))))))),
% 54.09/17.41 inference(or_proxy_clausification,[],[f280])).
% 54.09/17.41 thf(f282,plain,(
% 54.09/17.41 ($false = ((~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))))))))))))),
% 54.09/17.41 inference(or_proxy_clausification,[],[f280])).
% 54.09/17.41 thf(f283,plain,(
% 54.09/17.41 ($true = (((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))))))))))))),
% 54.09/17.41 inference(not_proxy_clausification,[],[f282])).
% 54.09/17.41 thf(f284,plain,(
% 54.09/17.41 ($true = (((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))))))))))),
% 54.09/17.41 inference(or_proxy_clausification,[],[f283])).
% 54.09/17.41 thf(f285,plain,(
% 54.09/17.41 ($true = (((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))))),
% 54.09/17.41 inference(or_proxy_clausification,[],[f284])).
% 54.09/17.41 thf(f286,plain,(
% 54.09/17.41 ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))),
% 54.09/17.41 inference(or_proxy_clausification,[],[f285])).
% 54.09/17.41 thf(f287,plain,(
% 54.09/17.41 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))),
% 54.09/17.41 inference(not_proxy_clausification,[],[f286])).
% 54.09/17.41 thf(f288,plain,(
% 54.09/17.41 ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))),
% 54.09/17.41 inference(or_proxy_clausification,[],[f287])).
% 54.09/17.41 thf(f289,plain,(
% 54.09/17.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))),
% 54.09/17.41 inference(or_proxy_clausification,[],[f287])).
% 54.09/17.41 thf(f290,plain,(
% 54.09/17.41 ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))),
% 54.09/17.41 inference(not_proxy_clausification,[],[f289])).
% 54.09/17.41 thf(f291,plain,(
% 54.09/17.41 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f290])).
% 54.09/17.41 thf(f292,plain,(
% 54.09/17.41 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f291])).
% 54.09/17.41 thf(f293,plain,(
% 54.09/17.41 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f292])).
% 54.09/17.41 thf(f294,plain,(
% 54.09/17.41 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f292])).
% 54.09/17.41 thf(f295,plain,(
% 54.09/17.41 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f294])).
% 54.09/17.41 thf(f296,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f295])).
% 54.09/17.41 thf(f297,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f296])).
% 54.09/17.41 thf(f298,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f297])).
% 54.09/17.41 thf(f299,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f297])).
% 54.09/17.41 thf(f300,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f299])).
% 54.09/17.41 thf(f301,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f300])).
% 54.09/17.41 thf(f302,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f301])).
% 54.09/17.41 thf(f303,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f302])).
% 54.09/17.41 thf(f304,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f302])).
% 54.09/17.41 thf(f305,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f304])).
% 54.09/17.41 thf(f306,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f305])).
% 54.09/17.41 thf(f307,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f306])).
% 54.09/17.41 thf(f308,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f307])).
% 54.09/17.41 thf(f309,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f308])).
% 54.09/17.41 thf(f310,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f309])).
% 54.09/17.41 thf(f311,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f310])).
% 54.09/17.41 thf(f312,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f311])).
% 54.09/17.41 thf(f313,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f312])).
% 54.09/17.41 thf(f314,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f313])).
% 54.09/17.41 thf(f315,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f314])).
% 54.09/17.41 thf(f316,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f303])).
% 54.09/17.41 thf(f317,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f316])).
% 54.09/17.41 thf(f318,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f317])).
% 54.09/17.41 thf(f319,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f317])).
% 54.09/17.41 thf(f320,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f319])).
% 54.09/17.41 thf(f321,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f320])).
% 54.09/17.41 thf(f322,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f321])).
% 54.09/17.41 thf(f323,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f322])).
% 54.09/17.41 thf(f324,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f323])).
% 54.09/17.41 thf(f325,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f324])).
% 54.09/17.41 thf(f326,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f325])).
% 54.09/17.41 thf(f327,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f326])).
% 54.09/17.41 thf(f328,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f327])).
% 54.09/17.41 thf(f329,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f328])).
% 54.09/17.41 thf(f330,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f329])).
% 54.09/17.41 thf(f331,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f318])).
% 54.09/17.41 thf(f332,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f331])).
% 54.09/17.41 thf(f333,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f332])).
% 54.09/17.41 thf(f334,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f332])).
% 54.09/17.41 thf(f335,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f334])).
% 54.09/17.41 thf(f336,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f335])).
% 54.09/17.41 thf(f337,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f336])).
% 54.09/17.41 thf(f338,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f337])).
% 54.09/17.41 thf(f339,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f338])).
% 54.09/17.41 thf(f340,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f339])).
% 54.09/17.41 thf(f341,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f340])).
% 54.09/17.41 thf(f342,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f341])).
% 54.09/17.41 thf(f343,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f342])).
% 54.09/17.41 thf(f344,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f343])).
% 54.09/17.41 thf(f345,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f344])).
% 54.09/17.41 thf(f346,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f333])).
% 54.09/17.41 thf(f347,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f346])).
% 54.09/17.41 thf(f348,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f347])).
% 54.09/17.41 thf(f349,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f348])).
% 54.09/17.41 thf(f350,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f349])).
% 54.09/17.41 thf(f351,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f350])).
% 54.09/17.41 thf(f352,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f351])).
% 54.09/17.41 thf(f353,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f352])).
% 54.09/17.41 thf(f354,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f353])).
% 54.09/17.41 thf(f355,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f354])).
% 54.09/17.41 thf(f356,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f355])).
% 54.09/17.41 thf(f357,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f298])).
% 54.09/17.41 thf(f358,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f357])).
% 54.09/17.41 thf(f359,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f358])).
% 54.09/17.41 thf(f360,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f358])).
% 54.09/17.41 thf(f361,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f360])).
% 54.09/17.41 thf(f362,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f361])).
% 54.09/17.41 thf(f363,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f362])).
% 54.09/17.41 thf(f364,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f363])).
% 54.09/17.41 thf(f365,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f363])).
% 54.09/17.41 thf(f366,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f365])).
% 54.09/17.41 thf(f367,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f366])).
% 54.09/17.41 thf(f368,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f367])).
% 54.09/17.41 thf(f369,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f368])).
% 54.09/17.41 thf(f370,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f369])).
% 54.09/17.41 thf(f371,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f370])).
% 54.09/17.41 thf(f372,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f371])).
% 54.09/17.41 thf(f373,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f372])).
% 54.09/17.41 thf(f374,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f373])).
% 54.09/17.41 thf(f375,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f374])).
% 54.09/17.41 thf(f376,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f375])).
% 54.09/17.41 thf(f377,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f364])).
% 54.09/17.41 thf(f378,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f377])).
% 54.09/17.41 thf(f379,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f378])).
% 54.09/17.41 thf(f380,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f378])).
% 54.09/17.41 thf(f381,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f380])).
% 54.09/17.41 thf(f382,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f381])).
% 54.09/17.41 thf(f383,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f382])).
% 54.09/17.41 thf(f384,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f383])).
% 54.09/17.41 thf(f385,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f384])).
% 54.09/17.41 thf(f386,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f385])).
% 54.09/17.41 thf(f387,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f386])).
% 54.09/17.41 thf(f388,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f387])).
% 54.09/17.41 thf(f389,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f388])).
% 54.09/17.41 thf(f390,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f389])).
% 54.09/17.41 thf(f391,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f390])).
% 54.09/17.41 thf(f392,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f379])).
% 54.09/17.41 thf(f393,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f392])).
% 54.09/17.41 thf(f394,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f393])).
% 54.09/17.41 thf(f395,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f393])).
% 54.09/17.41 thf(f396,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f395])).
% 54.09/17.41 thf(f397,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f396])).
% 54.09/17.41 thf(f398,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f397])).
% 54.09/17.41 thf(f399,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f398])).
% 54.09/17.41 thf(f400,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f399])).
% 54.09/17.41 thf(f401,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f400])).
% 54.09/17.41 thf(f402,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f401])).
% 54.09/17.41 thf(f403,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f402])).
% 54.09/17.41 thf(f404,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f403])).
% 54.09/17.41 thf(f405,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f404])).
% 54.09/17.41 thf(f406,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f405])).
% 54.09/17.41 thf(f407,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f394])).
% 54.09/17.41 thf(f408,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f407])).
% 54.09/17.41 thf(f409,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f408])).
% 54.09/17.41 thf(f410,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f409])).
% 54.09/17.41 thf(f411,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f410])).
% 54.09/17.41 thf(f412,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f411])).
% 54.09/17.41 thf(f413,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f412])).
% 54.09/17.41 thf(f414,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f413])).
% 54.09/17.41 thf(f415,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f414])).
% 54.09/17.41 thf(f416,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f415])).
% 54.09/17.41 thf(f417,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f416])).
% 54.09/17.41 thf(f418,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f359])).
% 54.09/17.41 thf(f419,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f418])).
% 54.09/17.41 thf(f420,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f419])).
% 54.09/17.41 thf(f421,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f419])).
% 54.09/17.41 thf(f422,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f421])).
% 54.09/17.41 thf(f423,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f422])).
% 54.09/17.41 thf(f424,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f423])).
% 54.09/17.41 thf(f425,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f424])).
% 54.09/17.41 thf(f426,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f424])).
% 54.09/17.41 thf(f427,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f426])).
% 54.09/17.41 thf(f428,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f427])).
% 54.09/17.41 thf(f429,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f428])).
% 54.09/17.41 thf(f430,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f429])).
% 54.09/17.41 thf(f431,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f430])).
% 54.09/17.41 thf(f432,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f431])).
% 54.09/17.41 thf(f433,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f432])).
% 54.09/17.41 thf(f434,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f433])).
% 54.09/17.41 thf(f435,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f434])).
% 54.09/17.41 thf(f436,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f435])).
% 54.09/17.41 thf(f437,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f436])).
% 54.09/17.41 thf(f438,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f425])).
% 54.09/17.41 thf(f439,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f438])).
% 54.09/17.41 thf(f440,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f439])).
% 54.09/17.41 thf(f441,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f439])).
% 54.09/17.41 thf(f442,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f441])).
% 54.09/17.41 thf(f443,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f442])).
% 54.09/17.41 thf(f444,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f443])).
% 54.09/17.41 thf(f445,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f444])).
% 54.09/17.41 thf(f446,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f445])).
% 54.09/17.41 thf(f447,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f446])).
% 54.09/17.41 thf(f448,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f447])).
% 54.09/17.41 thf(f449,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f448])).
% 54.09/17.41 thf(f450,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f449])).
% 54.09/17.41 thf(f451,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f450])).
% 54.09/17.41 thf(f452,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f451])).
% 54.09/17.41 thf(f453,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f440])).
% 54.09/17.41 thf(f454,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f453])).
% 54.09/17.41 thf(f455,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f454])).
% 54.09/17.41 thf(f456,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f454])).
% 54.09/17.41 thf(f457,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f456])).
% 54.09/17.41 thf(f458,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f457])).
% 54.09/17.41 thf(f459,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f458])).
% 54.09/17.41 thf(f460,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f459])).
% 54.09/17.41 thf(f461,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f460])).
% 54.09/17.41 thf(f462,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f461])).
% 54.09/17.41 thf(f463,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f462])).
% 54.09/17.41 thf(f464,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f463])).
% 54.09/17.41 thf(f465,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f464])).
% 54.09/17.41 thf(f466,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f465])).
% 54.09/17.41 thf(f467,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f466])).
% 54.09/17.41 thf(f468,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f455])).
% 54.09/17.41 thf(f469,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f468])).
% 54.09/17.41 thf(f470,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f469])).
% 54.09/17.41 thf(f471,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f470])).
% 54.09/17.41 thf(f472,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f471])).
% 54.09/17.41 thf(f473,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f472])).
% 54.09/17.41 thf(f474,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f473])).
% 54.09/17.41 thf(f475,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f474])).
% 54.09/17.41 thf(f476,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f475])).
% 54.09/17.41 thf(f477,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f476])).
% 54.09/17.41 thf(f478,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f477])).
% 54.09/17.41 thf(f479,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f420])).
% 54.09/17.41 thf(f480,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f479])).
% 54.09/17.41 thf(f481,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f480])).
% 54.09/17.41 thf(f482,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f481])).
% 54.09/17.41 thf(f483,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f481])).
% 54.09/17.41 thf(f484,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f483])).
% 54.09/17.41 thf(f485,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f484])).
% 54.09/17.41 thf(f486,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f485])).
% 54.09/17.41 thf(f487,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f486])).
% 54.09/17.41 thf(f488,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f487])).
% 54.09/17.41 thf(f489,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f488])).
% 54.09/17.41 thf(f490,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f489])).
% 54.09/17.41 thf(f491,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f490])).
% 54.09/17.41 thf(f492,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f491])).
% 54.09/17.41 thf(f493,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f492])).
% 54.09/17.41 thf(f494,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f493])).
% 54.09/17.41 thf(f495,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f482])).
% 54.09/17.41 thf(f496,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f495])).
% 54.09/17.41 thf(f497,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f496])).
% 54.09/17.41 thf(f498,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f496])).
% 54.09/17.41 thf(f499,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f498])).
% 54.09/17.41 thf(f500,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f499])).
% 54.09/17.41 thf(f501,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f500])).
% 54.09/17.41 thf(f502,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f501])).
% 54.09/17.41 thf(f503,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f502])).
% 54.09/17.41 thf(f504,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f503])).
% 54.09/17.41 thf(f505,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f504])).
% 54.09/17.41 thf(f506,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f505])).
% 54.09/17.41 thf(f507,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f506])).
% 54.09/17.41 thf(f508,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f507])).
% 54.09/17.41 thf(f509,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f508])).
% 54.09/17.41 thf(f510,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f497])).
% 54.09/17.41 thf(f511,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f510])).
% 54.09/17.41 thf(f512,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f511])).
% 54.09/17.41 thf(f513,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f511])).
% 54.09/17.41 thf(f514,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f513])).
% 54.09/17.41 thf(f515,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f514])).
% 54.09/17.41 thf(f516,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f515])).
% 54.09/17.41 thf(f517,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f516])).
% 54.09/17.41 thf(f518,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f517])).
% 54.09/17.41 thf(f519,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f518])).
% 54.09/17.41 thf(f520,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f519])).
% 54.09/17.41 thf(f521,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f520])).
% 54.09/17.41 thf(f522,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f521])).
% 54.09/17.41 thf(f523,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f522])).
% 54.09/17.41 thf(f524,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f523])).
% 54.09/17.41 thf(f525,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f512])).
% 54.09/17.41 thf(f526,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f525])).
% 54.09/17.41 thf(f527,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f526])).
% 54.09/17.41 thf(f528,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f527])).
% 54.09/17.41 thf(f529,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f528])).
% 54.09/17.41 thf(f530,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f529])).
% 54.09/17.41 thf(f531,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f530])).
% 54.09/17.41 thf(f532,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f531])).
% 54.09/17.41 thf(f533,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f532])).
% 54.09/17.41 thf(f534,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f533])).
% 54.09/17.41 thf(f535,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f534])).
% 54.09/17.41 thf(f536,plain,(
% 54.09/17.41 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f293])).
% 54.09/17.41 thf(f537,plain,(
% 54.09/17.41 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f536])).
% 54.09/17.41 thf(f538,plain,(
% 54.09/17.41 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f537])).
% 54.09/17.41 thf(f539,plain,(
% 54.09/17.41 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f537])).
% 54.09/17.41 thf(f540,plain,(
% 54.09/17.41 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f539])).
% 54.09/17.41 thf(f541,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f540])).
% 54.09/17.41 thf(f542,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f541])).
% 54.09/17.41 thf(f543,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f542])).
% 54.09/17.41 thf(f544,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f542])).
% 54.09/17.41 thf(f545,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f544])).
% 54.09/17.41 thf(f546,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f545])).
% 54.09/17.41 thf(f547,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f546])).
% 54.09/17.41 thf(f548,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f547])).
% 54.09/17.41 thf(f549,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f547])).
% 54.09/17.41 thf(f550,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f549])).
% 54.09/17.41 thf(f551,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f550])).
% 54.09/17.41 thf(f552,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f551])).
% 54.09/17.41 thf(f553,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f552])).
% 54.09/17.41 thf(f554,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f553])).
% 54.09/17.41 thf(f555,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f554])).
% 54.09/17.41 thf(f556,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f555])).
% 54.09/17.41 thf(f557,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f556])).
% 54.09/17.41 thf(f558,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f557])).
% 54.09/17.41 thf(f559,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f558])).
% 54.09/17.41 thf(f560,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f559])).
% 54.09/17.41 thf(f561,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f548])).
% 54.09/17.41 thf(f562,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f561])).
% 54.09/17.41 thf(f563,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f562])).
% 54.09/17.41 thf(f564,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f562])).
% 54.09/17.41 thf(f565,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f564])).
% 54.09/17.41 thf(f566,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f565])).
% 54.09/17.41 thf(f567,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f566])).
% 54.09/17.41 thf(f568,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f567])).
% 54.09/17.41 thf(f569,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f568])).
% 54.09/17.41 thf(f570,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f569])).
% 54.09/17.41 thf(f571,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f570])).
% 54.09/17.41 thf(f572,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f571])).
% 54.09/17.41 thf(f573,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f572])).
% 54.09/17.41 thf(f574,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f573])).
% 54.09/17.41 thf(f575,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f574])).
% 54.09/17.41 thf(f576,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f563])).
% 54.09/17.41 thf(f577,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f576])).
% 54.09/17.41 thf(f578,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f577])).
% 54.09/17.41 thf(f579,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f577])).
% 54.09/17.41 thf(f580,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f579])).
% 54.09/17.41 thf(f581,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f580])).
% 54.09/17.41 thf(f582,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f581])).
% 54.09/17.41 thf(f583,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f582])).
% 54.09/17.41 thf(f584,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f583])).
% 54.09/17.41 thf(f585,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f584])).
% 54.09/17.41 thf(f586,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f585])).
% 54.09/17.41 thf(f587,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f586])).
% 54.09/17.41 thf(f588,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f587])).
% 54.09/17.41 thf(f589,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f588])).
% 54.09/17.41 thf(f590,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f589])).
% 54.09/17.41 thf(f591,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f578])).
% 54.09/17.41 thf(f592,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f591])).
% 54.09/17.41 thf(f593,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f592])).
% 54.09/17.41 thf(f594,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f593])).
% 54.09/17.41 thf(f595,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f594])).
% 54.09/17.41 thf(f596,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f595])).
% 54.09/17.41 thf(f597,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f596])).
% 54.09/17.41 thf(f598,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f597])).
% 54.09/17.41 thf(f599,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f598])).
% 54.09/17.41 thf(f600,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f599])).
% 54.09/17.41 thf(f601,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f600])).
% 54.09/17.41 thf(f602,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f543])).
% 54.09/17.41 thf(f603,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f602])).
% 54.09/17.41 thf(f604,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f603])).
% 54.09/17.41 thf(f605,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f603])).
% 54.09/17.41 thf(f606,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f605])).
% 54.09/17.41 thf(f607,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f606])).
% 54.09/17.41 thf(f608,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f607])).
% 54.09/17.41 thf(f609,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f608])).
% 54.09/17.41 thf(f610,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f608])).
% 54.09/17.41 thf(f611,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f610])).
% 54.09/17.41 thf(f612,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f611])).
% 54.09/17.41 thf(f613,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f612])).
% 54.09/17.41 thf(f614,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f613])).
% 54.09/17.41 thf(f615,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f614])).
% 54.09/17.41 thf(f616,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f615])).
% 54.09/17.41 thf(f617,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f616])).
% 54.09/17.41 thf(f618,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f617])).
% 54.09/17.41 thf(f619,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f618])).
% 54.09/17.41 thf(f620,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f619])).
% 54.09/17.41 thf(f621,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f620])).
% 54.09/17.41 thf(f622,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f609])).
% 54.09/17.41 thf(f623,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f622])).
% 54.09/17.41 thf(f624,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f623])).
% 54.09/17.41 thf(f625,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f623])).
% 54.09/17.41 thf(f626,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f625])).
% 54.09/17.41 thf(f627,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f626])).
% 54.09/17.41 thf(f628,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f627])).
% 54.09/17.41 thf(f629,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f628])).
% 54.09/17.41 thf(f630,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f629])).
% 54.09/17.41 thf(f631,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f630])).
% 54.09/17.41 thf(f632,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f631])).
% 54.09/17.41 thf(f633,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f632])).
% 54.09/17.41 thf(f634,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f633])).
% 54.09/17.41 thf(f635,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f634])).
% 54.09/17.41 thf(f636,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f635])).
% 54.09/17.41 thf(f637,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f624])).
% 54.09/17.41 thf(f638,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f637])).
% 54.09/17.41 thf(f639,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f638])).
% 54.09/17.41 thf(f640,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f638])).
% 54.09/17.41 thf(f641,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f640])).
% 54.09/17.41 thf(f642,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f641])).
% 54.09/17.41 thf(f643,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f642])).
% 54.09/17.41 thf(f644,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f643])).
% 54.09/17.41 thf(f645,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f644])).
% 54.09/17.41 thf(f646,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f645])).
% 54.09/17.41 thf(f647,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f646])).
% 54.09/17.41 thf(f648,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f647])).
% 54.09/17.41 thf(f649,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f648])).
% 54.09/17.41 thf(f650,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f649])).
% 54.09/17.41 thf(f651,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f650])).
% 54.09/17.41 thf(f652,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f639])).
% 54.09/17.41 thf(f653,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f652])).
% 54.09/17.41 thf(f654,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f653])).
% 54.09/17.41 thf(f655,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f654])).
% 54.09/17.41 thf(f656,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f655])).
% 54.09/17.41 thf(f657,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f656])).
% 54.09/17.41 thf(f658,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f657])).
% 54.09/17.41 thf(f659,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f658])).
% 54.09/17.41 thf(f660,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f659])).
% 54.09/17.41 thf(f661,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f660])).
% 54.09/17.41 thf(f662,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f661])).
% 54.09/17.41 thf(f663,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f604])).
% 54.09/17.41 thf(f664,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f663])).
% 54.09/17.41 thf(f665,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f664])).
% 54.09/17.41 thf(f666,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f664])).
% 54.09/17.41 thf(f667,plain,(
% 54.09/17.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f666])).
% 54.09/17.41 thf(f668,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f667])).
% 54.09/17.41 thf(f669,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f668])).
% 54.09/17.41 thf(f670,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f669])).
% 54.09/17.41 thf(f671,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f669])).
% 54.09/17.41 thf(f672,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f671])).
% 54.09/17.41 thf(f673,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.41 inference(pi_proxy_clausification,[],[f672])).
% 54.09/17.41 thf(f674,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.41 inference(beta-eta_normalization,[],[f673])).
% 54.09/17.41 thf(f675,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f674])).
% 54.09/17.41 thf(f676,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f675])).
% 54.09/17.41 thf(f677,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f676])).
% 54.09/17.41 thf(f678,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f677])).
% 54.09/17.41 thf(f679,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f678])).
% 54.09/17.41 thf(f680,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f679])).
% 54.09/17.41 thf(f681,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f680])).
% 54.09/17.41 thf(f682,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f681])).
% 54.09/17.41 thf(f683,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f670])).
% 54.09/17.41 thf(f684,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.41 inference(not_proxy_clausification,[],[f683])).
% 54.09/17.41 thf(f685,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f684])).
% 54.09/17.41 thf(f686,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.41 inference(or_proxy_clausification,[],[f684])).
% 54.09/17.41 thf(f687,plain,(
% 54.09/17.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f686])).
% 54.09/17.42 thf(f688,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f687])).
% 54.09/17.42 thf(f689,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f688])).
% 54.09/17.42 thf(f690,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f689])).
% 54.09/17.42 thf(f691,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f690])).
% 54.09/17.42 thf(f692,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f691])).
% 54.09/17.42 thf(f693,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f692])).
% 54.09/17.42 thf(f694,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f693])).
% 54.09/17.42 thf(f695,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f694])).
% 54.09/17.42 thf(f696,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f695])).
% 54.09/17.42 thf(f697,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f696])).
% 54.09/17.42 thf(f698,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f685])).
% 54.09/17.42 thf(f699,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f698])).
% 54.09/17.42 thf(f700,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f699])).
% 54.09/17.42 thf(f701,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f699])).
% 54.09/17.42 thf(f702,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f701])).
% 54.09/17.42 thf(f703,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f702])).
% 54.09/17.42 thf(f704,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f703])).
% 54.09/17.42 thf(f705,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f704])).
% 54.09/17.42 thf(f706,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f705])).
% 54.09/17.42 thf(f707,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f706])).
% 54.09/17.42 thf(f708,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f707])).
% 54.09/17.42 thf(f709,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f708])).
% 54.09/17.42 thf(f710,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f709])).
% 54.09/17.42 thf(f711,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f710])).
% 54.09/17.42 thf(f712,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f711])).
% 54.09/17.42 thf(f713,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f700])).
% 54.09/17.42 thf(f714,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f713])).
% 54.09/17.42 thf(f715,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f714])).
% 54.09/17.42 thf(f716,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f715])).
% 54.09/17.42 thf(f717,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f716])).
% 54.09/17.42 thf(f718,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f717])).
% 54.09/17.42 thf(f719,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f718])).
% 54.09/17.42 thf(f720,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f719])).
% 54.09/17.42 thf(f721,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f720])).
% 54.09/17.42 thf(f722,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f721])).
% 54.09/17.42 thf(f723,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f722])).
% 54.09/17.42 thf(f724,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f665])).
% 54.09/17.42 thf(f725,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f724])).
% 54.09/17.42 thf(f726,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f725])).
% 54.09/17.42 thf(f727,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f726])).
% 54.09/17.42 thf(f728,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f726])).
% 54.09/17.42 thf(f729,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f728])).
% 54.09/17.42 thf(f730,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f729])).
% 54.09/17.42 thf(f731,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f730])).
% 54.09/17.42 thf(f732,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f731])).
% 54.09/17.42 thf(f733,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f732])).
% 54.09/17.42 thf(f734,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f733])).
% 54.09/17.42 thf(f735,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f734])).
% 54.09/17.42 thf(f736,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f735])).
% 54.09/17.42 thf(f737,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f736])).
% 54.09/17.42 thf(f738,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f737])).
% 54.09/17.42 thf(f739,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f738])).
% 54.09/17.42 thf(f740,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f727])).
% 54.09/17.42 thf(f741,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f740])).
% 54.09/17.42 thf(f742,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f741])).
% 54.09/17.42 thf(f743,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f741])).
% 54.09/17.42 thf(f744,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f743])).
% 54.09/17.42 thf(f745,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f744])).
% 54.09/17.42 thf(f746,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f745])).
% 54.09/17.42 thf(f747,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f746])).
% 54.09/17.42 thf(f748,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f747])).
% 54.09/17.42 thf(f749,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f748])).
% 54.09/17.42 thf(f750,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f749])).
% 54.09/17.42 thf(f751,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f750])).
% 54.09/17.42 thf(f752,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f751])).
% 54.09/17.42 thf(f753,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f752])).
% 54.09/17.42 thf(f754,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f753])).
% 54.09/17.42 thf(f755,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f742])).
% 54.09/17.42 thf(f756,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f755])).
% 54.09/17.42 thf(f757,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f756])).
% 54.09/17.42 thf(f758,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f756])).
% 54.09/17.42 thf(f759,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f758])).
% 54.09/17.42 thf(f760,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f759])).
% 54.09/17.42 thf(f761,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f760])).
% 54.09/17.42 thf(f762,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f761])).
% 54.09/17.42 thf(f763,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f762])).
% 54.09/17.42 thf(f764,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f763])).
% 54.09/17.42 thf(f765,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f764])).
% 54.09/17.42 thf(f766,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f765])).
% 54.09/17.42 thf(f767,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f766])).
% 54.09/17.42 thf(f768,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f767])).
% 54.09/17.42 thf(f769,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f768])).
% 54.09/17.42 thf(f770,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f757])).
% 54.09/17.42 thf(f771,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f770])).
% 54.09/17.42 thf(f772,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f771])).
% 54.09/17.42 thf(f773,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f772])).
% 54.09/17.42 thf(f774,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f773])).
% 54.09/17.42 thf(f775,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f774])).
% 54.09/17.42 thf(f776,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f775])).
% 54.09/17.42 thf(f777,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f776])).
% 54.09/17.42 thf(f778,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f777])).
% 54.09/17.42 thf(f779,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f778])).
% 54.09/17.42 thf(f780,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f779])).
% 54.09/17.42 thf(f781,plain,(
% 54.09/17.42 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f538])).
% 54.09/17.42 thf(f782,plain,(
% 54.09/17.42 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f781])).
% 54.09/17.42 thf(f783,plain,(
% 54.09/17.42 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f782])).
% 54.09/17.42 thf(f784,plain,(
% 54.09/17.42 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f782])).
% 54.09/17.42 thf(f785,plain,(
% 54.09/17.42 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f784])).
% 54.09/17.42 thf(f786,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f785])).
% 54.09/17.42 thf(f787,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f786])).
% 54.09/17.42 thf(f788,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f787])).
% 54.09/17.42 thf(f789,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f787])).
% 54.09/17.42 thf(f790,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f789])).
% 54.09/17.42 thf(f791,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f790])).
% 54.09/17.42 thf(f792,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f791])).
% 54.09/17.42 thf(f793,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f792])).
% 54.09/17.42 thf(f794,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f792])).
% 54.09/17.42 thf(f795,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f794])).
% 54.09/17.42 thf(f796,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f795])).
% 54.09/17.42 thf(f797,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f796])).
% 54.09/17.42 thf(f798,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f797])).
% 54.09/17.42 thf(f799,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f798])).
% 54.09/17.42 thf(f800,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f799])).
% 54.09/17.42 thf(f801,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f800])).
% 54.09/17.42 thf(f802,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f801])).
% 54.09/17.42 thf(f803,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f802])).
% 54.09/17.42 thf(f804,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f803])).
% 54.09/17.42 thf(f805,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f804])).
% 54.09/17.42 thf(f806,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f793])).
% 54.09/17.42 thf(f807,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f806])).
% 54.09/17.42 thf(f808,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f807])).
% 54.09/17.42 thf(f809,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f807])).
% 54.09/17.42 thf(f810,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f809])).
% 54.09/17.42 thf(f811,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f810])).
% 54.09/17.42 thf(f812,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f811])).
% 54.09/17.42 thf(f813,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f812])).
% 54.09/17.42 thf(f814,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f813])).
% 54.09/17.42 thf(f815,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f814])).
% 54.09/17.42 thf(f816,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f815])).
% 54.09/17.42 thf(f817,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f816])).
% 54.09/17.42 thf(f818,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f817])).
% 54.09/17.42 thf(f819,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f818])).
% 54.09/17.42 thf(f820,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f819])).
% 54.09/17.42 thf(f821,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f808])).
% 54.09/17.42 thf(f822,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f821])).
% 54.09/17.42 thf(f823,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f822])).
% 54.09/17.42 thf(f824,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f822])).
% 54.09/17.42 thf(f825,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f824])).
% 54.09/17.42 thf(f826,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f825])).
% 54.09/17.42 thf(f827,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f826])).
% 54.09/17.42 thf(f828,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f827])).
% 54.09/17.42 thf(f829,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f828])).
% 54.09/17.42 thf(f830,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f829])).
% 54.09/17.42 thf(f831,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f830])).
% 54.09/17.42 thf(f832,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f831])).
% 54.09/17.42 thf(f833,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f832])).
% 54.09/17.42 thf(f834,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f833])).
% 54.09/17.42 thf(f835,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f834])).
% 54.09/17.42 thf(f836,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f823])).
% 54.09/17.42 thf(f837,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f836])).
% 54.09/17.42 thf(f838,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f837])).
% 54.09/17.42 thf(f839,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f838])).
% 54.09/17.42 thf(f840,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f839])).
% 54.09/17.42 thf(f841,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f840])).
% 54.09/17.42 thf(f842,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f841])).
% 54.09/17.42 thf(f843,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f842])).
% 54.09/17.42 thf(f844,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f843])).
% 54.09/17.42 thf(f845,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f844])).
% 54.09/17.42 thf(f846,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f845])).
% 54.09/17.42 thf(f847,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f788])).
% 54.09/17.42 thf(f848,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f847])).
% 54.09/17.42 thf(f849,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f848])).
% 54.09/17.42 thf(f850,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f848])).
% 54.09/17.42 thf(f851,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f850])).
% 54.09/17.42 thf(f852,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f851])).
% 54.09/17.42 thf(f853,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f852])).
% 54.09/17.42 thf(f854,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f853])).
% 54.09/17.42 thf(f855,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f853])).
% 54.09/17.42 thf(f856,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f855])).
% 54.09/17.42 thf(f857,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f856])).
% 54.09/17.42 thf(f858,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f857])).
% 54.09/17.42 thf(f859,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f858])).
% 54.09/17.42 thf(f860,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f859])).
% 54.09/17.42 thf(f861,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f860])).
% 54.09/17.42 thf(f862,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f861])).
% 54.09/17.42 thf(f863,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f862])).
% 54.09/17.42 thf(f864,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f863])).
% 54.09/17.42 thf(f865,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f864])).
% 54.09/17.42 thf(f866,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f865])).
% 54.09/17.42 thf(f867,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f854])).
% 54.09/17.42 thf(f868,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f867])).
% 54.09/17.42 thf(f869,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f868])).
% 54.09/17.42 thf(f870,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f868])).
% 54.09/17.42 thf(f871,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f870])).
% 54.09/17.42 thf(f872,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f871])).
% 54.09/17.42 thf(f873,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f872])).
% 54.09/17.42 thf(f874,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f873])).
% 54.09/17.42 thf(f875,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f874])).
% 54.09/17.42 thf(f876,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f875])).
% 54.09/17.42 thf(f877,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f876])).
% 54.09/17.42 thf(f878,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f877])).
% 54.09/17.42 thf(f879,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f878])).
% 54.09/17.42 thf(f880,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f879])).
% 54.09/17.42 thf(f881,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f880])).
% 54.09/17.42 thf(f882,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f869])).
% 54.09/17.42 thf(f883,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f882])).
% 54.09/17.42 thf(f884,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f883])).
% 54.09/17.42 thf(f885,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f883])).
% 54.09/17.42 thf(f886,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f885])).
% 54.09/17.42 thf(f887,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f886])).
% 54.09/17.42 thf(f888,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f887])).
% 54.09/17.42 thf(f889,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f888])).
% 54.09/17.42 thf(f890,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f889])).
% 54.09/17.42 thf(f891,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f890])).
% 54.09/17.42 thf(f892,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f891])).
% 54.09/17.42 thf(f893,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f892])).
% 54.09/17.42 thf(f894,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f893])).
% 54.09/17.42 thf(f895,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f894])).
% 54.09/17.42 thf(f896,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f895])).
% 54.09/17.42 thf(f897,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f884])).
% 54.09/17.42 thf(f898,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f897])).
% 54.09/17.42 thf(f899,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f898])).
% 54.09/17.42 thf(f900,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f899])).
% 54.09/17.42 thf(f901,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f900])).
% 54.09/17.42 thf(f902,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f901])).
% 54.09/17.42 thf(f903,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f902])).
% 54.09/17.42 thf(f904,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f903])).
% 54.09/17.42 thf(f905,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f904])).
% 54.09/17.42 thf(f906,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f905])).
% 54.09/17.42 thf(f907,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f906])).
% 54.09/17.42 thf(f908,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f849])).
% 54.09/17.42 thf(f909,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f908])).
% 54.09/17.42 thf(f910,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f909])).
% 54.09/17.42 thf(f911,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f909])).
% 54.09/17.42 thf(f912,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f911])).
% 54.09/17.42 thf(f913,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f912])).
% 54.09/17.42 thf(f914,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f913])).
% 54.09/17.42 thf(f915,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f914])).
% 54.09/17.42 thf(f916,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f914])).
% 54.09/17.42 thf(f917,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f916])).
% 54.09/17.42 thf(f918,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f917])).
% 54.09/17.42 thf(f919,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f918])).
% 54.09/17.42 thf(f920,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f919])).
% 54.09/17.42 thf(f921,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f920])).
% 54.09/17.42 thf(f922,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f921])).
% 54.09/17.42 thf(f923,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f922])).
% 54.09/17.42 thf(f924,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f923])).
% 54.09/17.42 thf(f925,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f924])).
% 54.09/17.42 thf(f926,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f925])).
% 54.09/17.42 thf(f927,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f926])).
% 54.09/17.42 thf(f928,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f915])).
% 54.09/17.42 thf(f929,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f928])).
% 54.09/17.42 thf(f930,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f929])).
% 54.09/17.42 thf(f931,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f929])).
% 54.09/17.42 thf(f932,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f931])).
% 54.09/17.42 thf(f933,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f932])).
% 54.09/17.42 thf(f934,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f933])).
% 54.09/17.42 thf(f935,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f934])).
% 54.09/17.42 thf(f936,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f935])).
% 54.09/17.42 thf(f937,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f936])).
% 54.09/17.42 thf(f938,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f937])).
% 54.09/17.42 thf(f939,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f938])).
% 54.09/17.42 thf(f940,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f939])).
% 54.09/17.42 thf(f941,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f940])).
% 54.09/17.42 thf(f942,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f941])).
% 54.09/17.42 thf(f943,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f930])).
% 54.09/17.42 thf(f944,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f943])).
% 54.09/17.42 thf(f945,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f944])).
% 54.09/17.42 thf(f946,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f944])).
% 54.09/17.42 thf(f947,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f946])).
% 54.09/17.42 thf(f948,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f947])).
% 54.09/17.42 thf(f949,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f948])).
% 54.09/17.42 thf(f950,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f949])).
% 54.09/17.42 thf(f951,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f950])).
% 54.09/17.42 thf(f952,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f951])).
% 54.09/17.42 thf(f953,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f952])).
% 54.09/17.42 thf(f954,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f953])).
% 54.09/17.42 thf(f955,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f954])).
% 54.09/17.42 thf(f956,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f955])).
% 54.09/17.42 thf(f957,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f956])).
% 54.09/17.42 thf(f958,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f945])).
% 54.09/17.42 thf(f959,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f958])).
% 54.09/17.42 thf(f960,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f959])).
% 54.09/17.42 thf(f961,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f960])).
% 54.09/17.42 thf(f962,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f961])).
% 54.09/17.42 thf(f963,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f962])).
% 54.09/17.42 thf(f964,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f963])).
% 54.09/17.42 thf(f965,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f964])).
% 54.09/17.42 thf(f966,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f965])).
% 54.09/17.42 thf(f967,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f966])).
% 54.09/17.42 thf(f968,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f967])).
% 54.09/17.42 thf(f969,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f910])).
% 54.09/17.42 thf(f970,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f969])).
% 54.09/17.42 thf(f971,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f970])).
% 54.09/17.42 thf(f972,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f971])).
% 54.09/17.42 thf(f973,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f971])).
% 54.09/17.42 thf(f974,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f973])).
% 54.09/17.42 thf(f975,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f974])).
% 54.09/17.42 thf(f976,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f975])).
% 54.09/17.42 thf(f977,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f976])).
% 54.09/17.42 thf(f978,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f977])).
% 54.09/17.42 thf(f979,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f978])).
% 54.09/17.42 thf(f980,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f979])).
% 54.09/17.42 thf(f981,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f980])).
% 54.09/17.42 thf(f982,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f981])).
% 54.09/17.42 thf(f983,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f982])).
% 54.09/17.42 thf(f984,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f983])).
% 54.09/17.42 thf(f985,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f972])).
% 54.09/17.42 thf(f986,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f985])).
% 54.09/17.42 thf(f987,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f986])).
% 54.09/17.42 thf(f988,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f986])).
% 54.09/17.42 thf(f989,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f988])).
% 54.09/17.42 thf(f990,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f989])).
% 54.09/17.42 thf(f991,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f990])).
% 54.09/17.42 thf(f992,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f991])).
% 54.09/17.42 thf(f993,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f992])).
% 54.09/17.42 thf(f994,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f993])).
% 54.09/17.42 thf(f995,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f994])).
% 54.09/17.42 thf(f996,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f995])).
% 54.09/17.42 thf(f997,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f996])).
% 54.09/17.42 thf(f998,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f997])).
% 54.09/17.42 thf(f999,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f998])).
% 54.09/17.42 thf(f1000,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f987])).
% 54.09/17.42 thf(f1001,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1000])).
% 54.09/17.42 thf(f1002,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1001])).
% 54.09/17.42 thf(f1003,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1001])).
% 54.09/17.42 thf(f1004,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1003])).
% 54.09/17.42 thf(f1005,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f1004])).
% 54.09/17.42 thf(f1006,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f1005])).
% 54.09/17.42 thf(f1007,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1006])).
% 54.09/17.42 thf(f1008,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1007])).
% 54.09/17.42 thf(f1009,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1008])).
% 54.09/17.42 thf(f1010,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1009])).
% 54.09/17.42 thf(f1011,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1010])).
% 54.09/17.42 thf(f1012,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1011])).
% 54.09/17.42 thf(f1013,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1012])).
% 54.09/17.42 thf(f1014,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1013])).
% 54.09/17.42 thf(f1015,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1002])).
% 54.09/17.42 thf(f1016,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f1015])).
% 54.09/17.42 thf(f1017,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f1016])).
% 54.09/17.42 thf(f1018,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1017])).
% 54.09/17.42 thf(f1019,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1018])).
% 54.09/17.42 thf(f1020,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1019])).
% 54.09/17.42 thf(f1021,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1020])).
% 54.09/17.42 thf(f1022,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1021])).
% 54.09/17.42 thf(f1023,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1022])).
% 54.09/17.42 thf(f1024,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1023])).
% 54.09/17.42 thf(f1025,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1024])).
% 54.09/17.42 thf(f1026,plain,(
% 54.09/17.42 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f783])).
% 54.09/17.42 thf(f1027,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f1026])).
% 54.09/17.42 thf(f1028,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1027])).
% 54.09/17.42 thf(f1029,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1028])).
% 54.09/17.42 thf(f1030,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1028])).
% 54.09/17.42 thf(f1031,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1030])).
% 54.09/17.42 thf(f1032,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f1031])).
% 54.09/17.42 thf(f1033,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1032])).
% 54.09/17.42 thf(f1034,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1033])).
% 54.09/17.42 thf(f1035,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1033])).
% 54.09/17.42 thf(f1036,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1035])).
% 54.09/17.42 thf(f1037,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f1036])).
% 54.09/17.42 thf(f1038,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f1037])).
% 54.09/17.42 thf(f1039,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1038])).
% 54.09/17.42 thf(f1040,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1039])).
% 54.09/17.42 thf(f1041,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1040])).
% 54.09/17.42 thf(f1042,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1041])).
% 54.09/17.42 thf(f1043,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1042])).
% 54.09/17.42 thf(f1044,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1043])).
% 54.09/17.42 thf(f1045,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1044])).
% 54.09/17.42 thf(f1046,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1045])).
% 54.09/17.42 thf(f1047,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1034])).
% 54.09/17.42 thf(f1048,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1047])).
% 54.09/17.42 thf(f1049,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1048])).
% 54.09/17.42 thf(f1050,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1048])).
% 54.09/17.42 thf(f1051,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1050])).
% 54.09/17.42 thf(f1052,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f1051])).
% 54.09/17.42 thf(f1053,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f1052])).
% 54.09/17.42 thf(f1054,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1053])).
% 54.09/17.42 thf(f1055,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1054])).
% 54.09/17.42 thf(f1056,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1055])).
% 54.09/17.42 thf(f1057,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1056])).
% 54.09/17.42 thf(f1058,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1057])).
% 54.09/17.42 thf(f1059,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1058])).
% 54.09/17.42 thf(f1060,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1059])).
% 54.09/17.42 thf(f1061,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1060])).
% 54.09/17.42 thf(f1062,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1049])).
% 54.09/17.42 thf(f1063,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1062])).
% 54.09/17.42 thf(f1064,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1063])).
% 54.09/17.42 thf(f1065,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1063])).
% 54.09/17.42 thf(f1066,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1065])).
% 54.09/17.42 thf(f1067,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f1066])).
% 54.09/17.42 thf(f1068,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f1067])).
% 54.09/17.42 thf(f1069,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1068])).
% 54.09/17.42 thf(f1070,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1069])).
% 54.09/17.42 thf(f1071,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1070])).
% 54.09/17.42 thf(f1072,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1071])).
% 54.09/17.42 thf(f1073,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1072])).
% 54.09/17.42 thf(f1074,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1073])).
% 54.09/17.42 thf(f1075,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1074])).
% 54.09/17.42 thf(f1076,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1075])).
% 54.09/17.42 thf(f1077,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1064])).
% 54.09/17.42 thf(f1078,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f1077])).
% 54.09/17.42 thf(f1079,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f1078])).
% 54.09/17.42 thf(f1080,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1079])).
% 54.09/17.42 thf(f1081,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1080])).
% 54.09/17.42 thf(f1082,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1081])).
% 54.09/17.42 thf(f1083,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1082])).
% 54.09/17.42 thf(f1084,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1083])).
% 54.09/17.42 thf(f1085,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1084])).
% 54.09/17.42 thf(f1086,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1085])).
% 54.09/17.42 thf(f1087,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1086])).
% 54.09/17.42 thf(f1088,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1029])).
% 54.09/17.42 thf(f1089,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1088])).
% 54.09/17.42 thf(f1090,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1089])).
% 54.09/17.42 thf(f1091,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1089])).
% 54.09/17.42 thf(f1092,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1091])).
% 54.09/17.42 thf(f1093,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f1092])).
% 54.09/17.42 thf(f1094,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1093])).
% 54.09/17.42 thf(f1095,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1094])).
% 54.09/17.42 thf(f1096,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1094])).
% 54.09/17.42 thf(f1097,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1096])).
% 54.09/17.42 thf(f1098,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f1097])).
% 54.09/17.42 thf(f1099,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f1098])).
% 54.09/17.42 thf(f1100,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1099])).
% 54.09/17.42 thf(f1101,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1100])).
% 54.09/17.42 thf(f1102,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1101])).
% 54.09/17.42 thf(f1103,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1102])).
% 54.09/17.42 thf(f1104,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1103])).
% 54.09/17.42 thf(f1105,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1104])).
% 54.09/17.42 thf(f1106,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1105])).
% 54.09/17.42 thf(f1107,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1106])).
% 54.09/17.42 thf(f1108,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1095])).
% 54.09/17.42 thf(f1109,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1108])).
% 54.09/17.42 thf(f1110,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1109])).
% 54.09/17.42 thf(f1111,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1109])).
% 54.09/17.42 thf(f1112,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1111])).
% 54.09/17.42 thf(f1113,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f1112])).
% 54.09/17.42 thf(f1114,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f1113])).
% 54.09/17.42 thf(f1115,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1114])).
% 54.09/17.42 thf(f1116,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1115])).
% 54.09/17.42 thf(f1117,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1116])).
% 54.09/17.42 thf(f1118,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1117])).
% 54.09/17.42 thf(f1119,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1118])).
% 54.09/17.42 thf(f1120,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1119])).
% 54.09/17.42 thf(f1121,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1120])).
% 54.09/17.42 thf(f1122,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1121])).
% 54.09/17.42 thf(f1123,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1110])).
% 54.09/17.42 thf(f1124,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1123])).
% 54.09/17.42 thf(f1125,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1124])).
% 54.09/17.42 thf(f1126,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1124])).
% 54.09/17.42 thf(f1127,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1126])).
% 54.09/17.42 thf(f1128,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f1127])).
% 54.09/17.42 thf(f1129,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f1128])).
% 54.09/17.42 thf(f1130,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1129])).
% 54.09/17.42 thf(f1131,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1130])).
% 54.09/17.42 thf(f1132,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1131])).
% 54.09/17.42 thf(f1133,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1132])).
% 54.09/17.42 thf(f1134,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1133])).
% 54.09/17.42 thf(f1135,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1134])).
% 54.09/17.42 thf(f1136,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1135])).
% 54.09/17.42 thf(f1137,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1136])).
% 54.09/17.42 thf(f1138,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1125])).
% 54.09/17.42 thf(f1139,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f1138])).
% 54.09/17.42 thf(f1140,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f1139])).
% 54.09/17.42 thf(f1141,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1140])).
% 54.09/17.42 thf(f1142,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1141])).
% 54.09/17.42 thf(f1143,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1142])).
% 54.09/17.42 thf(f1144,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1143])).
% 54.09/17.42 thf(f1145,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1144])).
% 54.09/17.42 thf(f1146,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1145])).
% 54.09/17.42 thf(f1147,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1146])).
% 54.09/17.42 thf(f1148,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1147])).
% 54.09/17.42 thf(f1149,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1090])).
% 54.09/17.42 thf(f1150,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1149])).
% 54.09/17.42 thf(f1151,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1150])).
% 54.09/17.42 thf(f1152,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1150])).
% 54.09/17.42 thf(f1153,plain,(
% 54.09/17.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1152])).
% 54.09/17.42 thf(f1154,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f1153])).
% 54.09/17.42 thf(f1155,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1154])).
% 54.09/17.42 thf(f1156,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1155])).
% 54.09/17.42 thf(f1157,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1155])).
% 54.09/17.42 thf(f1158,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1157])).
% 54.09/17.42 thf(f1159,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f1158])).
% 54.09/17.42 thf(f1160,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f1159])).
% 54.09/17.42 thf(f1161,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1160])).
% 54.09/17.42 thf(f1162,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1161])).
% 54.09/17.42 thf(f1163,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1162])).
% 54.09/17.42 thf(f1164,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1163])).
% 54.09/17.42 thf(f1165,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1164])).
% 54.09/17.42 thf(f1166,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1165])).
% 54.09/17.42 thf(f1167,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1166])).
% 54.09/17.42 thf(f1168,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1167])).
% 54.09/17.42 thf(f1169,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1156])).
% 54.09/17.42 thf(f1170,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1169])).
% 54.09/17.42 thf(f1171,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1170])).
% 54.09/17.42 thf(f1172,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1170])).
% 54.09/17.42 thf(f1173,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1172])).
% 54.09/17.42 thf(f1174,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f1173])).
% 54.09/17.42 thf(f1175,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f1174])).
% 54.09/17.42 thf(f1176,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1175])).
% 54.09/17.42 thf(f1177,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1176])).
% 54.09/17.42 thf(f1178,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1177])).
% 54.09/17.42 thf(f1179,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1178])).
% 54.09/17.42 thf(f1180,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1179])).
% 54.09/17.42 thf(f1181,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1180])).
% 54.09/17.42 thf(f1182,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1181])).
% 54.09/17.42 thf(f1183,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1182])).
% 54.09/17.42 thf(f1184,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1171])).
% 54.09/17.42 thf(f1185,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1184])).
% 54.09/17.42 thf(f1186,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1185])).
% 54.09/17.42 thf(f1187,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1185])).
% 54.09/17.42 thf(f1188,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1187])).
% 54.09/17.42 thf(f1189,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.42 inference(pi_proxy_clausification,[],[f1188])).
% 54.09/17.42 thf(f1190,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.42 inference(beta-eta_normalization,[],[f1189])).
% 54.09/17.42 thf(f1191,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1190])).
% 54.09/17.42 thf(f1192,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1191])).
% 54.09/17.42 thf(f1193,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1192])).
% 54.09/17.42 thf(f1194,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(or_proxy_clausification,[],[f1193])).
% 54.09/17.42 thf(f1195,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1194])).
% 54.09/17.42 thf(f1196,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1195])).
% 54.09/17.42 thf(f1197,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.42 inference(not_proxy_clausification,[],[f1196])).
% 54.09/17.42 thf(f1198,plain,(
% 54.09/17.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1197])).
% 54.09/17.43 thf(f1199,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1186])).
% 54.09/17.43 thf(f1200,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1199])).
% 54.09/17.43 thf(f1201,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1200])).
% 54.09/17.43 thf(f1202,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1201])).
% 54.09/17.43 thf(f1203,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1202])).
% 54.09/17.43 thf(f1204,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1203])).
% 54.09/17.43 thf(f1205,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1204])).
% 54.09/17.43 thf(f1206,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1205])).
% 54.09/17.43 thf(f1207,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1206])).
% 54.09/17.43 thf(f1208,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1207])).
% 54.09/17.43 thf(f1209,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1208])).
% 54.09/17.43 thf(f1210,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1151])).
% 54.09/17.43 thf(f1211,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1210])).
% 54.09/17.43 thf(f1212,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1211])).
% 54.09/17.43 thf(f1213,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1212])).
% 54.09/17.43 thf(f1214,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1212])).
% 54.09/17.43 thf(f1215,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1214])).
% 54.09/17.43 thf(f1216,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1215])).
% 54.09/17.43 thf(f1217,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1216])).
% 54.09/17.43 thf(f1218,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1217])).
% 54.09/17.43 thf(f1219,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1218])).
% 54.09/17.43 thf(f1220,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1219])).
% 54.09/17.43 thf(f1221,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1220])).
% 54.09/17.43 thf(f1222,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1221])).
% 54.09/17.43 thf(f1223,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1222])).
% 54.09/17.43 thf(f1224,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1223])).
% 54.09/17.43 thf(f1225,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1224])).
% 54.09/17.43 thf(f1226,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1213])).
% 54.09/17.43 thf(f1227,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1226])).
% 54.09/17.43 thf(f1228,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1227])).
% 54.09/17.43 thf(f1229,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1227])).
% 54.09/17.43 thf(f1230,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1229])).
% 54.09/17.43 thf(f1231,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1230])).
% 54.09/17.43 thf(f1232,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1231])).
% 54.09/17.43 thf(f1233,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1232])).
% 54.09/17.43 thf(f1234,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1233])).
% 54.09/17.43 thf(f1235,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1234])).
% 54.09/17.43 thf(f1236,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1235])).
% 54.09/17.43 thf(f1237,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1236])).
% 54.09/17.43 thf(f1238,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1237])).
% 54.09/17.43 thf(f1239,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1238])).
% 54.09/17.43 thf(f1240,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1239])).
% 54.09/17.43 thf(f1241,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1228])).
% 54.09/17.43 thf(f1242,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1241])).
% 54.09/17.43 thf(f1243,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1242])).
% 54.09/17.43 thf(f1244,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1242])).
% 54.09/17.43 thf(f1245,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1244])).
% 54.09/17.43 thf(f1246,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1245])).
% 54.09/17.43 thf(f1247,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1246])).
% 54.09/17.43 thf(f1248,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1247])).
% 54.09/17.43 thf(f1249,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1248])).
% 54.09/17.43 thf(f1250,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1249])).
% 54.09/17.43 thf(f1251,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1250])).
% 54.09/17.43 thf(f1252,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1251])).
% 54.09/17.43 thf(f1253,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1252])).
% 54.09/17.43 thf(f1254,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1253])).
% 54.09/17.43 thf(f1255,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1254])).
% 54.09/17.43 thf(f1256,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1243])).
% 54.09/17.43 thf(f1257,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1256])).
% 54.09/17.43 thf(f1258,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1257])).
% 54.09/17.43 thf(f1259,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1258])).
% 54.09/17.43 thf(f1260,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1259])).
% 54.09/17.43 thf(f1261,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1260])).
% 54.09/17.43 thf(f1262,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1261])).
% 54.09/17.43 thf(f1263,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1262])).
% 54.09/17.43 thf(f1264,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1263])).
% 54.09/17.43 thf(f1265,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1264])).
% 54.09/17.43 thf(f1266,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1265])).
% 54.09/17.43 thf(f1267,plain,(
% 54.09/17.43 ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))),
% 54.09/17.43 inference(not_proxy_clausification,[],[f288])).
% 54.09/17.43 thf(f1268,plain,(
% 54.09/17.43 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1267])).
% 54.09/17.43 thf(f1269,plain,(
% 54.09/17.43 ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1268])).
% 54.09/17.43 thf(f1270,plain,(
% 54.09/17.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1268])).
% 54.09/17.43 thf(f1271,plain,(
% 54.09/17.43 ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1270])).
% 54.09/17.43 thf(f1272,plain,(
% 54.09/17.43 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1271])).
% 54.09/17.43 thf(f1273,plain,(
% 54.09/17.43 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1272])).
% 54.09/17.43 thf(f1274,plain,(
% 54.09/17.43 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1273])).
% 54.09/17.43 thf(f1275,plain,(
% 54.09/17.43 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1273])).
% 54.09/17.43 thf(f1276,plain,(
% 54.09/17.43 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1275])).
% 54.09/17.43 thf(f1277,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1276])).
% 54.09/17.43 thf(f1278,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1277])).
% 54.09/17.43 thf(f1279,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1278])).
% 54.09/17.43 thf(f1280,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1278])).
% 54.09/17.43 thf(f1281,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1280])).
% 54.09/17.43 thf(f1282,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1281])).
% 54.09/17.43 thf(f1283,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1282])).
% 54.09/17.43 thf(f1284,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1283])).
% 54.09/17.43 thf(f1285,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1283])).
% 54.09/17.43 thf(f1286,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1285])).
% 54.09/17.43 thf(f1287,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1286])).
% 54.09/17.43 thf(f1288,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1287])).
% 54.09/17.43 thf(f1289,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1288])).
% 54.09/17.43 thf(f1290,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1289])).
% 54.09/17.43 thf(f1291,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1290])).
% 54.09/17.43 thf(f1292,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1291])).
% 54.09/17.43 thf(f1293,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1292])).
% 54.09/17.43 thf(f1294,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1293])).
% 54.09/17.43 thf(f1295,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1294])).
% 54.09/17.43 thf(f1296,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1295])).
% 54.09/17.43 thf(f1297,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1284])).
% 54.09/17.43 thf(f1298,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1297])).
% 54.09/17.43 thf(f1299,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1298])).
% 54.09/17.43 thf(f1300,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1298])).
% 54.09/17.43 thf(f1301,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1300])).
% 54.09/17.43 thf(f1302,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1301])).
% 54.09/17.43 thf(f1303,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1302])).
% 54.09/17.43 thf(f1304,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1303])).
% 54.09/17.43 thf(f1305,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1304])).
% 54.09/17.43 thf(f1306,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1305])).
% 54.09/17.43 thf(f1307,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1306])).
% 54.09/17.43 thf(f1308,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1307])).
% 54.09/17.43 thf(f1309,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1308])).
% 54.09/17.43 thf(f1310,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1309])).
% 54.09/17.43 thf(f1311,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1310])).
% 54.09/17.43 thf(f1312,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1299])).
% 54.09/17.43 thf(f1313,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1312])).
% 54.09/17.43 thf(f1314,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1313])).
% 54.09/17.43 thf(f1315,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1313])).
% 54.09/17.43 thf(f1316,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1315])).
% 54.09/17.43 thf(f1317,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1316])).
% 54.09/17.43 thf(f1318,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1317])).
% 54.09/17.43 thf(f1319,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1318])).
% 54.09/17.43 thf(f1320,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1319])).
% 54.09/17.43 thf(f1321,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1320])).
% 54.09/17.43 thf(f1322,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1321])).
% 54.09/17.43 thf(f1323,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1322])).
% 54.09/17.43 thf(f1324,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1323])).
% 54.09/17.43 thf(f1325,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1324])).
% 54.09/17.43 thf(f1326,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1325])).
% 54.09/17.43 thf(f1327,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1314])).
% 54.09/17.43 thf(f1328,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1327])).
% 54.09/17.43 thf(f1329,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1328])).
% 54.09/17.43 thf(f1330,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1329])).
% 54.09/17.43 thf(f1331,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1330])).
% 54.09/17.43 thf(f1332,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1331])).
% 54.09/17.43 thf(f1333,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1332])).
% 54.09/17.43 thf(f1334,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1333])).
% 54.09/17.43 thf(f1335,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1334])).
% 54.09/17.43 thf(f1336,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1335])).
% 54.09/17.43 thf(f1337,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1336])).
% 54.09/17.43 thf(f1338,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1279])).
% 54.09/17.43 thf(f1339,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1338])).
% 54.09/17.43 thf(f1340,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1339])).
% 54.09/17.43 thf(f1341,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1339])).
% 54.09/17.43 thf(f1342,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1341])).
% 54.09/17.43 thf(f1343,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1342])).
% 54.09/17.43 thf(f1344,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1343])).
% 54.09/17.43 thf(f1345,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1344])).
% 54.09/17.43 thf(f1346,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1344])).
% 54.09/17.43 thf(f1347,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1346])).
% 54.09/17.43 thf(f1348,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1347])).
% 54.09/17.43 thf(f1349,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1348])).
% 54.09/17.43 thf(f1350,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1349])).
% 54.09/17.43 thf(f1351,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1350])).
% 54.09/17.43 thf(f1352,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1351])).
% 54.09/17.43 thf(f1353,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1352])).
% 54.09/17.43 thf(f1354,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1353])).
% 54.09/17.43 thf(f1355,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1354])).
% 54.09/17.43 thf(f1356,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1355])).
% 54.09/17.43 thf(f1357,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1356])).
% 54.09/17.43 thf(f1358,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1345])).
% 54.09/17.43 thf(f1359,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1358])).
% 54.09/17.43 thf(f1360,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1359])).
% 54.09/17.43 thf(f1361,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1359])).
% 54.09/17.43 thf(f1362,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1361])).
% 54.09/17.43 thf(f1363,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1362])).
% 54.09/17.43 thf(f1364,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1363])).
% 54.09/17.43 thf(f1365,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1364])).
% 54.09/17.43 thf(f1366,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1365])).
% 54.09/17.43 thf(f1367,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1366])).
% 54.09/17.43 thf(f1368,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1367])).
% 54.09/17.43 thf(f1369,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1368])).
% 54.09/17.43 thf(f1370,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1369])).
% 54.09/17.43 thf(f1371,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1370])).
% 54.09/17.43 thf(f1372,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1371])).
% 54.09/17.43 thf(f1373,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1360])).
% 54.09/17.43 thf(f1374,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1373])).
% 54.09/17.43 thf(f1375,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1374])).
% 54.09/17.43 thf(f1376,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1374])).
% 54.09/17.43 thf(f1377,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1376])).
% 54.09/17.43 thf(f1378,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1377])).
% 54.09/17.43 thf(f1379,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1378])).
% 54.09/17.43 thf(f1380,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1379])).
% 54.09/17.43 thf(f1381,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1380])).
% 54.09/17.43 thf(f1382,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1381])).
% 54.09/17.43 thf(f1383,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1382])).
% 54.09/17.43 thf(f1384,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1383])).
% 54.09/17.43 thf(f1385,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1384])).
% 54.09/17.43 thf(f1386,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1385])).
% 54.09/17.43 thf(f1387,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1386])).
% 54.09/17.43 thf(f1388,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1375])).
% 54.09/17.43 thf(f1389,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1388])).
% 54.09/17.43 thf(f1390,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1389])).
% 54.09/17.43 thf(f1391,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1390])).
% 54.09/17.43 thf(f1392,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1391])).
% 54.09/17.43 thf(f1393,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1392])).
% 54.09/17.43 thf(f1394,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1393])).
% 54.09/17.43 thf(f1395,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1394])).
% 54.09/17.43 thf(f1396,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1395])).
% 54.09/17.43 thf(f1397,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1396])).
% 54.09/17.43 thf(f1398,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1397])).
% 54.09/17.43 thf(f1399,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1340])).
% 54.09/17.43 thf(f1400,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1399])).
% 54.09/17.43 thf(f1401,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1400])).
% 54.09/17.43 thf(f1402,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1400])).
% 54.09/17.43 thf(f1403,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1402])).
% 54.09/17.43 thf(f1404,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1403])).
% 54.09/17.43 thf(f1405,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1404])).
% 54.09/17.43 thf(f1406,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1405])).
% 54.09/17.43 thf(f1407,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1405])).
% 54.09/17.43 thf(f1408,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1407])).
% 54.09/17.43 thf(f1409,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1408])).
% 54.09/17.43 thf(f1410,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1409])).
% 54.09/17.43 thf(f1411,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1410])).
% 54.09/17.43 thf(f1412,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1411])).
% 54.09/17.43 thf(f1413,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1412])).
% 54.09/17.43 thf(f1414,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1413])).
% 54.09/17.43 thf(f1415,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1414])).
% 54.09/17.43 thf(f1416,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1415])).
% 54.09/17.43 thf(f1417,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1416])).
% 54.09/17.43 thf(f1418,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1417])).
% 54.09/17.43 thf(f1419,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1406])).
% 54.09/17.43 thf(f1420,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1419])).
% 54.09/17.43 thf(f1421,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1420])).
% 54.09/17.43 thf(f1422,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1420])).
% 54.09/17.43 thf(f1423,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1422])).
% 54.09/17.43 thf(f1424,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1423])).
% 54.09/17.43 thf(f1425,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1424])).
% 54.09/17.43 thf(f1426,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1425])).
% 54.09/17.43 thf(f1427,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1426])).
% 54.09/17.43 thf(f1428,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1427])).
% 54.09/17.43 thf(f1429,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1428])).
% 54.09/17.43 thf(f1430,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1429])).
% 54.09/17.43 thf(f1431,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1430])).
% 54.09/17.43 thf(f1432,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1431])).
% 54.09/17.43 thf(f1433,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1432])).
% 54.09/17.43 thf(f1434,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1421])).
% 54.09/17.43 thf(f1435,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1434])).
% 54.09/17.43 thf(f1436,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1435])).
% 54.09/17.43 thf(f1437,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1435])).
% 54.09/17.43 thf(f1438,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1437])).
% 54.09/17.43 thf(f1439,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1438])).
% 54.09/17.43 thf(f1440,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1439])).
% 54.09/17.43 thf(f1441,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1440])).
% 54.09/17.43 thf(f1442,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1441])).
% 54.09/17.43 thf(f1443,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1442])).
% 54.09/17.43 thf(f1444,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1443])).
% 54.09/17.43 thf(f1445,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1444])).
% 54.09/17.43 thf(f1446,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1445])).
% 54.09/17.43 thf(f1447,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1446])).
% 54.09/17.43 thf(f1448,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1447])).
% 54.09/17.43 thf(f1449,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1436])).
% 54.09/17.43 thf(f1450,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1449])).
% 54.09/17.43 thf(f1451,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1450])).
% 54.09/17.43 thf(f1452,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1451])).
% 54.09/17.43 thf(f1453,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1452])).
% 54.09/17.43 thf(f1454,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1453])).
% 54.09/17.43 thf(f1455,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1454])).
% 54.09/17.43 thf(f1456,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1455])).
% 54.09/17.43 thf(f1457,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1456])).
% 54.09/17.43 thf(f1458,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1457])).
% 54.09/17.43 thf(f1459,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1458])).
% 54.09/17.43 thf(f1460,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1401])).
% 54.09/17.43 thf(f1461,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1460])).
% 54.09/17.43 thf(f1462,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1461])).
% 54.09/17.43 thf(f1463,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1462])).
% 54.09/17.43 thf(f1464,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1462])).
% 54.09/17.43 thf(f1465,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1464])).
% 54.09/17.43 thf(f1466,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1465])).
% 54.09/17.43 thf(f1467,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1466])).
% 54.09/17.43 thf(f1468,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1467])).
% 54.09/17.43 thf(f1469,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1468])).
% 54.09/17.43 thf(f1470,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1469])).
% 54.09/17.43 thf(f1471,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1470])).
% 54.09/17.43 thf(f1472,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1471])).
% 54.09/17.43 thf(f1473,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1472])).
% 54.09/17.43 thf(f1474,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1473])).
% 54.09/17.43 thf(f1475,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1474])).
% 54.09/17.43 thf(f1476,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1463])).
% 54.09/17.43 thf(f1477,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1476])).
% 54.09/17.43 thf(f1478,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1477])).
% 54.09/17.43 thf(f1479,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1477])).
% 54.09/17.43 thf(f1480,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1479])).
% 54.09/17.43 thf(f1481,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1480])).
% 54.09/17.43 thf(f1482,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1481])).
% 54.09/17.43 thf(f1483,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1482])).
% 54.09/17.43 thf(f1484,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1483])).
% 54.09/17.43 thf(f1485,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1484])).
% 54.09/17.43 thf(f1486,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1485])).
% 54.09/17.43 thf(f1487,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1486])).
% 54.09/17.43 thf(f1488,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1487])).
% 54.09/17.43 thf(f1489,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1488])).
% 54.09/17.43 thf(f1490,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1489])).
% 54.09/17.43 thf(f1491,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1478])).
% 54.09/17.43 thf(f1492,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1491])).
% 54.09/17.43 thf(f1493,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1492])).
% 54.09/17.43 thf(f1494,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1492])).
% 54.09/17.43 thf(f1495,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1494])).
% 54.09/17.43 thf(f1496,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1495])).
% 54.09/17.43 thf(f1497,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1496])).
% 54.09/17.43 thf(f1498,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1497])).
% 54.09/17.43 thf(f1499,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1498])).
% 54.09/17.43 thf(f1500,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1499])).
% 54.09/17.43 thf(f1501,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1500])).
% 54.09/17.43 thf(f1502,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1501])).
% 54.09/17.43 thf(f1503,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1502])).
% 54.09/17.43 thf(f1504,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1503])).
% 54.09/17.43 thf(f1505,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1504])).
% 54.09/17.43 thf(f1506,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1493])).
% 54.09/17.43 thf(f1507,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1506])).
% 54.09/17.43 thf(f1508,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1507])).
% 54.09/17.43 thf(f1509,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1508])).
% 54.09/17.43 thf(f1510,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1509])).
% 54.09/17.43 thf(f1511,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1510])).
% 54.09/17.43 thf(f1512,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1511])).
% 54.09/17.43 thf(f1513,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1512])).
% 54.09/17.43 thf(f1514,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1513])).
% 54.09/17.43 thf(f1515,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1514])).
% 54.09/17.43 thf(f1516,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1515])).
% 54.09/17.43 thf(f1517,plain,(
% 54.09/17.43 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1274])).
% 54.09/17.43 thf(f1518,plain,(
% 54.09/17.43 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1517])).
% 54.09/17.43 thf(f1519,plain,(
% 54.09/17.43 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1518])).
% 54.09/17.43 thf(f1520,plain,(
% 54.09/17.43 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1518])).
% 54.09/17.43 thf(f1521,plain,(
% 54.09/17.43 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1520])).
% 54.09/17.43 thf(f1522,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1521])).
% 54.09/17.43 thf(f1523,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1522])).
% 54.09/17.43 thf(f1524,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1523])).
% 54.09/17.43 thf(f1525,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1523])).
% 54.09/17.43 thf(f1526,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1525])).
% 54.09/17.43 thf(f1527,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1526])).
% 54.09/17.43 thf(f1528,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1527])).
% 54.09/17.43 thf(f1529,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1528])).
% 54.09/17.43 thf(f1530,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1528])).
% 54.09/17.43 thf(f1531,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1530])).
% 54.09/17.43 thf(f1532,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1531])).
% 54.09/17.43 thf(f1533,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1532])).
% 54.09/17.43 thf(f1534,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1533])).
% 54.09/17.43 thf(f1535,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1534])).
% 54.09/17.43 thf(f1536,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1535])).
% 54.09/17.43 thf(f1537,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1536])).
% 54.09/17.43 thf(f1538,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1537])).
% 54.09/17.43 thf(f1539,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1538])).
% 54.09/17.43 thf(f1540,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1539])).
% 54.09/17.43 thf(f1541,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1540])).
% 54.09/17.43 thf(f1542,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1529])).
% 54.09/17.43 thf(f1543,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1542])).
% 54.09/17.43 thf(f1544,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1543])).
% 54.09/17.43 thf(f1545,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1543])).
% 54.09/17.43 thf(f1546,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1545])).
% 54.09/17.43 thf(f1547,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1546])).
% 54.09/17.43 thf(f1548,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1547])).
% 54.09/17.43 thf(f1549,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1548])).
% 54.09/17.43 thf(f1550,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1549])).
% 54.09/17.43 thf(f1551,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1550])).
% 54.09/17.43 thf(f1552,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1551])).
% 54.09/17.43 thf(f1553,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1552])).
% 54.09/17.43 thf(f1554,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1553])).
% 54.09/17.43 thf(f1555,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1554])).
% 54.09/17.43 thf(f1556,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1555])).
% 54.09/17.43 thf(f1557,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1544])).
% 54.09/17.43 thf(f1558,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1557])).
% 54.09/17.43 thf(f1559,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1558])).
% 54.09/17.43 thf(f1560,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1558])).
% 54.09/17.43 thf(f1561,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1560])).
% 54.09/17.43 thf(f1562,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1561])).
% 54.09/17.43 thf(f1563,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1562])).
% 54.09/17.43 thf(f1564,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1563])).
% 54.09/17.43 thf(f1565,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1564])).
% 54.09/17.43 thf(f1566,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1565])).
% 54.09/17.43 thf(f1567,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1566])).
% 54.09/17.43 thf(f1568,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1567])).
% 54.09/17.43 thf(f1569,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1568])).
% 54.09/17.43 thf(f1570,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1569])).
% 54.09/17.43 thf(f1571,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1570])).
% 54.09/17.43 thf(f1572,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1559])).
% 54.09/17.43 thf(f1573,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1572])).
% 54.09/17.43 thf(f1574,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1573])).
% 54.09/17.43 thf(f1575,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1574])).
% 54.09/17.43 thf(f1576,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1575])).
% 54.09/17.43 thf(f1577,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1576])).
% 54.09/17.43 thf(f1578,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1577])).
% 54.09/17.43 thf(f1579,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1578])).
% 54.09/17.43 thf(f1580,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1579])).
% 54.09/17.43 thf(f1581,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1580])).
% 54.09/17.43 thf(f1582,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1581])).
% 54.09/17.43 thf(f1583,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1524])).
% 54.09/17.43 thf(f1584,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1583])).
% 54.09/17.43 thf(f1585,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1584])).
% 54.09/17.43 thf(f1586,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1584])).
% 54.09/17.43 thf(f1587,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1586])).
% 54.09/17.43 thf(f1588,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1587])).
% 54.09/17.43 thf(f1589,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1588])).
% 54.09/17.43 thf(f1590,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1589])).
% 54.09/17.43 thf(f1591,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1589])).
% 54.09/17.43 thf(f1592,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1591])).
% 54.09/17.43 thf(f1593,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1592])).
% 54.09/17.43 thf(f1594,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1593])).
% 54.09/17.43 thf(f1595,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1594])).
% 54.09/17.43 thf(f1596,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1595])).
% 54.09/17.43 thf(f1597,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1596])).
% 54.09/17.43 thf(f1598,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1597])).
% 54.09/17.43 thf(f1599,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1598])).
% 54.09/17.43 thf(f1600,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1599])).
% 54.09/17.43 thf(f1601,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1600])).
% 54.09/17.43 thf(f1602,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1601])).
% 54.09/17.43 thf(f1603,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1590])).
% 54.09/17.43 thf(f1604,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1603])).
% 54.09/17.43 thf(f1605,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1604])).
% 54.09/17.43 thf(f1606,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1604])).
% 54.09/17.43 thf(f1607,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1606])).
% 54.09/17.43 thf(f1608,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1607])).
% 54.09/17.43 thf(f1609,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1608])).
% 54.09/17.43 thf(f1610,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1609])).
% 54.09/17.43 thf(f1611,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1610])).
% 54.09/17.43 thf(f1612,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1611])).
% 54.09/17.43 thf(f1613,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1612])).
% 54.09/17.43 thf(f1614,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1613])).
% 54.09/17.43 thf(f1615,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1614])).
% 54.09/17.43 thf(f1616,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1615])).
% 54.09/17.43 thf(f1617,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1616])).
% 54.09/17.43 thf(f1618,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1605])).
% 54.09/17.43 thf(f1619,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1618])).
% 54.09/17.43 thf(f1620,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1619])).
% 54.09/17.43 thf(f1621,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1619])).
% 54.09/17.43 thf(f1622,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1621])).
% 54.09/17.43 thf(f1623,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1622])).
% 54.09/17.43 thf(f1624,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1623])).
% 54.09/17.43 thf(f1625,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1624])).
% 54.09/17.43 thf(f1626,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1625])).
% 54.09/17.43 thf(f1627,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1626])).
% 54.09/17.43 thf(f1628,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1627])).
% 54.09/17.43 thf(f1629,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1628])).
% 54.09/17.43 thf(f1630,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1629])).
% 54.09/17.43 thf(f1631,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1630])).
% 54.09/17.43 thf(f1632,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1631])).
% 54.09/17.43 thf(f1633,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1620])).
% 54.09/17.43 thf(f1634,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1633])).
% 54.09/17.43 thf(f1635,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1634])).
% 54.09/17.43 thf(f1636,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1635])).
% 54.09/17.43 thf(f1637,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1636])).
% 54.09/17.43 thf(f1638,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1637])).
% 54.09/17.43 thf(f1639,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1638])).
% 54.09/17.43 thf(f1640,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1639])).
% 54.09/17.43 thf(f1641,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1640])).
% 54.09/17.43 thf(f1642,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1641])).
% 54.09/17.43 thf(f1643,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1642])).
% 54.09/17.43 thf(f1644,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1585])).
% 54.09/17.43 thf(f1645,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1644])).
% 54.09/17.43 thf(f1646,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1645])).
% 54.09/17.43 thf(f1647,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1645])).
% 54.09/17.43 thf(f1648,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1647])).
% 54.09/17.43 thf(f1649,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1648])).
% 54.09/17.43 thf(f1650,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1649])).
% 54.09/17.43 thf(f1651,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1650])).
% 54.09/17.43 thf(f1652,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1650])).
% 54.09/17.43 thf(f1653,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1652])).
% 54.09/17.43 thf(f1654,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1653])).
% 54.09/17.43 thf(f1655,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1654])).
% 54.09/17.43 thf(f1656,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1655])).
% 54.09/17.43 thf(f1657,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1656])).
% 54.09/17.43 thf(f1658,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1657])).
% 54.09/17.43 thf(f1659,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1658])).
% 54.09/17.43 thf(f1660,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1659])).
% 54.09/17.43 thf(f1661,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1660])).
% 54.09/17.43 thf(f1662,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1661])).
% 54.09/17.43 thf(f1663,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1662])).
% 54.09/17.43 thf(f1664,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1651])).
% 54.09/17.43 thf(f1665,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1664])).
% 54.09/17.43 thf(f1666,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1665])).
% 54.09/17.43 thf(f1667,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1665])).
% 54.09/17.43 thf(f1668,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1667])).
% 54.09/17.43 thf(f1669,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1668])).
% 54.09/17.43 thf(f1670,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1669])).
% 54.09/17.43 thf(f1671,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1670])).
% 54.09/17.43 thf(f1672,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1671])).
% 54.09/17.43 thf(f1673,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1672])).
% 54.09/17.43 thf(f1674,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1673])).
% 54.09/17.43 thf(f1675,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1674])).
% 54.09/17.43 thf(f1676,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1675])).
% 54.09/17.43 thf(f1677,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1676])).
% 54.09/17.43 thf(f1678,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1677])).
% 54.09/17.43 thf(f1679,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1666])).
% 54.09/17.43 thf(f1680,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1679])).
% 54.09/17.43 thf(f1681,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1680])).
% 54.09/17.43 thf(f1682,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1680])).
% 54.09/17.43 thf(f1683,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1682])).
% 54.09/17.43 thf(f1684,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1683])).
% 54.09/17.43 thf(f1685,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1684])).
% 54.09/17.43 thf(f1686,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1685])).
% 54.09/17.43 thf(f1687,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1686])).
% 54.09/17.43 thf(f1688,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1687])).
% 54.09/17.43 thf(f1689,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1688])).
% 54.09/17.43 thf(f1690,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1689])).
% 54.09/17.43 thf(f1691,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1690])).
% 54.09/17.43 thf(f1692,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1691])).
% 54.09/17.43 thf(f1693,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1692])).
% 54.09/17.43 thf(f1694,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1681])).
% 54.09/17.43 thf(f1695,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1694])).
% 54.09/17.43 thf(f1696,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.43 inference(beta-eta_normalization,[],[f1695])).
% 54.09/17.43 thf(f1697,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1696])).
% 54.09/17.43 thf(f1698,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1697])).
% 54.09/17.43 thf(f1699,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1698])).
% 54.09/17.43 thf(f1700,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(or_proxy_clausification,[],[f1699])).
% 54.09/17.43 thf(f1701,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1700])).
% 54.09/17.43 thf(f1702,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1701])).
% 54.09/17.43 thf(f1703,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1702])).
% 54.09/17.43 thf(f1704,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1703])).
% 54.09/17.43 thf(f1705,plain,(
% 54.09/17.43 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(not_proxy_clausification,[],[f1646])).
% 54.09/17.43 thf(f1706,plain,(
% 54.09/17.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.43 inference(pi_proxy_clausification,[],[f1705])).
% 54.09/17.44 thf(f1707,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1706])).
% 54.09/17.44 thf(f1708,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1707])).
% 54.09/17.44 thf(f1709,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1707])).
% 54.09/17.44 thf(f1710,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1709])).
% 54.09/17.44 thf(f1711,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1710])).
% 54.09/17.44 thf(f1712,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1711])).
% 54.09/17.44 thf(f1713,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1712])).
% 54.09/17.44 thf(f1714,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1713])).
% 54.09/17.44 thf(f1715,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1714])).
% 54.09/17.44 thf(f1716,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1715])).
% 54.09/17.44 thf(f1717,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1716])).
% 54.09/17.44 thf(f1718,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1717])).
% 54.09/17.44 thf(f1719,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1718])).
% 54.09/17.44 thf(f1720,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1719])).
% 54.09/17.44 thf(f1721,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1708])).
% 54.09/17.44 thf(f1722,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1721])).
% 54.09/17.44 thf(f1723,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1722])).
% 54.09/17.44 thf(f1724,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1722])).
% 54.09/17.44 thf(f1725,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1724])).
% 54.09/17.44 thf(f1726,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1725])).
% 54.09/17.44 thf(f1727,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1726])).
% 54.09/17.44 thf(f1728,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1727])).
% 54.09/17.44 thf(f1729,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1728])).
% 54.09/17.44 thf(f1730,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1729])).
% 54.09/17.44 thf(f1731,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1730])).
% 54.09/17.44 thf(f1732,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1731])).
% 54.09/17.44 thf(f1733,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1732])).
% 54.09/17.44 thf(f1734,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1733])).
% 54.09/17.44 thf(f1735,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1734])).
% 54.09/17.44 thf(f1736,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1723])).
% 54.09/17.44 thf(f1737,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1736])).
% 54.09/17.44 thf(f1738,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1737])).
% 54.09/17.44 thf(f1739,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1737])).
% 54.09/17.44 thf(f1740,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1739])).
% 54.09/17.44 thf(f1741,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1740])).
% 54.09/17.44 thf(f1742,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1741])).
% 54.09/17.44 thf(f1743,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1742])).
% 54.09/17.44 thf(f1744,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1743])).
% 54.09/17.44 thf(f1745,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1744])).
% 54.09/17.44 thf(f1746,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1745])).
% 54.09/17.44 thf(f1747,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1746])).
% 54.09/17.44 thf(f1748,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1747])).
% 54.09/17.44 thf(f1749,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1748])).
% 54.09/17.44 thf(f1750,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1749])).
% 54.09/17.44 thf(f1751,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1738])).
% 54.09/17.44 thf(f1752,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1751])).
% 54.09/17.44 thf(f1753,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1752])).
% 54.09/17.44 thf(f1754,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1753])).
% 54.09/17.44 thf(f1755,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1754])).
% 54.09/17.44 thf(f1756,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1755])).
% 54.09/17.44 thf(f1757,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1756])).
% 54.09/17.44 thf(f1758,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1757])).
% 54.09/17.44 thf(f1759,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1758])).
% 54.09/17.44 thf(f1760,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1759])).
% 54.09/17.44 thf(f1761,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1760])).
% 54.09/17.44 thf(f1762,plain,(
% 54.09/17.44 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1519])).
% 54.09/17.44 thf(f1763,plain,(
% 54.09/17.44 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1762])).
% 54.09/17.44 thf(f1764,plain,(
% 54.09/17.44 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1763])).
% 54.09/17.44 thf(f1765,plain,(
% 54.09/17.44 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1763])).
% 54.09/17.44 thf(f1766,plain,(
% 54.09/17.44 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1765])).
% 54.09/17.44 thf(f1767,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1766])).
% 54.09/17.44 thf(f1768,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1767])).
% 54.09/17.44 thf(f1769,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1768])).
% 54.09/17.44 thf(f1770,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1768])).
% 54.09/17.44 thf(f1771,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1770])).
% 54.09/17.44 thf(f1772,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1771])).
% 54.09/17.44 thf(f1773,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1772])).
% 54.09/17.44 thf(f1774,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1773])).
% 54.09/17.44 thf(f1775,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1773])).
% 54.09/17.44 thf(f1776,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1775])).
% 54.09/17.44 thf(f1777,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1776])).
% 54.09/17.44 thf(f1778,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1777])).
% 54.09/17.44 thf(f1779,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1778])).
% 54.09/17.44 thf(f1780,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1779])).
% 54.09/17.44 thf(f1781,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1780])).
% 54.09/17.44 thf(f1782,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1781])).
% 54.09/17.44 thf(f1783,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1782])).
% 54.09/17.44 thf(f1784,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1783])).
% 54.09/17.44 thf(f1785,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1784])).
% 54.09/17.44 thf(f1786,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1785])).
% 54.09/17.44 thf(f1787,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1774])).
% 54.09/17.44 thf(f1788,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1787])).
% 54.09/17.44 thf(f1789,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1788])).
% 54.09/17.44 thf(f1790,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1788])).
% 54.09/17.44 thf(f1791,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1790])).
% 54.09/17.44 thf(f1792,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1791])).
% 54.09/17.44 thf(f1793,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1792])).
% 54.09/17.44 thf(f1794,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1793])).
% 54.09/17.44 thf(f1795,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1794])).
% 54.09/17.44 thf(f1796,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1795])).
% 54.09/17.44 thf(f1797,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1796])).
% 54.09/17.44 thf(f1798,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1797])).
% 54.09/17.44 thf(f1799,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1798])).
% 54.09/17.44 thf(f1800,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1799])).
% 54.09/17.44 thf(f1801,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1800])).
% 54.09/17.44 thf(f1802,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1789])).
% 54.09/17.44 thf(f1803,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1802])).
% 54.09/17.44 thf(f1804,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1803])).
% 54.09/17.44 thf(f1805,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1803])).
% 54.09/17.44 thf(f1806,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1805])).
% 54.09/17.44 thf(f1807,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1806])).
% 54.09/17.44 thf(f1808,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1807])).
% 54.09/17.44 thf(f1809,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1808])).
% 54.09/17.44 thf(f1810,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1809])).
% 54.09/17.44 thf(f1811,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1810])).
% 54.09/17.44 thf(f1812,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1811])).
% 54.09/17.44 thf(f1813,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1812])).
% 54.09/17.44 thf(f1814,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1813])).
% 54.09/17.44 thf(f1815,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1814])).
% 54.09/17.44 thf(f1816,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1815])).
% 54.09/17.44 thf(f1817,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1804])).
% 54.09/17.44 thf(f1818,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1817])).
% 54.09/17.44 thf(f1819,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1818])).
% 54.09/17.44 thf(f1820,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1819])).
% 54.09/17.44 thf(f1821,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1820])).
% 54.09/17.44 thf(f1822,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1821])).
% 54.09/17.44 thf(f1823,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1822])).
% 54.09/17.44 thf(f1824,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1823])).
% 54.09/17.44 thf(f1825,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1824])).
% 54.09/17.44 thf(f1826,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1825])).
% 54.09/17.44 thf(f1827,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1826])).
% 54.09/17.44 thf(f1828,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1769])).
% 54.09/17.44 thf(f1829,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1828])).
% 54.09/17.44 thf(f1830,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1829])).
% 54.09/17.44 thf(f1831,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1829])).
% 54.09/17.44 thf(f1832,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1831])).
% 54.09/17.44 thf(f1833,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1832])).
% 54.09/17.44 thf(f1834,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1833])).
% 54.09/17.44 thf(f1835,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1834])).
% 54.09/17.44 thf(f1836,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1834])).
% 54.09/17.44 thf(f1837,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1836])).
% 54.09/17.44 thf(f1838,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1837])).
% 54.09/17.44 thf(f1839,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1838])).
% 54.09/17.44 thf(f1840,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1839])).
% 54.09/17.44 thf(f1841,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1840])).
% 54.09/17.44 thf(f1842,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1841])).
% 54.09/17.44 thf(f1843,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1842])).
% 54.09/17.44 thf(f1844,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1843])).
% 54.09/17.44 thf(f1845,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1844])).
% 54.09/17.44 thf(f1846,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1845])).
% 54.09/17.44 thf(f1847,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1846])).
% 54.09/17.44 thf(f1848,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1835])).
% 54.09/17.44 thf(f1849,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1848])).
% 54.09/17.44 thf(f1850,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1849])).
% 54.09/17.44 thf(f1851,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1849])).
% 54.09/17.44 thf(f1852,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1851])).
% 54.09/17.44 thf(f1853,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1852])).
% 54.09/17.44 thf(f1854,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1853])).
% 54.09/17.44 thf(f1855,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1854])).
% 54.09/17.44 thf(f1856,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1855])).
% 54.09/17.44 thf(f1857,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1856])).
% 54.09/17.44 thf(f1858,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1857])).
% 54.09/17.44 thf(f1859,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1858])).
% 54.09/17.44 thf(f1860,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1859])).
% 54.09/17.44 thf(f1861,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1860])).
% 54.09/17.44 thf(f1862,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1861])).
% 54.09/17.44 thf(f1863,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1850])).
% 54.09/17.44 thf(f1864,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1863])).
% 54.09/17.44 thf(f1865,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1864])).
% 54.09/17.44 thf(f1866,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1864])).
% 54.09/17.44 thf(f1867,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1866])).
% 54.09/17.44 thf(f1868,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1867])).
% 54.09/17.44 thf(f1869,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1868])).
% 54.09/17.44 thf(f1870,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1869])).
% 54.09/17.44 thf(f1871,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1870])).
% 54.09/17.44 thf(f1872,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1871])).
% 54.09/17.44 thf(f1873,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1872])).
% 54.09/17.44 thf(f1874,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1873])).
% 54.09/17.44 thf(f1875,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1874])).
% 54.09/17.44 thf(f1876,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1875])).
% 54.09/17.44 thf(f1877,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1876])).
% 54.09/17.44 thf(f1878,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1865])).
% 54.09/17.44 thf(f1879,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1878])).
% 54.09/17.44 thf(f1880,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1879])).
% 54.09/17.44 thf(f1881,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1880])).
% 54.09/17.44 thf(f1882,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1881])).
% 54.09/17.44 thf(f1883,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1882])).
% 54.09/17.44 thf(f1884,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1883])).
% 54.09/17.44 thf(f1885,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1884])).
% 54.09/17.44 thf(f1886,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1885])).
% 54.09/17.44 thf(f1887,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1886])).
% 54.09/17.44 thf(f1888,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1887])).
% 54.09/17.44 thf(f1889,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1830])).
% 54.09/17.44 thf(f1890,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1889])).
% 54.09/17.44 thf(f1891,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1890])).
% 54.09/17.44 thf(f1892,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1890])).
% 54.09/17.44 thf(f1893,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1892])).
% 54.09/17.44 thf(f1894,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1893])).
% 54.09/17.44 thf(f1895,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1894])).
% 54.09/17.44 thf(f1896,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1895])).
% 54.09/17.44 thf(f1897,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1895])).
% 54.09/17.44 thf(f1898,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1897])).
% 54.09/17.44 thf(f1899,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1898])).
% 54.09/17.44 thf(f1900,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1899])).
% 54.09/17.44 thf(f1901,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1900])).
% 54.09/17.44 thf(f1902,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1901])).
% 54.09/17.44 thf(f1903,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1902])).
% 54.09/17.44 thf(f1904,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1903])).
% 54.09/17.44 thf(f1905,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1904])).
% 54.09/17.44 thf(f1906,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1905])).
% 54.09/17.44 thf(f1907,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1906])).
% 54.09/17.44 thf(f1908,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1907])).
% 54.09/17.44 thf(f1909,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1896])).
% 54.09/17.44 thf(f1910,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1909])).
% 54.09/17.44 thf(f1911,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1910])).
% 54.09/17.44 thf(f1912,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1910])).
% 54.09/17.44 thf(f1913,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1912])).
% 54.09/17.44 thf(f1914,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1913])).
% 54.09/17.44 thf(f1915,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1914])).
% 54.09/17.44 thf(f1916,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1915])).
% 54.09/17.44 thf(f1917,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1916])).
% 54.09/17.44 thf(f1918,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1917])).
% 54.09/17.44 thf(f1919,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1918])).
% 54.09/17.44 thf(f1920,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1919])).
% 54.09/17.44 thf(f1921,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1920])).
% 54.09/17.44 thf(f1922,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1921])).
% 54.09/17.44 thf(f1923,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1922])).
% 54.09/17.44 thf(f1924,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1911])).
% 54.09/17.44 thf(f1925,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1924])).
% 54.09/17.44 thf(f1926,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1925])).
% 54.09/17.44 thf(f1927,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1925])).
% 54.09/17.44 thf(f1928,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1927])).
% 54.09/17.44 thf(f1929,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1928])).
% 54.09/17.44 thf(f1930,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1929])).
% 54.09/17.44 thf(f1931,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1930])).
% 54.09/17.44 thf(f1932,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1931])).
% 54.09/17.44 thf(f1933,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1932])).
% 54.09/17.44 thf(f1934,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1933])).
% 54.09/17.44 thf(f1935,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1934])).
% 54.09/17.44 thf(f1936,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1935])).
% 54.09/17.44 thf(f1937,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1936])).
% 54.09/17.44 thf(f1938,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1937])).
% 54.09/17.44 thf(f1939,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1926])).
% 54.09/17.44 thf(f1940,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1939])).
% 54.09/17.44 thf(f1941,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1940])).
% 54.09/17.44 thf(f1942,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1941])).
% 54.09/17.44 thf(f1943,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1942])).
% 54.09/17.44 thf(f1944,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1943])).
% 54.09/17.44 thf(f1945,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1944])).
% 54.09/17.44 thf(f1946,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1945])).
% 54.09/17.44 thf(f1947,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1946])).
% 54.09/17.44 thf(f1948,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1947])).
% 54.09/17.44 thf(f1949,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1948])).
% 54.09/17.44 thf(f1950,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1891])).
% 54.09/17.44 thf(f1951,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1950])).
% 54.09/17.44 thf(f1952,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1951])).
% 54.09/17.44 thf(f1953,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1952])).
% 54.09/17.44 thf(f1954,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1952])).
% 54.09/17.44 thf(f1955,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1954])).
% 54.09/17.44 thf(f1956,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1955])).
% 54.09/17.44 thf(f1957,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1956])).
% 54.09/17.44 thf(f1958,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1957])).
% 54.09/17.44 thf(f1959,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1958])).
% 54.09/17.44 thf(f1960,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1959])).
% 54.09/17.44 thf(f1961,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1960])).
% 54.09/17.44 thf(f1962,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1961])).
% 54.09/17.44 thf(f1963,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1962])).
% 54.09/17.44 thf(f1964,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1963])).
% 54.09/17.44 thf(f1965,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1964])).
% 54.09/17.44 thf(f1966,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1953])).
% 54.09/17.44 thf(f1967,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1966])).
% 54.09/17.44 thf(f1968,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1967])).
% 54.09/17.44 thf(f1969,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1967])).
% 54.09/17.44 thf(f1970,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1969])).
% 54.09/17.44 thf(f1971,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1970])).
% 54.09/17.44 thf(f1972,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1971])).
% 54.09/17.44 thf(f1973,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1972])).
% 54.09/17.44 thf(f1974,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1973])).
% 54.09/17.44 thf(f1975,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1974])).
% 54.09/17.44 thf(f1976,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1975])).
% 54.09/17.44 thf(f1977,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1976])).
% 54.09/17.44 thf(f1978,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1977])).
% 54.09/17.44 thf(f1979,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1978])).
% 54.09/17.44 thf(f1980,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1979])).
% 54.09/17.44 thf(f1981,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1968])).
% 54.09/17.44 thf(f1982,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1981])).
% 54.09/17.44 thf(f1983,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1982])).
% 54.09/17.44 thf(f1984,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1982])).
% 54.09/17.44 thf(f1985,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1984])).
% 54.09/17.44 thf(f1986,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1985])).
% 54.09/17.44 thf(f1987,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1986])).
% 54.09/17.44 thf(f1988,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1987])).
% 54.09/17.44 thf(f1989,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1988])).
% 54.09/17.44 thf(f1990,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1989])).
% 54.09/17.44 thf(f1991,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1990])).
% 54.09/17.44 thf(f1992,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1991])).
% 54.09/17.44 thf(f1993,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1992])).
% 54.09/17.44 thf(f1994,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1993])).
% 54.09/17.44 thf(f1995,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1994])).
% 54.09/17.44 thf(f1996,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1983])).
% 54.09/17.44 thf(f1997,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f1996])).
% 54.09/17.44 thf(f1998,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f1997])).
% 54.09/17.44 thf(f1999,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1998])).
% 54.09/17.44 thf(f2000,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f1999])).
% 54.09/17.44 thf(f2001,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2000])).
% 54.09/17.44 thf(f2002,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2001])).
% 54.09/17.44 thf(f2003,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2002])).
% 54.09/17.44 thf(f2004,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2003])).
% 54.09/17.44 thf(f2005,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2004])).
% 54.09/17.44 thf(f2006,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2005])).
% 54.09/17.44 thf(f2007,plain,(
% 54.09/17.44 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f1764])).
% 54.09/17.44 thf(f2008,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2007])).
% 54.09/17.44 thf(f2009,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2008])).
% 54.09/17.44 thf(f2010,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2009])).
% 54.09/17.44 thf(f2011,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2009])).
% 54.09/17.44 thf(f2012,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2011])).
% 54.09/17.44 thf(f2013,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2012])).
% 54.09/17.44 thf(f2014,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2013])).
% 54.09/17.44 thf(f2015,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2014])).
% 54.09/17.44 thf(f2016,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2014])).
% 54.09/17.44 thf(f2017,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2016])).
% 54.09/17.44 thf(f2018,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2017])).
% 54.09/17.44 thf(f2019,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f2018])).
% 54.09/17.44 thf(f2020,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2019])).
% 54.09/17.44 thf(f2021,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2020])).
% 54.09/17.44 thf(f2022,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2021])).
% 54.09/17.44 thf(f2023,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2022])).
% 54.09/17.44 thf(f2024,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2023])).
% 54.09/17.44 thf(f2025,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2024])).
% 54.09/17.44 thf(f2026,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2025])).
% 54.09/17.44 thf(f2027,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2026])).
% 54.09/17.44 thf(f2028,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2015])).
% 54.09/17.44 thf(f2029,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2028])).
% 54.09/17.44 thf(f2030,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2029])).
% 54.09/17.44 thf(f2031,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2029])).
% 54.09/17.44 thf(f2032,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2031])).
% 54.09/17.44 thf(f2033,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2032])).
% 54.09/17.44 thf(f2034,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f2033])).
% 54.09/17.44 thf(f2035,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2034])).
% 54.09/17.44 thf(f2036,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2035])).
% 54.09/17.44 thf(f2037,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2036])).
% 54.09/17.44 thf(f2038,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2037])).
% 54.09/17.44 thf(f2039,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2038])).
% 54.09/17.44 thf(f2040,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2039])).
% 54.09/17.44 thf(f2041,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2040])).
% 54.09/17.44 thf(f2042,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2041])).
% 54.09/17.44 thf(f2043,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2030])).
% 54.09/17.44 thf(f2044,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2043])).
% 54.09/17.44 thf(f2045,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2044])).
% 54.09/17.44 thf(f2046,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2044])).
% 54.09/17.44 thf(f2047,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2046])).
% 54.09/17.44 thf(f2048,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2047])).
% 54.09/17.44 thf(f2049,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f2048])).
% 54.09/17.44 thf(f2050,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2049])).
% 54.09/17.44 thf(f2051,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2050])).
% 54.09/17.44 thf(f2052,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2051])).
% 54.09/17.44 thf(f2053,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2052])).
% 54.09/17.44 thf(f2054,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2053])).
% 54.09/17.44 thf(f2055,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2054])).
% 54.09/17.44 thf(f2056,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2055])).
% 54.09/17.44 thf(f2057,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2056])).
% 54.09/17.44 thf(f2058,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2045])).
% 54.09/17.44 thf(f2059,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2058])).
% 54.09/17.44 thf(f2060,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f2059])).
% 54.09/17.44 thf(f2061,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2060])).
% 54.09/17.44 thf(f2062,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2061])).
% 54.09/17.44 thf(f2063,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2062])).
% 54.09/17.44 thf(f2064,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2063])).
% 54.09/17.44 thf(f2065,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2064])).
% 54.09/17.44 thf(f2066,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2065])).
% 54.09/17.44 thf(f2067,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2066])).
% 54.09/17.44 thf(f2068,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2067])).
% 54.09/17.44 thf(f2069,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2010])).
% 54.09/17.44 thf(f2070,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2069])).
% 54.09/17.44 thf(f2071,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2070])).
% 54.09/17.44 thf(f2072,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2070])).
% 54.09/17.44 thf(f2073,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2072])).
% 54.09/17.44 thf(f2074,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2073])).
% 54.09/17.44 thf(f2075,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2074])).
% 54.09/17.44 thf(f2076,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2075])).
% 54.09/17.44 thf(f2077,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2075])).
% 54.09/17.44 thf(f2078,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2077])).
% 54.09/17.44 thf(f2079,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2078])).
% 54.09/17.44 thf(f2080,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f2079])).
% 54.09/17.44 thf(f2081,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2080])).
% 54.09/17.44 thf(f2082,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2081])).
% 54.09/17.44 thf(f2083,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2082])).
% 54.09/17.44 thf(f2084,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2083])).
% 54.09/17.44 thf(f2085,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2084])).
% 54.09/17.44 thf(f2086,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2085])).
% 54.09/17.44 thf(f2087,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2086])).
% 54.09/17.44 thf(f2088,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2087])).
% 54.09/17.44 thf(f2089,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2076])).
% 54.09/17.44 thf(f2090,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2089])).
% 54.09/17.44 thf(f2091,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2090])).
% 54.09/17.44 thf(f2092,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2090])).
% 54.09/17.44 thf(f2093,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2092])).
% 54.09/17.44 thf(f2094,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2093])).
% 54.09/17.44 thf(f2095,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f2094])).
% 54.09/17.44 thf(f2096,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2095])).
% 54.09/17.44 thf(f2097,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2096])).
% 54.09/17.44 thf(f2098,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2097])).
% 54.09/17.44 thf(f2099,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2098])).
% 54.09/17.44 thf(f2100,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2099])).
% 54.09/17.44 thf(f2101,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2100])).
% 54.09/17.44 thf(f2102,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2101])).
% 54.09/17.44 thf(f2103,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2102])).
% 54.09/17.44 thf(f2104,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2091])).
% 54.09/17.44 thf(f2105,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2104])).
% 54.09/17.44 thf(f2106,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2105])).
% 54.09/17.44 thf(f2107,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2105])).
% 54.09/17.44 thf(f2108,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2107])).
% 54.09/17.44 thf(f2109,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2108])).
% 54.09/17.44 thf(f2110,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f2109])).
% 54.09/17.44 thf(f2111,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2110])).
% 54.09/17.44 thf(f2112,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2111])).
% 54.09/17.44 thf(f2113,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2112])).
% 54.09/17.44 thf(f2114,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2113])).
% 54.09/17.44 thf(f2115,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2114])).
% 54.09/17.44 thf(f2116,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2115])).
% 54.09/17.44 thf(f2117,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2116])).
% 54.09/17.44 thf(f2118,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2117])).
% 54.09/17.44 thf(f2119,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2106])).
% 54.09/17.44 thf(f2120,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2119])).
% 54.09/17.44 thf(f2121,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f2120])).
% 54.09/17.44 thf(f2122,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2121])).
% 54.09/17.44 thf(f2123,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2122])).
% 54.09/17.44 thf(f2124,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2123])).
% 54.09/17.44 thf(f2125,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2124])).
% 54.09/17.44 thf(f2126,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2125])).
% 54.09/17.44 thf(f2127,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2126])).
% 54.09/17.44 thf(f2128,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2127])).
% 54.09/17.44 thf(f2129,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2128])).
% 54.09/17.44 thf(f2130,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2071])).
% 54.09/17.44 thf(f2131,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2130])).
% 54.09/17.44 thf(f2132,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2131])).
% 54.09/17.44 thf(f2133,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2131])).
% 54.09/17.44 thf(f2134,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2133])).
% 54.09/17.44 thf(f2135,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2134])).
% 54.09/17.44 thf(f2136,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2135])).
% 54.09/17.44 thf(f2137,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2136])).
% 54.09/17.44 thf(f2138,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2136])).
% 54.09/17.44 thf(f2139,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2138])).
% 54.09/17.44 thf(f2140,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2139])).
% 54.09/17.44 thf(f2141,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f2140])).
% 54.09/17.44 thf(f2142,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2141])).
% 54.09/17.44 thf(f2143,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2142])).
% 54.09/17.44 thf(f2144,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2143])).
% 54.09/17.44 thf(f2145,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2144])).
% 54.09/17.44 thf(f2146,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2145])).
% 54.09/17.44 thf(f2147,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2146])).
% 54.09/17.44 thf(f2148,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2147])).
% 54.09/17.44 thf(f2149,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2148])).
% 54.09/17.44 thf(f2150,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2137])).
% 54.09/17.44 thf(f2151,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2150])).
% 54.09/17.44 thf(f2152,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2151])).
% 54.09/17.44 thf(f2153,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2151])).
% 54.09/17.44 thf(f2154,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2153])).
% 54.09/17.44 thf(f2155,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2154])).
% 54.09/17.44 thf(f2156,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f2155])).
% 54.09/17.44 thf(f2157,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2156])).
% 54.09/17.44 thf(f2158,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2157])).
% 54.09/17.44 thf(f2159,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2158])).
% 54.09/17.44 thf(f2160,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2159])).
% 54.09/17.44 thf(f2161,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2160])).
% 54.09/17.44 thf(f2162,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2161])).
% 54.09/17.44 thf(f2163,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2162])).
% 54.09/17.44 thf(f2164,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2163])).
% 54.09/17.44 thf(f2165,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2152])).
% 54.09/17.44 thf(f2166,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2165])).
% 54.09/17.44 thf(f2167,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2166])).
% 54.09/17.44 thf(f2168,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2166])).
% 54.09/17.44 thf(f2169,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2168])).
% 54.09/17.44 thf(f2170,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2169])).
% 54.09/17.44 thf(f2171,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f2170])).
% 54.09/17.44 thf(f2172,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2171])).
% 54.09/17.44 thf(f2173,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2172])).
% 54.09/17.44 thf(f2174,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2173])).
% 54.09/17.44 thf(f2175,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2174])).
% 54.09/17.44 thf(f2176,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2175])).
% 54.09/17.44 thf(f2177,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2176])).
% 54.09/17.44 thf(f2178,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2177])).
% 54.09/17.44 thf(f2179,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2178])).
% 54.09/17.44 thf(f2180,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2167])).
% 54.09/17.44 thf(f2181,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2180])).
% 54.09/17.44 thf(f2182,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f2181])).
% 54.09/17.44 thf(f2183,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2182])).
% 54.09/17.44 thf(f2184,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2183])).
% 54.09/17.44 thf(f2185,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2184])).
% 54.09/17.44 thf(f2186,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2185])).
% 54.09/17.44 thf(f2187,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2186])).
% 54.09/17.44 thf(f2188,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2187])).
% 54.09/17.44 thf(f2189,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2188])).
% 54.09/17.44 thf(f2190,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2189])).
% 54.09/17.44 thf(f2191,plain,(
% 54.09/17.44 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2132])).
% 54.09/17.44 thf(f2192,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2191])).
% 54.09/17.44 thf(f2193,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2192])).
% 54.09/17.44 thf(f2194,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2193])).
% 54.09/17.44 thf(f2195,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2193])).
% 54.09/17.44 thf(f2196,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2195])).
% 54.09/17.44 thf(f2197,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2196])).
% 54.09/17.44 thf(f2198,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f2197])).
% 54.09/17.44 thf(f2199,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2198])).
% 54.09/17.44 thf(f2200,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2199])).
% 54.09/17.44 thf(f2201,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2200])).
% 54.09/17.44 thf(f2202,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2201])).
% 54.09/17.44 thf(f2203,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2202])).
% 54.09/17.44 thf(f2204,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2203])).
% 54.09/17.44 thf(f2205,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2204])).
% 54.09/17.44 thf(f2206,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2205])).
% 54.09/17.44 thf(f2207,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2194])).
% 54.09/17.44 thf(f2208,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2207])).
% 54.09/17.44 thf(f2209,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2208])).
% 54.09/17.44 thf(f2210,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2208])).
% 54.09/17.44 thf(f2211,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2210])).
% 54.09/17.44 thf(f2212,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.44 inference(pi_proxy_clausification,[],[f2211])).
% 54.09/17.44 thf(f2213,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.44 inference(beta-eta_normalization,[],[f2212])).
% 54.09/17.44 thf(f2214,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2213])).
% 54.09/17.44 thf(f2215,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2214])).
% 54.09/17.44 thf(f2216,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2215])).
% 54.09/17.44 thf(f2217,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(or_proxy_clausification,[],[f2216])).
% 54.09/17.44 thf(f2218,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2217])).
% 54.09/17.44 thf(f2219,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.44 inference(not_proxy_clausification,[],[f2218])).
% 54.09/17.44 thf(f2220,plain,(
% 54.09/17.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2219])).
% 54.09/17.45 thf(f2221,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2220])).
% 54.09/17.45 thf(f2222,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2209])).
% 54.09/17.45 thf(f2223,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2222])).
% 54.09/17.45 thf(f2224,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2223])).
% 54.09/17.45 thf(f2225,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2223])).
% 54.09/17.45 thf(f2226,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2225])).
% 54.09/17.45 thf(f2227,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2226])).
% 54.09/17.45 thf(f2228,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2227])).
% 54.09/17.45 thf(f2229,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2228])).
% 54.09/17.45 thf(f2230,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2229])).
% 54.09/17.45 thf(f2231,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2230])).
% 54.09/17.45 thf(f2232,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2231])).
% 54.09/17.45 thf(f2233,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2232])).
% 54.09/17.45 thf(f2234,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2233])).
% 54.09/17.45 thf(f2235,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2234])).
% 54.09/17.45 thf(f2236,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2235])).
% 54.09/17.45 thf(f2237,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2224])).
% 54.09/17.45 thf(f2238,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2237])).
% 54.09/17.45 thf(f2239,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2238])).
% 54.09/17.45 thf(f2240,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2239])).
% 54.09/17.45 thf(f2241,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2240])).
% 54.09/17.45 thf(f2242,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2241])).
% 54.09/17.45 thf(f2243,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2242])).
% 54.09/17.45 thf(f2244,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2243])).
% 54.09/17.45 thf(f2245,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2244])).
% 54.09/17.45 thf(f2246,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2245])).
% 54.09/17.45 thf(f2247,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2246])).
% 54.09/17.45 thf(f2248,plain,(
% 54.09/17.45 ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))),
% 54.09/17.45 inference(not_proxy_clausification,[],[f1269])).
% 54.09/17.45 thf(f2249,plain,(
% 54.09/17.45 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2248])).
% 54.09/17.45 thf(f2250,plain,(
% 54.09/17.45 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2249])).
% 54.09/17.45 thf(f2251,plain,(
% 54.09/17.45 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2249])).
% 54.09/17.45 thf(f2252,plain,(
% 54.09/17.45 ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2251])).
% 54.09/17.45 thf(f2253,plain,(
% 54.09/17.45 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2252])).
% 54.09/17.45 thf(f2254,plain,(
% 54.09/17.45 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2253])).
% 54.09/17.45 thf(f2255,plain,(
% 54.09/17.45 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2254])).
% 54.09/17.45 thf(f2256,plain,(
% 54.09/17.45 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2254])).
% 54.09/17.45 thf(f2257,plain,(
% 54.09/17.45 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2256])).
% 54.09/17.45 thf(f2258,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2257])).
% 54.09/17.45 thf(f2259,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2258])).
% 54.09/17.45 thf(f2260,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2259])).
% 54.09/17.45 thf(f2261,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2259])).
% 54.09/17.45 thf(f2262,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2261])).
% 54.09/17.45 thf(f2263,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2262])).
% 54.09/17.45 thf(f2264,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2263])).
% 54.09/17.45 thf(f2265,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2264])).
% 54.09/17.45 thf(f2266,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2264])).
% 54.09/17.45 thf(f2267,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2266])).
% 54.09/17.45 thf(f2268,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2267])).
% 54.09/17.45 thf(f2269,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2268])).
% 54.09/17.45 thf(f2270,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2269])).
% 54.09/17.45 thf(f2271,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2270])).
% 54.09/17.45 thf(f2272,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2271])).
% 54.09/17.45 thf(f2273,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2272])).
% 54.09/17.45 thf(f2274,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2273])).
% 54.09/17.45 thf(f2275,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2274])).
% 54.09/17.45 thf(f2276,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2275])).
% 54.09/17.45 thf(f2277,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2276])).
% 54.09/17.45 thf(f2278,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2265])).
% 54.09/17.45 thf(f2279,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2278])).
% 54.09/17.45 thf(f2280,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2279])).
% 54.09/17.45 thf(f2281,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2279])).
% 54.09/17.45 thf(f2282,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2281])).
% 54.09/17.45 thf(f2283,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2282])).
% 54.09/17.45 thf(f2284,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2283])).
% 54.09/17.45 thf(f2285,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2284])).
% 54.09/17.45 thf(f2286,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2285])).
% 54.09/17.45 thf(f2287,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2286])).
% 54.09/17.45 thf(f2288,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2287])).
% 54.09/17.45 thf(f2289,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2288])).
% 54.09/17.45 thf(f2290,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2289])).
% 54.09/17.45 thf(f2291,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2290])).
% 54.09/17.45 thf(f2292,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2291])).
% 54.09/17.45 thf(f2293,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2280])).
% 54.09/17.45 thf(f2294,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2293])).
% 54.09/17.45 thf(f2295,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2294])).
% 54.09/17.45 thf(f2296,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2294])).
% 54.09/17.45 thf(f2297,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2296])).
% 54.09/17.45 thf(f2298,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2297])).
% 54.09/17.45 thf(f2299,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2298])).
% 54.09/17.45 thf(f2300,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2299])).
% 54.09/17.45 thf(f2301,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2300])).
% 54.09/17.45 thf(f2302,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2301])).
% 54.09/17.45 thf(f2303,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2302])).
% 54.09/17.45 thf(f2304,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2303])).
% 54.09/17.45 thf(f2305,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2304])).
% 54.09/17.45 thf(f2306,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2305])).
% 54.09/17.45 thf(f2307,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2306])).
% 54.09/17.45 thf(f2308,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2295])).
% 54.09/17.45 thf(f2309,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2308])).
% 54.09/17.45 thf(f2310,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2309])).
% 54.09/17.45 thf(f2311,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2310])).
% 54.09/17.45 thf(f2312,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2311])).
% 54.09/17.45 thf(f2313,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2312])).
% 54.09/17.45 thf(f2314,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2313])).
% 54.09/17.45 thf(f2315,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2314])).
% 54.09/17.45 thf(f2316,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2315])).
% 54.09/17.45 thf(f2317,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2316])).
% 54.09/17.45 thf(f2318,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2317])).
% 54.09/17.45 thf(f2319,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2260])).
% 54.09/17.45 thf(f2320,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2319])).
% 54.09/17.45 thf(f2321,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2320])).
% 54.09/17.45 thf(f2322,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2320])).
% 54.09/17.45 thf(f2323,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2322])).
% 54.09/17.45 thf(f2324,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2323])).
% 54.09/17.45 thf(f2325,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2324])).
% 54.09/17.45 thf(f2326,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2325])).
% 54.09/17.45 thf(f2327,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2325])).
% 54.09/17.45 thf(f2328,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2327])).
% 54.09/17.45 thf(f2329,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2328])).
% 54.09/17.45 thf(f2330,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2329])).
% 54.09/17.45 thf(f2331,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2330])).
% 54.09/17.45 thf(f2332,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2331])).
% 54.09/17.45 thf(f2333,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2332])).
% 54.09/17.45 thf(f2334,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2333])).
% 54.09/17.45 thf(f2335,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2334])).
% 54.09/17.45 thf(f2336,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2335])).
% 54.09/17.45 thf(f2337,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2336])).
% 54.09/17.45 thf(f2338,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2337])).
% 54.09/17.45 thf(f2339,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2326])).
% 54.09/17.45 thf(f2340,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2339])).
% 54.09/17.45 thf(f2341,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2340])).
% 54.09/17.45 thf(f2342,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2340])).
% 54.09/17.45 thf(f2343,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2342])).
% 54.09/17.45 thf(f2344,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2343])).
% 54.09/17.45 thf(f2345,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2344])).
% 54.09/17.45 thf(f2346,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2345])).
% 54.09/17.45 thf(f2347,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2346])).
% 54.09/17.45 thf(f2348,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2347])).
% 54.09/17.45 thf(f2349,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2348])).
% 54.09/17.45 thf(f2350,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2349])).
% 54.09/17.45 thf(f2351,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2350])).
% 54.09/17.45 thf(f2352,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2351])).
% 54.09/17.45 thf(f2353,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2352])).
% 54.09/17.45 thf(f2354,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2341])).
% 54.09/17.45 thf(f2355,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2354])).
% 54.09/17.45 thf(f2356,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2355])).
% 54.09/17.45 thf(f2357,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2355])).
% 54.09/17.45 thf(f2358,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2357])).
% 54.09/17.45 thf(f2359,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2358])).
% 54.09/17.45 thf(f2360,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2359])).
% 54.09/17.45 thf(f2361,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2360])).
% 54.09/17.45 thf(f2362,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2361])).
% 54.09/17.45 thf(f2363,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2362])).
% 54.09/17.45 thf(f2364,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2363])).
% 54.09/17.45 thf(f2365,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2364])).
% 54.09/17.45 thf(f2366,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2365])).
% 54.09/17.45 thf(f2367,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2366])).
% 54.09/17.45 thf(f2368,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2367])).
% 54.09/17.45 thf(f2369,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2356])).
% 54.09/17.45 thf(f2370,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2369])).
% 54.09/17.45 thf(f2371,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2370])).
% 54.09/17.45 thf(f2372,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2371])).
% 54.09/17.45 thf(f2373,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2372])).
% 54.09/17.45 thf(f2374,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2373])).
% 54.09/17.45 thf(f2375,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2374])).
% 54.09/17.45 thf(f2376,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2375])).
% 54.09/17.45 thf(f2377,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2376])).
% 54.09/17.45 thf(f2378,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2377])).
% 54.09/17.45 thf(f2379,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2378])).
% 54.09/17.45 thf(f2380,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2321])).
% 54.09/17.45 thf(f2381,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2380])).
% 54.09/17.45 thf(f2382,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2381])).
% 54.09/17.45 thf(f2383,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2381])).
% 54.09/17.45 thf(f2384,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2383])).
% 54.09/17.45 thf(f2385,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2384])).
% 54.09/17.45 thf(f2386,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2385])).
% 54.09/17.45 thf(f2387,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2386])).
% 54.09/17.45 thf(f2388,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2386])).
% 54.09/17.45 thf(f2389,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2388])).
% 54.09/17.45 thf(f2390,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2389])).
% 54.09/17.45 thf(f2391,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2390])).
% 54.09/17.45 thf(f2392,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2391])).
% 54.09/17.45 thf(f2393,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2392])).
% 54.09/17.45 thf(f2394,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2393])).
% 54.09/17.45 thf(f2395,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2394])).
% 54.09/17.45 thf(f2396,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2395])).
% 54.09/17.45 thf(f2397,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2396])).
% 54.09/17.45 thf(f2398,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2397])).
% 54.09/17.45 thf(f2399,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2398])).
% 54.09/17.45 thf(f2400,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2387])).
% 54.09/17.45 thf(f2401,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2400])).
% 54.09/17.45 thf(f2402,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2401])).
% 54.09/17.45 thf(f2403,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2401])).
% 54.09/17.45 thf(f2404,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2403])).
% 54.09/17.45 thf(f2405,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2404])).
% 54.09/17.45 thf(f2406,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2405])).
% 54.09/17.45 thf(f2407,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2406])).
% 54.09/17.45 thf(f2408,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2407])).
% 54.09/17.45 thf(f2409,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2408])).
% 54.09/17.45 thf(f2410,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2409])).
% 54.09/17.45 thf(f2411,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2410])).
% 54.09/17.45 thf(f2412,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2411])).
% 54.09/17.45 thf(f2413,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2412])).
% 54.09/17.45 thf(f2414,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2413])).
% 54.09/17.45 thf(f2415,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2402])).
% 54.09/17.45 thf(f2416,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2415])).
% 54.09/17.45 thf(f2417,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2416])).
% 54.09/17.45 thf(f2418,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2416])).
% 54.09/17.45 thf(f2419,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2418])).
% 54.09/17.45 thf(f2420,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2419])).
% 54.09/17.45 thf(f2421,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2420])).
% 54.09/17.45 thf(f2422,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2421])).
% 54.09/17.45 thf(f2423,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2422])).
% 54.09/17.45 thf(f2424,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2423])).
% 54.09/17.45 thf(f2425,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2424])).
% 54.09/17.45 thf(f2426,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2425])).
% 54.09/17.45 thf(f2427,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2426])).
% 54.09/17.45 thf(f2428,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2427])).
% 54.09/17.45 thf(f2429,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2428])).
% 54.09/17.45 thf(f2430,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2417])).
% 54.09/17.45 thf(f2431,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2430])).
% 54.09/17.45 thf(f2432,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2431])).
% 54.09/17.45 thf(f2433,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2432])).
% 54.09/17.45 thf(f2434,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2433])).
% 54.09/17.45 thf(f2435,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2434])).
% 54.09/17.45 thf(f2436,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2435])).
% 54.09/17.45 thf(f2437,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2436])).
% 54.09/17.45 thf(f2438,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2437])).
% 54.09/17.45 thf(f2439,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2438])).
% 54.09/17.45 thf(f2440,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2439])).
% 54.09/17.45 thf(f2441,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2382])).
% 54.09/17.45 thf(f2442,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2441])).
% 54.09/17.45 thf(f2443,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2442])).
% 54.09/17.45 thf(f2444,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2443])).
% 54.09/17.45 thf(f2445,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2443])).
% 54.09/17.45 thf(f2446,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2445])).
% 54.09/17.45 thf(f2447,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2446])).
% 54.09/17.45 thf(f2448,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2447])).
% 54.09/17.45 thf(f2449,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2448])).
% 54.09/17.45 thf(f2450,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2449])).
% 54.09/17.45 thf(f2451,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2450])).
% 54.09/17.45 thf(f2452,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2451])).
% 54.09/17.45 thf(f2453,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2452])).
% 54.09/17.45 thf(f2454,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2453])).
% 54.09/17.45 thf(f2455,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2454])).
% 54.09/17.45 thf(f2456,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2455])).
% 54.09/17.45 thf(f2457,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2444])).
% 54.09/17.45 thf(f2458,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2457])).
% 54.09/17.45 thf(f2459,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2458])).
% 54.09/17.45 thf(f2460,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2458])).
% 54.09/17.45 thf(f2461,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2460])).
% 54.09/17.45 thf(f2462,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2461])).
% 54.09/17.45 thf(f2463,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2462])).
% 54.09/17.45 thf(f2464,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2463])).
% 54.09/17.45 thf(f2465,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2464])).
% 54.09/17.45 thf(f2466,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2465])).
% 54.09/17.45 thf(f2467,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2466])).
% 54.09/17.45 thf(f2468,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2467])).
% 54.09/17.45 thf(f2469,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2468])).
% 54.09/17.45 thf(f2470,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2469])).
% 54.09/17.45 thf(f2471,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2470])).
% 54.09/17.45 thf(f2472,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2459])).
% 54.09/17.45 thf(f2473,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2472])).
% 54.09/17.45 thf(f2474,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2473])).
% 54.09/17.45 thf(f2475,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2473])).
% 54.09/17.45 thf(f2476,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2475])).
% 54.09/17.45 thf(f2477,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2476])).
% 54.09/17.45 thf(f2478,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2477])).
% 54.09/17.45 thf(f2479,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2478])).
% 54.09/17.45 thf(f2480,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2479])).
% 54.09/17.45 thf(f2481,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2480])).
% 54.09/17.45 thf(f2482,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2481])).
% 54.09/17.45 thf(f2483,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2482])).
% 54.09/17.45 thf(f2484,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2483])).
% 54.09/17.45 thf(f2485,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2484])).
% 54.09/17.45 thf(f2486,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2485])).
% 54.09/17.45 thf(f2487,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2474])).
% 54.09/17.45 thf(f2488,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2487])).
% 54.09/17.45 thf(f2489,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2488])).
% 54.09/17.45 thf(f2490,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2489])).
% 54.09/17.45 thf(f2491,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2490])).
% 54.09/17.45 thf(f2492,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2491])).
% 54.09/17.45 thf(f2493,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2492])).
% 54.09/17.45 thf(f2494,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2493])).
% 54.09/17.45 thf(f2495,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2494])).
% 54.09/17.45 thf(f2496,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2495])).
% 54.09/17.45 thf(f2497,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2496])).
% 54.09/17.45 thf(f2498,plain,(
% 54.09/17.45 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2255])).
% 54.09/17.45 thf(f2499,plain,(
% 54.09/17.45 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2498])).
% 54.09/17.45 thf(f2500,plain,(
% 54.09/17.45 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2499])).
% 54.09/17.45 thf(f2501,plain,(
% 54.09/17.45 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2499])).
% 54.09/17.45 thf(f2502,plain,(
% 54.09/17.45 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2501])).
% 54.09/17.45 thf(f2503,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2502])).
% 54.09/17.45 thf(f2504,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2503])).
% 54.09/17.45 thf(f2505,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2504])).
% 54.09/17.45 thf(f2506,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2504])).
% 54.09/17.45 thf(f2507,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2506])).
% 54.09/17.45 thf(f2508,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2507])).
% 54.09/17.45 thf(f2509,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2508])).
% 54.09/17.45 thf(f2510,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2509])).
% 54.09/17.45 thf(f2511,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2509])).
% 54.09/17.45 thf(f2512,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2511])).
% 54.09/17.45 thf(f2513,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2512])).
% 54.09/17.45 thf(f2514,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2513])).
% 54.09/17.45 thf(f2515,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2514])).
% 54.09/17.45 thf(f2516,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2515])).
% 54.09/17.45 thf(f2517,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2516])).
% 54.09/17.45 thf(f2518,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2517])).
% 54.09/17.45 thf(f2519,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2518])).
% 54.09/17.45 thf(f2520,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2519])).
% 54.09/17.45 thf(f2521,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2520])).
% 54.09/17.45 thf(f2522,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2521])).
% 54.09/17.45 thf(f2523,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2510])).
% 54.09/17.45 thf(f2524,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2523])).
% 54.09/17.45 thf(f2525,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2524])).
% 54.09/17.45 thf(f2526,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2524])).
% 54.09/17.45 thf(f2527,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2526])).
% 54.09/17.45 thf(f2528,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2527])).
% 54.09/17.45 thf(f2529,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2528])).
% 54.09/17.45 thf(f2530,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2529])).
% 54.09/17.45 thf(f2531,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2530])).
% 54.09/17.45 thf(f2532,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2531])).
% 54.09/17.45 thf(f2533,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2532])).
% 54.09/17.45 thf(f2534,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2533])).
% 54.09/17.45 thf(f2535,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2534])).
% 54.09/17.45 thf(f2536,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2535])).
% 54.09/17.45 thf(f2537,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2536])).
% 54.09/17.45 thf(f2538,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2525])).
% 54.09/17.45 thf(f2539,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2538])).
% 54.09/17.45 thf(f2540,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2539])).
% 54.09/17.45 thf(f2541,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2539])).
% 54.09/17.45 thf(f2542,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2541])).
% 54.09/17.45 thf(f2543,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2542])).
% 54.09/17.45 thf(f2544,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2543])).
% 54.09/17.45 thf(f2545,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2544])).
% 54.09/17.45 thf(f2546,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2545])).
% 54.09/17.45 thf(f2547,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2546])).
% 54.09/17.45 thf(f2548,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2547])).
% 54.09/17.45 thf(f2549,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2548])).
% 54.09/17.45 thf(f2550,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2549])).
% 54.09/17.45 thf(f2551,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2550])).
% 54.09/17.45 thf(f2552,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2551])).
% 54.09/17.45 thf(f2553,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2540])).
% 54.09/17.45 thf(f2554,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2553])).
% 54.09/17.45 thf(f2555,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2554])).
% 54.09/17.45 thf(f2556,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2555])).
% 54.09/17.45 thf(f2557,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2556])).
% 54.09/17.45 thf(f2558,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2557])).
% 54.09/17.45 thf(f2559,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2558])).
% 54.09/17.45 thf(f2560,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2559])).
% 54.09/17.45 thf(f2561,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2560])).
% 54.09/17.45 thf(f2562,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2561])).
% 54.09/17.45 thf(f2563,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2562])).
% 54.09/17.45 thf(f2564,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2505])).
% 54.09/17.45 thf(f2565,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2564])).
% 54.09/17.45 thf(f2566,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2565])).
% 54.09/17.45 thf(f2567,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2565])).
% 54.09/17.45 thf(f2568,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2567])).
% 54.09/17.45 thf(f2569,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2568])).
% 54.09/17.45 thf(f2570,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2569])).
% 54.09/17.45 thf(f2571,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2570])).
% 54.09/17.45 thf(f2572,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2570])).
% 54.09/17.45 thf(f2573,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2572])).
% 54.09/17.45 thf(f2574,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2573])).
% 54.09/17.45 thf(f2575,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2574])).
% 54.09/17.45 thf(f2576,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2575])).
% 54.09/17.45 thf(f2577,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2576])).
% 54.09/17.45 thf(f2578,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2577])).
% 54.09/17.45 thf(f2579,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2578])).
% 54.09/17.45 thf(f2580,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2579])).
% 54.09/17.45 thf(f2581,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2580])).
% 54.09/17.45 thf(f2582,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2581])).
% 54.09/17.45 thf(f2583,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2582])).
% 54.09/17.45 thf(f2584,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2571])).
% 54.09/17.45 thf(f2585,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2584])).
% 54.09/17.45 thf(f2586,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2585])).
% 54.09/17.45 thf(f2587,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2585])).
% 54.09/17.45 thf(f2588,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2587])).
% 54.09/17.45 thf(f2589,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2588])).
% 54.09/17.45 thf(f2590,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2589])).
% 54.09/17.45 thf(f2591,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2590])).
% 54.09/17.45 thf(f2592,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2591])).
% 54.09/17.45 thf(f2593,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2592])).
% 54.09/17.45 thf(f2594,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2593])).
% 54.09/17.45 thf(f2595,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2594])).
% 54.09/17.45 thf(f2596,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2595])).
% 54.09/17.45 thf(f2597,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2596])).
% 54.09/17.45 thf(f2598,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2597])).
% 54.09/17.45 thf(f2599,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2586])).
% 54.09/17.45 thf(f2600,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2599])).
% 54.09/17.45 thf(f2601,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2600])).
% 54.09/17.45 thf(f2602,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2600])).
% 54.09/17.45 thf(f2603,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2602])).
% 54.09/17.45 thf(f2604,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2603])).
% 54.09/17.45 thf(f2605,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2604])).
% 54.09/17.45 thf(f2606,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2605])).
% 54.09/17.45 thf(f2607,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2606])).
% 54.09/17.45 thf(f2608,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2607])).
% 54.09/17.45 thf(f2609,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2608])).
% 54.09/17.45 thf(f2610,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2609])).
% 54.09/17.45 thf(f2611,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2610])).
% 54.09/17.45 thf(f2612,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2611])).
% 54.09/17.45 thf(f2613,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2612])).
% 54.09/17.45 thf(f2614,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2601])).
% 54.09/17.45 thf(f2615,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2614])).
% 54.09/17.45 thf(f2616,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2615])).
% 54.09/17.45 thf(f2617,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2616])).
% 54.09/17.45 thf(f2618,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2617])).
% 54.09/17.45 thf(f2619,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2618])).
% 54.09/17.45 thf(f2620,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2619])).
% 54.09/17.45 thf(f2621,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2620])).
% 54.09/17.45 thf(f2622,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2621])).
% 54.09/17.45 thf(f2623,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2622])).
% 54.09/17.45 thf(f2624,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2623])).
% 54.09/17.45 thf(f2625,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2566])).
% 54.09/17.45 thf(f2626,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2625])).
% 54.09/17.45 thf(f2627,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2626])).
% 54.09/17.45 thf(f2628,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2626])).
% 54.09/17.45 thf(f2629,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2628])).
% 54.09/17.45 thf(f2630,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2629])).
% 54.09/17.45 thf(f2631,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2630])).
% 54.09/17.45 thf(f2632,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2631])).
% 54.09/17.45 thf(f2633,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2631])).
% 54.09/17.45 thf(f2634,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2633])).
% 54.09/17.45 thf(f2635,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2634])).
% 54.09/17.45 thf(f2636,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2635])).
% 54.09/17.45 thf(f2637,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2636])).
% 54.09/17.45 thf(f2638,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2637])).
% 54.09/17.45 thf(f2639,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2638])).
% 54.09/17.45 thf(f2640,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2639])).
% 54.09/17.45 thf(f2641,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2640])).
% 54.09/17.45 thf(f2642,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2641])).
% 54.09/17.45 thf(f2643,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2642])).
% 54.09/17.45 thf(f2644,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2643])).
% 54.09/17.45 thf(f2645,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2632])).
% 54.09/17.45 thf(f2646,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2645])).
% 54.09/17.45 thf(f2647,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2646])).
% 54.09/17.45 thf(f2648,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2646])).
% 54.09/17.45 thf(f2649,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2648])).
% 54.09/17.45 thf(f2650,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2649])).
% 54.09/17.45 thf(f2651,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2650])).
% 54.09/17.45 thf(f2652,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2651])).
% 54.09/17.45 thf(f2653,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2652])).
% 54.09/17.45 thf(f2654,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2653])).
% 54.09/17.45 thf(f2655,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2654])).
% 54.09/17.45 thf(f2656,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2655])).
% 54.09/17.45 thf(f2657,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2656])).
% 54.09/17.45 thf(f2658,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2657])).
% 54.09/17.45 thf(f2659,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2658])).
% 54.09/17.45 thf(f2660,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2647])).
% 54.09/17.45 thf(f2661,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2660])).
% 54.09/17.45 thf(f2662,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2661])).
% 54.09/17.45 thf(f2663,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2661])).
% 54.09/17.45 thf(f2664,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2663])).
% 54.09/17.45 thf(f2665,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2664])).
% 54.09/17.45 thf(f2666,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2665])).
% 54.09/17.45 thf(f2667,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2666])).
% 54.09/17.45 thf(f2668,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2667])).
% 54.09/17.45 thf(f2669,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2668])).
% 54.09/17.45 thf(f2670,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2669])).
% 54.09/17.45 thf(f2671,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2670])).
% 54.09/17.45 thf(f2672,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2671])).
% 54.09/17.45 thf(f2673,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2672])).
% 54.09/17.45 thf(f2674,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2673])).
% 54.09/17.45 thf(f2675,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2662])).
% 54.09/17.45 thf(f2676,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2675])).
% 54.09/17.45 thf(f2677,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2676])).
% 54.09/17.45 thf(f2678,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2677])).
% 54.09/17.45 thf(f2679,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2678])).
% 54.09/17.45 thf(f2680,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2679])).
% 54.09/17.45 thf(f2681,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2680])).
% 54.09/17.45 thf(f2682,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2681])).
% 54.09/17.45 thf(f2683,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2682])).
% 54.09/17.45 thf(f2684,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2683])).
% 54.09/17.45 thf(f2685,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2684])).
% 54.09/17.45 thf(f2686,plain,(
% 54.09/17.45 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2627])).
% 54.09/17.45 thf(f2687,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2686])).
% 54.09/17.45 thf(f2688,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2687])).
% 54.09/17.45 thf(f2689,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2688])).
% 54.09/17.45 thf(f2690,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2688])).
% 54.09/17.45 thf(f2691,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2690])).
% 54.09/17.45 thf(f2692,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2691])).
% 54.09/17.45 thf(f2693,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2692])).
% 54.09/17.45 thf(f2694,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2693])).
% 54.09/17.45 thf(f2695,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2694])).
% 54.09/17.45 thf(f2696,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2695])).
% 54.09/17.45 thf(f2697,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2696])).
% 54.09/17.45 thf(f2698,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2697])).
% 54.09/17.45 thf(f2699,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2698])).
% 54.09/17.45 thf(f2700,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2699])).
% 54.09/17.45 thf(f2701,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2700])).
% 54.09/17.45 thf(f2702,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2689])).
% 54.09/17.45 thf(f2703,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2702])).
% 54.09/17.45 thf(f2704,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2703])).
% 54.09/17.45 thf(f2705,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2703])).
% 54.09/17.45 thf(f2706,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2705])).
% 54.09/17.45 thf(f2707,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2706])).
% 54.09/17.45 thf(f2708,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2707])).
% 54.09/17.45 thf(f2709,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2708])).
% 54.09/17.45 thf(f2710,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2709])).
% 54.09/17.45 thf(f2711,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2710])).
% 54.09/17.45 thf(f2712,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2711])).
% 54.09/17.45 thf(f2713,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2712])).
% 54.09/17.45 thf(f2714,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2713])).
% 54.09/17.45 thf(f2715,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2714])).
% 54.09/17.45 thf(f2716,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2715])).
% 54.09/17.45 thf(f2717,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2704])).
% 54.09/17.45 thf(f2718,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2717])).
% 54.09/17.45 thf(f2719,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2718])).
% 54.09/17.45 thf(f2720,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2718])).
% 54.09/17.45 thf(f2721,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.45 inference(not_proxy_clausification,[],[f2720])).
% 54.09/17.45 thf(f2722,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.45 inference(pi_proxy_clausification,[],[f2721])).
% 54.09/17.45 thf(f2723,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.45 inference(beta-eta_normalization,[],[f2722])).
% 54.09/17.45 thf(f2724,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2723])).
% 54.09/17.45 thf(f2725,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2724])).
% 54.09/17.45 thf(f2726,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2725])).
% 54.09/17.45 thf(f2727,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.45 inference(or_proxy_clausification,[],[f2726])).
% 54.09/17.45 thf(f2728,plain,(
% 54.09/17.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2727])).
% 54.09/17.46 thf(f2729,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2728])).
% 54.09/17.46 thf(f2730,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2729])).
% 54.09/17.46 thf(f2731,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2730])).
% 54.09/17.46 thf(f2732,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2719])).
% 54.09/17.46 thf(f2733,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2732])).
% 54.09/17.46 thf(f2734,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2733])).
% 54.09/17.46 thf(f2735,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2734])).
% 54.09/17.46 thf(f2736,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2735])).
% 54.09/17.46 thf(f2737,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2736])).
% 54.09/17.46 thf(f2738,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2737])).
% 54.09/17.46 thf(f2739,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2738])).
% 54.09/17.46 thf(f2740,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2739])).
% 54.09/17.46 thf(f2741,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2740])).
% 54.09/17.46 thf(f2742,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2741])).
% 54.09/17.46 thf(f2743,plain,(
% 54.09/17.46 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2500])).
% 54.09/17.46 thf(f2744,plain,(
% 54.09/17.46 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2743])).
% 54.09/17.46 thf(f2745,plain,(
% 54.09/17.46 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2744])).
% 54.09/17.46 thf(f2746,plain,(
% 54.09/17.46 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2744])).
% 54.09/17.46 thf(f2747,plain,(
% 54.09/17.46 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2746])).
% 54.09/17.46 thf(f2748,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2747])).
% 54.09/17.46 thf(f2749,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2748])).
% 54.09/17.46 thf(f2750,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2749])).
% 54.09/17.46 thf(f2751,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2749])).
% 54.09/17.46 thf(f2752,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2751])).
% 54.09/17.46 thf(f2753,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2752])).
% 54.09/17.46 thf(f2754,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2753])).
% 54.09/17.46 thf(f2755,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2754])).
% 54.09/17.46 thf(f2756,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2754])).
% 54.09/17.46 thf(f2757,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2756])).
% 54.09/17.46 thf(f2758,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2757])).
% 54.09/17.46 thf(f2759,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2758])).
% 54.09/17.46 thf(f2760,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2759])).
% 54.09/17.46 thf(f2761,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2760])).
% 54.09/17.46 thf(f2762,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2761])).
% 54.09/17.46 thf(f2763,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2762])).
% 54.09/17.46 thf(f2764,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2763])).
% 54.09/17.46 thf(f2765,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2764])).
% 54.09/17.46 thf(f2766,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2765])).
% 54.09/17.46 thf(f2767,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2766])).
% 54.09/17.46 thf(f2768,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2755])).
% 54.09/17.46 thf(f2769,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2768])).
% 54.09/17.46 thf(f2770,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2769])).
% 54.09/17.46 thf(f2771,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2769])).
% 54.09/17.46 thf(f2772,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2771])).
% 54.09/17.46 thf(f2773,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2772])).
% 54.09/17.46 thf(f2774,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2773])).
% 54.09/17.46 thf(f2775,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2774])).
% 54.09/17.46 thf(f2776,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2775])).
% 54.09/17.46 thf(f2777,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2776])).
% 54.09/17.46 thf(f2778,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2777])).
% 54.09/17.46 thf(f2779,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2778])).
% 54.09/17.46 thf(f2780,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2779])).
% 54.09/17.46 thf(f2781,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2780])).
% 54.09/17.46 thf(f2782,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2781])).
% 54.09/17.46 thf(f2783,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2770])).
% 54.09/17.46 thf(f2784,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2783])).
% 54.09/17.46 thf(f2785,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2784])).
% 54.09/17.46 thf(f2786,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2784])).
% 54.09/17.46 thf(f2787,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2786])).
% 54.09/17.46 thf(f2788,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2787])).
% 54.09/17.46 thf(f2789,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2788])).
% 54.09/17.46 thf(f2790,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2789])).
% 54.09/17.46 thf(f2791,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2790])).
% 54.09/17.46 thf(f2792,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2791])).
% 54.09/17.46 thf(f2793,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2792])).
% 54.09/17.46 thf(f2794,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2793])).
% 54.09/17.46 thf(f2795,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2794])).
% 54.09/17.46 thf(f2796,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2795])).
% 54.09/17.46 thf(f2797,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2796])).
% 54.09/17.46 thf(f2798,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2785])).
% 54.09/17.46 thf(f2799,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2798])).
% 54.09/17.46 thf(f2800,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2799])).
% 54.09/17.46 thf(f2801,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2800])).
% 54.09/17.46 thf(f2802,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2801])).
% 54.09/17.46 thf(f2803,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2802])).
% 54.09/17.46 thf(f2804,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2803])).
% 54.09/17.46 thf(f2805,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2804])).
% 54.09/17.46 thf(f2806,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2805])).
% 54.09/17.46 thf(f2807,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2806])).
% 54.09/17.46 thf(f2808,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2807])).
% 54.09/17.46 thf(f2809,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2750])).
% 54.09/17.46 thf(f2810,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2809])).
% 54.09/17.46 thf(f2811,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2810])).
% 54.09/17.46 thf(f2812,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2810])).
% 54.09/17.46 thf(f2813,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2812])).
% 54.09/17.46 thf(f2814,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2813])).
% 54.09/17.46 thf(f2815,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2814])).
% 54.09/17.46 thf(f2816,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2815])).
% 54.09/17.46 thf(f2817,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2815])).
% 54.09/17.46 thf(f2818,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2817])).
% 54.09/17.46 thf(f2819,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2818])).
% 54.09/17.46 thf(f2820,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2819])).
% 54.09/17.46 thf(f2821,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2820])).
% 54.09/17.46 thf(f2822,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2821])).
% 54.09/17.46 thf(f2823,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2822])).
% 54.09/17.46 thf(f2824,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2823])).
% 54.09/17.46 thf(f2825,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2824])).
% 54.09/17.46 thf(f2826,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2825])).
% 54.09/17.46 thf(f2827,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2826])).
% 54.09/17.46 thf(f2828,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2827])).
% 54.09/17.46 thf(f2829,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2816])).
% 54.09/17.46 thf(f2830,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2829])).
% 54.09/17.46 thf(f2831,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2830])).
% 54.09/17.46 thf(f2832,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2830])).
% 54.09/17.46 thf(f2833,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2832])).
% 54.09/17.46 thf(f2834,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2833])).
% 54.09/17.46 thf(f2835,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2834])).
% 54.09/17.46 thf(f2836,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2835])).
% 54.09/17.46 thf(f2837,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2836])).
% 54.09/17.46 thf(f2838,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2837])).
% 54.09/17.46 thf(f2839,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2838])).
% 54.09/17.46 thf(f2840,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2839])).
% 54.09/17.46 thf(f2841,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2840])).
% 54.09/17.46 thf(f2842,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2841])).
% 54.09/17.46 thf(f2843,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2842])).
% 54.09/17.46 thf(f2844,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2831])).
% 54.09/17.46 thf(f2845,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2844])).
% 54.09/17.46 thf(f2846,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2845])).
% 54.09/17.46 thf(f2847,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2845])).
% 54.09/17.46 thf(f2848,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2847])).
% 54.09/17.46 thf(f2849,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2848])).
% 54.09/17.46 thf(f2850,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2849])).
% 54.09/17.46 thf(f2851,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2850])).
% 54.09/17.46 thf(f2852,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2851])).
% 54.09/17.46 thf(f2853,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2852])).
% 54.09/17.46 thf(f2854,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2853])).
% 54.09/17.46 thf(f2855,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2854])).
% 54.09/17.46 thf(f2856,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2855])).
% 54.09/17.46 thf(f2857,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2856])).
% 54.09/17.46 thf(f2858,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2857])).
% 54.09/17.46 thf(f2859,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2846])).
% 54.09/17.46 thf(f2860,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2859])).
% 54.09/17.46 thf(f2861,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2860])).
% 54.09/17.46 thf(f2862,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2861])).
% 54.09/17.46 thf(f2863,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2862])).
% 54.09/17.46 thf(f2864,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2863])).
% 54.09/17.46 thf(f2865,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2864])).
% 54.09/17.46 thf(f2866,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2865])).
% 54.09/17.46 thf(f2867,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2866])).
% 54.09/17.46 thf(f2868,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2867])).
% 54.09/17.46 thf(f2869,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2868])).
% 54.09/17.46 thf(f2870,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2811])).
% 54.09/17.46 thf(f2871,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2870])).
% 54.09/17.46 thf(f2872,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2871])).
% 54.09/17.46 thf(f2873,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2871])).
% 54.09/17.46 thf(f2874,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2873])).
% 54.09/17.46 thf(f2875,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2874])).
% 54.09/17.46 thf(f2876,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2875])).
% 54.09/17.46 thf(f2877,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2876])).
% 54.09/17.46 thf(f2878,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2876])).
% 54.09/17.46 thf(f2879,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2878])).
% 54.09/17.46 thf(f2880,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2879])).
% 54.09/17.46 thf(f2881,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2880])).
% 54.09/17.46 thf(f2882,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2881])).
% 54.09/17.46 thf(f2883,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2882])).
% 54.09/17.46 thf(f2884,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2883])).
% 54.09/17.46 thf(f2885,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2884])).
% 54.09/17.46 thf(f2886,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2885])).
% 54.09/17.46 thf(f2887,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2886])).
% 54.09/17.46 thf(f2888,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2887])).
% 54.09/17.46 thf(f2889,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2888])).
% 54.09/17.46 thf(f2890,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2877])).
% 54.09/17.46 thf(f2891,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2890])).
% 54.09/17.46 thf(f2892,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2891])).
% 54.09/17.46 thf(f2893,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2891])).
% 54.09/17.46 thf(f2894,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2893])).
% 54.09/17.46 thf(f2895,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2894])).
% 54.09/17.46 thf(f2896,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2895])).
% 54.09/17.46 thf(f2897,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2896])).
% 54.09/17.46 thf(f2898,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2897])).
% 54.09/17.46 thf(f2899,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2898])).
% 54.09/17.46 thf(f2900,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2899])).
% 54.09/17.46 thf(f2901,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2900])).
% 54.09/17.46 thf(f2902,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2901])).
% 54.09/17.46 thf(f2903,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2902])).
% 54.09/17.46 thf(f2904,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2903])).
% 54.09/17.46 thf(f2905,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2892])).
% 54.09/17.46 thf(f2906,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2905])).
% 54.09/17.46 thf(f2907,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2906])).
% 54.09/17.46 thf(f2908,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2906])).
% 54.09/17.46 thf(f2909,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2908])).
% 54.09/17.46 thf(f2910,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2909])).
% 54.09/17.46 thf(f2911,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2910])).
% 54.09/17.46 thf(f2912,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2911])).
% 54.09/17.46 thf(f2913,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2912])).
% 54.09/17.46 thf(f2914,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2913])).
% 54.09/17.46 thf(f2915,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2914])).
% 54.09/17.46 thf(f2916,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2915])).
% 54.09/17.46 thf(f2917,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2916])).
% 54.09/17.46 thf(f2918,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2917])).
% 54.09/17.46 thf(f2919,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2918])).
% 54.09/17.46 thf(f2920,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2907])).
% 54.09/17.46 thf(f2921,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2920])).
% 54.09/17.46 thf(f2922,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2921])).
% 54.09/17.46 thf(f2923,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2922])).
% 54.09/17.46 thf(f2924,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2923])).
% 54.09/17.46 thf(f2925,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2924])).
% 54.09/17.46 thf(f2926,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2925])).
% 54.09/17.46 thf(f2927,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2926])).
% 54.09/17.46 thf(f2928,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2927])).
% 54.09/17.46 thf(f2929,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2928])).
% 54.09/17.46 thf(f2930,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2929])).
% 54.09/17.46 thf(f2931,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2872])).
% 54.09/17.46 thf(f2932,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2931])).
% 54.09/17.46 thf(f2933,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2932])).
% 54.09/17.46 thf(f2934,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2933])).
% 54.09/17.46 thf(f2935,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2933])).
% 54.09/17.46 thf(f2936,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2935])).
% 54.09/17.46 thf(f2937,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2936])).
% 54.09/17.46 thf(f2938,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2937])).
% 54.09/17.46 thf(f2939,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2938])).
% 54.09/17.46 thf(f2940,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2939])).
% 54.09/17.46 thf(f2941,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2940])).
% 54.09/17.46 thf(f2942,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2941])).
% 54.09/17.46 thf(f2943,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2942])).
% 54.09/17.46 thf(f2944,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2943])).
% 54.09/17.46 thf(f2945,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2944])).
% 54.09/17.46 thf(f2946,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2945])).
% 54.09/17.46 thf(f2947,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2934])).
% 54.09/17.46 thf(f2948,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2947])).
% 54.09/17.46 thf(f2949,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2948])).
% 54.09/17.46 thf(f2950,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2948])).
% 54.09/17.46 thf(f2951,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2950])).
% 54.09/17.46 thf(f2952,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2951])).
% 54.09/17.46 thf(f2953,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2952])).
% 54.09/17.46 thf(f2954,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2953])).
% 54.09/17.46 thf(f2955,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2954])).
% 54.09/17.46 thf(f2956,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2955])).
% 54.09/17.46 thf(f2957,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2956])).
% 54.09/17.46 thf(f2958,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2957])).
% 54.09/17.46 thf(f2959,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2958])).
% 54.09/17.46 thf(f2960,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2959])).
% 54.09/17.46 thf(f2961,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2960])).
% 54.09/17.46 thf(f2962,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2949])).
% 54.09/17.46 thf(f2963,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2962])).
% 54.09/17.46 thf(f2964,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2963])).
% 54.09/17.46 thf(f2965,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2963])).
% 54.09/17.46 thf(f2966,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2965])).
% 54.09/17.46 thf(f2967,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2966])).
% 54.09/17.46 thf(f2968,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2967])).
% 54.09/17.46 thf(f2969,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2968])).
% 54.09/17.46 thf(f2970,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2969])).
% 54.09/17.46 thf(f2971,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2970])).
% 54.09/17.46 thf(f2972,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2971])).
% 54.09/17.46 thf(f2973,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2972])).
% 54.09/17.46 thf(f2974,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2973])).
% 54.09/17.46 thf(f2975,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2974])).
% 54.09/17.46 thf(f2976,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2975])).
% 54.09/17.46 thf(f2977,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2964])).
% 54.09/17.46 thf(f2978,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2977])).
% 54.09/17.46 thf(f2979,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2978])).
% 54.09/17.46 thf(f2980,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2979])).
% 54.09/17.46 thf(f2981,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2980])).
% 54.09/17.46 thf(f2982,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2981])).
% 54.09/17.46 thf(f2983,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2982])).
% 54.09/17.46 thf(f2984,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2983])).
% 54.09/17.46 thf(f2985,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2984])).
% 54.09/17.46 thf(f2986,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2985])).
% 54.09/17.46 thf(f2987,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2986])).
% 54.09/17.46 thf(f2988,plain,(
% 54.09/17.46 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2745])).
% 54.09/17.46 thf(f2989,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2988])).
% 54.09/17.46 thf(f2990,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2989])).
% 54.09/17.46 thf(f2991,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2990])).
% 54.09/17.46 thf(f2992,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2990])).
% 54.09/17.46 thf(f2993,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2992])).
% 54.09/17.46 thf(f2994,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2993])).
% 54.09/17.46 thf(f2995,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2994])).
% 54.09/17.46 thf(f2996,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2995])).
% 54.09/17.46 thf(f2997,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f2995])).
% 54.09/17.46 thf(f2998,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2997])).
% 54.09/17.46 thf(f2999,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f2998])).
% 54.09/17.46 thf(f3000,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f2999])).
% 54.09/17.46 thf(f3001,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3000])).
% 54.09/17.46 thf(f3002,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3001])).
% 54.09/17.46 thf(f3003,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3002])).
% 54.09/17.46 thf(f3004,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3003])).
% 54.09/17.46 thf(f3005,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3004])).
% 54.09/17.46 thf(f3006,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3005])).
% 54.09/17.46 thf(f3007,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3006])).
% 54.09/17.46 thf(f3008,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3007])).
% 54.09/17.46 thf(f3009,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2996])).
% 54.09/17.46 thf(f3010,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3009])).
% 54.09/17.46 thf(f3011,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3010])).
% 54.09/17.46 thf(f3012,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3010])).
% 54.09/17.46 thf(f3013,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3012])).
% 54.09/17.46 thf(f3014,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f3013])).
% 54.09/17.46 thf(f3015,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f3014])).
% 54.09/17.46 thf(f3016,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3015])).
% 54.09/17.46 thf(f3017,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3016])).
% 54.09/17.46 thf(f3018,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3017])).
% 54.09/17.46 thf(f3019,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3018])).
% 54.09/17.46 thf(f3020,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3019])).
% 54.09/17.46 thf(f3021,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3020])).
% 54.09/17.46 thf(f3022,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3021])).
% 54.09/17.46 thf(f3023,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3022])).
% 54.09/17.46 thf(f3024,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3011])).
% 54.09/17.46 thf(f3025,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3024])).
% 54.09/17.46 thf(f3026,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3025])).
% 54.09/17.46 thf(f3027,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3025])).
% 54.09/17.46 thf(f3028,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3027])).
% 54.09/17.46 thf(f3029,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f3028])).
% 54.09/17.46 thf(f3030,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f3029])).
% 54.09/17.46 thf(f3031,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3030])).
% 54.09/17.46 thf(f3032,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3031])).
% 54.09/17.46 thf(f3033,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3032])).
% 54.09/17.46 thf(f3034,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3033])).
% 54.09/17.46 thf(f3035,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3034])).
% 54.09/17.46 thf(f3036,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3035])).
% 54.09/17.46 thf(f3037,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3036])).
% 54.09/17.46 thf(f3038,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3037])).
% 54.09/17.46 thf(f3039,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3026])).
% 54.09/17.46 thf(f3040,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f3039])).
% 54.09/17.46 thf(f3041,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f3040])).
% 54.09/17.46 thf(f3042,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3041])).
% 54.09/17.46 thf(f3043,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3042])).
% 54.09/17.46 thf(f3044,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3043])).
% 54.09/17.46 thf(f3045,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3044])).
% 54.09/17.46 thf(f3046,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3045])).
% 54.09/17.46 thf(f3047,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3046])).
% 54.09/17.46 thf(f3048,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3047])).
% 54.09/17.46 thf(f3049,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3048])).
% 54.09/17.46 thf(f3050,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f2991])).
% 54.09/17.46 thf(f3051,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3050])).
% 54.09/17.46 thf(f3052,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3051])).
% 54.09/17.46 thf(f3053,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3051])).
% 54.09/17.46 thf(f3054,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3053])).
% 54.09/17.46 thf(f3055,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f3054])).
% 54.09/17.46 thf(f3056,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3055])).
% 54.09/17.46 thf(f3057,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3056])).
% 54.09/17.46 thf(f3058,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3056])).
% 54.09/17.46 thf(f3059,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3058])).
% 54.09/17.46 thf(f3060,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f3059])).
% 54.09/17.46 thf(f3061,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f3060])).
% 54.09/17.46 thf(f3062,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3061])).
% 54.09/17.46 thf(f3063,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3062])).
% 54.09/17.46 thf(f3064,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3063])).
% 54.09/17.46 thf(f3065,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3064])).
% 54.09/17.46 thf(f3066,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3065])).
% 54.09/17.46 thf(f3067,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3066])).
% 54.09/17.46 thf(f3068,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3067])).
% 54.09/17.46 thf(f3069,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3068])).
% 54.09/17.46 thf(f3070,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3057])).
% 54.09/17.46 thf(f3071,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3070])).
% 54.09/17.46 thf(f3072,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3071])).
% 54.09/17.46 thf(f3073,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3071])).
% 54.09/17.46 thf(f3074,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3073])).
% 54.09/17.46 thf(f3075,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f3074])).
% 54.09/17.46 thf(f3076,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f3075])).
% 54.09/17.46 thf(f3077,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3076])).
% 54.09/17.46 thf(f3078,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3077])).
% 54.09/17.46 thf(f3079,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3078])).
% 54.09/17.46 thf(f3080,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3079])).
% 54.09/17.46 thf(f3081,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3080])).
% 54.09/17.46 thf(f3082,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3081])).
% 54.09/17.46 thf(f3083,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3082])).
% 54.09/17.46 thf(f3084,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3083])).
% 54.09/17.46 thf(f3085,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3072])).
% 54.09/17.46 thf(f3086,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3085])).
% 54.09/17.46 thf(f3087,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3086])).
% 54.09/17.46 thf(f3088,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3086])).
% 54.09/17.46 thf(f3089,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3088])).
% 54.09/17.46 thf(f3090,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f3089])).
% 54.09/17.46 thf(f3091,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f3090])).
% 54.09/17.46 thf(f3092,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3091])).
% 54.09/17.46 thf(f3093,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3092])).
% 54.09/17.46 thf(f3094,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3093])).
% 54.09/17.46 thf(f3095,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3094])).
% 54.09/17.46 thf(f3096,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3095])).
% 54.09/17.46 thf(f3097,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3096])).
% 54.09/17.46 thf(f3098,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3097])).
% 54.09/17.46 thf(f3099,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3098])).
% 54.09/17.46 thf(f3100,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3087])).
% 54.09/17.46 thf(f3101,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f3100])).
% 54.09/17.46 thf(f3102,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f3101])).
% 54.09/17.46 thf(f3103,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3102])).
% 54.09/17.46 thf(f3104,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3103])).
% 54.09/17.46 thf(f3105,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3104])).
% 54.09/17.46 thf(f3106,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3105])).
% 54.09/17.46 thf(f3107,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3106])).
% 54.09/17.46 thf(f3108,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3107])).
% 54.09/17.46 thf(f3109,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3108])).
% 54.09/17.46 thf(f3110,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3109])).
% 54.09/17.46 thf(f3111,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3052])).
% 54.09/17.46 thf(f3112,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3111])).
% 54.09/17.46 thf(f3113,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3112])).
% 54.09/17.46 thf(f3114,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3112])).
% 54.09/17.46 thf(f3115,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3114])).
% 54.09/17.46 thf(f3116,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f3115])).
% 54.09/17.46 thf(f3117,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3116])).
% 54.09/17.46 thf(f3118,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3117])).
% 54.09/17.46 thf(f3119,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3117])).
% 54.09/17.46 thf(f3120,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3119])).
% 54.09/17.46 thf(f3121,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f3120])).
% 54.09/17.46 thf(f3122,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f3121])).
% 54.09/17.46 thf(f3123,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3122])).
% 54.09/17.46 thf(f3124,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3123])).
% 54.09/17.46 thf(f3125,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3124])).
% 54.09/17.46 thf(f3126,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3125])).
% 54.09/17.46 thf(f3127,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3126])).
% 54.09/17.46 thf(f3128,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3127])).
% 54.09/17.46 thf(f3129,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3128])).
% 54.09/17.46 thf(f3130,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3129])).
% 54.09/17.46 thf(f3131,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3118])).
% 54.09/17.46 thf(f3132,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3131])).
% 54.09/17.46 thf(f3133,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3132])).
% 54.09/17.46 thf(f3134,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3132])).
% 54.09/17.46 thf(f3135,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3134])).
% 54.09/17.46 thf(f3136,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f3135])).
% 54.09/17.46 thf(f3137,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f3136])).
% 54.09/17.46 thf(f3138,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3137])).
% 54.09/17.46 thf(f3139,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3138])).
% 54.09/17.46 thf(f3140,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3139])).
% 54.09/17.46 thf(f3141,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3140])).
% 54.09/17.46 thf(f3142,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3141])).
% 54.09/17.46 thf(f3143,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3142])).
% 54.09/17.46 thf(f3144,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3143])).
% 54.09/17.46 thf(f3145,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3144])).
% 54.09/17.46 thf(f3146,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3133])).
% 54.09/17.46 thf(f3147,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3146])).
% 54.09/17.46 thf(f3148,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3147])).
% 54.09/17.46 thf(f3149,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3147])).
% 54.09/17.46 thf(f3150,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3149])).
% 54.09/17.46 thf(f3151,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f3150])).
% 54.09/17.46 thf(f3152,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f3151])).
% 54.09/17.46 thf(f3153,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3152])).
% 54.09/17.46 thf(f3154,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3153])).
% 54.09/17.46 thf(f3155,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3154])).
% 54.09/17.46 thf(f3156,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3155])).
% 54.09/17.46 thf(f3157,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3156])).
% 54.09/17.46 thf(f3158,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3157])).
% 54.09/17.46 thf(f3159,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3158])).
% 54.09/17.46 thf(f3160,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3159])).
% 54.09/17.46 thf(f3161,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3148])).
% 54.09/17.46 thf(f3162,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f3161])).
% 54.09/17.46 thf(f3163,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f3162])).
% 54.09/17.46 thf(f3164,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3163])).
% 54.09/17.46 thf(f3165,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3164])).
% 54.09/17.46 thf(f3166,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3165])).
% 54.09/17.46 thf(f3167,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3166])).
% 54.09/17.46 thf(f3168,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3167])).
% 54.09/17.46 thf(f3169,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3168])).
% 54.09/17.46 thf(f3170,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3169])).
% 54.09/17.46 thf(f3171,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3170])).
% 54.09/17.46 thf(f3172,plain,(
% 54.09/17.46 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3113])).
% 54.09/17.46 thf(f3173,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f3172])).
% 54.09/17.46 thf(f3174,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3173])).
% 54.09/17.46 thf(f3175,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3174])).
% 54.09/17.46 thf(f3176,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3174])).
% 54.09/17.46 thf(f3177,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3176])).
% 54.09/17.46 thf(f3178,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f3177])).
% 54.09/17.46 thf(f3179,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f3178])).
% 54.09/17.46 thf(f3180,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3179])).
% 54.09/17.46 thf(f3181,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3180])).
% 54.09/17.46 thf(f3182,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3181])).
% 54.09/17.46 thf(f3183,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3182])).
% 54.09/17.46 thf(f3184,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3183])).
% 54.09/17.46 thf(f3185,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3184])).
% 54.09/17.46 thf(f3186,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3185])).
% 54.09/17.46 thf(f3187,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3186])).
% 54.09/17.46 thf(f3188,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3175])).
% 54.09/17.46 thf(f3189,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3188])).
% 54.09/17.46 thf(f3190,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3189])).
% 54.09/17.46 thf(f3191,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3189])).
% 54.09/17.46 thf(f3192,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3191])).
% 54.09/17.46 thf(f3193,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.46 inference(pi_proxy_clausification,[],[f3192])).
% 54.09/17.46 thf(f3194,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.46 inference(beta-eta_normalization,[],[f3193])).
% 54.09/17.46 thf(f3195,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3194])).
% 54.09/17.46 thf(f3196,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3195])).
% 54.09/17.46 thf(f3197,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3196])).
% 54.09/17.46 thf(f3198,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(or_proxy_clausification,[],[f3197])).
% 54.09/17.46 thf(f3199,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3198])).
% 54.09/17.46 thf(f3200,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3199])).
% 54.09/17.46 thf(f3201,plain,(
% 54.09/17.46 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.46 inference(not_proxy_clausification,[],[f3200])).
% 54.09/17.46 thf(f3202,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3201])).
% 54.09/17.47 thf(f3203,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3190])).
% 54.09/17.47 thf(f3204,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3203])).
% 54.09/17.47 thf(f3205,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3204])).
% 54.09/17.47 thf(f3206,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3204])).
% 54.09/17.47 thf(f3207,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3206])).
% 54.09/17.47 thf(f3208,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3207])).
% 54.09/17.47 thf(f3209,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3208])).
% 54.09/17.47 thf(f3210,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3209])).
% 54.09/17.47 thf(f3211,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3210])).
% 54.09/17.47 thf(f3212,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3211])).
% 54.09/17.47 thf(f3213,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3212])).
% 54.09/17.47 thf(f3214,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3213])).
% 54.09/17.47 thf(f3215,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3214])).
% 54.09/17.47 thf(f3216,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3215])).
% 54.09/17.47 thf(f3217,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3216])).
% 54.09/17.47 thf(f3218,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3205])).
% 54.09/17.47 thf(f3219,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3218])).
% 54.09/17.47 thf(f3220,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3219])).
% 54.09/17.47 thf(f3221,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3220])).
% 54.09/17.47 thf(f3222,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3221])).
% 54.09/17.47 thf(f3223,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3222])).
% 54.09/17.47 thf(f3224,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3223])).
% 54.09/17.47 thf(f3225,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3224])).
% 54.09/17.47 thf(f3226,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3225])).
% 54.09/17.47 thf(f3227,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3226])).
% 54.09/17.47 thf(f3228,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3227])).
% 54.09/17.47 thf(f3229,plain,(
% 54.09/17.47 ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))),
% 54.09/17.47 inference(not_proxy_clausification,[],[f2250])).
% 54.09/17.47 thf(f3230,plain,(
% 54.09/17.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3229])).
% 54.09/17.47 thf(f3231,plain,(
% 54.09/17.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3230])).
% 54.09/17.47 thf(f3232,plain,(
% 54.09/17.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3231])).
% 54.09/17.47 thf(f3233,plain,(
% 54.09/17.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3231])).
% 54.09/17.47 thf(f3234,plain,(
% 54.09/17.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3233])).
% 54.09/17.47 thf(f3235,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3234])).
% 54.09/17.47 thf(f3236,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3235])).
% 54.09/17.47 thf(f3237,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3236])).
% 54.09/17.47 thf(f3238,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3236])).
% 54.09/17.47 thf(f3239,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3238])).
% 54.09/17.47 thf(f3240,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3239])).
% 54.09/17.47 thf(f3241,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3240])).
% 54.09/17.47 thf(f3242,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3241])).
% 54.09/17.47 thf(f3243,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3241])).
% 54.09/17.47 thf(f3244,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3243])).
% 54.09/17.47 thf(f3245,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3244])).
% 54.09/17.47 thf(f3246,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3245])).
% 54.09/17.47 thf(f3247,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3246])).
% 54.09/17.47 thf(f3248,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3247])).
% 54.09/17.47 thf(f3249,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3248])).
% 54.09/17.47 thf(f3250,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3249])).
% 54.09/17.47 thf(f3251,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3250])).
% 54.09/17.47 thf(f3252,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3251])).
% 54.09/17.47 thf(f3253,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3252])).
% 54.09/17.47 thf(f3254,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3253])).
% 54.09/17.47 thf(f3255,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3242])).
% 54.09/17.47 thf(f3256,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3255])).
% 54.09/17.47 thf(f3257,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3256])).
% 54.09/17.47 thf(f3258,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3256])).
% 54.09/17.47 thf(f3259,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3258])).
% 54.09/17.47 thf(f3260,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3259])).
% 54.09/17.47 thf(f3261,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3260])).
% 54.09/17.47 thf(f3262,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3261])).
% 54.09/17.47 thf(f3263,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3262])).
% 54.09/17.47 thf(f3264,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3263])).
% 54.09/17.47 thf(f3265,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3264])).
% 54.09/17.47 thf(f3266,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3265])).
% 54.09/17.47 thf(f3267,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3266])).
% 54.09/17.47 thf(f3268,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3267])).
% 54.09/17.47 thf(f3269,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3268])).
% 54.09/17.47 thf(f3270,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3257])).
% 54.09/17.47 thf(f3271,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3270])).
% 54.09/17.47 thf(f3272,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3271])).
% 54.09/17.47 thf(f3273,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3271])).
% 54.09/17.47 thf(f3274,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3273])).
% 54.09/17.47 thf(f3275,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3274])).
% 54.09/17.47 thf(f3276,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3275])).
% 54.09/17.47 thf(f3277,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3276])).
% 54.09/17.47 thf(f3278,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3277])).
% 54.09/17.47 thf(f3279,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3278])).
% 54.09/17.47 thf(f3280,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3279])).
% 54.09/17.47 thf(f3281,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3280])).
% 54.09/17.47 thf(f3282,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3281])).
% 54.09/17.47 thf(f3283,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3282])).
% 54.09/17.47 thf(f3284,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3283])).
% 54.09/17.47 thf(f3285,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3272])).
% 54.09/17.47 thf(f3286,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3285])).
% 54.09/17.47 thf(f3287,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3286])).
% 54.09/17.47 thf(f3288,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3287])).
% 54.09/17.47 thf(f3289,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3288])).
% 54.09/17.47 thf(f3290,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3289])).
% 54.09/17.47 thf(f3291,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3290])).
% 54.09/17.47 thf(f3292,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3291])).
% 54.09/17.47 thf(f3293,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3292])).
% 54.09/17.47 thf(f3294,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3293])).
% 54.09/17.47 thf(f3295,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3294])).
% 54.09/17.47 thf(f3296,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3237])).
% 54.09/17.47 thf(f3297,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3296])).
% 54.09/17.47 thf(f3298,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3297])).
% 54.09/17.47 thf(f3299,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3297])).
% 54.09/17.47 thf(f3300,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3299])).
% 54.09/17.47 thf(f3301,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3300])).
% 54.09/17.47 thf(f3302,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3301])).
% 54.09/17.47 thf(f3303,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3302])).
% 54.09/17.47 thf(f3304,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3302])).
% 54.09/17.47 thf(f3305,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3304])).
% 54.09/17.47 thf(f3306,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3305])).
% 54.09/17.47 thf(f3307,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3306])).
% 54.09/17.47 thf(f3308,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3307])).
% 54.09/17.47 thf(f3309,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3308])).
% 54.09/17.47 thf(f3310,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3309])).
% 54.09/17.47 thf(f3311,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3310])).
% 54.09/17.47 thf(f3312,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3311])).
% 54.09/17.47 thf(f3313,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3312])).
% 54.09/17.47 thf(f3314,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3313])).
% 54.09/17.47 thf(f3315,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3314])).
% 54.09/17.47 thf(f3316,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3303])).
% 54.09/17.47 thf(f3317,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3316])).
% 54.09/17.47 thf(f3318,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3317])).
% 54.09/17.47 thf(f3319,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3317])).
% 54.09/17.47 thf(f3320,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3319])).
% 54.09/17.47 thf(f3321,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3320])).
% 54.09/17.47 thf(f3322,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3321])).
% 54.09/17.47 thf(f3323,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3322])).
% 54.09/17.47 thf(f3324,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3323])).
% 54.09/17.47 thf(f3325,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3324])).
% 54.09/17.47 thf(f3326,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3325])).
% 54.09/17.47 thf(f3327,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3326])).
% 54.09/17.47 thf(f3328,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3327])).
% 54.09/17.47 thf(f3329,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3328])).
% 54.09/17.47 thf(f3330,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3329])).
% 54.09/17.47 thf(f3331,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3318])).
% 54.09/17.47 thf(f3332,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3331])).
% 54.09/17.47 thf(f3333,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3332])).
% 54.09/17.47 thf(f3334,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3332])).
% 54.09/17.47 thf(f3335,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3334])).
% 54.09/17.47 thf(f3336,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3335])).
% 54.09/17.47 thf(f3337,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3336])).
% 54.09/17.47 thf(f3338,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3337])).
% 54.09/17.47 thf(f3339,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3338])).
% 54.09/17.47 thf(f3340,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3339])).
% 54.09/17.47 thf(f3341,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3340])).
% 54.09/17.47 thf(f3342,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3341])).
% 54.09/17.47 thf(f3343,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3342])).
% 54.09/17.47 thf(f3344,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3343])).
% 54.09/17.47 thf(f3345,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3344])).
% 54.09/17.47 thf(f3346,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3333])).
% 54.09/17.47 thf(f3347,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3346])).
% 54.09/17.47 thf(f3348,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3347])).
% 54.09/17.47 thf(f3349,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3348])).
% 54.09/17.47 thf(f3350,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3349])).
% 54.09/17.47 thf(f3351,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3350])).
% 54.09/17.47 thf(f3352,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3351])).
% 54.09/17.47 thf(f3353,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3352])).
% 54.09/17.47 thf(f3354,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3353])).
% 54.09/17.47 thf(f3355,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3354])).
% 54.09/17.47 thf(f3356,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3355])).
% 54.09/17.47 thf(f3357,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3298])).
% 54.09/17.47 thf(f3358,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3357])).
% 54.09/17.47 thf(f3359,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3358])).
% 54.09/17.47 thf(f3360,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3358])).
% 54.09/17.47 thf(f3361,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3360])).
% 54.09/17.47 thf(f3362,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3361])).
% 54.09/17.47 thf(f3363,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3362])).
% 54.09/17.47 thf(f3364,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3363])).
% 54.09/17.47 thf(f3365,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3363])).
% 54.09/17.47 thf(f3366,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3365])).
% 54.09/17.47 thf(f3367,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3366])).
% 54.09/17.47 thf(f3368,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3367])).
% 54.09/17.47 thf(f3369,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3368])).
% 54.09/17.47 thf(f3370,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3369])).
% 54.09/17.47 thf(f3371,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3370])).
% 54.09/17.47 thf(f3372,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3371])).
% 54.09/17.47 thf(f3373,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3372])).
% 54.09/17.47 thf(f3374,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3373])).
% 54.09/17.47 thf(f3375,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3374])).
% 54.09/17.47 thf(f3376,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3375])).
% 54.09/17.47 thf(f3377,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3364])).
% 54.09/17.47 thf(f3378,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3377])).
% 54.09/17.47 thf(f3379,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3378])).
% 54.09/17.47 thf(f3380,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3378])).
% 54.09/17.47 thf(f3381,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3380])).
% 54.09/17.47 thf(f3382,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3381])).
% 54.09/17.47 thf(f3383,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3382])).
% 54.09/17.47 thf(f3384,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3383])).
% 54.09/17.47 thf(f3385,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3384])).
% 54.09/17.47 thf(f3386,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3385])).
% 54.09/17.47 thf(f3387,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3386])).
% 54.09/17.47 thf(f3388,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3387])).
% 54.09/17.47 thf(f3389,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3388])).
% 54.09/17.47 thf(f3390,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3389])).
% 54.09/17.47 thf(f3391,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3390])).
% 54.09/17.47 thf(f3392,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3379])).
% 54.09/17.47 thf(f3393,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3392])).
% 54.09/17.47 thf(f3394,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3393])).
% 54.09/17.47 thf(f3395,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3393])).
% 54.09/17.47 thf(f3396,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3395])).
% 54.09/17.47 thf(f3397,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3396])).
% 54.09/17.47 thf(f3398,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3397])).
% 54.09/17.47 thf(f3399,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3398])).
% 54.09/17.47 thf(f3400,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3399])).
% 54.09/17.47 thf(f3401,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3400])).
% 54.09/17.47 thf(f3402,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3401])).
% 54.09/17.47 thf(f3403,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3402])).
% 54.09/17.47 thf(f3404,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3403])).
% 54.09/17.47 thf(f3405,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3404])).
% 54.09/17.47 thf(f3406,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3405])).
% 54.09/17.47 thf(f3407,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3394])).
% 54.09/17.47 thf(f3408,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3407])).
% 54.09/17.47 thf(f3409,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3408])).
% 54.09/17.47 thf(f3410,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3409])).
% 54.09/17.47 thf(f3411,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3410])).
% 54.09/17.47 thf(f3412,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3411])).
% 54.09/17.47 thf(f3413,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3412])).
% 54.09/17.47 thf(f3414,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3413])).
% 54.09/17.47 thf(f3415,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3414])).
% 54.09/17.47 thf(f3416,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3415])).
% 54.09/17.47 thf(f3417,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3416])).
% 54.09/17.47 thf(f3418,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3359])).
% 54.09/17.47 thf(f3419,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3418])).
% 54.09/17.47 thf(f3420,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3419])).
% 54.09/17.47 thf(f3421,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3420])).
% 54.09/17.47 thf(f3422,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3420])).
% 54.09/17.47 thf(f3423,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3422])).
% 54.09/17.47 thf(f3424,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3423])).
% 54.09/17.47 thf(f3425,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3424])).
% 54.09/17.47 thf(f3426,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3425])).
% 54.09/17.47 thf(f3427,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3426])).
% 54.09/17.47 thf(f3428,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3427])).
% 54.09/17.47 thf(f3429,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3428])).
% 54.09/17.47 thf(f3430,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3429])).
% 54.09/17.47 thf(f3431,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3430])).
% 54.09/17.47 thf(f3432,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3431])).
% 54.09/17.47 thf(f3433,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3432])).
% 54.09/17.47 thf(f3434,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3421])).
% 54.09/17.47 thf(f3435,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3434])).
% 54.09/17.47 thf(f3436,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3435])).
% 54.09/17.47 thf(f3437,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3435])).
% 54.09/17.47 thf(f3438,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3437])).
% 54.09/17.47 thf(f3439,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3438])).
% 54.09/17.47 thf(f3440,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3439])).
% 54.09/17.47 thf(f3441,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3440])).
% 54.09/17.47 thf(f3442,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3441])).
% 54.09/17.47 thf(f3443,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3442])).
% 54.09/17.47 thf(f3444,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3443])).
% 54.09/17.47 thf(f3445,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3444])).
% 54.09/17.47 thf(f3446,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3445])).
% 54.09/17.47 thf(f3447,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3446])).
% 54.09/17.47 thf(f3448,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3447])).
% 54.09/17.47 thf(f3449,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3436])).
% 54.09/17.47 thf(f3450,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3449])).
% 54.09/17.47 thf(f3451,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3450])).
% 54.09/17.47 thf(f3452,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3450])).
% 54.09/17.47 thf(f3453,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3452])).
% 54.09/17.47 thf(f3454,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3453])).
% 54.09/17.47 thf(f3455,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3454])).
% 54.09/17.47 thf(f3456,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3455])).
% 54.09/17.47 thf(f3457,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3456])).
% 54.09/17.47 thf(f3458,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3457])).
% 54.09/17.47 thf(f3459,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3458])).
% 54.09/17.47 thf(f3460,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3459])).
% 54.09/17.47 thf(f3461,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3460])).
% 54.09/17.47 thf(f3462,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3461])).
% 54.09/17.47 thf(f3463,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3462])).
% 54.09/17.47 thf(f3464,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3451])).
% 54.09/17.47 thf(f3465,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3464])).
% 54.09/17.47 thf(f3466,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3465])).
% 54.09/17.47 thf(f3467,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3466])).
% 54.09/17.47 thf(f3468,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3467])).
% 54.09/17.47 thf(f3469,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3468])).
% 54.09/17.47 thf(f3470,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3469])).
% 54.09/17.47 thf(f3471,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3470])).
% 54.09/17.47 thf(f3472,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3471])).
% 54.09/17.47 thf(f3473,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3472])).
% 54.09/17.47 thf(f3474,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3473])).
% 54.09/17.47 thf(f3475,plain,(
% 54.09/17.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3232])).
% 54.09/17.47 thf(f3476,plain,(
% 54.09/17.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3475])).
% 54.09/17.47 thf(f3477,plain,(
% 54.09/17.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3476])).
% 54.09/17.47 thf(f3478,plain,(
% 54.09/17.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3476])).
% 54.09/17.47 thf(f3479,plain,(
% 54.09/17.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3478])).
% 54.09/17.47 thf(f3480,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3479])).
% 54.09/17.47 thf(f3481,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3480])).
% 54.09/17.47 thf(f3482,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3481])).
% 54.09/17.47 thf(f3483,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3481])).
% 54.09/17.47 thf(f3484,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3483])).
% 54.09/17.47 thf(f3485,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3484])).
% 54.09/17.47 thf(f3486,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3485])).
% 54.09/17.47 thf(f3487,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3486])).
% 54.09/17.47 thf(f3488,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3486])).
% 54.09/17.47 thf(f3489,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3488])).
% 54.09/17.47 thf(f3490,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3489])).
% 54.09/17.47 thf(f3491,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3490])).
% 54.09/17.47 thf(f3492,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3491])).
% 54.09/17.47 thf(f3493,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3492])).
% 54.09/17.47 thf(f3494,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3493])).
% 54.09/17.47 thf(f3495,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3494])).
% 54.09/17.47 thf(f3496,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3495])).
% 54.09/17.47 thf(f3497,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3496])).
% 54.09/17.47 thf(f3498,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3497])).
% 54.09/17.47 thf(f3499,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3498])).
% 54.09/17.47 thf(f3500,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3487])).
% 54.09/17.47 thf(f3501,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3500])).
% 54.09/17.47 thf(f3502,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3501])).
% 54.09/17.47 thf(f3503,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3501])).
% 54.09/17.47 thf(f3504,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3503])).
% 54.09/17.47 thf(f3505,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3504])).
% 54.09/17.47 thf(f3506,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3505])).
% 54.09/17.47 thf(f3507,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3506])).
% 54.09/17.47 thf(f3508,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3507])).
% 54.09/17.47 thf(f3509,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3508])).
% 54.09/17.47 thf(f3510,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3509])).
% 54.09/17.47 thf(f3511,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3510])).
% 54.09/17.47 thf(f3512,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3511])).
% 54.09/17.47 thf(f3513,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3512])).
% 54.09/17.47 thf(f3514,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3513])).
% 54.09/17.47 thf(f3515,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3502])).
% 54.09/17.47 thf(f3516,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3515])).
% 54.09/17.47 thf(f3517,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3516])).
% 54.09/17.47 thf(f3518,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3516])).
% 54.09/17.47 thf(f3519,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3518])).
% 54.09/17.47 thf(f3520,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3519])).
% 54.09/17.47 thf(f3521,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3520])).
% 54.09/17.47 thf(f3522,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3521])).
% 54.09/17.47 thf(f3523,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3522])).
% 54.09/17.47 thf(f3524,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3523])).
% 54.09/17.47 thf(f3525,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3524])).
% 54.09/17.47 thf(f3526,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3525])).
% 54.09/17.47 thf(f3527,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3526])).
% 54.09/17.47 thf(f3528,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3527])).
% 54.09/17.47 thf(f3529,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3528])).
% 54.09/17.47 thf(f3530,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3517])).
% 54.09/17.47 thf(f3531,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3530])).
% 54.09/17.47 thf(f3532,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3531])).
% 54.09/17.47 thf(f3533,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3532])).
% 54.09/17.47 thf(f3534,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3533])).
% 54.09/17.47 thf(f3535,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3534])).
% 54.09/17.47 thf(f3536,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3535])).
% 54.09/17.47 thf(f3537,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3536])).
% 54.09/17.47 thf(f3538,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3537])).
% 54.09/17.47 thf(f3539,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3538])).
% 54.09/17.47 thf(f3540,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3539])).
% 54.09/17.47 thf(f3541,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3482])).
% 54.09/17.47 thf(f3542,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3541])).
% 54.09/17.47 thf(f3543,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3542])).
% 54.09/17.47 thf(f3544,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3542])).
% 54.09/17.47 thf(f3545,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3544])).
% 54.09/17.47 thf(f3546,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3545])).
% 54.09/17.47 thf(f3547,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3546])).
% 54.09/17.47 thf(f3548,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3547])).
% 54.09/17.47 thf(f3549,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3547])).
% 54.09/17.47 thf(f3550,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3549])).
% 54.09/17.47 thf(f3551,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3550])).
% 54.09/17.47 thf(f3552,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3551])).
% 54.09/17.47 thf(f3553,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3552])).
% 54.09/17.47 thf(f3554,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3553])).
% 54.09/17.47 thf(f3555,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3554])).
% 54.09/17.47 thf(f3556,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3555])).
% 54.09/17.47 thf(f3557,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3556])).
% 54.09/17.47 thf(f3558,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3557])).
% 54.09/17.47 thf(f3559,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3558])).
% 54.09/17.47 thf(f3560,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3559])).
% 54.09/17.47 thf(f3561,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3548])).
% 54.09/17.47 thf(f3562,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3561])).
% 54.09/17.47 thf(f3563,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3562])).
% 54.09/17.47 thf(f3564,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3562])).
% 54.09/17.47 thf(f3565,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3564])).
% 54.09/17.47 thf(f3566,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3565])).
% 54.09/17.47 thf(f3567,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3566])).
% 54.09/17.47 thf(f3568,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3567])).
% 54.09/17.47 thf(f3569,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3568])).
% 54.09/17.47 thf(f3570,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3569])).
% 54.09/17.47 thf(f3571,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3570])).
% 54.09/17.47 thf(f3572,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3571])).
% 54.09/17.47 thf(f3573,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3572])).
% 54.09/17.47 thf(f3574,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3573])).
% 54.09/17.47 thf(f3575,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3574])).
% 54.09/17.47 thf(f3576,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3563])).
% 54.09/17.47 thf(f3577,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3576])).
% 54.09/17.47 thf(f3578,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3577])).
% 54.09/17.47 thf(f3579,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3577])).
% 54.09/17.47 thf(f3580,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3579])).
% 54.09/17.47 thf(f3581,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3580])).
% 54.09/17.47 thf(f3582,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3581])).
% 54.09/17.47 thf(f3583,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3582])).
% 54.09/17.47 thf(f3584,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3583])).
% 54.09/17.47 thf(f3585,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3584])).
% 54.09/17.47 thf(f3586,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3585])).
% 54.09/17.47 thf(f3587,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3586])).
% 54.09/17.47 thf(f3588,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3587])).
% 54.09/17.47 thf(f3589,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3588])).
% 54.09/17.47 thf(f3590,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3589])).
% 54.09/17.47 thf(f3591,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3578])).
% 54.09/17.47 thf(f3592,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3591])).
% 54.09/17.47 thf(f3593,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3592])).
% 54.09/17.47 thf(f3594,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3593])).
% 54.09/17.47 thf(f3595,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3594])).
% 54.09/17.47 thf(f3596,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3595])).
% 54.09/17.47 thf(f3597,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3596])).
% 54.09/17.47 thf(f3598,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3597])).
% 54.09/17.47 thf(f3599,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3598])).
% 54.09/17.47 thf(f3600,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3599])).
% 54.09/17.47 thf(f3601,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3600])).
% 54.09/17.47 thf(f3602,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3543])).
% 54.09/17.47 thf(f3603,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3602])).
% 54.09/17.47 thf(f3604,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3603])).
% 54.09/17.47 thf(f3605,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3603])).
% 54.09/17.47 thf(f3606,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3605])).
% 54.09/17.47 thf(f3607,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3606])).
% 54.09/17.47 thf(f3608,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3607])).
% 54.09/17.47 thf(f3609,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3608])).
% 54.09/17.47 thf(f3610,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3608])).
% 54.09/17.47 thf(f3611,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3610])).
% 54.09/17.47 thf(f3612,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3611])).
% 54.09/17.47 thf(f3613,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3612])).
% 54.09/17.47 thf(f3614,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3613])).
% 54.09/17.47 thf(f3615,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3614])).
% 54.09/17.47 thf(f3616,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3615])).
% 54.09/17.47 thf(f3617,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3616])).
% 54.09/17.47 thf(f3618,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3617])).
% 54.09/17.47 thf(f3619,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3618])).
% 54.09/17.47 thf(f3620,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3619])).
% 54.09/17.47 thf(f3621,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3620])).
% 54.09/17.47 thf(f3622,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3609])).
% 54.09/17.47 thf(f3623,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3622])).
% 54.09/17.47 thf(f3624,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3623])).
% 54.09/17.47 thf(f3625,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3623])).
% 54.09/17.47 thf(f3626,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3625])).
% 54.09/17.47 thf(f3627,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3626])).
% 54.09/17.47 thf(f3628,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3627])).
% 54.09/17.47 thf(f3629,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3628])).
% 54.09/17.47 thf(f3630,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3629])).
% 54.09/17.47 thf(f3631,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3630])).
% 54.09/17.47 thf(f3632,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3631])).
% 54.09/17.47 thf(f3633,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3632])).
% 54.09/17.47 thf(f3634,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3633])).
% 54.09/17.47 thf(f3635,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3634])).
% 54.09/17.47 thf(f3636,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3635])).
% 54.09/17.47 thf(f3637,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3624])).
% 54.09/17.47 thf(f3638,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3637])).
% 54.09/17.47 thf(f3639,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3638])).
% 54.09/17.47 thf(f3640,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3638])).
% 54.09/17.47 thf(f3641,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3640])).
% 54.09/17.47 thf(f3642,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3641])).
% 54.09/17.47 thf(f3643,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3642])).
% 54.09/17.47 thf(f3644,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3643])).
% 54.09/17.47 thf(f3645,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3644])).
% 54.09/17.47 thf(f3646,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3645])).
% 54.09/17.47 thf(f3647,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3646])).
% 54.09/17.47 thf(f3648,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3647])).
% 54.09/17.47 thf(f3649,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3648])).
% 54.09/17.47 thf(f3650,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3649])).
% 54.09/17.47 thf(f3651,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3650])).
% 54.09/17.47 thf(f3652,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3639])).
% 54.09/17.47 thf(f3653,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3652])).
% 54.09/17.47 thf(f3654,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3653])).
% 54.09/17.47 thf(f3655,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3654])).
% 54.09/17.47 thf(f3656,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3655])).
% 54.09/17.47 thf(f3657,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3656])).
% 54.09/17.47 thf(f3658,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3657])).
% 54.09/17.47 thf(f3659,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3658])).
% 54.09/17.47 thf(f3660,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3659])).
% 54.09/17.47 thf(f3661,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3660])).
% 54.09/17.47 thf(f3662,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3661])).
% 54.09/17.47 thf(f3663,plain,(
% 54.09/17.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3604])).
% 54.09/17.47 thf(f3664,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3663])).
% 54.09/17.47 thf(f3665,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3664])).
% 54.09/17.47 thf(f3666,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3665])).
% 54.09/17.47 thf(f3667,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3665])).
% 54.09/17.47 thf(f3668,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3667])).
% 54.09/17.47 thf(f3669,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3668])).
% 54.09/17.47 thf(f3670,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3669])).
% 54.09/17.47 thf(f3671,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3670])).
% 54.09/17.47 thf(f3672,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3671])).
% 54.09/17.47 thf(f3673,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3672])).
% 54.09/17.47 thf(f3674,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3673])).
% 54.09/17.47 thf(f3675,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3674])).
% 54.09/17.47 thf(f3676,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3675])).
% 54.09/17.47 thf(f3677,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3676])).
% 54.09/17.47 thf(f3678,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3677])).
% 54.09/17.47 thf(f3679,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3666])).
% 54.09/17.47 thf(f3680,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3679])).
% 54.09/17.47 thf(f3681,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3680])).
% 54.09/17.47 thf(f3682,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3680])).
% 54.09/17.47 thf(f3683,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3682])).
% 54.09/17.47 thf(f3684,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3683])).
% 54.09/17.47 thf(f3685,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3684])).
% 54.09/17.47 thf(f3686,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3685])).
% 54.09/17.47 thf(f3687,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3686])).
% 54.09/17.47 thf(f3688,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3687])).
% 54.09/17.47 thf(f3689,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3688])).
% 54.09/17.47 thf(f3690,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3689])).
% 54.09/17.47 thf(f3691,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3690])).
% 54.09/17.47 thf(f3692,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3691])).
% 54.09/17.47 thf(f3693,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3692])).
% 54.09/17.47 thf(f3694,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3681])).
% 54.09/17.47 thf(f3695,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3694])).
% 54.09/17.47 thf(f3696,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3695])).
% 54.09/17.47 thf(f3697,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3695])).
% 54.09/17.47 thf(f3698,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3697])).
% 54.09/17.47 thf(f3699,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3698])).
% 54.09/17.47 thf(f3700,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3699])).
% 54.09/17.47 thf(f3701,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3700])).
% 54.09/17.47 thf(f3702,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3701])).
% 54.09/17.47 thf(f3703,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3702])).
% 54.09/17.47 thf(f3704,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3703])).
% 54.09/17.47 thf(f3705,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3704])).
% 54.09/17.47 thf(f3706,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3705])).
% 54.09/17.47 thf(f3707,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3706])).
% 54.09/17.47 thf(f3708,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3707])).
% 54.09/17.47 thf(f3709,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.47 inference(not_proxy_clausification,[],[f3696])).
% 54.09/17.47 thf(f3710,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.47 inference(pi_proxy_clausification,[],[f3709])).
% 54.09/17.47 thf(f3711,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.47 inference(beta-eta_normalization,[],[f3710])).
% 54.09/17.47 thf(f3712,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3711])).
% 54.09/17.47 thf(f3713,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.47 inference(or_proxy_clausification,[],[f3712])).
% 54.09/17.47 thf(f3714,plain,(
% 54.09/17.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3713])).
% 54.09/17.48 thf(f3715,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3714])).
% 54.09/17.48 thf(f3716,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3715])).
% 54.09/17.48 thf(f3717,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3716])).
% 54.09/17.48 thf(f3718,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3717])).
% 54.09/17.48 thf(f3719,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3718])).
% 54.09/17.48 thf(f3720,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3477])).
% 54.09/17.48 thf(f3721,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3720])).
% 54.09/17.48 thf(f3722,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3721])).
% 54.09/17.48 thf(f3723,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3721])).
% 54.09/17.48 thf(f3724,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3723])).
% 54.09/17.48 thf(f3725,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3724])).
% 54.09/17.48 thf(f3726,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3725])).
% 54.09/17.48 thf(f3727,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3726])).
% 54.09/17.48 thf(f3728,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3726])).
% 54.09/17.48 thf(f3729,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3728])).
% 54.09/17.48 thf(f3730,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3729])).
% 54.09/17.48 thf(f3731,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3730])).
% 54.09/17.48 thf(f3732,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3731])).
% 54.09/17.48 thf(f3733,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3731])).
% 54.09/17.48 thf(f3734,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3733])).
% 54.09/17.48 thf(f3735,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3734])).
% 54.09/17.48 thf(f3736,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3735])).
% 54.09/17.48 thf(f3737,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3736])).
% 54.09/17.48 thf(f3738,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3737])).
% 54.09/17.48 thf(f3739,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3738])).
% 54.09/17.48 thf(f3740,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3739])).
% 54.09/17.48 thf(f3741,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3740])).
% 54.09/17.48 thf(f3742,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3741])).
% 54.09/17.48 thf(f3743,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3742])).
% 54.09/17.48 thf(f3744,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3743])).
% 54.09/17.48 thf(f3745,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3732])).
% 54.09/17.48 thf(f3746,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3745])).
% 54.09/17.48 thf(f3747,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3746])).
% 54.09/17.48 thf(f3748,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3746])).
% 54.09/17.48 thf(f3749,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3748])).
% 54.09/17.48 thf(f3750,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3749])).
% 54.09/17.48 thf(f3751,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3750])).
% 54.09/17.48 thf(f3752,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3751])).
% 54.09/17.48 thf(f3753,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3752])).
% 54.09/17.48 thf(f3754,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3753])).
% 54.09/17.48 thf(f3755,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3754])).
% 54.09/17.48 thf(f3756,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3755])).
% 54.09/17.48 thf(f3757,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3756])).
% 54.09/17.48 thf(f3758,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3757])).
% 54.09/17.48 thf(f3759,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3758])).
% 54.09/17.48 thf(f3760,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3747])).
% 54.09/17.48 thf(f3761,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3760])).
% 54.09/17.48 thf(f3762,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3761])).
% 54.09/17.48 thf(f3763,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3761])).
% 54.09/17.48 thf(f3764,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3763])).
% 54.09/17.48 thf(f3765,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3764])).
% 54.09/17.48 thf(f3766,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3765])).
% 54.09/17.48 thf(f3767,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3766])).
% 54.09/17.48 thf(f3768,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3767])).
% 54.09/17.48 thf(f3769,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3768])).
% 54.09/17.48 thf(f3770,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3769])).
% 54.09/17.48 thf(f3771,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3770])).
% 54.09/17.48 thf(f3772,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3771])).
% 54.09/17.48 thf(f3773,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3772])).
% 54.09/17.48 thf(f3774,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3773])).
% 54.09/17.48 thf(f3775,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3762])).
% 54.09/17.48 thf(f3776,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3775])).
% 54.09/17.48 thf(f3777,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3776])).
% 54.09/17.48 thf(f3778,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3777])).
% 54.09/17.48 thf(f3779,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3778])).
% 54.09/17.48 thf(f3780,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3779])).
% 54.09/17.48 thf(f3781,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3780])).
% 54.09/17.48 thf(f3782,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3781])).
% 54.09/17.48 thf(f3783,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3782])).
% 54.09/17.48 thf(f3784,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3783])).
% 54.09/17.48 thf(f3785,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3784])).
% 54.09/17.48 thf(f3786,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3727])).
% 54.09/17.48 thf(f3787,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3786])).
% 54.09/17.48 thf(f3788,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3787])).
% 54.09/17.48 thf(f3789,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3787])).
% 54.09/17.48 thf(f3790,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3789])).
% 54.09/17.48 thf(f3791,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3790])).
% 54.09/17.48 thf(f3792,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3791])).
% 54.09/17.48 thf(f3793,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3792])).
% 54.09/17.48 thf(f3794,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3792])).
% 54.09/17.48 thf(f3795,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3794])).
% 54.09/17.48 thf(f3796,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3795])).
% 54.09/17.48 thf(f3797,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3796])).
% 54.09/17.48 thf(f3798,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3797])).
% 54.09/17.48 thf(f3799,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3798])).
% 54.09/17.48 thf(f3800,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3799])).
% 54.09/17.48 thf(f3801,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3800])).
% 54.09/17.48 thf(f3802,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3801])).
% 54.09/17.48 thf(f3803,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3802])).
% 54.09/17.48 thf(f3804,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3803])).
% 54.09/17.48 thf(f3805,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3804])).
% 54.09/17.48 thf(f3806,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3793])).
% 54.09/17.48 thf(f3807,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3806])).
% 54.09/17.48 thf(f3808,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3807])).
% 54.09/17.48 thf(f3809,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3807])).
% 54.09/17.48 thf(f3810,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3809])).
% 54.09/17.48 thf(f3811,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3810])).
% 54.09/17.48 thf(f3812,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3811])).
% 54.09/17.48 thf(f3813,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3812])).
% 54.09/17.48 thf(f3814,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3813])).
% 54.09/17.48 thf(f3815,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3814])).
% 54.09/17.48 thf(f3816,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3815])).
% 54.09/17.48 thf(f3817,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3816])).
% 54.09/17.48 thf(f3818,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3817])).
% 54.09/17.48 thf(f3819,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3818])).
% 54.09/17.48 thf(f3820,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3819])).
% 54.09/17.48 thf(f3821,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3808])).
% 54.09/17.48 thf(f3822,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3821])).
% 54.09/17.48 thf(f3823,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3822])).
% 54.09/17.48 thf(f3824,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3822])).
% 54.09/17.48 thf(f3825,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3824])).
% 54.09/17.48 thf(f3826,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3825])).
% 54.09/17.48 thf(f3827,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3826])).
% 54.09/17.48 thf(f3828,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3827])).
% 54.09/17.48 thf(f3829,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3828])).
% 54.09/17.48 thf(f3830,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3829])).
% 54.09/17.48 thf(f3831,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3830])).
% 54.09/17.48 thf(f3832,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3831])).
% 54.09/17.48 thf(f3833,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3832])).
% 54.09/17.48 thf(f3834,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3833])).
% 54.09/17.48 thf(f3835,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3834])).
% 54.09/17.48 thf(f3836,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3823])).
% 54.09/17.48 thf(f3837,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3836])).
% 54.09/17.48 thf(f3838,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3837])).
% 54.09/17.48 thf(f3839,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3838])).
% 54.09/17.48 thf(f3840,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3839])).
% 54.09/17.48 thf(f3841,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3840])).
% 54.09/17.48 thf(f3842,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3841])).
% 54.09/17.48 thf(f3843,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3842])).
% 54.09/17.48 thf(f3844,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3843])).
% 54.09/17.48 thf(f3845,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3844])).
% 54.09/17.48 thf(f3846,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3845])).
% 54.09/17.48 thf(f3847,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3788])).
% 54.09/17.48 thf(f3848,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3847])).
% 54.09/17.48 thf(f3849,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3848])).
% 54.09/17.48 thf(f3850,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3848])).
% 54.09/17.48 thf(f3851,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3850])).
% 54.09/17.48 thf(f3852,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3851])).
% 54.09/17.48 thf(f3853,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3852])).
% 54.09/17.48 thf(f3854,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3853])).
% 54.09/17.48 thf(f3855,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3853])).
% 54.09/17.48 thf(f3856,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3855])).
% 54.09/17.48 thf(f3857,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3856])).
% 54.09/17.48 thf(f3858,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3857])).
% 54.09/17.48 thf(f3859,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3858])).
% 54.09/17.48 thf(f3860,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3859])).
% 54.09/17.48 thf(f3861,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3860])).
% 54.09/17.48 thf(f3862,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3861])).
% 54.09/17.48 thf(f3863,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3862])).
% 54.09/17.48 thf(f3864,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3863])).
% 54.09/17.48 thf(f3865,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3864])).
% 54.09/17.48 thf(f3866,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3865])).
% 54.09/17.48 thf(f3867,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3854])).
% 54.09/17.48 thf(f3868,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3867])).
% 54.09/17.48 thf(f3869,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3868])).
% 54.09/17.48 thf(f3870,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3868])).
% 54.09/17.48 thf(f3871,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3870])).
% 54.09/17.48 thf(f3872,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3871])).
% 54.09/17.48 thf(f3873,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3872])).
% 54.09/17.48 thf(f3874,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3873])).
% 54.09/17.48 thf(f3875,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3874])).
% 54.09/17.48 thf(f3876,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3875])).
% 54.09/17.48 thf(f3877,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3876])).
% 54.09/17.48 thf(f3878,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3877])).
% 54.09/17.48 thf(f3879,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3878])).
% 54.09/17.48 thf(f3880,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3879])).
% 54.09/17.48 thf(f3881,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3880])).
% 54.09/17.48 thf(f3882,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3869])).
% 54.09/17.48 thf(f3883,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3882])).
% 54.09/17.48 thf(f3884,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3883])).
% 54.09/17.48 thf(f3885,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3883])).
% 54.09/17.48 thf(f3886,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3885])).
% 54.09/17.48 thf(f3887,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3886])).
% 54.09/17.48 thf(f3888,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3887])).
% 54.09/17.48 thf(f3889,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3888])).
% 54.09/17.48 thf(f3890,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3889])).
% 54.09/17.48 thf(f3891,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3890])).
% 54.09/17.48 thf(f3892,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3891])).
% 54.09/17.48 thf(f3893,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3892])).
% 54.09/17.48 thf(f3894,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3893])).
% 54.09/17.48 thf(f3895,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3894])).
% 54.09/17.48 thf(f3896,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3895])).
% 54.09/17.48 thf(f3897,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3884])).
% 54.09/17.48 thf(f3898,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3897])).
% 54.09/17.48 thf(f3899,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3898])).
% 54.09/17.48 thf(f3900,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3899])).
% 54.09/17.48 thf(f3901,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3900])).
% 54.09/17.48 thf(f3902,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3901])).
% 54.09/17.48 thf(f3903,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3902])).
% 54.09/17.48 thf(f3904,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3903])).
% 54.09/17.48 thf(f3905,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3904])).
% 54.09/17.48 thf(f3906,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3905])).
% 54.09/17.48 thf(f3907,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3906])).
% 54.09/17.48 thf(f3908,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3849])).
% 54.09/17.48 thf(f3909,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3908])).
% 54.09/17.48 thf(f3910,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3909])).
% 54.09/17.48 thf(f3911,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3910])).
% 54.09/17.48 thf(f3912,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3910])).
% 54.09/17.48 thf(f3913,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3912])).
% 54.09/17.48 thf(f3914,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3913])).
% 54.09/17.48 thf(f3915,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3914])).
% 54.09/17.48 thf(f3916,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3915])).
% 54.09/17.48 thf(f3917,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3916])).
% 54.09/17.48 thf(f3918,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3917])).
% 54.09/17.48 thf(f3919,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3918])).
% 54.09/17.48 thf(f3920,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3919])).
% 54.09/17.48 thf(f3921,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3920])).
% 54.09/17.48 thf(f3922,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3921])).
% 54.09/17.48 thf(f3923,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3922])).
% 54.09/17.48 thf(f3924,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3911])).
% 54.09/17.48 thf(f3925,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3924])).
% 54.09/17.48 thf(f3926,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3925])).
% 54.09/17.48 thf(f3927,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3925])).
% 54.09/17.48 thf(f3928,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3927])).
% 54.09/17.48 thf(f3929,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3928])).
% 54.09/17.48 thf(f3930,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3929])).
% 54.09/17.48 thf(f3931,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3930])).
% 54.09/17.48 thf(f3932,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3931])).
% 54.09/17.48 thf(f3933,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3932])).
% 54.09/17.48 thf(f3934,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3933])).
% 54.09/17.48 thf(f3935,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3934])).
% 54.09/17.48 thf(f3936,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3935])).
% 54.09/17.48 thf(f3937,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3936])).
% 54.09/17.48 thf(f3938,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3937])).
% 54.09/17.48 thf(f3939,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3926])).
% 54.09/17.48 thf(f3940,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3939])).
% 54.09/17.48 thf(f3941,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3940])).
% 54.09/17.48 thf(f3942,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3940])).
% 54.09/17.48 thf(f3943,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3942])).
% 54.09/17.48 thf(f3944,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3943])).
% 54.09/17.48 thf(f3945,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3944])).
% 54.09/17.48 thf(f3946,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3945])).
% 54.09/17.48 thf(f3947,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3946])).
% 54.09/17.48 thf(f3948,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3947])).
% 54.09/17.48 thf(f3949,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3948])).
% 54.09/17.48 thf(f3950,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3949])).
% 54.09/17.48 thf(f3951,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3950])).
% 54.09/17.48 thf(f3952,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3951])).
% 54.09/17.48 thf(f3953,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3952])).
% 54.09/17.48 thf(f3954,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3941])).
% 54.09/17.48 thf(f3955,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3954])).
% 54.09/17.48 thf(f3956,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3955])).
% 54.09/17.48 thf(f3957,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3956])).
% 54.09/17.48 thf(f3958,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3957])).
% 54.09/17.48 thf(f3959,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3958])).
% 54.09/17.48 thf(f3960,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3959])).
% 54.09/17.48 thf(f3961,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3960])).
% 54.09/17.48 thf(f3962,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3961])).
% 54.09/17.48 thf(f3963,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3962])).
% 54.09/17.48 thf(f3964,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3963])).
% 54.09/17.48 thf(f3965,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3722])).
% 54.09/17.48 thf(f3966,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3965])).
% 54.09/17.48 thf(f3967,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3966])).
% 54.09/17.48 thf(f3968,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3967])).
% 54.09/17.48 thf(f3969,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3967])).
% 54.09/17.48 thf(f3970,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3969])).
% 54.09/17.48 thf(f3971,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3970])).
% 54.09/17.48 thf(f3972,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3971])).
% 54.09/17.48 thf(f3973,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3972])).
% 54.09/17.48 thf(f3974,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3972])).
% 54.09/17.48 thf(f3975,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3974])).
% 54.09/17.48 thf(f3976,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3975])).
% 54.09/17.48 thf(f3977,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3976])).
% 54.09/17.48 thf(f3978,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3977])).
% 54.09/17.48 thf(f3979,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3978])).
% 54.09/17.48 thf(f3980,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3979])).
% 54.09/17.48 thf(f3981,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3980])).
% 54.09/17.48 thf(f3982,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3981])).
% 54.09/17.48 thf(f3983,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3982])).
% 54.09/17.48 thf(f3984,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3983])).
% 54.09/17.48 thf(f3985,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3984])).
% 54.09/17.48 thf(f3986,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3973])).
% 54.09/17.48 thf(f3987,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3986])).
% 54.09/17.48 thf(f3988,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3987])).
% 54.09/17.48 thf(f3989,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3987])).
% 54.09/17.48 thf(f3990,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3989])).
% 54.09/17.48 thf(f3991,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f3990])).
% 54.09/17.48 thf(f3992,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f3991])).
% 54.09/17.48 thf(f3993,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3992])).
% 54.09/17.48 thf(f3994,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3993])).
% 54.09/17.48 thf(f3995,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3994])).
% 54.09/17.48 thf(f3996,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f3995])).
% 54.09/17.48 thf(f3997,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3996])).
% 54.09/17.48 thf(f3998,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3997])).
% 54.09/17.48 thf(f3999,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3998])).
% 54.09/17.48 thf(f4000,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3999])).
% 54.09/17.48 thf(f4001,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3988])).
% 54.09/17.48 thf(f4002,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4001])).
% 54.09/17.48 thf(f4003,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4002])).
% 54.09/17.48 thf(f4004,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4002])).
% 54.09/17.48 thf(f4005,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4004])).
% 54.09/17.48 thf(f4006,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4005])).
% 54.09/17.48 thf(f4007,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f4006])).
% 54.09/17.48 thf(f4008,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4007])).
% 54.09/17.48 thf(f4009,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4008])).
% 54.09/17.48 thf(f4010,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4009])).
% 54.09/17.48 thf(f4011,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4010])).
% 54.09/17.48 thf(f4012,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4011])).
% 54.09/17.48 thf(f4013,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4012])).
% 54.09/17.48 thf(f4014,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4013])).
% 54.09/17.48 thf(f4015,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4014])).
% 54.09/17.48 thf(f4016,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4003])).
% 54.09/17.48 thf(f4017,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4016])).
% 54.09/17.48 thf(f4018,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f4017])).
% 54.09/17.48 thf(f4019,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4018])).
% 54.09/17.48 thf(f4020,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4019])).
% 54.09/17.48 thf(f4021,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4020])).
% 54.09/17.48 thf(f4022,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4021])).
% 54.09/17.48 thf(f4023,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4022])).
% 54.09/17.48 thf(f4024,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4023])).
% 54.09/17.48 thf(f4025,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4024])).
% 54.09/17.48 thf(f4026,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4025])).
% 54.09/17.48 thf(f4027,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f3968])).
% 54.09/17.48 thf(f4028,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4027])).
% 54.09/17.48 thf(f4029,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4028])).
% 54.09/17.48 thf(f4030,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4028])).
% 54.09/17.48 thf(f4031,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4030])).
% 54.09/17.48 thf(f4032,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4031])).
% 54.09/17.48 thf(f4033,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4032])).
% 54.09/17.48 thf(f4034,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4033])).
% 54.09/17.48 thf(f4035,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4033])).
% 54.09/17.48 thf(f4036,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4035])).
% 54.09/17.48 thf(f4037,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4036])).
% 54.09/17.48 thf(f4038,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f4037])).
% 54.09/17.48 thf(f4039,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4038])).
% 54.09/17.48 thf(f4040,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4039])).
% 54.09/17.48 thf(f4041,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4040])).
% 54.09/17.48 thf(f4042,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4041])).
% 54.09/17.48 thf(f4043,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4042])).
% 54.09/17.48 thf(f4044,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4043])).
% 54.09/17.48 thf(f4045,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4044])).
% 54.09/17.48 thf(f4046,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4045])).
% 54.09/17.48 thf(f4047,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4034])).
% 54.09/17.48 thf(f4048,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4047])).
% 54.09/17.48 thf(f4049,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4048])).
% 54.09/17.48 thf(f4050,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4048])).
% 54.09/17.48 thf(f4051,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4050])).
% 54.09/17.48 thf(f4052,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4051])).
% 54.09/17.48 thf(f4053,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f4052])).
% 54.09/17.48 thf(f4054,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4053])).
% 54.09/17.48 thf(f4055,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4054])).
% 54.09/17.48 thf(f4056,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4055])).
% 54.09/17.48 thf(f4057,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4056])).
% 54.09/17.48 thf(f4058,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4057])).
% 54.09/17.48 thf(f4059,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4058])).
% 54.09/17.48 thf(f4060,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4059])).
% 54.09/17.48 thf(f4061,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4060])).
% 54.09/17.48 thf(f4062,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4049])).
% 54.09/17.48 thf(f4063,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4062])).
% 54.09/17.48 thf(f4064,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4063])).
% 54.09/17.48 thf(f4065,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4063])).
% 54.09/17.48 thf(f4066,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4065])).
% 54.09/17.48 thf(f4067,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4066])).
% 54.09/17.48 thf(f4068,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f4067])).
% 54.09/17.48 thf(f4069,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4068])).
% 54.09/17.48 thf(f4070,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4069])).
% 54.09/17.48 thf(f4071,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4070])).
% 54.09/17.48 thf(f4072,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4071])).
% 54.09/17.48 thf(f4073,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4072])).
% 54.09/17.48 thf(f4074,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4073])).
% 54.09/17.48 thf(f4075,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4074])).
% 54.09/17.48 thf(f4076,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4075])).
% 54.09/17.48 thf(f4077,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4064])).
% 54.09/17.48 thf(f4078,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4077])).
% 54.09/17.48 thf(f4079,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f4078])).
% 54.09/17.48 thf(f4080,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4079])).
% 54.09/17.48 thf(f4081,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4080])).
% 54.09/17.48 thf(f4082,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4081])).
% 54.09/17.48 thf(f4083,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4082])).
% 54.09/17.48 thf(f4084,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4083])).
% 54.09/17.48 thf(f4085,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4084])).
% 54.09/17.48 thf(f4086,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4085])).
% 54.09/17.48 thf(f4087,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4086])).
% 54.09/17.48 thf(f4088,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4029])).
% 54.09/17.48 thf(f4089,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4088])).
% 54.09/17.48 thf(f4090,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4089])).
% 54.09/17.48 thf(f4091,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4089])).
% 54.09/17.48 thf(f4092,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4091])).
% 54.09/17.48 thf(f4093,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4092])).
% 54.09/17.48 thf(f4094,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4093])).
% 54.09/17.48 thf(f4095,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4094])).
% 54.09/17.48 thf(f4096,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4094])).
% 54.09/17.48 thf(f4097,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4096])).
% 54.09/17.48 thf(f4098,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4097])).
% 54.09/17.48 thf(f4099,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f4098])).
% 54.09/17.48 thf(f4100,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4099])).
% 54.09/17.48 thf(f4101,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4100])).
% 54.09/17.48 thf(f4102,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4101])).
% 54.09/17.48 thf(f4103,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4102])).
% 54.09/17.48 thf(f4104,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4103])).
% 54.09/17.48 thf(f4105,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4104])).
% 54.09/17.48 thf(f4106,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4105])).
% 54.09/17.48 thf(f4107,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4106])).
% 54.09/17.48 thf(f4108,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4095])).
% 54.09/17.48 thf(f4109,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4108])).
% 54.09/17.48 thf(f4110,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4109])).
% 54.09/17.48 thf(f4111,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4109])).
% 54.09/17.48 thf(f4112,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4111])).
% 54.09/17.48 thf(f4113,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4112])).
% 54.09/17.48 thf(f4114,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f4113])).
% 54.09/17.48 thf(f4115,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4114])).
% 54.09/17.48 thf(f4116,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4115])).
% 54.09/17.48 thf(f4117,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4116])).
% 54.09/17.48 thf(f4118,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4117])).
% 54.09/17.48 thf(f4119,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4118])).
% 54.09/17.48 thf(f4120,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4119])).
% 54.09/17.48 thf(f4121,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4120])).
% 54.09/17.48 thf(f4122,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4121])).
% 54.09/17.48 thf(f4123,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4110])).
% 54.09/17.48 thf(f4124,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4123])).
% 54.09/17.48 thf(f4125,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4124])).
% 54.09/17.48 thf(f4126,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4124])).
% 54.09/17.48 thf(f4127,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4126])).
% 54.09/17.48 thf(f4128,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4127])).
% 54.09/17.48 thf(f4129,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f4128])).
% 54.09/17.48 thf(f4130,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4129])).
% 54.09/17.48 thf(f4131,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4130])).
% 54.09/17.48 thf(f4132,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4131])).
% 54.09/17.48 thf(f4133,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4132])).
% 54.09/17.48 thf(f4134,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4133])).
% 54.09/17.48 thf(f4135,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4134])).
% 54.09/17.48 thf(f4136,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4135])).
% 54.09/17.48 thf(f4137,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4136])).
% 54.09/17.48 thf(f4138,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4125])).
% 54.09/17.48 thf(f4139,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4138])).
% 54.09/17.48 thf(f4140,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f4139])).
% 54.09/17.48 thf(f4141,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4140])).
% 54.09/17.48 thf(f4142,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4141])).
% 54.09/17.48 thf(f4143,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4142])).
% 54.09/17.48 thf(f4144,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4143])).
% 54.09/17.48 thf(f4145,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4144])).
% 54.09/17.48 thf(f4146,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4145])).
% 54.09/17.48 thf(f4147,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4146])).
% 54.09/17.48 thf(f4148,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4147])).
% 54.09/17.48 thf(f4149,plain,(
% 54.09/17.48 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4090])).
% 54.09/17.48 thf(f4150,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4149])).
% 54.09/17.48 thf(f4151,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4150])).
% 54.09/17.48 thf(f4152,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4151])).
% 54.09/17.48 thf(f4153,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4151])).
% 54.09/17.48 thf(f4154,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4153])).
% 54.09/17.48 thf(f4155,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4154])).
% 54.09/17.48 thf(f4156,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f4155])).
% 54.09/17.48 thf(f4157,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4156])).
% 54.09/17.48 thf(f4158,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4157])).
% 54.09/17.48 thf(f4159,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4158])).
% 54.09/17.48 thf(f4160,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4159])).
% 54.09/17.48 thf(f4161,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4160])).
% 54.09/17.48 thf(f4162,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4161])).
% 54.09/17.48 thf(f4163,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4162])).
% 54.09/17.48 thf(f4164,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4163])).
% 54.09/17.48 thf(f4165,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4152])).
% 54.09/17.48 thf(f4166,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4165])).
% 54.09/17.48 thf(f4167,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4166])).
% 54.09/17.48 thf(f4168,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4166])).
% 54.09/17.48 thf(f4169,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4168])).
% 54.09/17.48 thf(f4170,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4169])).
% 54.09/17.48 thf(f4171,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f4170])).
% 54.09/17.48 thf(f4172,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4171])).
% 54.09/17.48 thf(f4173,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4172])).
% 54.09/17.48 thf(f4174,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4173])).
% 54.09/17.48 thf(f4175,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4174])).
% 54.09/17.48 thf(f4176,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4175])).
% 54.09/17.48 thf(f4177,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4176])).
% 54.09/17.48 thf(f4178,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4177])).
% 54.09/17.48 thf(f4179,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4178])).
% 54.09/17.48 thf(f4180,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4167])).
% 54.09/17.48 thf(f4181,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4180])).
% 54.09/17.48 thf(f4182,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4181])).
% 54.09/17.48 thf(f4183,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4181])).
% 54.09/17.48 thf(f4184,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4183])).
% 54.09/17.48 thf(f4185,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4184])).
% 54.09/17.48 thf(f4186,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f4185])).
% 54.09/17.48 thf(f4187,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4186])).
% 54.09/17.48 thf(f4188,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4187])).
% 54.09/17.48 thf(f4189,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4188])).
% 54.09/17.48 thf(f4190,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4189])).
% 54.09/17.48 thf(f4191,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4190])).
% 54.09/17.48 thf(f4192,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4191])).
% 54.09/17.48 thf(f4193,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4192])).
% 54.09/17.48 thf(f4194,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4193])).
% 54.09/17.48 thf(f4195,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4182])).
% 54.09/17.48 thf(f4196,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4195])).
% 54.09/17.48 thf(f4197,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X1)))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f4196])).
% 54.09/17.48 thf(f4198,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = (((~ (rel_s4 @ sK2 @ X2)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4197])).
% 54.09/17.48 thf(f4199,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((~ (rel_s4 @ sK2 @ X3)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4198])).
% 54.09/17.48 thf(f4200,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = (((~ (rel_s4 @ sK2 @ X4)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4199])).
% 54.09/17.48 thf(f4201,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4200])).
% 54.09/17.48 thf(f4202,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (rel_s4 @ sK2 @ X2)))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4201])).
% 54.09/17.48 thf(f4203,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($true = ((~ (rel_s4 @ sK2 @ X3)))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4202])).
% 54.09/17.48 thf(f4204,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($true = ((~ (rel_s4 @ sK2 @ X4))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4203])).
% 54.09/17.48 thf(f4205,plain,(
% 54.09/17.48 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((rel_s4 @ sK2 @ X2))) | ($false = ((rel_s4 @ sK2 @ X3))) | ($false = ((rel_s4 @ sK2 @ X4)))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4204])).
% 54.09/17.48 thf(f4206,plain,(
% 54.09/17.48 ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y1))))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y1))))))))))))))))))))))),
% 54.09/17.48 inference(not_proxy_clausification,[],[f281])).
% 54.09/17.48 thf(f4207,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y1))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y1))))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y1))))))))))))))))))) @ X1)))) )),
% 54.09/17.48 inference(pi_proxy_clausification,[],[f4206])).
% 54.09/17.48 thf(f4208,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($true = (((~ (rel_s4 @ sK2 @ X1)) | (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))))))))))))))) )),
% 54.09/17.48 inference(beta-eta_normalization,[],[f4207])).
% 54.09/17.48 thf(f4209,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($true = ((~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4208])).
% 54.09/17.48 thf(f4210,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($false = (((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4209])).
% 54.09/17.48 thf(f4211,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($false = (((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4210])).
% 54.09/17.48 thf(f4212,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4210])).
% 54.09/17.48 thf(f4213,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4212])).
% 54.09/17.48 thf(f4214,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($true = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4213])).
% 54.09/17.48 thf(f4215,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0)))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4214])).
% 54.09/17.48 thf(f4216,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0)))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4215])).
% 54.09/17.48 thf(f4217,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($true = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4216])).
% 54.09/17.48 thf(f4218,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4217])).
% 54.09/17.48 thf(f4219,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))))))) )),
% 54.09/17.48 inference(not_proxy_clausification,[],[f4218])).
% 54.09/17.48 thf(f4220,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))))) )),
% 54.09/17.48 inference(or_proxy_clausification,[],[f4219])).
% 54.09/17.48 thf(f4221,plain,(
% 54.09/17.48 ( ! [X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4220])).
% 54.09/17.49 thf(f4222,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ (sK3 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))))) )),
% 54.09/17.49 inference(sigma_proxy_clausification,[],[f4221])).
% 54.09/17.49 thf(f4223,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4222])).
% 54.09/17.49 thf(f4224,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0)))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4223])).
% 54.09/17.49 thf(f4225,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ (sK4 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))))) )),
% 54.09/17.49 inference(sigma_proxy_clausification,[],[f4224])).
% 54.09/17.49 thf(f4226,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ (sK4 @ X1)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4225])).
% 54.09/17.49 thf(f4227,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ (sK4 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ (sK5 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))))) )),
% 54.09/17.49 inference(sigma_proxy_clausification,[],[f4226])).
% 54.09/17.49 thf(f4228,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ (sK4 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ (sK5 @ X1)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4227])).
% 54.09/17.49 thf(f4229,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ (sK4 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ (sK5 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ (sK6 @ X1))))) )),
% 54.09/17.49 inference(sigma_proxy_clausification,[],[f4228])).
% 54.09/17.49 thf(f4230,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((~ (rel_s4 @ X1 @ (sK3 @ X1))) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1))))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((~ (rel_s4 @ X1 @ (sK4 @ X1))) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK5 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(beta-eta_normalization,[],[f4229])).
% 54.09/17.49 thf(f4231,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((~ (rel_s4 @ X1 @ (sK4 @ X1))) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK5 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4230])).
% 54.09/17.49 thf(f4232,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((~ (rel_s4 @ X1 @ (sK3 @ X1))))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((~ (rel_s4 @ X1 @ (sK4 @ X1))) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK5 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4230])).
% 54.09/17.49 thf(f4233,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((~ (rel_s4 @ X1 @ (sK4 @ X1))) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK5 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4232])).
% 54.09/17.49 thf(f4234,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK5 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4233])).
% 54.09/17.49 thf(f4235,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((~ (rel_s4 @ X1 @ (sK4 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK5 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4233])).
% 54.09/17.49 thf(f4236,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK5 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4235])).
% 54.09/17.49 thf(f4237,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4236])).
% 54.09/17.49 thf(f4238,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK5 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4236])).
% 54.09/17.49 thf(f4239,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK5 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4238])).
% 54.09/17.49 thf(f4240,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK5 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK3 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4239])).
% 54.09/17.49 thf(f4241,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK5 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4239])).
% 54.09/17.49 thf(f4242,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK6 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK5 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK3 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4241])).
% 54.09/17.49 thf(f4243,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK3 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4237])).
% 54.09/17.49 thf(f4244,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4237])).
% 54.09/17.49 thf(f4245,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK6 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK3 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4244])).
% 54.09/17.49 thf(f4246,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4234])).
% 54.09/17.49 thf(f4247,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK5 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4234])).
% 54.09/17.49 thf(f4248,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK5 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4247])).
% 54.09/17.49 thf(f4249,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK5 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK3 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4248])).
% 54.09/17.49 thf(f4250,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK5 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4248])).
% 54.09/17.49 thf(f4251,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK6 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK5 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK3 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4250])).
% 54.09/17.49 thf(f4252,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4246])).
% 54.09/17.49 thf(f4253,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4246])).
% 54.09/17.49 thf(f4254,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK6 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK3 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4253])).
% 54.09/17.49 thf(f4255,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK5 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4231])).
% 54.09/17.49 thf(f4256,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((~ (rel_s4 @ X1 @ (sK4 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK5 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4231])).
% 54.09/17.49 thf(f4257,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK5 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4256])).
% 54.09/17.49 thf(f4258,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4257])).
% 54.09/17.49 thf(f4259,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK5 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4257])).
% 54.09/17.49 thf(f4260,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK5 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4259])).
% 54.09/17.49 thf(f4261,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK5 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4260])).
% 54.09/17.49 thf(f4262,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK5 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4260])).
% 54.09/17.49 thf(f4263,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK6 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK5 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1)))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4262])).
% 54.09/17.49 thf(f4264,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4258])).
% 54.09/17.49 thf(f4265,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4258])).
% 54.09/17.49 thf(f4266,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK6 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK4 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4265])).
% 54.09/17.49 thf(f4267,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4255])).
% 54.09/17.49 thf(f4268,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK5 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4255])).
% 54.09/17.49 thf(f4269,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK5 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK6 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4268])).
% 54.09/17.49 thf(f4270,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK5 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4269])).
% 54.09/17.49 thf(f4271,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK5 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4269])).
% 54.09/17.49 thf(f4272,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK6 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK5 @ X1)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4271])).
% 54.09/17.49 thf(f4273,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4267])).
% 54.09/17.49 thf(f4274,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK6 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4267])).
% 54.09/17.49 thf(f4275,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ (sK4 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK6 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X1)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4274])).
% 54.09/17.49 thf(f4276,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4211])).
% 54.09/17.49 thf(f4277,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4211])).
% 54.09/17.49 thf(f4278,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4277])).
% 54.09/17.49 thf(f4279,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4278])).
% 54.09/17.49 thf(f4280,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4279])).
% 54.09/17.49 thf(f4281,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4280])).
% 54.09/17.49 thf(f4282,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4281])).
% 54.09/17.49 thf(f4283,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4282])).
% 54.09/17.49 thf(f4284,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4283])).
% 54.09/17.49 thf(f4285,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4284])).
% 54.09/17.49 thf(f4286,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4285])).
% 54.09/17.49 thf(f4287,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ (sK7 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))))) )),
% 54.09/17.49 inference(sigma_proxy_clausification,[],[f4286])).
% 54.09/17.49 thf(f4288,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4287])).
% 54.09/17.49 thf(f4289,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4288])).
% 54.09/17.49 thf(f4290,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ (sK8 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))))) )),
% 54.09/17.49 inference(sigma_proxy_clausification,[],[f4289])).
% 54.09/17.49 thf(f4291,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ (sK8 @ X1)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4290])).
% 54.09/17.49 thf(f4292,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ (sK8 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ (sK9 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))))) )),
% 54.09/17.49 inference(sigma_proxy_clausification,[],[f4291])).
% 54.09/17.49 thf(f4293,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ (sK8 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ (sK9 @ X1)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4292])).
% 54.09/17.49 thf(f4294,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ (sK8 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ (sK9 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ (sK10 @ X1))))) )),
% 54.09/17.49 inference(sigma_proxy_clausification,[],[f4293])).
% 54.09/17.49 thf(f4295,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((~ (rel_s4 @ X1 @ (sK7 @ X1))) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1))))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((~ (rel_s4 @ X1 @ (sK8 @ X1))) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK9 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(beta-eta_normalization,[],[f4294])).
% 54.09/17.49 thf(f4296,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((~ (rel_s4 @ X1 @ (sK8 @ X1))) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK9 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4295])).
% 54.09/17.49 thf(f4297,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((~ (rel_s4 @ X1 @ (sK7 @ X1))))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((~ (rel_s4 @ X1 @ (sK8 @ X1))) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK9 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4295])).
% 54.09/17.49 thf(f4298,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((~ (rel_s4 @ X1 @ (sK8 @ X1))) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK9 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4297])).
% 54.09/17.49 thf(f4299,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK9 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4298])).
% 54.09/17.49 thf(f4300,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((~ (rel_s4 @ X1 @ (sK8 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK9 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4298])).
% 54.09/17.49 thf(f4301,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK9 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4300])).
% 54.09/17.49 thf(f4302,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4301])).
% 54.09/17.49 thf(f4303,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK9 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4301])).
% 54.09/17.49 thf(f4304,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK9 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4303])).
% 54.09/17.49 thf(f4305,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK9 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK7 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4304])).
% 54.09/17.49 thf(f4306,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK9 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4304])).
% 54.09/17.49 thf(f4307,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK10 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK9 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK7 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4306])).
% 54.09/17.49 thf(f4308,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK7 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4302])).
% 54.09/17.49 thf(f4309,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4302])).
% 54.09/17.49 thf(f4310,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK10 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK7 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4309])).
% 54.09/17.49 thf(f4311,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4299])).
% 54.09/17.49 thf(f4312,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK9 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4299])).
% 54.09/17.49 thf(f4313,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK9 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4312])).
% 54.09/17.49 thf(f4314,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK9 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK7 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4313])).
% 54.09/17.49 thf(f4315,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK9 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4313])).
% 54.09/17.49 thf(f4316,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK10 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK9 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK7 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4315])).
% 54.09/17.49 thf(f4317,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4311])).
% 54.09/17.49 thf(f4318,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4311])).
% 54.09/17.49 thf(f4319,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK10 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK7 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4318])).
% 54.09/17.49 thf(f4320,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK9 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4296])).
% 54.09/17.49 thf(f4321,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((~ (rel_s4 @ X1 @ (sK8 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK9 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4296])).
% 54.09/17.49 thf(f4322,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK9 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4321])).
% 54.09/17.49 thf(f4323,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4322])).
% 54.09/17.49 thf(f4324,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK9 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4322])).
% 54.09/17.49 thf(f4325,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK9 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4324])).
% 54.09/17.49 thf(f4326,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK9 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4325])).
% 54.09/17.49 thf(f4327,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK9 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4325])).
% 54.09/17.49 thf(f4328,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK10 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK9 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1)))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4327])).
% 54.09/17.49 thf(f4329,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4323])).
% 54.09/17.49 thf(f4330,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4323])).
% 54.09/17.49 thf(f4331,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK10 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK8 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4330])).
% 54.09/17.49 thf(f4332,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4320])).
% 54.09/17.49 thf(f4333,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK9 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4320])).
% 54.09/17.49 thf(f4334,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK9 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK10 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4333])).
% 54.09/17.49 thf(f4335,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK9 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4334])).
% 54.09/17.49 thf(f4336,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK9 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4334])).
% 54.09/17.49 thf(f4337,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK10 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK9 @ X1)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4336])).
% 54.09/17.49 thf(f4338,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4332])).
% 54.09/17.49 thf(f4339,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK10 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4332])).
% 54.09/17.49 thf(f4340,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ (sK8 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK10 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X1)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4339])).
% 54.09/17.49 thf(f4341,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4276])).
% 54.09/17.49 thf(f4342,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4276])).
% 54.09/17.49 thf(f4343,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4342])).
% 54.09/17.49 thf(f4344,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4343])).
% 54.09/17.49 thf(f4345,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4344])).
% 54.09/17.49 thf(f4346,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4345])).
% 54.09/17.49 thf(f4347,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4346])).
% 54.09/17.49 thf(f4348,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4347])).
% 54.09/17.49 thf(f4349,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4348])).
% 54.09/17.49 thf(f4350,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4349])).
% 54.09/17.49 thf(f4351,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4350])).
% 54.09/17.49 thf(f4352,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ (sK11 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.49 inference(sigma_proxy_clausification,[],[f4351])).
% 54.09/17.49 thf(f4353,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4352])).
% 54.09/17.49 thf(f4354,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4353])).
% 54.09/17.49 thf(f4355,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ (sK12 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.49 inference(sigma_proxy_clausification,[],[f4354])).
% 54.09/17.49 thf(f4356,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ (sK12 @ X1)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4355])).
% 54.09/17.49 thf(f4357,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ (sK12 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ (sK13 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))))) )),
% 54.09/17.49 inference(sigma_proxy_clausification,[],[f4356])).
% 54.09/17.49 thf(f4358,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ (sK12 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ (sK13 @ X1)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4357])).
% 54.09/17.49 thf(f4359,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ (sK12 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ (sK13 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ (sK14 @ X1))))) )),
% 54.09/17.49 inference(sigma_proxy_clausification,[],[f4358])).
% 54.09/17.49 thf(f4360,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((~ (rel_s4 @ X1 @ (sK11 @ X1))) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1))))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((~ (rel_s4 @ X1 @ (sK12 @ X1))) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK13 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(beta-eta_normalization,[],[f4359])).
% 54.09/17.49 thf(f4361,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((~ (rel_s4 @ X1 @ (sK12 @ X1))) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK13 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4360])).
% 54.09/17.49 thf(f4362,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((~ (rel_s4 @ X1 @ (sK11 @ X1))))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((~ (rel_s4 @ X1 @ (sK12 @ X1))) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK13 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4360])).
% 54.09/17.49 thf(f4363,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((~ (rel_s4 @ X1 @ (sK12 @ X1))) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK13 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4362])).
% 54.09/17.49 thf(f4364,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK13 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4363])).
% 54.09/17.49 thf(f4365,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((~ (rel_s4 @ X1 @ (sK12 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK13 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4363])).
% 54.09/17.49 thf(f4366,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK13 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4365])).
% 54.09/17.49 thf(f4367,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4366])).
% 54.09/17.49 thf(f4368,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK13 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4366])).
% 54.09/17.49 thf(f4369,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK13 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4368])).
% 54.09/17.49 thf(f4370,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK13 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK11 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4369])).
% 54.09/17.49 thf(f4371,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK13 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4369])).
% 54.09/17.49 thf(f4372,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK14 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK13 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK11 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4371])).
% 54.09/17.49 thf(f4373,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK11 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4367])).
% 54.09/17.49 thf(f4374,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4367])).
% 54.09/17.49 thf(f4375,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK14 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK11 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4374])).
% 54.09/17.49 thf(f4376,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4364])).
% 54.09/17.49 thf(f4377,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK13 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4364])).
% 54.09/17.49 thf(f4378,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK13 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4377])).
% 54.09/17.49 thf(f4379,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK13 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK11 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4378])).
% 54.09/17.49 thf(f4380,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK13 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4378])).
% 54.09/17.49 thf(f4381,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK14 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK13 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK11 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4380])).
% 54.09/17.49 thf(f4382,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4376])).
% 54.09/17.49 thf(f4383,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4376])).
% 54.09/17.49 thf(f4384,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK14 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK11 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4383])).
% 54.09/17.49 thf(f4385,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK13 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4361])).
% 54.09/17.49 thf(f4386,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((~ (rel_s4 @ X1 @ (sK12 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK13 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4361])).
% 54.09/17.49 thf(f4387,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK13 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4386])).
% 54.09/17.49 thf(f4388,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4387])).
% 54.09/17.49 thf(f4389,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK13 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4387])).
% 54.09/17.49 thf(f4390,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK13 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4389])).
% 54.09/17.49 thf(f4391,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK13 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4390])).
% 54.09/17.49 thf(f4392,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK13 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4390])).
% 54.09/17.49 thf(f4393,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK14 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK13 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1)))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4392])).
% 54.09/17.49 thf(f4394,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4388])).
% 54.09/17.49 thf(f4395,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4388])).
% 54.09/17.49 thf(f4396,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK14 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK12 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4395])).
% 54.09/17.49 thf(f4397,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4385])).
% 54.09/17.49 thf(f4398,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK13 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4385])).
% 54.09/17.49 thf(f4399,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK13 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK14 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4398])).
% 54.09/17.49 thf(f4400,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK13 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4399])).
% 54.09/17.49 thf(f4401,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK13 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4399])).
% 54.09/17.49 thf(f4402,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK14 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK13 @ X1)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4401])).
% 54.09/17.49 thf(f4403,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4397])).
% 54.09/17.49 thf(f4404,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK14 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4397])).
% 54.09/17.49 thf(f4405,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ (sK12 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK14 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X1)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4404])).
% 54.09/17.49 thf(f4406,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4341])).
% 54.09/17.49 thf(f4407,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4406])).
% 54.09/17.49 thf(f4408,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4407])).
% 54.09/17.49 thf(f4409,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))) | (~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4408])).
% 54.09/17.49 thf(f4410,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((~ (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4409])).
% 54.09/17.49 thf(f4411,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4410])).
% 54.09/17.49 thf(f4412,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4411])).
% 54.09/17.49 thf(f4413,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4412])).
% 54.09/17.49 thf(f4414,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4413])).
% 54.09/17.49 thf(f4415,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ (sK15 @ X1)))) | ($true = ((~ (rel_s4 @ sK2 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))))) )),
% 54.09/17.49 inference(sigma_proxy_clausification,[],[f4414])).
% 54.09/17.49 thf(f4416,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4415])).
% 54.09/17.49 thf(f4417,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4416])).
% 54.09/17.49 thf(f4418,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ (sK16 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))))) )),
% 54.09/17.49 inference(sigma_proxy_clausification,[],[f4417])).
% 54.09/17.49 thf(f4419,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ (sK16 @ X1)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4418])).
% 54.09/17.49 thf(f4420,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ (sK16 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ (sK17 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))))) )),
% 54.09/17.49 inference(sigma_proxy_clausification,[],[f4419])).
% 54.09/17.49 thf(f4421,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ (sK16 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ (sK17 @ X1)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4420])).
% 54.09/17.49 thf(f4422,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ (sK16 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ (sK17 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ (sK18 @ X1))))) )),
% 54.09/17.49 inference(sigma_proxy_clausification,[],[f4421])).
% 54.09/17.49 thf(f4423,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = (((~ (rel_s4 @ X1 @ (sK15 @ X1))) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1))))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((~ (rel_s4 @ X1 @ (sK16 @ X1))) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK17 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(beta-eta_normalization,[],[f4422])).
% 54.09/17.49 thf(f4424,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((~ (rel_s4 @ X1 @ (sK16 @ X1))) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK17 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4423])).
% 54.09/17.49 thf(f4425,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((~ (rel_s4 @ X1 @ (sK15 @ X1))))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((~ (rel_s4 @ X1 @ (sK16 @ X1))) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK17 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4423])).
% 54.09/17.49 thf(f4426,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = (((~ (rel_s4 @ X1 @ (sK16 @ X1))) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK17 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4425])).
% 54.09/17.49 thf(f4427,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK17 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4426])).
% 54.09/17.49 thf(f4428,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((~ (rel_s4 @ X1 @ (sK16 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK17 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4426])).
% 54.09/17.49 thf(f4429,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK17 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4428])).
% 54.09/17.49 thf(f4430,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4429])).
% 54.09/17.49 thf(f4431,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK17 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4429])).
% 54.09/17.49 thf(f4432,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK17 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4431])).
% 54.09/17.49 thf(f4433,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK17 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK15 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4432])).
% 54.09/17.49 thf(f4434,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK17 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4432])).
% 54.09/17.49 thf(f4435,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK18 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK17 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK15 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4434])).
% 54.09/17.49 thf(f4436,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK15 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4430])).
% 54.09/17.49 thf(f4437,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4430])).
% 54.09/17.49 thf(f4438,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK18 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK15 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4437])).
% 54.09/17.49 thf(f4439,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4427])).
% 54.09/17.49 thf(f4440,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK17 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4427])).
% 54.09/17.49 thf(f4441,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK17 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4440])).
% 54.09/17.49 thf(f4442,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK17 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK15 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4441])).
% 54.09/17.49 thf(f4443,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK17 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4441])).
% 54.09/17.49 thf(f4444,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK18 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK17 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK15 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4443])).
% 54.09/17.49 thf(f4445,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4439])).
% 54.09/17.49 thf(f4446,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4439])).
% 54.09/17.49 thf(f4447,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK18 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK15 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4446])).
% 54.09/17.49 thf(f4448,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK17 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4424])).
% 54.09/17.49 thf(f4449,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((~ (rel_s4 @ X1 @ (sK16 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK17 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4424])).
% 54.09/17.49 thf(f4450,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK17 @ X1))) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4449])).
% 54.09/17.49 thf(f4451,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4450])).
% 54.09/17.49 thf(f4452,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK17 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4450])).
% 54.09/17.49 thf(f4453,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK17 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4452])).
% 54.09/17.49 thf(f4454,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK17 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4453])).
% 54.09/17.49 thf(f4455,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK17 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4453])).
% 54.09/17.49 thf(f4456,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK18 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK17 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1)))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4455])).
% 54.09/17.49 thf(f4457,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4451])).
% 54.09/17.49 thf(f4458,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4451])).
% 54.09/17.49 thf(f4459,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK18 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK16 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4458])).
% 54.09/17.49 thf(f4460,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4448])).
% 54.09/17.49 thf(f4461,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK17 @ X1))))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4448])).
% 54.09/17.49 thf(f4462,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK17 @ X1)))) | ($false = (((~ (rel_s4 @ X1 @ (sK18 @ X1))) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4461])).
% 54.09/17.49 thf(f4463,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK17 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4462])).
% 54.09/17.49 thf(f4464,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK17 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4462])).
% 54.09/17.49 thf(f4465,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK18 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($true = ((rel_s4 @ X1 @ (sK17 @ X1)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4464])).
% 54.09/17.49 thf(f4466,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X1))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4460])).
% 54.09/17.49 thf(f4467,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1)))) | ($false = ((~ (rel_s4 @ X1 @ (sK18 @ X1)))))) )),
% 54.09/17.49 inference(or_proxy_clausification,[],[f4460])).
% 54.09/17.49 thf(f4468,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ (sK16 @ X1)))) | ($true = ((rel_s4 @ X1 @ (sK18 @ X1)))) | ($false = ((rel_s4 @ sK2 @ X1))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X1)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X1))))) )),
% 54.09/17.49 inference(not_proxy_clausification,[],[f4467])).
% 54.09/17.49 thf(f7108,plain,(
% 54.09/17.49 ($true = ((!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)))))),
% 54.09/17.49 inference(beta-eta_normalization,[],[f251])).
% 54.09/17.49 thf(f7109,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1)))) )),
% 54.09/17.49 inference(pi_proxy_clausification,[],[f7108])).
% 54.09/17.49 thf(f7110,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ X1)))) )),
% 54.09/17.49 inference(beta-eta_normalization,[],[f7109])).
% 54.09/17.49 thf(f7112,definition,(
% 54.09/17.49 spl101_1 <=> ! [X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X4))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_1])],[avatar_definition])).
% 54.09/17.49 thf(f7113,plain,(
% 54.09/17.49 ( ! [X4 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X4)))) ) | ~spl101_1),
% 54.09/17.49 inference(avatar_component_clause,[],[f7112])).
% 54.09/17.49 thf(f7115,definition,(
% 54.09/17.49 spl101_2 <=> ! [X3 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($false = ((rel_s4 @ sK2 @ X3))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_2])],[avatar_definition])).
% 54.09/17.49 thf(f7116,plain,(
% 54.09/17.49 ( ! [X3 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) | ($false = ((rel_s4 @ sK2 @ X3)))) ) | ~spl101_2),
% 54.09/17.49 inference(avatar_component_clause,[],[f7115])).
% 54.09/17.49 thf(f7118,definition,(
% 54.09/17.49 spl101_3 <=> ! [X2 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((rel_s4 @ sK2 @ X2))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_3])],[avatar_definition])).
% 54.09/17.49 thf(f7119,plain,(
% 54.09/17.49 ( ! [X2 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((rel_s4 @ sK2 @ X2)))) ) | ~spl101_3),
% 54.09/17.49 inference(avatar_component_clause,[],[f7118])).
% 54.09/17.49 thf(f7121,definition,(
% 54.09/17.49 spl101_4 <=> ! [X1 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($false = ((rel_s4 @ sK2 @ X1))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_4])],[avatar_definition])).
% 54.09/17.49 thf(f7122,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X1))) | ($false = ((rel_s4 @ sK2 @ X1)))) ) | ~spl101_4),
% 54.09/17.49 inference(avatar_component_clause,[],[f7121])).
% 54.09/17.49 thf(f7123,plain,(
% 54.09/17.49 spl101_1 | spl101_2 | spl101_3 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f315,f7121,f7118,f7115,f7112])).
% 54.09/17.49 thf(f7125,definition,(
% 54.09/17.49 spl101_5 <=> ! [X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X4))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_5])],[avatar_definition])).
% 54.09/17.49 thf(f7126,plain,(
% 54.09/17.49 ( ! [X4 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X4)))) ) | ~spl101_5),
% 54.09/17.49 inference(avatar_component_clause,[],[f7125])).
% 54.09/17.49 thf(f7127,plain,(
% 54.09/17.49 spl101_5 | spl101_2 | spl101_3 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f330,f7121,f7118,f7115,f7125])).
% 54.09/17.49 thf(f7129,definition,(
% 54.09/17.49 spl101_6 <=> ! [X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X4))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_6])],[avatar_definition])).
% 54.09/17.49 thf(f7130,plain,(
% 54.09/17.49 ( ! [X4 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X4)))) ) | ~spl101_6),
% 54.09/17.49 inference(avatar_component_clause,[],[f7129])).
% 54.09/17.49 thf(f7131,plain,(
% 54.09/17.49 spl101_6 | spl101_2 | spl101_3 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f345,f7121,f7118,f7115,f7129])).
% 54.09/17.49 thf(f7133,definition,(
% 54.09/17.49 spl101_7 <=> ! [X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X4))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_7])],[avatar_definition])).
% 54.09/17.49 thf(f7134,plain,(
% 54.09/17.49 ( ! [X4 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))) | ($false = ((rel_s4 @ sK2 @ X4)))) ) | ~spl101_7),
% 54.09/17.49 inference(avatar_component_clause,[],[f7133])).
% 54.09/17.49 thf(f7135,plain,(
% 54.09/17.49 spl101_7 | spl101_2 | spl101_3 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f356,f7121,f7118,f7115,f7133])).
% 54.09/17.49 thf(f7137,definition,(
% 54.09/17.49 spl101_8 <=> ! [X3 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((rel_s4 @ sK2 @ X3))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_8])],[avatar_definition])).
% 54.09/17.49 thf(f7138,plain,(
% 54.09/17.49 ( ! [X3 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((rel_s4 @ sK2 @ X3)))) ) | ~spl101_8),
% 54.09/17.49 inference(avatar_component_clause,[],[f7137])).
% 54.09/17.49 thf(f7139,plain,(
% 54.09/17.49 spl101_1 | spl101_8 | spl101_3 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f376,f7121,f7118,f7137,f7112])).
% 54.09/17.49 thf(f7140,plain,(
% 54.09/17.49 spl101_5 | spl101_8 | spl101_3 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f391,f7121,f7118,f7137,f7125])).
% 54.09/17.49 thf(f7141,plain,(
% 54.09/17.49 spl101_6 | spl101_8 | spl101_3 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f406,f7121,f7118,f7137,f7129])).
% 54.09/17.49 thf(f7142,plain,(
% 54.09/17.49 spl101_7 | spl101_8 | spl101_3 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f417,f7121,f7118,f7137,f7133])).
% 54.09/17.49 thf(f7144,definition,(
% 54.09/17.49 spl101_9 <=> ! [X3 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((rel_s4 @ sK2 @ X3))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_9])],[avatar_definition])).
% 54.09/17.49 thf(f7145,plain,(
% 54.09/17.49 ( ! [X3 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((rel_s4 @ sK2 @ X3)))) ) | ~spl101_9),
% 54.09/17.49 inference(avatar_component_clause,[],[f7144])).
% 54.09/17.49 thf(f7146,plain,(
% 54.09/17.49 spl101_1 | spl101_9 | spl101_3 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f437,f7121,f7118,f7144,f7112])).
% 54.09/17.49 thf(f7147,plain,(
% 54.09/17.49 spl101_5 | spl101_9 | spl101_3 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f452,f7121,f7118,f7144,f7125])).
% 54.09/17.49 thf(f7148,plain,(
% 54.09/17.49 spl101_6 | spl101_9 | spl101_3 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f467,f7121,f7118,f7144,f7129])).
% 54.09/17.49 thf(f7149,plain,(
% 54.09/17.49 spl101_7 | spl101_9 | spl101_3 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f478,f7121,f7118,f7144,f7133])).
% 54.09/17.49 thf(f7151,definition,(
% 54.09/17.49 spl101_10 <=> ! [X3 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($false = ((rel_s4 @ sK2 @ X3))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_10])],[avatar_definition])).
% 54.09/17.49 thf(f7152,plain,(
% 54.09/17.49 ( ! [X3 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))) | ($false = ((rel_s4 @ sK2 @ X3)))) ) | ~spl101_10),
% 54.09/17.49 inference(avatar_component_clause,[],[f7151])).
% 54.09/17.49 thf(f7153,plain,(
% 54.09/17.49 spl101_1 | spl101_10 | spl101_3 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f494,f7121,f7118,f7151,f7112])).
% 54.09/17.49 thf(f7154,plain,(
% 54.09/17.49 spl101_5 | spl101_10 | spl101_3 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f509,f7121,f7118,f7151,f7125])).
% 54.09/17.49 thf(f7155,plain,(
% 54.09/17.49 spl101_6 | spl101_10 | spl101_3 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f524,f7121,f7118,f7151,f7129])).
% 54.09/17.49 thf(f7156,plain,(
% 54.09/17.49 spl101_7 | spl101_10 | spl101_3 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f535,f7121,f7118,f7151,f7133])).
% 54.09/17.49 thf(f7158,definition,(
% 54.09/17.49 spl101_11 <=> ! [X2 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($false = ((rel_s4 @ sK2 @ X2))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_11])],[avatar_definition])).
% 54.09/17.49 thf(f7159,plain,(
% 54.09/17.49 ( ! [X2 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) | ($false = ((rel_s4 @ sK2 @ X2)))) ) | ~spl101_11),
% 54.09/17.49 inference(avatar_component_clause,[],[f7158])).
% 54.09/17.49 thf(f7160,plain,(
% 54.09/17.49 spl101_1 | spl101_2 | spl101_11 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f560,f7121,f7158,f7115,f7112])).
% 54.09/17.49 thf(f7161,plain,(
% 54.09/17.49 spl101_5 | spl101_2 | spl101_11 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f575,f7121,f7158,f7115,f7125])).
% 54.09/17.49 thf(f7162,plain,(
% 54.09/17.49 spl101_6 | spl101_2 | spl101_11 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f590,f7121,f7158,f7115,f7129])).
% 54.09/17.49 thf(f7163,plain,(
% 54.09/17.49 spl101_7 | spl101_2 | spl101_11 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f601,f7121,f7158,f7115,f7133])).
% 54.09/17.49 thf(f7164,plain,(
% 54.09/17.49 spl101_1 | spl101_8 | spl101_11 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f621,f7121,f7158,f7137,f7112])).
% 54.09/17.49 thf(f7165,plain,(
% 54.09/17.49 spl101_5 | spl101_8 | spl101_11 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f636,f7121,f7158,f7137,f7125])).
% 54.09/17.49 thf(f7166,plain,(
% 54.09/17.49 spl101_6 | spl101_8 | spl101_11 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f651,f7121,f7158,f7137,f7129])).
% 54.09/17.49 thf(f7167,plain,(
% 54.09/17.49 spl101_7 | spl101_8 | spl101_11 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f662,f7121,f7158,f7137,f7133])).
% 54.09/17.49 thf(f7168,plain,(
% 54.09/17.49 spl101_1 | spl101_9 | spl101_11 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f682,f7121,f7158,f7144,f7112])).
% 54.09/17.49 thf(f7169,plain,(
% 54.09/17.49 spl101_5 | spl101_9 | spl101_11 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f697,f7121,f7158,f7144,f7125])).
% 54.09/17.49 thf(f7170,plain,(
% 54.09/17.49 spl101_6 | spl101_9 | spl101_11 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f712,f7121,f7158,f7144,f7129])).
% 54.09/17.49 thf(f7171,plain,(
% 54.09/17.49 spl101_7 | spl101_9 | spl101_11 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f723,f7121,f7158,f7144,f7133])).
% 54.09/17.49 thf(f7172,plain,(
% 54.09/17.49 spl101_1 | spl101_10 | spl101_11 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f739,f7121,f7158,f7151,f7112])).
% 54.09/17.49 thf(f7173,plain,(
% 54.09/17.49 spl101_5 | spl101_10 | spl101_11 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f754,f7121,f7158,f7151,f7125])).
% 54.09/17.49 thf(f7174,plain,(
% 54.09/17.49 spl101_6 | spl101_10 | spl101_11 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f769,f7121,f7158,f7151,f7129])).
% 54.09/17.49 thf(f7175,plain,(
% 54.09/17.49 spl101_7 | spl101_10 | spl101_11 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f780,f7121,f7158,f7151,f7133])).
% 54.09/17.49 thf(f7177,definition,(
% 54.09/17.49 spl101_12 <=> ! [X2 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($false = ((rel_s4 @ sK2 @ X2))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_12])],[avatar_definition])).
% 54.09/17.49 thf(f7178,plain,(
% 54.09/17.49 ( ! [X2 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) | ($false = ((rel_s4 @ sK2 @ X2)))) ) | ~spl101_12),
% 54.09/17.49 inference(avatar_component_clause,[],[f7177])).
% 54.09/17.49 thf(f7179,plain,(
% 54.09/17.49 spl101_1 | spl101_2 | spl101_12 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f805,f7121,f7177,f7115,f7112])).
% 54.09/17.49 thf(f7180,plain,(
% 54.09/17.49 spl101_5 | spl101_2 | spl101_12 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f820,f7121,f7177,f7115,f7125])).
% 54.09/17.49 thf(f7181,plain,(
% 54.09/17.49 spl101_6 | spl101_2 | spl101_12 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f835,f7121,f7177,f7115,f7129])).
% 54.09/17.49 thf(f7182,plain,(
% 54.09/17.49 spl101_7 | spl101_2 | spl101_12 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f846,f7121,f7177,f7115,f7133])).
% 54.09/17.49 thf(f7183,plain,(
% 54.09/17.49 spl101_1 | spl101_8 | spl101_12 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f866,f7121,f7177,f7137,f7112])).
% 54.09/17.49 thf(f7184,plain,(
% 54.09/17.49 spl101_5 | spl101_8 | spl101_12 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f881,f7121,f7177,f7137,f7125])).
% 54.09/17.49 thf(f7185,plain,(
% 54.09/17.49 spl101_6 | spl101_8 | spl101_12 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f896,f7121,f7177,f7137,f7129])).
% 54.09/17.49 thf(f7186,plain,(
% 54.09/17.49 spl101_7 | spl101_8 | spl101_12 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f907,f7121,f7177,f7137,f7133])).
% 54.09/17.49 thf(f7187,plain,(
% 54.09/17.49 spl101_1 | spl101_9 | spl101_12 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f927,f7121,f7177,f7144,f7112])).
% 54.09/17.49 thf(f7188,plain,(
% 54.09/17.49 spl101_5 | spl101_9 | spl101_12 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f942,f7121,f7177,f7144,f7125])).
% 54.09/17.49 thf(f7189,plain,(
% 54.09/17.49 spl101_6 | spl101_9 | spl101_12 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f957,f7121,f7177,f7144,f7129])).
% 54.09/17.49 thf(f7190,plain,(
% 54.09/17.49 spl101_7 | spl101_9 | spl101_12 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f968,f7121,f7177,f7144,f7133])).
% 54.09/17.49 thf(f7191,plain,(
% 54.09/17.49 spl101_1 | spl101_10 | spl101_12 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f984,f7121,f7177,f7151,f7112])).
% 54.09/17.49 thf(f7192,plain,(
% 54.09/17.49 spl101_5 | spl101_10 | spl101_12 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f999,f7121,f7177,f7151,f7125])).
% 54.09/17.49 thf(f7193,plain,(
% 54.09/17.49 spl101_6 | spl101_10 | spl101_12 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1014,f7121,f7177,f7151,f7129])).
% 54.09/17.49 thf(f7194,plain,(
% 54.09/17.49 spl101_7 | spl101_10 | spl101_12 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1025,f7121,f7177,f7151,f7133])).
% 54.09/17.49 thf(f7196,definition,(
% 54.09/17.49 spl101_13 <=> ! [X2 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((rel_s4 @ sK2 @ X2))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_13])],[avatar_definition])).
% 54.09/17.49 thf(f7197,plain,(
% 54.09/17.49 ( ! [X2 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((rel_s4 @ sK2 @ X2)))) ) | ~spl101_13),
% 54.09/17.49 inference(avatar_component_clause,[],[f7196])).
% 54.09/17.49 thf(f7198,plain,(
% 54.09/17.49 spl101_1 | spl101_2 | spl101_13 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1046,f7121,f7196,f7115,f7112])).
% 54.09/17.49 thf(f7199,plain,(
% 54.09/17.49 spl101_5 | spl101_2 | spl101_13 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1061,f7121,f7196,f7115,f7125])).
% 54.09/17.49 thf(f7200,plain,(
% 54.09/17.49 spl101_6 | spl101_2 | spl101_13 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1076,f7121,f7196,f7115,f7129])).
% 54.09/17.49 thf(f7201,plain,(
% 54.09/17.49 spl101_7 | spl101_2 | spl101_13 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1087,f7121,f7196,f7115,f7133])).
% 54.09/17.49 thf(f7202,plain,(
% 54.09/17.49 spl101_1 | spl101_8 | spl101_13 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1107,f7121,f7196,f7137,f7112])).
% 54.09/17.49 thf(f7203,plain,(
% 54.09/17.49 spl101_5 | spl101_8 | spl101_13 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1122,f7121,f7196,f7137,f7125])).
% 54.09/17.49 thf(f7204,plain,(
% 54.09/17.49 spl101_6 | spl101_8 | spl101_13 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1137,f7121,f7196,f7137,f7129])).
% 54.09/17.49 thf(f7205,plain,(
% 54.09/17.49 spl101_7 | spl101_8 | spl101_13 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1148,f7121,f7196,f7137,f7133])).
% 54.09/17.49 thf(f7206,plain,(
% 54.09/17.49 spl101_1 | spl101_9 | spl101_13 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1168,f7121,f7196,f7144,f7112])).
% 54.09/17.49 thf(f7207,plain,(
% 54.09/17.49 spl101_5 | spl101_9 | spl101_13 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1183,f7121,f7196,f7144,f7125])).
% 54.09/17.49 thf(f7208,plain,(
% 54.09/17.49 spl101_6 | spl101_9 | spl101_13 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1198,f7121,f7196,f7144,f7129])).
% 54.09/17.49 thf(f7209,plain,(
% 54.09/17.49 spl101_7 | spl101_9 | spl101_13 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1209,f7121,f7196,f7144,f7133])).
% 54.09/17.49 thf(f7210,plain,(
% 54.09/17.49 spl101_1 | spl101_10 | spl101_13 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1225,f7121,f7196,f7151,f7112])).
% 54.09/17.49 thf(f7211,plain,(
% 54.09/17.49 spl101_5 | spl101_10 | spl101_13 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1240,f7121,f7196,f7151,f7125])).
% 54.09/17.49 thf(f7212,plain,(
% 54.09/17.49 spl101_6 | spl101_10 | spl101_13 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1255,f7121,f7196,f7151,f7129])).
% 54.09/17.49 thf(f7213,plain,(
% 54.09/17.49 spl101_7 | spl101_10 | spl101_13 | spl101_4),
% 54.09/17.49 inference(avatar_split_clause,[],[f1266,f7121,f7196,f7151,f7133])).
% 54.09/17.49 thf(f7215,definition,(
% 54.09/17.49 spl101_14 <=> ! [X1 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($false = ((rel_s4 @ sK2 @ X1))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_14])],[avatar_definition])).
% 54.09/17.49 thf(f7216,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($false = ((rel_s4 @ sK2 @ X1)))) ) | ~spl101_14),
% 54.09/17.49 inference(avatar_component_clause,[],[f7215])).
% 54.09/17.49 thf(f7217,plain,(
% 54.09/17.49 spl101_1 | spl101_2 | spl101_3 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1296,f7215,f7118,f7115,f7112])).
% 54.09/17.49 thf(f7218,plain,(
% 54.09/17.49 spl101_5 | spl101_2 | spl101_3 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1311,f7215,f7118,f7115,f7125])).
% 54.09/17.49 thf(f7219,plain,(
% 54.09/17.49 spl101_6 | spl101_2 | spl101_3 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1326,f7215,f7118,f7115,f7129])).
% 54.09/17.49 thf(f7220,plain,(
% 54.09/17.49 spl101_7 | spl101_2 | spl101_3 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1337,f7215,f7118,f7115,f7133])).
% 54.09/17.49 thf(f7221,plain,(
% 54.09/17.49 spl101_1 | spl101_8 | spl101_3 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1357,f7215,f7118,f7137,f7112])).
% 54.09/17.49 thf(f7222,plain,(
% 54.09/17.49 spl101_5 | spl101_8 | spl101_3 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1372,f7215,f7118,f7137,f7125])).
% 54.09/17.49 thf(f7223,plain,(
% 54.09/17.49 spl101_6 | spl101_8 | spl101_3 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1387,f7215,f7118,f7137,f7129])).
% 54.09/17.49 thf(f7224,plain,(
% 54.09/17.49 spl101_7 | spl101_8 | spl101_3 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1398,f7215,f7118,f7137,f7133])).
% 54.09/17.49 thf(f7225,plain,(
% 54.09/17.49 spl101_1 | spl101_9 | spl101_3 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1418,f7215,f7118,f7144,f7112])).
% 54.09/17.49 thf(f7226,plain,(
% 54.09/17.49 spl101_5 | spl101_9 | spl101_3 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1433,f7215,f7118,f7144,f7125])).
% 54.09/17.49 thf(f7227,plain,(
% 54.09/17.49 spl101_6 | spl101_9 | spl101_3 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1448,f7215,f7118,f7144,f7129])).
% 54.09/17.49 thf(f7228,plain,(
% 54.09/17.49 spl101_7 | spl101_9 | spl101_3 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1459,f7215,f7118,f7144,f7133])).
% 54.09/17.49 thf(f7229,plain,(
% 54.09/17.49 spl101_1 | spl101_10 | spl101_3 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1475,f7215,f7118,f7151,f7112])).
% 54.09/17.49 thf(f7230,plain,(
% 54.09/17.49 spl101_5 | spl101_10 | spl101_3 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1490,f7215,f7118,f7151,f7125])).
% 54.09/17.49 thf(f7231,plain,(
% 54.09/17.49 spl101_6 | spl101_10 | spl101_3 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1505,f7215,f7118,f7151,f7129])).
% 54.09/17.49 thf(f7232,plain,(
% 54.09/17.49 spl101_7 | spl101_10 | spl101_3 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1516,f7215,f7118,f7151,f7133])).
% 54.09/17.49 thf(f7233,plain,(
% 54.09/17.49 spl101_1 | spl101_2 | spl101_11 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1541,f7215,f7158,f7115,f7112])).
% 54.09/17.49 thf(f7234,plain,(
% 54.09/17.49 spl101_5 | spl101_2 | spl101_11 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1556,f7215,f7158,f7115,f7125])).
% 54.09/17.49 thf(f7235,plain,(
% 54.09/17.49 spl101_6 | spl101_2 | spl101_11 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1571,f7215,f7158,f7115,f7129])).
% 54.09/17.49 thf(f7236,plain,(
% 54.09/17.49 spl101_7 | spl101_2 | spl101_11 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1582,f7215,f7158,f7115,f7133])).
% 54.09/17.49 thf(f7237,plain,(
% 54.09/17.49 spl101_1 | spl101_8 | spl101_11 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1602,f7215,f7158,f7137,f7112])).
% 54.09/17.49 thf(f7238,plain,(
% 54.09/17.49 spl101_5 | spl101_8 | spl101_11 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1617,f7215,f7158,f7137,f7125])).
% 54.09/17.49 thf(f7239,plain,(
% 54.09/17.49 spl101_6 | spl101_8 | spl101_11 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1632,f7215,f7158,f7137,f7129])).
% 54.09/17.49 thf(f7240,plain,(
% 54.09/17.49 spl101_7 | spl101_8 | spl101_11 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1643,f7215,f7158,f7137,f7133])).
% 54.09/17.49 thf(f7241,plain,(
% 54.09/17.49 spl101_1 | spl101_9 | spl101_11 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1663,f7215,f7158,f7144,f7112])).
% 54.09/17.49 thf(f7242,plain,(
% 54.09/17.49 spl101_5 | spl101_9 | spl101_11 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1678,f7215,f7158,f7144,f7125])).
% 54.09/17.49 thf(f7243,plain,(
% 54.09/17.49 spl101_6 | spl101_9 | spl101_11 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1693,f7215,f7158,f7144,f7129])).
% 54.09/17.49 thf(f7244,plain,(
% 54.09/17.49 spl101_7 | spl101_9 | spl101_11 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1704,f7215,f7158,f7144,f7133])).
% 54.09/17.49 thf(f7245,plain,(
% 54.09/17.49 spl101_1 | spl101_10 | spl101_11 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1720,f7215,f7158,f7151,f7112])).
% 54.09/17.49 thf(f7246,plain,(
% 54.09/17.49 spl101_5 | spl101_10 | spl101_11 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1735,f7215,f7158,f7151,f7125])).
% 54.09/17.49 thf(f7247,plain,(
% 54.09/17.49 spl101_6 | spl101_10 | spl101_11 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1750,f7215,f7158,f7151,f7129])).
% 54.09/17.49 thf(f7248,plain,(
% 54.09/17.49 spl101_7 | spl101_10 | spl101_11 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1761,f7215,f7158,f7151,f7133])).
% 54.09/17.49 thf(f7249,plain,(
% 54.09/17.49 spl101_1 | spl101_2 | spl101_12 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1786,f7215,f7177,f7115,f7112])).
% 54.09/17.49 thf(f7250,plain,(
% 54.09/17.49 spl101_5 | spl101_2 | spl101_12 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1801,f7215,f7177,f7115,f7125])).
% 54.09/17.49 thf(f7251,plain,(
% 54.09/17.49 spl101_6 | spl101_2 | spl101_12 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1816,f7215,f7177,f7115,f7129])).
% 54.09/17.49 thf(f7252,plain,(
% 54.09/17.49 spl101_7 | spl101_2 | spl101_12 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1827,f7215,f7177,f7115,f7133])).
% 54.09/17.49 thf(f7253,plain,(
% 54.09/17.49 spl101_1 | spl101_8 | spl101_12 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1847,f7215,f7177,f7137,f7112])).
% 54.09/17.49 thf(f7254,plain,(
% 54.09/17.49 spl101_5 | spl101_8 | spl101_12 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1862,f7215,f7177,f7137,f7125])).
% 54.09/17.49 thf(f7255,plain,(
% 54.09/17.49 spl101_6 | spl101_8 | spl101_12 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1877,f7215,f7177,f7137,f7129])).
% 54.09/17.49 thf(f7256,plain,(
% 54.09/17.49 spl101_7 | spl101_8 | spl101_12 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1888,f7215,f7177,f7137,f7133])).
% 54.09/17.49 thf(f7257,plain,(
% 54.09/17.49 spl101_1 | spl101_9 | spl101_12 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1908,f7215,f7177,f7144,f7112])).
% 54.09/17.49 thf(f7258,plain,(
% 54.09/17.49 spl101_5 | spl101_9 | spl101_12 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1923,f7215,f7177,f7144,f7125])).
% 54.09/17.49 thf(f7259,plain,(
% 54.09/17.49 spl101_6 | spl101_9 | spl101_12 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1938,f7215,f7177,f7144,f7129])).
% 54.09/17.49 thf(f7260,plain,(
% 54.09/17.49 spl101_7 | spl101_9 | spl101_12 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1949,f7215,f7177,f7144,f7133])).
% 54.09/17.49 thf(f7261,plain,(
% 54.09/17.49 spl101_1 | spl101_10 | spl101_12 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1965,f7215,f7177,f7151,f7112])).
% 54.09/17.49 thf(f7262,plain,(
% 54.09/17.49 spl101_5 | spl101_10 | spl101_12 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1980,f7215,f7177,f7151,f7125])).
% 54.09/17.49 thf(f7263,plain,(
% 54.09/17.49 spl101_6 | spl101_10 | spl101_12 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f1995,f7215,f7177,f7151,f7129])).
% 54.09/17.49 thf(f7264,plain,(
% 54.09/17.49 spl101_7 | spl101_10 | spl101_12 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f2006,f7215,f7177,f7151,f7133])).
% 54.09/17.49 thf(f7265,plain,(
% 54.09/17.49 spl101_1 | spl101_2 | spl101_13 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f2027,f7215,f7196,f7115,f7112])).
% 54.09/17.49 thf(f7266,plain,(
% 54.09/17.49 spl101_5 | spl101_2 | spl101_13 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f2042,f7215,f7196,f7115,f7125])).
% 54.09/17.49 thf(f7267,plain,(
% 54.09/17.49 spl101_6 | spl101_2 | spl101_13 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f2057,f7215,f7196,f7115,f7129])).
% 54.09/17.49 thf(f7268,plain,(
% 54.09/17.49 spl101_7 | spl101_2 | spl101_13 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f2068,f7215,f7196,f7115,f7133])).
% 54.09/17.49 thf(f7269,plain,(
% 54.09/17.49 spl101_1 | spl101_8 | spl101_13 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f2088,f7215,f7196,f7137,f7112])).
% 54.09/17.49 thf(f7270,plain,(
% 54.09/17.49 spl101_5 | spl101_8 | spl101_13 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f2103,f7215,f7196,f7137,f7125])).
% 54.09/17.49 thf(f7271,plain,(
% 54.09/17.49 spl101_6 | spl101_8 | spl101_13 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f2118,f7215,f7196,f7137,f7129])).
% 54.09/17.49 thf(f7272,plain,(
% 54.09/17.49 spl101_7 | spl101_8 | spl101_13 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f2129,f7215,f7196,f7137,f7133])).
% 54.09/17.49 thf(f7273,plain,(
% 54.09/17.49 spl101_1 | spl101_9 | spl101_13 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f2149,f7215,f7196,f7144,f7112])).
% 54.09/17.49 thf(f7274,plain,(
% 54.09/17.49 spl101_5 | spl101_9 | spl101_13 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f2164,f7215,f7196,f7144,f7125])).
% 54.09/17.49 thf(f7275,plain,(
% 54.09/17.49 spl101_6 | spl101_9 | spl101_13 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f2179,f7215,f7196,f7144,f7129])).
% 54.09/17.49 thf(f7276,plain,(
% 54.09/17.49 spl101_7 | spl101_9 | spl101_13 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f2190,f7215,f7196,f7144,f7133])).
% 54.09/17.49 thf(f7277,plain,(
% 54.09/17.49 spl101_1 | spl101_10 | spl101_13 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f2206,f7215,f7196,f7151,f7112])).
% 54.09/17.49 thf(f7278,plain,(
% 54.09/17.49 spl101_5 | spl101_10 | spl101_13 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f2221,f7215,f7196,f7151,f7125])).
% 54.09/17.49 thf(f7279,plain,(
% 54.09/17.49 spl101_6 | spl101_10 | spl101_13 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f2236,f7215,f7196,f7151,f7129])).
% 54.09/17.49 thf(f7280,plain,(
% 54.09/17.49 spl101_7 | spl101_10 | spl101_13 | spl101_14),
% 54.09/17.49 inference(avatar_split_clause,[],[f2247,f7215,f7196,f7151,f7133])).
% 54.09/17.49 thf(f7282,definition,(
% 54.09/17.49 spl101_15 <=> ! [X1 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($false = ((rel_s4 @ sK2 @ X1))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_15])],[avatar_definition])).
% 54.09/17.49 thf(f7283,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X1))) | ($false = ((rel_s4 @ sK2 @ X1)))) ) | ~spl101_15),
% 54.09/17.49 inference(avatar_component_clause,[],[f7282])).
% 54.09/17.49 thf(f7284,plain,(
% 54.09/17.49 spl101_1 | spl101_2 | spl101_3 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2277,f7282,f7118,f7115,f7112])).
% 54.09/17.49 thf(f7285,plain,(
% 54.09/17.49 spl101_5 | spl101_2 | spl101_3 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2292,f7282,f7118,f7115,f7125])).
% 54.09/17.49 thf(f7286,plain,(
% 54.09/17.49 spl101_6 | spl101_2 | spl101_3 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2307,f7282,f7118,f7115,f7129])).
% 54.09/17.49 thf(f7287,plain,(
% 54.09/17.49 spl101_7 | spl101_2 | spl101_3 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2318,f7282,f7118,f7115,f7133])).
% 54.09/17.49 thf(f7288,plain,(
% 54.09/17.49 spl101_1 | spl101_8 | spl101_3 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2338,f7282,f7118,f7137,f7112])).
% 54.09/17.49 thf(f7289,plain,(
% 54.09/17.49 spl101_5 | spl101_8 | spl101_3 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2353,f7282,f7118,f7137,f7125])).
% 54.09/17.49 thf(f7290,plain,(
% 54.09/17.49 spl101_6 | spl101_8 | spl101_3 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2368,f7282,f7118,f7137,f7129])).
% 54.09/17.49 thf(f7291,plain,(
% 54.09/17.49 spl101_7 | spl101_8 | spl101_3 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2379,f7282,f7118,f7137,f7133])).
% 54.09/17.49 thf(f7292,plain,(
% 54.09/17.49 spl101_1 | spl101_9 | spl101_3 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2399,f7282,f7118,f7144,f7112])).
% 54.09/17.49 thf(f7293,plain,(
% 54.09/17.49 spl101_5 | spl101_9 | spl101_3 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2414,f7282,f7118,f7144,f7125])).
% 54.09/17.49 thf(f7294,plain,(
% 54.09/17.49 spl101_6 | spl101_9 | spl101_3 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2429,f7282,f7118,f7144,f7129])).
% 54.09/17.49 thf(f7295,plain,(
% 54.09/17.49 spl101_7 | spl101_9 | spl101_3 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2440,f7282,f7118,f7144,f7133])).
% 54.09/17.49 thf(f7296,plain,(
% 54.09/17.49 spl101_1 | spl101_10 | spl101_3 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2456,f7282,f7118,f7151,f7112])).
% 54.09/17.49 thf(f7297,plain,(
% 54.09/17.49 spl101_5 | spl101_10 | spl101_3 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2471,f7282,f7118,f7151,f7125])).
% 54.09/17.49 thf(f7298,plain,(
% 54.09/17.49 spl101_6 | spl101_10 | spl101_3 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2486,f7282,f7118,f7151,f7129])).
% 54.09/17.49 thf(f7299,plain,(
% 54.09/17.49 spl101_7 | spl101_10 | spl101_3 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2497,f7282,f7118,f7151,f7133])).
% 54.09/17.49 thf(f7300,plain,(
% 54.09/17.49 spl101_1 | spl101_2 | spl101_11 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2522,f7282,f7158,f7115,f7112])).
% 54.09/17.49 thf(f7301,plain,(
% 54.09/17.49 spl101_5 | spl101_2 | spl101_11 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2537,f7282,f7158,f7115,f7125])).
% 54.09/17.49 thf(f7302,plain,(
% 54.09/17.49 spl101_6 | spl101_2 | spl101_11 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2552,f7282,f7158,f7115,f7129])).
% 54.09/17.49 thf(f7303,plain,(
% 54.09/17.49 spl101_7 | spl101_2 | spl101_11 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2563,f7282,f7158,f7115,f7133])).
% 54.09/17.49 thf(f7304,plain,(
% 54.09/17.49 spl101_1 | spl101_8 | spl101_11 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2583,f7282,f7158,f7137,f7112])).
% 54.09/17.49 thf(f7305,plain,(
% 54.09/17.49 spl101_5 | spl101_8 | spl101_11 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2598,f7282,f7158,f7137,f7125])).
% 54.09/17.49 thf(f7306,plain,(
% 54.09/17.49 spl101_6 | spl101_8 | spl101_11 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2613,f7282,f7158,f7137,f7129])).
% 54.09/17.49 thf(f7307,plain,(
% 54.09/17.49 spl101_7 | spl101_8 | spl101_11 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2624,f7282,f7158,f7137,f7133])).
% 54.09/17.49 thf(f7308,plain,(
% 54.09/17.49 spl101_1 | spl101_9 | spl101_11 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2644,f7282,f7158,f7144,f7112])).
% 54.09/17.49 thf(f7309,plain,(
% 54.09/17.49 spl101_5 | spl101_9 | spl101_11 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2659,f7282,f7158,f7144,f7125])).
% 54.09/17.49 thf(f7310,plain,(
% 54.09/17.49 spl101_6 | spl101_9 | spl101_11 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2674,f7282,f7158,f7144,f7129])).
% 54.09/17.49 thf(f7311,plain,(
% 54.09/17.49 spl101_7 | spl101_9 | spl101_11 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2685,f7282,f7158,f7144,f7133])).
% 54.09/17.49 thf(f7312,plain,(
% 54.09/17.49 spl101_1 | spl101_10 | spl101_11 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2701,f7282,f7158,f7151,f7112])).
% 54.09/17.49 thf(f7313,plain,(
% 54.09/17.49 spl101_5 | spl101_10 | spl101_11 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2716,f7282,f7158,f7151,f7125])).
% 54.09/17.49 thf(f7314,plain,(
% 54.09/17.49 spl101_6 | spl101_10 | spl101_11 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2731,f7282,f7158,f7151,f7129])).
% 54.09/17.49 thf(f7315,plain,(
% 54.09/17.49 spl101_7 | spl101_10 | spl101_11 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2742,f7282,f7158,f7151,f7133])).
% 54.09/17.49 thf(f7316,plain,(
% 54.09/17.49 spl101_1 | spl101_2 | spl101_12 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2767,f7282,f7177,f7115,f7112])).
% 54.09/17.49 thf(f7317,plain,(
% 54.09/17.49 spl101_5 | spl101_2 | spl101_12 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2782,f7282,f7177,f7115,f7125])).
% 54.09/17.49 thf(f7318,plain,(
% 54.09/17.49 spl101_6 | spl101_2 | spl101_12 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2797,f7282,f7177,f7115,f7129])).
% 54.09/17.49 thf(f7319,plain,(
% 54.09/17.49 spl101_7 | spl101_2 | spl101_12 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2808,f7282,f7177,f7115,f7133])).
% 54.09/17.49 thf(f7320,plain,(
% 54.09/17.49 spl101_1 | spl101_8 | spl101_12 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2828,f7282,f7177,f7137,f7112])).
% 54.09/17.49 thf(f7321,plain,(
% 54.09/17.49 spl101_5 | spl101_8 | spl101_12 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2843,f7282,f7177,f7137,f7125])).
% 54.09/17.49 thf(f7322,plain,(
% 54.09/17.49 spl101_6 | spl101_8 | spl101_12 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2858,f7282,f7177,f7137,f7129])).
% 54.09/17.49 thf(f7323,plain,(
% 54.09/17.49 spl101_7 | spl101_8 | spl101_12 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2869,f7282,f7177,f7137,f7133])).
% 54.09/17.49 thf(f7324,plain,(
% 54.09/17.49 spl101_1 | spl101_9 | spl101_12 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2889,f7282,f7177,f7144,f7112])).
% 54.09/17.49 thf(f7325,plain,(
% 54.09/17.49 spl101_5 | spl101_9 | spl101_12 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2904,f7282,f7177,f7144,f7125])).
% 54.09/17.49 thf(f7326,plain,(
% 54.09/17.49 spl101_6 | spl101_9 | spl101_12 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2919,f7282,f7177,f7144,f7129])).
% 54.09/17.49 thf(f7327,plain,(
% 54.09/17.49 spl101_7 | spl101_9 | spl101_12 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2930,f7282,f7177,f7144,f7133])).
% 54.09/17.49 thf(f7328,plain,(
% 54.09/17.49 spl101_1 | spl101_10 | spl101_12 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2946,f7282,f7177,f7151,f7112])).
% 54.09/17.49 thf(f7329,plain,(
% 54.09/17.49 spl101_5 | spl101_10 | spl101_12 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2961,f7282,f7177,f7151,f7125])).
% 54.09/17.49 thf(f7330,plain,(
% 54.09/17.49 spl101_6 | spl101_10 | spl101_12 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2976,f7282,f7177,f7151,f7129])).
% 54.09/17.49 thf(f7331,plain,(
% 54.09/17.49 spl101_7 | spl101_10 | spl101_12 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f2987,f7282,f7177,f7151,f7133])).
% 54.09/17.49 thf(f7332,plain,(
% 54.09/17.49 spl101_1 | spl101_2 | spl101_13 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f3008,f7282,f7196,f7115,f7112])).
% 54.09/17.49 thf(f7333,plain,(
% 54.09/17.49 spl101_5 | spl101_2 | spl101_13 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f3023,f7282,f7196,f7115,f7125])).
% 54.09/17.49 thf(f7334,plain,(
% 54.09/17.49 spl101_6 | spl101_2 | spl101_13 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f3038,f7282,f7196,f7115,f7129])).
% 54.09/17.49 thf(f7335,plain,(
% 54.09/17.49 spl101_7 | spl101_2 | spl101_13 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f3049,f7282,f7196,f7115,f7133])).
% 54.09/17.49 thf(f7336,plain,(
% 54.09/17.49 spl101_1 | spl101_8 | spl101_13 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f3069,f7282,f7196,f7137,f7112])).
% 54.09/17.49 thf(f7337,plain,(
% 54.09/17.49 spl101_5 | spl101_8 | spl101_13 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f3084,f7282,f7196,f7137,f7125])).
% 54.09/17.49 thf(f7338,plain,(
% 54.09/17.49 spl101_6 | spl101_8 | spl101_13 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f3099,f7282,f7196,f7137,f7129])).
% 54.09/17.49 thf(f7339,plain,(
% 54.09/17.49 spl101_7 | spl101_8 | spl101_13 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f3110,f7282,f7196,f7137,f7133])).
% 54.09/17.49 thf(f7340,plain,(
% 54.09/17.49 spl101_1 | spl101_9 | spl101_13 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f3130,f7282,f7196,f7144,f7112])).
% 54.09/17.49 thf(f7341,plain,(
% 54.09/17.49 spl101_5 | spl101_9 | spl101_13 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f3145,f7282,f7196,f7144,f7125])).
% 54.09/17.49 thf(f7342,plain,(
% 54.09/17.49 spl101_6 | spl101_9 | spl101_13 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f3160,f7282,f7196,f7144,f7129])).
% 54.09/17.49 thf(f7343,plain,(
% 54.09/17.49 spl101_7 | spl101_9 | spl101_13 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f3171,f7282,f7196,f7144,f7133])).
% 54.09/17.49 thf(f7344,plain,(
% 54.09/17.49 spl101_1 | spl101_10 | spl101_13 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f3187,f7282,f7196,f7151,f7112])).
% 54.09/17.49 thf(f7345,plain,(
% 54.09/17.49 spl101_5 | spl101_10 | spl101_13 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f3202,f7282,f7196,f7151,f7125])).
% 54.09/17.49 thf(f7346,plain,(
% 54.09/17.49 spl101_6 | spl101_10 | spl101_13 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f3217,f7282,f7196,f7151,f7129])).
% 54.09/17.49 thf(f7347,plain,(
% 54.09/17.49 spl101_7 | spl101_10 | spl101_13 | spl101_15),
% 54.09/17.49 inference(avatar_split_clause,[],[f3228,f7282,f7196,f7151,f7133])).
% 54.09/17.49 thf(f7349,definition,(
% 54.09/17.49 spl101_16 <=> ! [X1 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($false = ((rel_s4 @ sK2 @ X1))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_16])],[avatar_definition])).
% 54.09/17.49 thf(f7350,plain,(
% 54.09/17.49 ( ! [X1 : $i] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X1))) | ($false = ((rel_s4 @ sK2 @ X1)))) ) | ~spl101_16),
% 54.09/17.49 inference(avatar_component_clause,[],[f7349])).
% 54.09/17.49 thf(f7351,plain,(
% 54.09/17.49 spl101_1 | spl101_2 | spl101_3 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3254,f7349,f7118,f7115,f7112])).
% 54.09/17.49 thf(f7352,plain,(
% 54.09/17.49 spl101_5 | spl101_2 | spl101_3 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3269,f7349,f7118,f7115,f7125])).
% 54.09/17.49 thf(f7353,plain,(
% 54.09/17.49 spl101_6 | spl101_2 | spl101_3 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3284,f7349,f7118,f7115,f7129])).
% 54.09/17.49 thf(f7354,plain,(
% 54.09/17.49 spl101_7 | spl101_2 | spl101_3 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3295,f7349,f7118,f7115,f7133])).
% 54.09/17.49 thf(f7355,plain,(
% 54.09/17.49 spl101_1 | spl101_8 | spl101_3 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3315,f7349,f7118,f7137,f7112])).
% 54.09/17.49 thf(f7356,plain,(
% 54.09/17.49 spl101_5 | spl101_8 | spl101_3 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3330,f7349,f7118,f7137,f7125])).
% 54.09/17.49 thf(f7357,plain,(
% 54.09/17.49 spl101_6 | spl101_8 | spl101_3 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3345,f7349,f7118,f7137,f7129])).
% 54.09/17.49 thf(f7358,plain,(
% 54.09/17.49 spl101_7 | spl101_8 | spl101_3 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3356,f7349,f7118,f7137,f7133])).
% 54.09/17.49 thf(f7359,plain,(
% 54.09/17.49 spl101_1 | spl101_9 | spl101_3 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3376,f7349,f7118,f7144,f7112])).
% 54.09/17.49 thf(f7360,plain,(
% 54.09/17.49 spl101_5 | spl101_9 | spl101_3 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3391,f7349,f7118,f7144,f7125])).
% 54.09/17.49 thf(f7361,plain,(
% 54.09/17.49 spl101_6 | spl101_9 | spl101_3 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3406,f7349,f7118,f7144,f7129])).
% 54.09/17.49 thf(f7362,plain,(
% 54.09/17.49 spl101_7 | spl101_9 | spl101_3 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3417,f7349,f7118,f7144,f7133])).
% 54.09/17.49 thf(f7363,plain,(
% 54.09/17.49 spl101_1 | spl101_10 | spl101_3 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3433,f7349,f7118,f7151,f7112])).
% 54.09/17.49 thf(f7364,plain,(
% 54.09/17.49 spl101_5 | spl101_10 | spl101_3 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3448,f7349,f7118,f7151,f7125])).
% 54.09/17.49 thf(f7365,plain,(
% 54.09/17.49 spl101_6 | spl101_10 | spl101_3 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3463,f7349,f7118,f7151,f7129])).
% 54.09/17.49 thf(f7366,plain,(
% 54.09/17.49 spl101_7 | spl101_10 | spl101_3 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3474,f7349,f7118,f7151,f7133])).
% 54.09/17.49 thf(f7367,plain,(
% 54.09/17.49 spl101_1 | spl101_2 | spl101_11 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3499,f7349,f7158,f7115,f7112])).
% 54.09/17.49 thf(f7368,plain,(
% 54.09/17.49 spl101_5 | spl101_2 | spl101_11 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3514,f7349,f7158,f7115,f7125])).
% 54.09/17.49 thf(f7369,plain,(
% 54.09/17.49 spl101_6 | spl101_2 | spl101_11 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3529,f7349,f7158,f7115,f7129])).
% 54.09/17.49 thf(f7370,plain,(
% 54.09/17.49 spl101_7 | spl101_2 | spl101_11 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3540,f7349,f7158,f7115,f7133])).
% 54.09/17.49 thf(f7371,plain,(
% 54.09/17.49 spl101_1 | spl101_8 | spl101_11 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3560,f7349,f7158,f7137,f7112])).
% 54.09/17.49 thf(f7372,plain,(
% 54.09/17.49 spl101_5 | spl101_8 | spl101_11 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3575,f7349,f7158,f7137,f7125])).
% 54.09/17.49 thf(f7373,plain,(
% 54.09/17.49 spl101_6 | spl101_8 | spl101_11 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3590,f7349,f7158,f7137,f7129])).
% 54.09/17.49 thf(f7374,plain,(
% 54.09/17.49 spl101_7 | spl101_8 | spl101_11 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3601,f7349,f7158,f7137,f7133])).
% 54.09/17.49 thf(f7375,plain,(
% 54.09/17.49 spl101_1 | spl101_9 | spl101_11 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3621,f7349,f7158,f7144,f7112])).
% 54.09/17.49 thf(f7376,plain,(
% 54.09/17.49 spl101_5 | spl101_9 | spl101_11 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3636,f7349,f7158,f7144,f7125])).
% 54.09/17.49 thf(f7377,plain,(
% 54.09/17.49 spl101_6 | spl101_9 | spl101_11 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3651,f7349,f7158,f7144,f7129])).
% 54.09/17.49 thf(f7378,plain,(
% 54.09/17.49 spl101_7 | spl101_9 | spl101_11 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3662,f7349,f7158,f7144,f7133])).
% 54.09/17.49 thf(f7379,plain,(
% 54.09/17.49 spl101_1 | spl101_10 | spl101_11 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3678,f7349,f7158,f7151,f7112])).
% 54.09/17.49 thf(f7380,plain,(
% 54.09/17.49 spl101_5 | spl101_10 | spl101_11 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3693,f7349,f7158,f7151,f7125])).
% 54.09/17.49 thf(f7381,plain,(
% 54.09/17.49 spl101_6 | spl101_10 | spl101_11 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3708,f7349,f7158,f7151,f7129])).
% 54.09/17.49 thf(f7382,plain,(
% 54.09/17.49 spl101_7 | spl101_10 | spl101_11 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3719,f7349,f7158,f7151,f7133])).
% 54.09/17.49 thf(f7383,plain,(
% 54.09/17.49 spl101_1 | spl101_2 | spl101_12 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3744,f7349,f7177,f7115,f7112])).
% 54.09/17.49 thf(f7384,plain,(
% 54.09/17.49 spl101_5 | spl101_2 | spl101_12 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3759,f7349,f7177,f7115,f7125])).
% 54.09/17.49 thf(f7385,plain,(
% 54.09/17.49 spl101_6 | spl101_2 | spl101_12 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3774,f7349,f7177,f7115,f7129])).
% 54.09/17.49 thf(f7386,plain,(
% 54.09/17.49 spl101_7 | spl101_2 | spl101_12 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3785,f7349,f7177,f7115,f7133])).
% 54.09/17.49 thf(f7387,plain,(
% 54.09/17.49 spl101_1 | spl101_8 | spl101_12 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3805,f7349,f7177,f7137,f7112])).
% 54.09/17.49 thf(f7388,plain,(
% 54.09/17.49 spl101_5 | spl101_8 | spl101_12 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3820,f7349,f7177,f7137,f7125])).
% 54.09/17.49 thf(f7389,plain,(
% 54.09/17.49 spl101_6 | spl101_8 | spl101_12 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3835,f7349,f7177,f7137,f7129])).
% 54.09/17.49 thf(f7390,plain,(
% 54.09/17.49 spl101_7 | spl101_8 | spl101_12 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3846,f7349,f7177,f7137,f7133])).
% 54.09/17.49 thf(f7391,plain,(
% 54.09/17.49 spl101_1 | spl101_9 | spl101_12 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3866,f7349,f7177,f7144,f7112])).
% 54.09/17.49 thf(f7392,plain,(
% 54.09/17.49 spl101_5 | spl101_9 | spl101_12 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3881,f7349,f7177,f7144,f7125])).
% 54.09/17.49 thf(f7393,plain,(
% 54.09/17.49 spl101_6 | spl101_9 | spl101_12 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3896,f7349,f7177,f7144,f7129])).
% 54.09/17.49 thf(f7394,plain,(
% 54.09/17.49 spl101_7 | spl101_9 | spl101_12 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3907,f7349,f7177,f7144,f7133])).
% 54.09/17.49 thf(f7395,plain,(
% 54.09/17.49 spl101_1 | spl101_10 | spl101_12 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3923,f7349,f7177,f7151,f7112])).
% 54.09/17.49 thf(f7396,plain,(
% 54.09/17.49 spl101_5 | spl101_10 | spl101_12 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3938,f7349,f7177,f7151,f7125])).
% 54.09/17.49 thf(f7397,plain,(
% 54.09/17.49 spl101_6 | spl101_10 | spl101_12 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3953,f7349,f7177,f7151,f7129])).
% 54.09/17.49 thf(f7398,plain,(
% 54.09/17.49 spl101_7 | spl101_10 | spl101_12 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3964,f7349,f7177,f7151,f7133])).
% 54.09/17.49 thf(f7399,plain,(
% 54.09/17.49 spl101_1 | spl101_2 | spl101_13 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f3985,f7349,f7196,f7115,f7112])).
% 54.09/17.49 thf(f7400,plain,(
% 54.09/17.49 spl101_5 | spl101_2 | spl101_13 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f4000,f7349,f7196,f7115,f7125])).
% 54.09/17.49 thf(f7401,plain,(
% 54.09/17.49 spl101_6 | spl101_2 | spl101_13 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f4015,f7349,f7196,f7115,f7129])).
% 54.09/17.49 thf(f7402,plain,(
% 54.09/17.49 spl101_7 | spl101_2 | spl101_13 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f4026,f7349,f7196,f7115,f7133])).
% 54.09/17.49 thf(f7403,plain,(
% 54.09/17.49 spl101_1 | spl101_8 | spl101_13 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f4046,f7349,f7196,f7137,f7112])).
% 54.09/17.49 thf(f7404,plain,(
% 54.09/17.49 spl101_5 | spl101_8 | spl101_13 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f4061,f7349,f7196,f7137,f7125])).
% 54.09/17.49 thf(f7405,plain,(
% 54.09/17.49 spl101_6 | spl101_8 | spl101_13 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f4076,f7349,f7196,f7137,f7129])).
% 54.09/17.49 thf(f7406,plain,(
% 54.09/17.49 spl101_7 | spl101_8 | spl101_13 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f4087,f7349,f7196,f7137,f7133])).
% 54.09/17.49 thf(f7407,plain,(
% 54.09/17.49 spl101_1 | spl101_9 | spl101_13 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f4107,f7349,f7196,f7144,f7112])).
% 54.09/17.49 thf(f7408,plain,(
% 54.09/17.49 spl101_5 | spl101_9 | spl101_13 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f4122,f7349,f7196,f7144,f7125])).
% 54.09/17.49 thf(f7409,plain,(
% 54.09/17.49 spl101_6 | spl101_9 | spl101_13 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f4137,f7349,f7196,f7144,f7129])).
% 54.09/17.49 thf(f7410,plain,(
% 54.09/17.49 spl101_7 | spl101_9 | spl101_13 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f4148,f7349,f7196,f7144,f7133])).
% 54.09/17.49 thf(f7411,plain,(
% 54.09/17.49 spl101_1 | spl101_10 | spl101_13 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f4164,f7349,f7196,f7151,f7112])).
% 54.09/17.49 thf(f7412,plain,(
% 54.09/17.49 spl101_5 | spl101_10 | spl101_13 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f4179,f7349,f7196,f7151,f7125])).
% 54.09/17.49 thf(f7413,plain,(
% 54.09/17.49 spl101_6 | spl101_10 | spl101_13 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f4194,f7349,f7196,f7151,f7129])).
% 54.09/17.49 thf(f7414,plain,(
% 54.09/17.49 spl101_7 | spl101_10 | spl101_13 | spl101_16),
% 54.09/17.49 inference(avatar_split_clause,[],[f4205,f7349,f7196,f7151,f7133])).
% 54.09/17.49 thf(f7432,plain,(
% 54.09/17.49 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0))))) ) | ~spl101_9),
% 54.09/17.49 inference(constrained_superposition,[],[f7145,f4305])).
% 54.09/17.49 thf(f7433,plain,(
% 54.09/17.49 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0))))) ) | ~spl101_9),
% 54.09/17.49 inference(trivial_inequality_removal,[],[f7432])).
% 54.09/17.49 thf(f7436,plain,(
% 54.09/17.49 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ~spl101_9),
% 54.09/17.49 inference(constrained_superposition,[],[f7433,f4307])).
% 54.09/17.49 thf(f7442,plain,(
% 54.09/17.49 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ~spl101_9),
% 54.09/17.49 inference(duplicate_literal_removal,[],[f7436])).
% 54.09/17.49 thf(f7443,plain,(
% 54.09/17.49 ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ~spl101_9),
% 54.09/17.49 inference(trivial_inequality_removal,[],[f7442])).
% 54.09/17.49 thf(f7445,definition,(
% 54.09/17.49 spl101_17 <=> ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_17])],[avatar_definition])).
% 54.09/17.49 thf(f7446,plain,(
% 54.09/17.49 ($true != ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | spl101_17),
% 54.09/17.49 inference(avatar_component_clause,[],[f7445])).
% 54.09/17.49 thf(f7447,plain,(
% 54.09/17.49 ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ~spl101_17),
% 54.09/17.49 inference(avatar_component_clause,[],[f7445])).
% 54.09/17.49 thf(f7449,definition,(
% 54.09/17.49 spl101_18 <=> ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_18])],[avatar_definition])).
% 54.09/17.49 thf(f7451,plain,(
% 54.09/17.49 ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ~spl101_18),
% 54.09/17.49 inference(avatar_component_clause,[],[f7449])).
% 54.09/17.49 thf(f7453,definition,(
% 54.09/17.49 spl101_19 <=> ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_19])],[avatar_definition])).
% 54.09/17.49 thf(f7454,plain,(
% 54.09/17.49 ($true != ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | spl101_19),
% 54.09/17.49 inference(avatar_component_clause,[],[f7453])).
% 54.09/17.49 thf(f7455,plain,(
% 54.09/17.49 ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ~spl101_19),
% 54.09/17.49 inference(avatar_component_clause,[],[f7453])).
% 54.09/17.49 thf(f7457,definition,(
% 54.09/17.49 spl101_20 <=> ($false = ((rel_s4 @ sK2 @ sK2)))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_20])],[avatar_definition])).
% 54.09/17.49 thf(f7458,plain,(
% 54.09/17.49 ($false != ((rel_s4 @ sK2 @ sK2))) | spl101_20),
% 54.09/17.49 inference(avatar_component_clause,[],[f7457])).
% 54.09/17.49 thf(f7459,plain,(
% 54.09/17.49 ($false = ((rel_s4 @ sK2 @ sK2))) | ~spl101_20),
% 54.09/17.49 inference(avatar_component_clause,[],[f7457])).
% 54.09/17.49 thf(f7461,plain,(
% 54.09/17.49 spl101_17 | spl101_20 | spl101_19 | spl101_18 | ~spl101_9),
% 54.09/17.49 inference(avatar_split_clause,[],[f7443,f7144,f7449,f7453,f7457,f7445])).
% 54.09/17.49 thf(f7496,plain,(
% 54.09/17.49 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK7 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0)))) ) | ~spl101_10),
% 54.09/17.49 inference(constrained_superposition,[],[f7152,f4328])).
% 54.09/17.49 thf(f7497,plain,(
% 54.09/17.49 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK7 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0)))) ) | ~spl101_10),
% 54.09/17.49 inference(trivial_inequality_removal,[],[f7496])).
% 54.09/17.49 thf(f7527,definition,(
% 54.09/17.49 spl101_21 <=> ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_21])],[avatar_definition])).
% 54.09/17.49 thf(f7528,plain,(
% 54.09/17.49 ($true != ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | spl101_21),
% 54.09/17.49 inference(avatar_component_clause,[],[f7527])).
% 54.09/17.49 thf(f7529,plain,(
% 54.09/17.49 ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ~spl101_21),
% 54.09/17.49 inference(avatar_component_clause,[],[f7527])).
% 54.09/17.49 thf(f7531,definition,(
% 54.09/17.49 spl101_22 <=> ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_22])],[avatar_definition])).
% 54.09/17.49 thf(f7532,plain,(
% 54.09/17.49 ($true != ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | spl101_22),
% 54.09/17.49 inference(avatar_component_clause,[],[f7531])).
% 54.09/17.49 thf(f7533,plain,(
% 54.09/17.49 ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ~spl101_22),
% 54.09/17.49 inference(avatar_component_clause,[],[f7531])).
% 54.09/17.49 thf(f7535,definition,(
% 54.09/17.49 spl101_23 <=> ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2))))),
% 54.09/17.49 introduced(definition,[new_symbols(definition,[spl101_23])],[avatar_definition])).
% 54.09/17.49 thf(f7536,plain,(
% 54.09/17.49 ($true != ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | spl101_23),
% 54.09/17.49 inference(avatar_component_clause,[],[f7535])).
% 54.09/17.49 thf(f7537,plain,(
% 54.09/17.49 ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ~spl101_23),
% 54.09/17.49 inference(avatar_component_clause,[],[f7535])).
% 54.09/17.49 thf(f7595,plain,(
% 54.09/17.49 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0))))) ) | ~spl101_4),
% 54.09/17.49 inference(constrained_superposition,[],[f7122,f4444])).
% 54.09/17.49 thf(f7596,plain,(
% 54.09/17.49 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0))))) ) | ~spl101_4),
% 54.09/17.49 inference(trivial_inequality_removal,[],[f7595])).
% 54.09/17.49 thf(f7603,plain,(
% 54.09/17.49 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK15 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0)))) ) | ~spl101_16),
% 54.09/17.49 inference(constrained_superposition,[],[f7350,f4456])).
% 54.09/17.49 thf(f7604,plain,(
% 54.09/17.49 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK15 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0)))) ) | ~spl101_16),
% 54.09/17.49 inference(trivial_inequality_removal,[],[f7603])).
% 54.09/17.49 thf(f7731,plain,(
% 54.09/17.49 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0))))) ) | ~spl101_9),
% 54.09/17.49 inference(constrained_superposition,[],[f7145,f4326])).
% 54.09/17.49 thf(f7732,plain,(
% 54.09/17.49 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK10 @ X0))))) ) | ~spl101_9),
% 54.09/17.49 inference(trivial_inequality_removal,[],[f7731])).
% 54.09/17.49 thf(f7737,plain,(
% 54.09/17.49 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK7 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK10 @ X0))))) ) | (~spl101_9 | ~spl101_10)),
% 54.09/17.49 inference(constrained_superposition,[],[f7152,f7732])).
% 54.09/17.49 thf(f7738,plain,(
% 54.09/17.49 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ X0))))) ) | (~spl101_9 | ~spl101_10)),
% 54.09/17.49 inference(trivial_inequality_removal,[],[f7737])).
% 54.09/17.49 thf(f7750,plain,(
% 54.09/17.49 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_9 | ~spl101_10)),
% 54.09/17.49 inference(constrained_superposition,[],[f7497,f7738])).
% 54.09/17.49 thf(f7754,plain,(
% 54.09/17.49 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_9 | ~spl101_10)),
% 54.09/17.49 inference(duplicate_literal_removal,[],[f7750])).
% 54.09/17.49 thf(f7755,plain,(
% 54.09/17.49 ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_9 | ~spl101_10)),
% 54.09/17.49 inference(trivial_inequality_removal,[],[f7754])).
% 54.09/17.49 thf(f7773,plain,(
% 54.09/17.49 ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_9 | ~spl101_10 | spl101_19)),
% 54.09/17.49 inference(forward_subsumption_resolution,[],[f7755,f7454])).
% 54.09/17.49 thf(f7781,plain,(
% 54.09/17.49 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0))))) ) | ~spl101_8),
% 54.09/17.49 inference(constrained_superposition,[],[f7138,f4331])).
% 54.09/17.49 thf(f7782,plain,(
% 54.09/17.49 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | ~spl101_8),
% 54.09/17.49 inference(trivial_inequality_removal,[],[f7781])).
% 54.09/17.49 thf(f7794,plain,(
% 54.09/17.49 ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | (~spl101_9 | ~spl101_10 | spl101_19 | spl101_20)),
% 54.09/17.49 inference(forward_subsumption_resolution,[],[f7773,f7458])).
% 54.09/17.49 thf(f7796,plain,(
% 54.09/17.49 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | (~spl101_9 | ~spl101_10 | ~spl101_17 | spl101_19 | spl101_20)),
% 54.09/17.49 inference(forward_demodulation,[],[f7794,f7447])).
% 54.09/17.49 thf(f7797,plain,(
% 54.09/17.49 ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | (~spl101_9 | ~spl101_10 | ~spl101_17 | spl101_19 | spl101_20)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f7796])).
% 54.09/17.50 thf(f7800,plain,(
% 54.09/17.50 spl101_18 | ~spl101_9 | ~spl101_10 | ~spl101_17 | spl101_19 | spl101_20),
% 54.09/17.50 inference(avatar_split_clause,[],[f7797,f7457,f7453,f7445,f7151,f7144,f7449])).
% 54.09/17.50 thf(f7803,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK7 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | (~spl101_8 | ~spl101_10)),
% 54.09/17.50 inference(constrained_superposition,[],[f7152,f7782])).
% 54.09/17.50 thf(f7804,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ X0))))) ) | (~spl101_8 | ~spl101_10)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f7803])).
% 54.09/17.50 thf(f7893,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X0))))) ) | ~spl101_4),
% 54.09/17.50 inference(constrained_superposition,[],[f7122,f4442])).
% 54.09/17.50 thf(f7894,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0))))) ) | ~spl101_4),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f7893])).
% 54.09/17.50 thf(f7901,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0))))) ) | ~spl101_4),
% 54.09/17.50 inference(constrained_superposition,[],[f7122,f4447])).
% 54.09/17.50 thf(f7902,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0))))) ) | ~spl101_4),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f7901])).
% 54.09/17.50 thf(f7917,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0))))) ) | ~spl101_14),
% 54.09/17.50 inference(constrained_superposition,[],[f7216,f4459])).
% 54.09/17.50 thf(f7918,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | ~spl101_14),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f7917])).
% 54.09/17.50 thf(f7931,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0))))) ) | ~spl101_4),
% 54.09/17.50 inference(constrained_superposition,[],[f7122,f4465])).
% 54.09/17.50 thf(f7932,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0))))) ) | ~spl101_4),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f7931])).
% 54.09/17.50 thf(f7972,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X0))))) ) | ~spl101_8),
% 54.09/17.50 inference(constrained_superposition,[],[f7138,f4329])).
% 54.09/17.50 thf(f7973,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | ~spl101_8),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f7972])).
% 54.09/17.50 thf(f8022,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | (~spl101_8 | ~spl101_9)),
% 54.09/17.50 inference(constrained_superposition,[],[f7145,f7973])).
% 54.09/17.50 thf(f8023,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | (~spl101_8 | ~spl101_9)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8022])).
% 54.09/17.50 thf(f8034,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK7 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | (~spl101_8 | ~spl101_9 | ~spl101_10)),
% 54.09/17.50 inference(constrained_superposition,[],[f7152,f8023])).
% 54.09/17.50 thf(f8035,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | (~spl101_8 | ~spl101_9 | ~spl101_10)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8034])).
% 54.09/17.50 thf(f8057,plain,(
% 54.09/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | (~spl101_8 | ~spl101_9 | ~spl101_10)),
% 54.09/17.50 inference(constrained_superposition,[],[f7804,f8035])).
% 54.09/17.50 thf(f8061,plain,(
% 54.09/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_8 | ~spl101_9 | ~spl101_10)),
% 54.09/17.50 inference(duplicate_literal_removal,[],[f8057])).
% 54.09/17.50 thf(f8062,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_8 | ~spl101_9 | ~spl101_10)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8061])).
% 54.09/17.50 thf(f8088,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_8 | ~spl101_9 | ~spl101_10 | spl101_19)),
% 54.09/17.50 inference(forward_subsumption_resolution,[],[f8062,f7454])).
% 54.09/17.50 thf(f8090,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_8 | ~spl101_9 | ~spl101_10 | spl101_19 | spl101_20)),
% 54.09/17.50 inference(forward_subsumption_resolution,[],[f8088,f7458])).
% 54.09/17.50 thf(f8092,plain,(
% 54.09/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_8 | ~spl101_9 | ~spl101_10 | ~spl101_18 | spl101_19 | spl101_20)),
% 54.09/17.50 inference(forward_demodulation,[],[f8090,f7451])).
% 54.09/17.50 thf(f8093,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_8 | ~spl101_9 | ~spl101_10 | ~spl101_18 | spl101_19 | spl101_20)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8092])).
% 54.09/17.50 thf(f8096,plain,(
% 54.09/17.50 ($true = $false) | (~spl101_8 | ~spl101_9 | ~spl101_10 | ~spl101_17 | ~spl101_18 | spl101_19 | spl101_20)),
% 54.09/17.50 inference(constrained_superposition,[],[f8093,f7447])).
% 54.09/17.50 thf(f8102,plain,(
% 54.09/17.50 $false | (~spl101_8 | ~spl101_9 | ~spl101_10 | ~spl101_17 | ~spl101_18 | spl101_19 | spl101_20)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8096])).
% 54.09/17.50 thf(f8103,plain,(
% 54.09/17.50 ~spl101_8 | ~spl101_9 | ~spl101_10 | ~spl101_17 | ~spl101_18 | spl101_19 | spl101_20),
% 54.09/17.50 inference(avatar_contradiction_clause,[],[f8102])).
% 54.09/17.50 thf(f8108,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK18 @ X0))))) ) | ~spl101_15),
% 54.09/17.50 inference(constrained_superposition,[],[f4454,f7283])).
% 54.09/17.50 thf(f8109,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK18 @ X0))))) ) | (~spl101_4 | ~spl101_15)),
% 54.09/17.50 inference(constrained_superposition,[],[f7894,f7283])).
% 54.09/17.50 thf(f8111,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK18 @ X0))))) ) | ~spl101_15),
% 54.09/17.50 inference(constrained_superposition,[],[f4433,f7283])).
% 54.09/17.50 thf(f8112,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0))))) ) | ~spl101_15),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8111])).
% 54.09/17.50 thf(f8114,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0)))) ) | (~spl101_4 | ~spl101_15)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8109])).
% 54.09/17.50 thf(f8115,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK18 @ X0))))) ) | ~spl101_15),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8108])).
% 54.09/17.50 thf(f8120,plain,(
% 54.09/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ~spl101_15),
% 54.09/17.50 inference(constrained_superposition,[],[f8112,f4435])).
% 54.09/17.50 thf(f8162,plain,(
% 54.09/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ~spl101_15),
% 54.09/17.50 inference(duplicate_literal_removal,[],[f8120])).
% 54.09/17.50 thf(f8163,plain,(
% 54.09/17.50 ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ~spl101_15),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8162])).
% 54.09/17.50 thf(f8166,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK15 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK18 @ X0))))) ) | (~spl101_15 | ~spl101_16)),
% 54.09/17.50 inference(constrained_superposition,[],[f7350,f8115])).
% 54.09/17.50 thf(f8167,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ X0))))) ) | (~spl101_15 | ~spl101_16)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8166])).
% 54.09/17.50 thf(f8224,plain,(
% 54.09/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_4 | ~spl101_15)),
% 54.09/17.50 inference(constrained_superposition,[],[f7596,f8114])).
% 54.09/17.50 thf(f8237,plain,(
% 54.09/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_15)),
% 54.09/17.50 inference(duplicate_literal_removal,[],[f8224])).
% 54.09/17.50 thf(f8238,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_15)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8237])).
% 54.09/17.50 thf(f8258,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_15 | spl101_20)),
% 54.09/17.50 inference(forward_subsumption_resolution,[],[f8238,f7458])).
% 54.09/17.50 thf(f8260,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_15 | spl101_20 | spl101_22)),
% 54.09/17.50 inference(forward_subsumption_resolution,[],[f8258,f7532])).
% 54.09/17.50 thf(f8262,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | (~spl101_4 | ~spl101_15 | spl101_20 | spl101_21 | spl101_22)),
% 54.09/17.50 inference(forward_subsumption_resolution,[],[f8260,f7528])).
% 54.09/17.50 thf(f8266,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0))))) ) | ~spl101_2),
% 54.09/17.50 inference(constrained_superposition,[],[f7116,f4340])).
% 54.09/17.50 thf(f8267,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0))))) ) | ~spl101_2),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8266])).
% 54.09/17.50 thf(f8270,plain,(
% 54.09/17.50 ($true = $false) | (~spl101_4 | ~spl101_15 | spl101_20 | spl101_21 | spl101_22 | ~spl101_23)),
% 54.09/17.50 inference(constrained_superposition,[],[f8262,f7537])).
% 54.09/17.50 thf(f8276,plain,(
% 54.09/17.50 $false | (~spl101_4 | ~spl101_15 | spl101_20 | spl101_21 | spl101_22 | ~spl101_23)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8270])).
% 54.09/17.50 thf(f8277,plain,(
% 54.09/17.50 ~spl101_4 | ~spl101_15 | spl101_20 | spl101_21 | spl101_22 | ~spl101_23),
% 54.09/17.50 inference(avatar_contradiction_clause,[],[f8276])).
% 54.09/17.50 thf(f8279,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | (~spl101_15 | spl101_22)),
% 54.09/17.50 inference(forward_subsumption_resolution,[],[f8163,f7532])).
% 54.09/17.50 thf(f8287,plain,(
% 54.09/17.50 ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | (~spl101_15 | spl101_20 | spl101_22)),
% 54.09/17.50 inference(forward_subsumption_resolution,[],[f8279,f7458])).
% 54.09/17.50 thf(f8290,plain,(
% 54.09/17.50 spl101_23 | spl101_21 | ~spl101_15 | spl101_20 | spl101_22),
% 54.09/17.50 inference(avatar_split_clause,[],[f8287,f7531,f7457,f7282,f7527,f7535])).
% 54.09/17.50 thf(f8310,plain,(
% 54.09/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_15 | ~spl101_16)),
% 54.09/17.50 inference(constrained_superposition,[],[f7604,f8167])).
% 54.09/17.50 thf(f8320,plain,(
% 54.09/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_15 | ~spl101_16)),
% 54.09/17.50 inference(duplicate_literal_removal,[],[f8310])).
% 54.09/17.50 thf(f8321,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_15 | ~spl101_16)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8320])).
% 54.09/17.50 thf(f8343,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_15 | ~spl101_16 | spl101_23)),
% 54.09/17.50 inference(forward_subsumption_resolution,[],[f8321,f7536])).
% 54.09/17.50 thf(f8345,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_15 | ~spl101_16 | spl101_22 | spl101_23)),
% 54.09/17.50 inference(forward_subsumption_resolution,[],[f8343,f7532])).
% 54.09/17.50 thf(f8347,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_15 | ~spl101_16 | spl101_20 | spl101_22 | spl101_23)),
% 54.09/17.50 inference(forward_subsumption_resolution,[],[f8345,f7458])).
% 54.09/17.50 thf(f8351,plain,(
% 54.09/17.50 ($true = $false) | (~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_21 | spl101_22 | spl101_23)),
% 54.09/17.50 inference(constrained_superposition,[],[f8347,f7529])).
% 54.09/17.50 thf(f8357,plain,(
% 54.09/17.50 $false | (~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_21 | spl101_22 | spl101_23)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8351])).
% 54.09/17.50 thf(f8358,plain,(
% 54.09/17.50 ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_21 | spl101_22 | spl101_23),
% 54.09/17.50 inference(avatar_contradiction_clause,[],[f8357])).
% 54.09/17.50 thf(f8364,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0))))) ) | ~spl101_1),
% 54.09/17.50 inference(constrained_superposition,[],[f4382,f7113])).
% 54.09/17.50 thf(f8365,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0))))) ) | ~spl101_1),
% 54.09/17.50 inference(constrained_superposition,[],[f4402,f7113])).
% 54.09/17.50 thf(f8366,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0))))) ) | ~spl101_1),
% 54.09/17.50 inference(constrained_superposition,[],[f4384,f7113])).
% 54.09/17.50 thf(f8367,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0))))) ) | ~spl101_1),
% 54.09/17.50 inference(constrained_superposition,[],[f4379,f7113])).
% 54.09/17.50 thf(f8368,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0))))) ) | ~spl101_1),
% 54.09/17.50 inference(constrained_superposition,[],[f4381,f7113])).
% 54.09/17.50 thf(f8369,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0)))) ) | ~spl101_1),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8368])).
% 54.09/17.50 thf(f8370,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0))))) ) | ~spl101_1),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8367])).
% 54.09/17.50 thf(f8371,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0))))) ) | ~spl101_1),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8366])).
% 54.09/17.50 thf(f8372,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0))))) ) | ~spl101_1),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8365])).
% 54.09/17.50 thf(f8373,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0))))) ) | ~spl101_1),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8364])).
% 54.09/17.50 thf(f8393,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK14 @ X0))))) ) | ~spl101_6),
% 54.09/17.50 inference(constrained_superposition,[],[f4391,f7130])).
% 54.09/17.50 thf(f8394,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK14 @ X0))))) ) | ~spl101_6),
% 54.09/17.50 inference(constrained_superposition,[],[f4370,f7130])).
% 54.09/17.50 thf(f8395,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0))))) ) | ~spl101_6),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8394])).
% 54.09/17.50 thf(f8396,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK14 @ X0))))) ) | ~spl101_6),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8393])).
% 54.09/17.50 thf(f8400,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ X0))))) ) | ~spl101_7),
% 54.09/17.50 inference(constrained_superposition,[],[f4393,f7134])).
% 54.09/17.50 thf(f8401,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK11 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0))))) ) | ~spl101_7),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8400])).
% 54.09/17.50 thf(f8407,plain,(
% 54.09/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ~spl101_6),
% 54.09/17.50 inference(constrained_superposition,[],[f8395,f4372])).
% 54.09/17.50 thf(f8425,plain,(
% 54.09/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ~spl101_6),
% 54.09/17.50 inference(duplicate_literal_removal,[],[f8407])).
% 54.09/17.50 thf(f8426,plain,(
% 54.09/17.50 ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ~spl101_6),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8425])).
% 54.09/17.50 thf(f8430,definition,(
% 54.09/17.50 spl101_25 <=> ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2))))),
% 54.09/17.50 introduced(definition,[new_symbols(definition,[spl101_25])],[avatar_definition])).
% 54.09/17.50 thf(f8431,plain,(
% 54.09/17.50 ($true != ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | spl101_25),
% 54.09/17.50 inference(avatar_component_clause,[],[f8430])).
% 54.09/17.50 thf(f8432,plain,(
% 54.09/17.50 ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ~spl101_25),
% 54.09/17.50 inference(avatar_component_clause,[],[f8430])).
% 54.09/17.50 thf(f8434,definition,(
% 54.09/17.50 spl101_26 <=> ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2))))),
% 54.09/17.50 introduced(definition,[new_symbols(definition,[spl101_26])],[avatar_definition])).
% 54.09/17.50 thf(f8435,plain,(
% 54.09/17.50 ($true != ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | spl101_26),
% 54.09/17.50 inference(avatar_component_clause,[],[f8434])).
% 54.09/17.50 thf(f8436,plain,(
% 54.09/17.50 ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ~spl101_26),
% 54.09/17.50 inference(avatar_component_clause,[],[f8434])).
% 54.09/17.50 thf(f8438,definition,(
% 54.09/17.50 spl101_27 <=> ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2))))),
% 54.09/17.50 introduced(definition,[new_symbols(definition,[spl101_27])],[avatar_definition])).
% 54.09/17.50 thf(f8440,plain,(
% 54.09/17.50 ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ~spl101_27),
% 54.09/17.50 inference(avatar_component_clause,[],[f8438])).
% 54.09/17.50 thf(f8469,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0))))) ) | (~spl101_1 | ~spl101_6)),
% 54.09/17.50 inference(constrained_superposition,[],[f7130,f8370])).
% 54.09/17.50 thf(f8470,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0))))) ) | (~spl101_1 | ~spl101_6)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8469])).
% 54.09/17.50 thf(f8507,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK11 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0))))) ) | (~spl101_1 | ~spl101_7)),
% 54.09/17.50 inference(constrained_superposition,[],[f7134,f8372])).
% 54.09/17.50 thf(f8508,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ X0))))) ) | (~spl101_1 | ~spl101_7)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8507])).
% 54.09/17.50 thf(f8517,plain,(
% 54.09/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | (~spl101_1 | ~spl101_6)),
% 54.09/17.50 inference(constrained_superposition,[],[f8369,f8470])).
% 54.09/17.50 thf(f8524,plain,(
% 54.09/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_1 | ~spl101_6)),
% 54.09/17.50 inference(duplicate_literal_removal,[],[f8517])).
% 54.09/17.50 thf(f8525,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_1 | ~spl101_6)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8524])).
% 54.09/17.50 thf(f8617,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK11 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK14 @ X0))))) ) | (~spl101_6 | ~spl101_7)),
% 54.09/17.50 inference(constrained_superposition,[],[f7134,f8396])).
% 54.09/17.50 thf(f8618,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ X0))))) ) | (~spl101_6 | ~spl101_7)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8617])).
% 54.09/17.50 thf(f8650,plain,(
% 54.09/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | (~spl101_6 | ~spl101_7)),
% 54.09/17.50 inference(constrained_superposition,[],[f8618,f8401])).
% 54.09/17.50 thf(f8683,plain,(
% 54.09/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | (~spl101_6 | ~spl101_7)),
% 54.09/17.50 inference(duplicate_literal_removal,[],[f8650])).
% 54.09/17.50 thf(f8684,plain,(
% 54.09/17.50 ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | (~spl101_6 | ~spl101_7)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8683])).
% 54.09/17.50 thf(f8774,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X0))))) ) | ~spl101_1),
% 54.09/17.50 inference(constrained_superposition,[],[f7113,f4400])).
% 54.09/17.50 thf(f8775,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0))))) ) | ~spl101_1),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8774])).
% 54.09/17.50 thf(f8780,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0))))) ) | (~spl101_1 | ~spl101_6)),
% 54.09/17.50 inference(constrained_superposition,[],[f7130,f8775])).
% 54.09/17.50 thf(f8781,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0))))) ) | (~spl101_1 | ~spl101_6)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8780])).
% 54.09/17.50 thf(f8792,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0))))) ) | ~spl101_1),
% 54.09/17.50 inference(constrained_superposition,[],[f7113,f4405])).
% 54.09/17.50 thf(f8793,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0))))) ) | ~spl101_1),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8792])).
% 54.09/17.50 thf(f8848,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X0))))) ) | ~spl101_4),
% 54.09/17.50 inference(constrained_superposition,[],[f7122,f4445])).
% 54.09/17.50 thf(f8849,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X0))))) ) | ~spl101_4),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8848])).
% 54.09/17.50 thf(f8854,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK11 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0))))) ) | (~spl101_1 | ~spl101_6 | ~spl101_7)),
% 54.09/17.50 inference(constrained_superposition,[],[f7134,f8781])).
% 54.09/17.50 thf(f8855,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK13 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0))))) ) | (~spl101_1 | ~spl101_6 | ~spl101_7)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8854])).
% 54.09/17.50 thf(f8877,plain,(
% 54.09/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | (~spl101_1 | ~spl101_6 | ~spl101_7)),
% 54.09/17.50 inference(constrained_superposition,[],[f8508,f8855])).
% 54.09/17.50 thf(f8881,plain,(
% 54.09/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | (~spl101_1 | ~spl101_6 | ~spl101_7)),
% 54.09/17.50 inference(duplicate_literal_removal,[],[f8877])).
% 54.09/17.50 thf(f8882,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | (~spl101_1 | ~spl101_6 | ~spl101_7)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8881])).
% 54.09/17.50 thf(f8908,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | (~spl101_1 | ~spl101_6 | ~spl101_7 | spl101_26)),
% 54.09/17.50 inference(forward_subsumption_resolution,[],[f8882,f8435])).
% 54.09/17.50 thf(f8910,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | (~spl101_1 | ~spl101_6 | ~spl101_7 | spl101_20 | spl101_26)),
% 54.09/17.50 inference(forward_subsumption_resolution,[],[f8908,f7458])).
% 54.09/17.50 thf(f8912,plain,(
% 54.09/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | (~spl101_1 | ~spl101_6 | ~spl101_7 | spl101_20 | spl101_26 | ~spl101_27)),
% 54.09/17.50 inference(forward_demodulation,[],[f8910,f8440])).
% 54.09/17.50 thf(f8913,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | (~spl101_1 | ~spl101_6 | ~spl101_7 | spl101_20 | spl101_26 | ~spl101_27)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8912])).
% 54.09/17.50 thf(f8916,plain,(
% 54.09/17.50 ($true = $false) | (~spl101_1 | ~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_25 | spl101_26 | ~spl101_27)),
% 54.09/17.50 inference(constrained_superposition,[],[f8913,f8432])).
% 54.09/17.50 thf(f8922,plain,(
% 54.09/17.50 $false | (~spl101_1 | ~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_25 | spl101_26 | ~spl101_27)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8916])).
% 54.09/17.50 thf(f8923,plain,(
% 54.09/17.50 ~spl101_1 | ~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_25 | spl101_26 | ~spl101_27),
% 54.09/17.50 inference(avatar_contradiction_clause,[],[f8922])).
% 54.09/17.50 thf(f8926,plain,(
% 54.09/17.50 ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | (~spl101_6 | ~spl101_7 | spl101_20)),
% 54.09/17.50 inference(forward_subsumption_resolution,[],[f8684,f7458])).
% 54.09/17.50 thf(f8934,plain,(
% 54.09/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | (~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_25)),
% 54.09/17.50 inference(forward_demodulation,[],[f8926,f8432])).
% 54.09/17.50 thf(f8935,plain,(
% 54.09/17.50 ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | (~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_25)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8934])).
% 54.09/17.50 thf(f8943,definition,(
% 54.09/17.50 spl101_28 <=> ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2))))),
% 54.09/17.50 introduced(definition,[new_symbols(definition,[spl101_28])],[avatar_definition])).
% 54.09/17.50 thf(f8945,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ~spl101_28),
% 54.09/17.50 inference(avatar_component_clause,[],[f8943])).
% 54.09/17.50 thf(f8948,plain,(
% 54.09/17.50 spl101_27 | spl101_26 | ~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_25),
% 54.09/17.50 inference(avatar_split_clause,[],[f8935,f8430,f7457,f7133,f7129,f8434,f8438])).
% 54.09/17.50 thf(f8951,definition,(
% 54.09/17.50 spl101_29 <=> ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2))))),
% 54.09/17.50 introduced(definition,[new_symbols(definition,[spl101_29])],[avatar_definition])).
% 54.09/17.50 thf(f8953,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ~spl101_29),
% 54.09/17.50 inference(avatar_component_clause,[],[f8951])).
% 54.09/17.50 thf(f8959,plain,(
% 54.09/17.50 ($true = $false) | (~spl101_26 | ~spl101_28)),
% 54.09/17.50 inference(constrained_superposition,[],[f8945,f8436])).
% 54.09/17.50 thf(f8965,plain,(
% 54.09/17.50 $false | (~spl101_26 | ~spl101_28)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8959])).
% 54.09/17.50 thf(f8966,plain,(
% 54.09/17.50 ~spl101_26 | ~spl101_28),
% 54.09/17.50 inference(avatar_contradiction_clause,[],[f8965])).
% 54.09/17.50 thf(f8978,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | ~spl101_3),
% 54.09/17.50 inference(constrained_superposition,[],[f4249,f7119])).
% 54.09/17.50 thf(f8979,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | ~spl101_3),
% 54.09/17.50 inference(constrained_superposition,[],[f4251,f7119])).
% 54.09/17.50 thf(f8980,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | ~spl101_3),
% 54.09/17.50 inference(constrained_superposition,[],[f4252,f7119])).
% 54.09/17.50 thf(f8981,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | ~spl101_3),
% 54.09/17.50 inference(constrained_superposition,[],[f4254,f7119])).
% 54.09/17.50 thf(f8982,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | ~spl101_3),
% 54.09/17.50 inference(constrained_superposition,[],[f4270,f7119])).
% 54.09/17.50 thf(f8983,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | ~spl101_3),
% 54.09/17.50 inference(constrained_superposition,[],[f4272,f7119])).
% 54.09/17.50 thf(f8984,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | ~spl101_3),
% 54.09/17.50 inference(constrained_superposition,[],[f4275,f7119])).
% 54.09/17.50 thf(f8985,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | ~spl101_3),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8984])).
% 54.09/17.50 thf(f8986,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | ~spl101_3),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8983])).
% 54.09/17.50 thf(f8987,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | ~spl101_3),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8982])).
% 54.09/17.50 thf(f8988,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | ~spl101_3),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8981])).
% 54.09/17.50 thf(f8989,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | ~spl101_3),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8980])).
% 54.09/17.50 thf(f8990,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0)))) ) | ~spl101_3),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8979])).
% 54.09/17.50 thf(f8991,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | ~spl101_3),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f8978])).
% 54.09/17.50 thf(f9005,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | ~spl101_11),
% 54.09/17.50 inference(constrained_superposition,[],[f4243,f7159])).
% 54.09/17.50 thf(f9006,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | ~spl101_11),
% 54.09/17.50 inference(constrained_superposition,[],[f4245,f7159])).
% 54.09/17.50 thf(f9007,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK5 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0))))) ) | ~spl101_11),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f9006])).
% 54.09/17.50 thf(f9008,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | ~spl101_11),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f9005])).
% 54.09/17.50 thf(f9017,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK6 @ X0))))) ) | ~spl101_12),
% 54.09/17.50 inference(constrained_superposition,[],[f4261,f7178])).
% 54.09/17.50 thf(f9018,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK6 @ X0))))) ) | ~spl101_12),
% 54.09/17.50 inference(constrained_superposition,[],[f4240,f7178])).
% 54.09/17.50 thf(f9019,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0))))) ) | ~spl101_12),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f9018])).
% 54.09/17.50 thf(f9020,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK6 @ X0))))) ) | ~spl101_12),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f9017])).
% 54.09/17.50 thf(f9024,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ X0))))) ) | ~spl101_13),
% 54.09/17.50 inference(constrained_superposition,[],[f4263,f7197])).
% 54.09/17.50 thf(f9025,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK3 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0))))) ) | ~spl101_13),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f9024])).
% 54.09/17.50 thf(f9031,plain,(
% 54.09/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ~spl101_12),
% 54.09/17.50 inference(constrained_superposition,[],[f9019,f4242])).
% 54.09/17.50 thf(f9049,plain,(
% 54.09/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ~spl101_12),
% 54.09/17.50 inference(duplicate_literal_removal,[],[f9031])).
% 54.09/17.50 thf(f9050,plain,(
% 54.09/17.50 ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ~spl101_12),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f9049])).
% 54.09/17.50 thf(f9052,plain,(
% 54.09/17.50 ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_12 | spl101_20)),
% 54.09/17.50 inference(forward_subsumption_resolution,[],[f9050,f7458])).
% 54.09/17.50 thf(f9054,definition,(
% 54.09/17.50 spl101_30 <=> ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2))))),
% 54.09/17.50 introduced(definition,[new_symbols(definition,[spl101_30])],[avatar_definition])).
% 54.09/17.50 thf(f9055,plain,(
% 54.09/17.50 ($true != ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | spl101_30),
% 54.09/17.50 inference(avatar_component_clause,[],[f9054])).
% 54.09/17.50 thf(f9056,plain,(
% 54.09/17.50 ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ~spl101_30),
% 54.09/17.50 inference(avatar_component_clause,[],[f9054])).
% 54.09/17.50 thf(f9058,definition,(
% 54.09/17.50 spl101_31 <=> ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2))))),
% 54.09/17.50 introduced(definition,[new_symbols(definition,[spl101_31])],[avatar_definition])).
% 54.09/17.50 thf(f9060,plain,(
% 54.09/17.50 ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ~spl101_31),
% 54.09/17.50 inference(avatar_component_clause,[],[f9058])).
% 54.09/17.50 thf(f9062,definition,(
% 54.09/17.50 spl101_32 <=> ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2))))),
% 54.09/17.50 introduced(definition,[new_symbols(definition,[spl101_32])],[avatar_definition])).
% 54.09/17.50 thf(f9063,plain,(
% 54.09/17.50 ($true != ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | spl101_32),
% 54.09/17.50 inference(avatar_component_clause,[],[f9062])).
% 54.09/17.50 thf(f9064,plain,(
% 54.09/17.50 ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ~spl101_32),
% 54.09/17.50 inference(avatar_component_clause,[],[f9062])).
% 54.09/17.50 thf(f9066,plain,(
% 54.09/17.50 spl101_32 | spl101_30 | spl101_31 | ~spl101_12 | spl101_20),
% 54.09/17.50 inference(avatar_split_clause,[],[f9052,f7457,f7177,f9058,f9054,f9062])).
% 54.09/17.50 thf(f9087,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK3 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | (~spl101_3 | ~spl101_13)),
% 54.09/17.50 inference(constrained_superposition,[],[f7197,f8986])).
% 54.09/17.50 thf(f9088,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ X0))))) ) | (~spl101_3 | ~spl101_13)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f9087])).
% 54.09/17.50 thf(f9107,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | (~spl101_3 | ~spl101_12)),
% 54.09/17.50 inference(constrained_superposition,[],[f7178,f8991])).
% 54.09/17.50 thf(f9108,plain,(
% 54.09/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | (~spl101_3 | ~spl101_12)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f9107])).
% 54.09/17.50 thf(f9120,plain,(
% 54.09/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_3 | ~spl101_12)),
% 54.09/17.50 inference(constrained_superposition,[],[f9108,f8990])).
% 54.09/17.50 thf(f9153,plain,(
% 54.09/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_3 | ~spl101_12)),
% 54.09/17.50 inference(duplicate_literal_removal,[],[f9120])).
% 54.09/17.50 thf(f9154,plain,(
% 54.09/17.50 ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_3 | ~spl101_12)),
% 54.09/17.50 inference(trivial_inequality_removal,[],[f9153])).
% 54.09/17.50 thf(f9176,definition,(
% 54.09/17.50 spl101_33 <=> ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2))))),
% 54.09/17.50 introduced(definition,[new_symbols(definition,[spl101_33])],[avatar_definition])).
% 54.09/17.50 thf(f9178,plain,(
% 54.09/17.50 ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ~spl101_33),
% 54.09/17.50 inference(avatar_component_clause,[],[f9176])).
% 54.09/17.50 thf(f9189,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_11 | ~spl101_12)),
% 121.38/17.50 inference(constrained_superposition,[],[f7178,f9008])).
% 121.38/17.50 thf(f9190,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_11 | ~spl101_12)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9189])).
% 121.38/17.50 thf(f9202,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | (~spl101_11 | ~spl101_12)),
% 121.38/17.50 inference(constrained_superposition,[],[f9007,f9190])).
% 121.38/17.50 thf(f9212,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_11 | ~spl101_12)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f9202])).
% 121.38/17.50 thf(f9213,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_11 | ~spl101_12)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9212])).
% 121.38/17.50 thf(f9231,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_11 | ~spl101_12 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f9213,f7458])).
% 121.38/17.50 thf(f9233,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_11 | ~spl101_12 | spl101_20 | spl101_30)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f9231,f9055])).
% 121.38/17.50 thf(f9235,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | (~spl101_11 | ~spl101_12 | spl101_20 | spl101_30 | spl101_32)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f9233,f9063])).
% 121.38/17.50 thf(f9243,plain,(
% 121.38/17.50 ($true = $false) | (~spl101_11 | ~spl101_12 | spl101_20 | spl101_30 | ~spl101_31 | spl101_32)),
% 121.38/17.50 inference(constrained_superposition,[],[f9235,f9060])).
% 121.38/17.50 thf(f9249,plain,(
% 121.38/17.50 $false | (~spl101_11 | ~spl101_12 | spl101_20 | spl101_30 | ~spl101_31 | spl101_32)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9243])).
% 121.38/17.50 thf(f9250,plain,(
% 121.38/17.50 ~spl101_11 | ~spl101_12 | spl101_20 | spl101_30 | ~spl101_31 | spl101_32),
% 121.38/17.50 inference(avatar_contradiction_clause,[],[f9249])).
% 121.38/17.50 thf(f9263,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | ~spl101_8),
% 121.38/17.50 inference(constrained_superposition,[],[f4308,f7138])).
% 121.38/17.50 thf(f9264,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | ~spl101_8),
% 121.38/17.50 inference(constrained_superposition,[],[f4310,f7138])).
% 121.38/17.50 thf(f9269,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | (~spl101_2 | ~spl101_8)),
% 121.38/17.50 inference(constrained_superposition,[],[f8267,f7138])).
% 121.38/17.50 thf(f9270,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | (~spl101_2 | ~spl101_8)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9269])).
% 121.38/17.50 thf(f9275,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0))))) ) | ~spl101_8),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9264])).
% 121.38/17.50 thf(f9276,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | ~spl101_8),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9263])).
% 121.38/17.50 thf(f9338,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK3 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK6 @ X0))))) ) | (~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(constrained_superposition,[],[f7197,f9020])).
% 121.38/17.50 thf(f9339,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ X0))))) ) | (~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9338])).
% 121.38/17.50 thf(f9349,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | (~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(constrained_superposition,[],[f9025,f9339])).
% 121.38/17.50 thf(f9353,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f9349])).
% 121.38/17.50 thf(f9354,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9353])).
% 121.38/17.50 thf(f9376,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | (~spl101_8 | ~spl101_9)),
% 121.38/17.50 inference(constrained_superposition,[],[f7145,f9276])).
% 121.38/17.50 thf(f9377,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK8 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | (~spl101_8 | ~spl101_9)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9376])).
% 121.38/17.50 thf(f9411,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | (~spl101_8 | ~spl101_9)),
% 121.38/17.50 inference(constrained_superposition,[],[f9377,f9275])).
% 121.38/17.50 thf(f9438,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | (~spl101_8 | ~spl101_9)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f9411])).
% 121.38/17.50 thf(f9439,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | (~spl101_8 | ~spl101_9)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9438])).
% 121.38/17.50 thf(f9466,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | (~spl101_8 | ~spl101_9 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f9439,f7458])).
% 121.38/17.50 thf(f9469,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_8 | ~spl101_9 | ~spl101_18 | spl101_20)),
% 121.38/17.50 inference(forward_demodulation,[],[f9466,f7451])).
% 121.38/17.50 thf(f9470,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_8 | ~spl101_9 | ~spl101_18 | spl101_20)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9469])).
% 121.38/17.50 thf(f9472,plain,(
% 121.38/17.50 spl101_17 | spl101_19 | ~spl101_8 | ~spl101_9 | ~spl101_18 | spl101_20),
% 121.38/17.50 inference(avatar_split_clause,[],[f9470,f7457,f7449,f7144,f7137,f7453,f7445])).
% 121.38/17.50 thf(f9475,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | (~spl101_3 | ~spl101_12)),
% 121.38/17.50 inference(constrained_superposition,[],[f7178,f8987])).
% 121.38/17.50 thf(f9476,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | (~spl101_3 | ~spl101_12)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9475])).
% 121.38/17.50 thf(f9483,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK3 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | (~spl101_3 | ~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(constrained_superposition,[],[f7197,f9476])).
% 121.38/17.50 thf(f9484,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK5 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0))))) ) | (~spl101_3 | ~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9483])).
% 121.38/17.50 thf(f9490,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | (~spl101_3 | ~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(constrained_superposition,[],[f9484,f9088])).
% 121.38/17.50 thf(f9505,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_3 | ~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f9490])).
% 121.38/17.50 thf(f9506,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_3 | ~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9505])).
% 121.38/17.50 thf(f9521,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK7 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | (~spl101_2 | ~spl101_8 | ~spl101_10)),
% 121.38/17.50 inference(constrained_superposition,[],[f7152,f9270])).
% 121.38/17.50 thf(f9522,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ X0))))) ) | (~spl101_2 | ~spl101_8 | ~spl101_10)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9521])).
% 121.38/17.50 thf(f9559,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X0))))) ) | ~spl101_14),
% 121.38/17.50 inference(constrained_superposition,[],[f7216,f4457])).
% 121.38/17.50 thf(f9560,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | ~spl101_14),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9559])).
% 121.38/17.50 thf(f9565,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_14 | ~spl101_15)),
% 121.38/17.50 inference(constrained_superposition,[],[f7283,f9560])).
% 121.38/17.50 thf(f9566,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_14 | ~spl101_15)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9565])).
% 121.38/17.50 thf(f9627,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X0))))) ) | ~spl101_4),
% 121.38/17.50 inference(constrained_superposition,[],[f7122,f4463])).
% 121.38/17.50 thf(f9628,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0))))) ) | ~spl101_4),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9627])).
% 121.38/17.50 thf(f9633,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0))))) ) | (~spl101_4 | ~spl101_15)),
% 121.38/17.50 inference(constrained_superposition,[],[f7283,f9628])).
% 121.38/17.50 thf(f9634,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0))))) ) | (~spl101_4 | ~spl101_15)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9633])).
% 121.38/17.50 thf(f9639,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0))))) ) | ~spl101_4),
% 121.38/17.50 inference(constrained_superposition,[],[f7122,f4468])).
% 121.38/17.50 thf(f9640,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0))))) ) | ~spl101_4),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9639])).
% 121.38/17.50 thf(f9707,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X0))))) ) | ~spl101_3),
% 121.38/17.50 inference(constrained_superposition,[],[f7119,f4273])).
% 121.38/17.50 thf(f9708,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ (sK5 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X0))))) ) | ~spl101_3),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9707])).
% 121.38/17.50 thf(f9721,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X0))))) ) | ~spl101_2),
% 121.38/17.50 inference(constrained_superposition,[],[f7116,f4338])).
% 121.38/17.50 thf(f9722,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X0))))) ) | ~spl101_2),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9721])).
% 121.38/17.50 thf(f9753,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X0))))) ) | (~spl101_2 | ~spl101_8)),
% 121.38/17.50 inference(constrained_superposition,[],[f7138,f9722])).
% 121.38/17.50 thf(f9754,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | (~spl101_2 | ~spl101_8)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9753])).
% 121.38/17.50 thf(f9759,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X0))))) ) | ~spl101_1),
% 121.38/17.50 inference(constrained_superposition,[],[f7113,f4403])).
% 121.38/17.50 thf(f9760,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ (sK13 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X0))))) ) | ~spl101_1),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9759])).
% 121.38/17.50 thf(f9771,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X0))))) ) | ~spl101_4),
% 121.38/17.50 inference(constrained_superposition,[],[f7122,f4466])).
% 121.38/17.50 thf(f9772,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X0))))) ) | ~spl101_4),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9771])).
% 121.38/17.50 thf(f9785,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | (~spl101_2 | ~spl101_8 | ~spl101_9)),
% 121.38/17.50 inference(constrained_superposition,[],[f7145,f9754])).
% 121.38/17.50 thf(f9786,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | (~spl101_2 | ~spl101_8 | ~spl101_9)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9785])).
% 121.38/17.50 thf(f9791,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | (~spl101_2 | ~spl101_8 | ~spl101_9 | ~spl101_10)),
% 121.38/17.50 inference(constrained_superposition,[],[f7152,f9786])).
% 121.38/17.50 thf(f9792,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0))))) ) | (~spl101_2 | ~spl101_8 | ~spl101_9 | ~spl101_10)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9791])).
% 121.38/17.50 thf(f9811,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | (~spl101_2 | ~spl101_8 | ~spl101_9 | ~spl101_10)),
% 121.38/17.50 inference(constrained_superposition,[],[f9522,f9792])).
% 121.38/17.50 thf(f9812,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_2 | ~spl101_8 | ~spl101_9 | ~spl101_10)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f9811])).
% 121.38/17.50 thf(f9813,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_2 | ~spl101_8 | ~spl101_9 | ~spl101_10)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9812])).
% 121.38/17.50 thf(f9845,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_2 | ~spl101_8 | ~spl101_9 | ~spl101_10 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f9813,f7458])).
% 121.38/17.50 thf(f9847,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_2 | ~spl101_8 | ~spl101_9 | ~spl101_10 | ~spl101_18 | spl101_20)),
% 121.38/17.50 inference(forward_demodulation,[],[f9845,f7451])).
% 121.38/17.50 thf(f9848,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_2 | ~spl101_8 | ~spl101_9 | ~spl101_10 | ~spl101_18 | spl101_20)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9847])).
% 121.38/17.50 thf(f9851,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_2 | ~spl101_8 | ~spl101_9 | ~spl101_10 | ~spl101_18 | ~spl101_19 | spl101_20)),
% 121.38/17.50 inference(forward_demodulation,[],[f9848,f7455])).
% 121.38/17.50 thf(f9852,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_2 | ~spl101_8 | ~spl101_9 | ~spl101_10 | ~spl101_18 | ~spl101_19 | spl101_20)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9851])).
% 121.38/17.50 thf(f9857,plain,(
% 121.38/17.50 ($true = $false) | (~spl101_2 | ~spl101_8 | ~spl101_9 | ~spl101_10 | ~spl101_17 | ~spl101_18 | ~spl101_19 | spl101_20)),
% 121.38/17.50 inference(constrained_superposition,[],[f9852,f7447])).
% 121.38/17.50 thf(f9863,plain,(
% 121.38/17.50 $false | (~spl101_2 | ~spl101_8 | ~spl101_9 | ~spl101_10 | ~spl101_17 | ~spl101_18 | ~spl101_19 | spl101_20)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9857])).
% 121.38/17.50 thf(f9864,plain,(
% 121.38/17.50 ~spl101_2 | ~spl101_8 | ~spl101_9 | ~spl101_10 | ~spl101_17 | ~spl101_18 | ~spl101_19 | spl101_20),
% 121.38/17.50 inference(avatar_contradiction_clause,[],[f9863])).
% 121.38/17.50 thf(f9873,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ X0))))) ) | (~spl101_14 | ~spl101_16)),
% 121.38/17.50 inference(constrained_superposition,[],[f7918,f7350])).
% 121.38/17.50 thf(f9876,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ X0))))) ) | (~spl101_14 | ~spl101_15 | ~spl101_16)),
% 121.38/17.50 inference(constrained_superposition,[],[f9566,f7350])).
% 121.38/17.50 thf(f9881,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ X0))))) ) | (~spl101_14 | ~spl101_15 | ~spl101_16)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9876])).
% 121.38/17.50 thf(f9884,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK17 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ X0))))) ) | (~spl101_14 | ~spl101_16)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f9873])).
% 121.38/17.50 thf(f10130,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_14 | ~spl101_15 | ~spl101_16)),
% 121.38/17.50 inference(constrained_superposition,[],[f9884,f9881])).
% 121.38/17.50 thf(f10134,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_14 | ~spl101_15 | ~spl101_16)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f10130])).
% 121.38/17.50 thf(f10135,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_14 | ~spl101_15 | ~spl101_16)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10134])).
% 121.38/17.50 thf(f10165,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_14 | ~spl101_15 | ~spl101_16 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f10135,f7458])).
% 121.38/17.50 thf(f10167,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_14 | ~spl101_15 | ~spl101_16 | spl101_20 | spl101_23)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f10165,f7536])).
% 121.38/17.50 thf(f10169,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_14 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_22 | spl101_23)),
% 121.38/17.50 inference(forward_demodulation,[],[f10167,f7533])).
% 121.38/17.50 thf(f10170,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_14 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_22 | spl101_23)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10169])).
% 121.38/17.50 thf(f10175,plain,(
% 121.38/17.50 ($true = $false) | (~spl101_14 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_21 | ~spl101_22 | spl101_23)),
% 121.38/17.50 inference(constrained_superposition,[],[f10170,f7529])).
% 121.38/17.50 thf(f10181,plain,(
% 121.38/17.50 $false | (~spl101_14 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_21 | ~spl101_22 | spl101_23)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10175])).
% 121.38/17.50 thf(f10182,plain,(
% 121.38/17.50 ~spl101_14 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_21 | ~spl101_22 | spl101_23),
% 121.38/17.50 inference(avatar_contradiction_clause,[],[f10181])).
% 121.38/17.50 thf(f10183,plain,(
% 121.38/17.50 ($true = $false) | (~spl101_27 | ~spl101_29)),
% 121.38/17.50 inference(forward_demodulation,[],[f8440,f8953])).
% 121.38/17.50 thf(f10184,plain,(
% 121.38/17.50 $false | (~spl101_27 | ~spl101_29)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10183])).
% 121.38/17.50 thf(f10185,plain,(
% 121.38/17.50 ~spl101_27 | ~spl101_29),
% 121.38/17.50 inference(avatar_contradiction_clause,[],[f10184])).
% 121.38/17.50 thf(f10195,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | ~spl101_5),
% 121.38/17.50 inference(constrained_superposition,[],[f4373,f7126])).
% 121.38/17.50 thf(f10196,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | ~spl101_5),
% 121.38/17.50 inference(constrained_superposition,[],[f4375,f7126])).
% 121.38/17.50 thf(f10197,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | ~spl101_5),
% 121.38/17.50 inference(constrained_superposition,[],[f4394,f7126])).
% 121.38/17.50 thf(f10198,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | ~spl101_5),
% 121.38/17.50 inference(constrained_superposition,[],[f4396,f7126])).
% 121.38/17.50 thf(f10199,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_1 | ~spl101_5)),
% 121.38/17.50 inference(constrained_superposition,[],[f8371,f7126])).
% 121.38/17.50 thf(f10200,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_1 | ~spl101_5)),
% 121.38/17.50 inference(constrained_superposition,[],[f8373,f7126])).
% 121.38/17.50 thf(f10201,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_1 | ~spl101_5)),
% 121.38/17.50 inference(constrained_superposition,[],[f8793,f7126])).
% 121.38/17.50 thf(f10202,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_1 | ~spl101_5)),
% 121.38/17.50 inference(constrained_superposition,[],[f9760,f7126])).
% 121.38/17.50 thf(f10203,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_1 | ~spl101_5)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10202])).
% 121.38/17.50 thf(f10204,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_1 | ~spl101_5)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10201])).
% 121.38/17.50 thf(f10205,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_1 | ~spl101_5)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10200])).
% 121.38/17.50 thf(f10206,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK13 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0)))) ) | (~spl101_1 | ~spl101_5)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10199])).
% 121.38/17.50 thf(f10207,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | ~spl101_5),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10198])).
% 121.38/17.50 thf(f10208,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | ~spl101_5),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10197])).
% 121.38/17.50 thf(f10209,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK13 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0))))) ) | ~spl101_5),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10196])).
% 121.38/17.50 thf(f10210,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | ~spl101_5),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10195])).
% 121.38/17.50 thf(f10273,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK11 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_5 | ~spl101_7)),
% 121.38/17.50 inference(constrained_superposition,[],[f7134,f10207])).
% 121.38/17.50 thf(f10274,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK13 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ X0))))) ) | (~spl101_5 | ~spl101_7)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10273])).
% 121.38/17.50 thf(f10279,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_5 | ~spl101_6)),
% 121.38/17.50 inference(constrained_superposition,[],[f7130,f10210])).
% 121.38/17.50 thf(f10280,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_5 | ~spl101_6)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10279])).
% 121.38/17.50 thf(f10322,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | (~spl101_5 | ~spl101_6)),
% 121.38/17.50 inference(constrained_superposition,[],[f10209,f10280])).
% 121.38/17.50 thf(f10326,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | (~spl101_5 | ~spl101_6)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f10322])).
% 121.38/17.50 thf(f10327,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | (~spl101_5 | ~spl101_6)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10326])).
% 121.38/17.50 thf(f10355,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_5 | ~spl101_6)),
% 121.38/17.50 inference(constrained_superposition,[],[f7130,f10208])).
% 121.38/17.50 thf(f10356,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_5 | ~spl101_6)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10355])).
% 121.38/17.50 thf(f10363,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK11 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_1 | ~spl101_5 | ~spl101_7)),
% 121.38/17.50 inference(constrained_superposition,[],[f7134,f10204])).
% 121.38/17.50 thf(f10364,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK13 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ X0))))) ) | (~spl101_1 | ~spl101_5 | ~spl101_7)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10363])).
% 121.38/17.50 thf(f10407,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_1 | ~spl101_5 | ~spl101_6)),
% 121.38/17.50 inference(constrained_superposition,[],[f7130,f10205])).
% 121.38/17.50 thf(f10408,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_1 | ~spl101_5 | ~spl101_6)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10407])).
% 121.38/17.50 thf(f10417,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_1 | ~spl101_5 | ~spl101_6)),
% 121.38/17.50 inference(constrained_superposition,[],[f10408,f10206])).
% 121.38/17.50 thf(f10453,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | (~spl101_1 | ~spl101_5 | ~spl101_6)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f10417])).
% 121.38/17.50 thf(f10454,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | (~spl101_1 | ~spl101_5 | ~spl101_6)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10453])).
% 121.38/17.50 thf(f10473,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK11 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_5 | ~spl101_6 | ~spl101_7)),
% 121.38/17.50 inference(constrained_superposition,[],[f7134,f10356])).
% 121.38/17.50 thf(f10474,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_5 | ~spl101_6 | ~spl101_7)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10473])).
% 121.38/17.50 thf(f10485,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | (~spl101_5 | ~spl101_6 | ~spl101_7)),
% 121.38/17.50 inference(constrained_superposition,[],[f10474,f10274])).
% 121.38/17.50 thf(f10515,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | (~spl101_5 | ~spl101_6 | ~spl101_7)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f10485])).
% 121.38/17.50 thf(f10516,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | (~spl101_5 | ~spl101_6 | ~spl101_7)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10515])).
% 121.38/17.50 thf(f10537,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_1 | ~spl101_5 | ~spl101_6)),
% 121.38/17.50 inference(constrained_superposition,[],[f7130,f10203])).
% 121.38/17.50 thf(f10538,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_1 | ~spl101_5 | ~spl101_6)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10537])).
% 121.38/17.50 thf(f10545,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_1 | ~spl101_5 | ~spl101_6 | ~spl101_7)),
% 121.38/17.50 inference(constrained_superposition,[],[f7134,f10538])).
% 121.38/17.50 thf(f10546,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK14 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ X0))))) ) | (~spl101_1 | ~spl101_5 | ~spl101_6 | ~spl101_7)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10545])).
% 121.38/17.50 thf(f10558,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | (~spl101_1 | ~spl101_5 | ~spl101_6 | ~spl101_7)),
% 121.38/17.50 inference(constrained_superposition,[],[f10546,f10364])).
% 121.38/17.50 thf(f10585,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | (~spl101_1 | ~spl101_5 | ~spl101_6 | ~spl101_7)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f10558])).
% 121.38/17.50 thf(f10586,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | (~spl101_1 | ~spl101_5 | ~spl101_6 | ~spl101_7)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10585])).
% 121.38/17.50 thf(f10602,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | (~spl101_1 | ~spl101_5 | ~spl101_6 | ~spl101_7 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f10586,f7458])).
% 121.38/17.50 thf(f10605,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | (~spl101_1 | ~spl101_5 | ~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_25)),
% 121.38/17.50 inference(forward_demodulation,[],[f10602,f8432])).
% 121.38/17.50 thf(f10606,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | (~spl101_1 | ~spl101_5 | ~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_25)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10605])).
% 121.38/17.50 thf(f10609,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | (~spl101_1 | ~spl101_5 | ~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_25 | ~spl101_27)),
% 121.38/17.50 inference(forward_demodulation,[],[f10606,f8440])).
% 121.38/17.50 thf(f10610,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | (~spl101_1 | ~spl101_5 | ~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_25 | ~spl101_27)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10609])).
% 121.38/17.50 thf(f10611,plain,(
% 121.38/17.50 spl101_28 | ~spl101_1 | ~spl101_5 | ~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_25 | ~spl101_27),
% 121.38/17.50 inference(avatar_split_clause,[],[f10610,f8438,f8430,f7457,f7133,f7129,f7125,f7112,f8943])).
% 121.38/17.50 thf(f10614,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | (~spl101_5 | ~spl101_6 | ~spl101_7 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f10516,f7458])).
% 121.38/17.50 thf(f10616,definition,(
% 121.38/17.50 spl101_34 <=> ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2))))),
% 121.38/17.50 introduced(definition,[new_symbols(definition,[spl101_34])],[avatar_definition])).
% 121.38/17.50 thf(f10618,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ~spl101_34),
% 121.38/17.50 inference(avatar_component_clause,[],[f10616])).
% 121.38/17.50 thf(f10620,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | (~spl101_5 | ~spl101_6 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f10327,f7458])).
% 121.38/17.50 thf(f10622,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | (~spl101_1 | ~spl101_5 | ~spl101_6 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f10454,f7458])).
% 121.38/17.50 thf(f10629,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | (~spl101_5 | ~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_26)),
% 121.38/17.50 inference(forward_demodulation,[],[f10614,f8436])).
% 121.38/17.50 thf(f10630,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | (~spl101_5 | ~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_26)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10629])).
% 121.38/17.50 thf(f10631,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | (~spl101_5 | ~spl101_6 | spl101_20 | ~spl101_26)),
% 121.38/17.50 inference(forward_demodulation,[],[f10620,f8436])).
% 121.38/17.50 thf(f10632,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | (~spl101_5 | ~spl101_6 | spl101_20 | ~spl101_26)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10631])).
% 121.38/17.50 thf(f10635,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | (~spl101_1 | ~spl101_5 | ~spl101_6 | spl101_20 | ~spl101_26)),
% 121.38/17.50 inference(forward_demodulation,[],[f10622,f8436])).
% 121.38/17.50 thf(f10636,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | (~spl101_1 | ~spl101_5 | ~spl101_6 | spl101_20 | ~spl101_26)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10635])).
% 121.38/17.50 thf(f10640,plain,(
% 121.38/17.50 spl101_34 | spl101_27 | ~spl101_5 | ~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_26),
% 121.38/17.50 inference(avatar_split_clause,[],[f10630,f8434,f7457,f7133,f7129,f7125,f8438,f10616])).
% 121.38/17.50 thf(f10641,plain,(
% 121.38/17.50 spl101_27 | spl101_25 | ~spl101_5 | ~spl101_6 | spl101_20 | ~spl101_26),
% 121.38/17.50 inference(avatar_split_clause,[],[f10632,f8434,f7457,f7129,f7125,f8430,f8438])).
% 121.38/17.50 thf(f10643,plain,(
% 121.38/17.50 spl101_29 | spl101_25 | ~spl101_1 | ~spl101_5 | ~spl101_6 | spl101_20 | ~spl101_26),
% 121.38/17.50 inference(avatar_split_clause,[],[f10636,f8434,f7457,f7129,f7125,f7112,f8430,f8951])).
% 121.38/17.50 thf(f10644,plain,(
% 121.38/17.50 ($true != $true) | ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | spl101_25),
% 121.38/17.50 inference(constrained_superposition,[],[f8431,f240])).
% 121.38/17.50 thf(f10645,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | spl101_25),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10644])).
% 121.38/17.50 thf(f10646,plain,(
% 121.38/17.50 spl101_34 | spl101_25),
% 121.38/17.50 inference(avatar_split_clause,[],[f10645,f8430,f10616])).
% 121.38/17.50 thf(f10665,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | ~spl101_11),
% 121.38/17.50 inference(constrained_superposition,[],[f4264,f7159])).
% 121.38/17.50 thf(f10666,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | ~spl101_11),
% 121.38/17.50 inference(constrained_superposition,[],[f4266,f7159])).
% 121.38/17.50 thf(f10667,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_3 | ~spl101_11)),
% 121.38/17.50 inference(constrained_superposition,[],[f8985,f7159])).
% 121.38/17.50 thf(f10668,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_3 | ~spl101_11)),
% 121.38/17.50 inference(constrained_superposition,[],[f8988,f7159])).
% 121.38/17.50 thf(f10669,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_3 | ~spl101_11)),
% 121.38/17.50 inference(constrained_superposition,[],[f8989,f7159])).
% 121.38/17.50 thf(f10670,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_3 | ~spl101_11)),
% 121.38/17.50 inference(constrained_superposition,[],[f9708,f7159])).
% 121.38/17.50 thf(f10671,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_3 | ~spl101_11)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10670])).
% 121.38/17.50 thf(f10672,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_3 | ~spl101_11)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10669])).
% 121.38/17.50 thf(f10673,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK5 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0)))) ) | (~spl101_3 | ~spl101_11)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10668])).
% 121.38/17.50 thf(f10674,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_3 | ~spl101_11)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10667])).
% 121.38/17.50 thf(f10675,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | ~spl101_11),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10666])).
% 121.38/17.50 thf(f10676,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | ~spl101_11),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10665])).
% 121.38/17.50 thf(f10715,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK3 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_11 | ~spl101_13)),
% 121.38/17.50 inference(constrained_superposition,[],[f7197,f10675])).
% 121.38/17.50 thf(f10716,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK5 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ X0))))) ) | (~spl101_11 | ~spl101_13)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10715])).
% 121.38/17.50 thf(f10779,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_11 | ~spl101_12)),
% 121.38/17.50 inference(constrained_superposition,[],[f7178,f10676])).
% 121.38/17.50 thf(f10780,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_11 | ~spl101_12)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10779])).
% 121.38/17.50 thf(f10831,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_3 | ~spl101_11 | ~spl101_12)),
% 121.38/17.50 inference(constrained_superposition,[],[f7178,f10672])).
% 121.38/17.50 thf(f10832,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_3 | ~spl101_11 | ~spl101_12)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10831])).
% 121.38/17.50 thf(f10841,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_3 | ~spl101_11 | ~spl101_12)),
% 121.38/17.50 inference(constrained_superposition,[],[f10832,f10673])).
% 121.38/17.50 thf(f10871,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | (~spl101_3 | ~spl101_11 | ~spl101_12)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f10841])).
% 121.38/17.50 thf(f10872,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | (~spl101_3 | ~spl101_11 | ~spl101_12)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10871])).
% 121.38/17.50 thf(f10887,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK3 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_3 | ~spl101_11 | ~spl101_13)),
% 121.38/17.50 inference(constrained_superposition,[],[f7197,f10674])).
% 121.38/17.50 thf(f10888,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK5 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ X0))))) ) | (~spl101_3 | ~spl101_11 | ~spl101_13)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10887])).
% 121.38/17.50 thf(f10941,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK3 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_11 | ~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(constrained_superposition,[],[f7197,f10780])).
% 121.38/17.50 thf(f10942,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_11 | ~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10941])).
% 121.38/17.50 thf(f10962,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | (~spl101_11 | ~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(constrained_superposition,[],[f10716,f10942])).
% 121.38/17.50 thf(f10966,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | (~spl101_11 | ~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f10962])).
% 121.38/17.50 thf(f10967,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | (~spl101_11 | ~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f10966])).
% 121.38/17.50 thf(f10997,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | (~spl101_11 | ~spl101_12 | ~spl101_13 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f10967,f7458])).
% 121.38/17.50 thf(f11015,plain,(
% 121.38/17.50 ($true = $false) | (~spl101_32 | ~spl101_33)),
% 121.38/17.50 inference(forward_demodulation,[],[f9064,f9178])).
% 121.38/17.50 thf(f11016,plain,(
% 121.38/17.50 $false | (~spl101_32 | ~spl101_33)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11015])).
% 121.38/17.50 thf(f11017,plain,(
% 121.38/17.50 ~spl101_32 | ~spl101_33),
% 121.38/17.50 inference(avatar_contradiction_clause,[],[f11016])).
% 121.38/17.50 thf(f11019,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | (~spl101_11 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_31)),
% 121.38/17.50 inference(forward_demodulation,[],[f10997,f9060])).
% 121.38/17.50 thf(f11020,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | (~spl101_11 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_31)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11019])).
% 121.38/17.50 thf(f11029,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_11 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30 | ~spl101_31)),
% 121.38/17.50 inference(forward_demodulation,[],[f11020,f9056])).
% 121.38/17.50 thf(f11030,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_11 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30 | ~spl101_31)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11029])).
% 121.38/17.50 thf(f11033,plain,(
% 121.38/17.50 spl101_32 | ~spl101_11 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30 | ~spl101_31),
% 121.38/17.50 inference(avatar_split_clause,[],[f11030,f9058,f9054,f7457,f7196,f7177,f7158,f9062])).
% 121.38/17.50 thf(f11043,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_3 | ~spl101_11 | ~spl101_12)),
% 121.38/17.50 inference(constrained_superposition,[],[f7178,f10671])).
% 121.38/17.50 thf(f11044,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_3 | ~spl101_11 | ~spl101_12)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11043])).
% 121.38/17.50 thf(f11051,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_3 | ~spl101_11 | ~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(constrained_superposition,[],[f7197,f11044])).
% 121.38/17.50 thf(f11052,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK6 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ X0))))) ) | (~spl101_3 | ~spl101_11 | ~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11051])).
% 121.38/17.50 thf(f11073,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | (~spl101_3 | ~spl101_11 | ~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(constrained_superposition,[],[f10888,f11052])).
% 121.38/17.50 thf(f11074,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | (~spl101_3 | ~spl101_11 | ~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f11073])).
% 121.38/17.50 thf(f11075,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | (~spl101_3 | ~spl101_11 | ~spl101_12 | ~spl101_13)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11074])).
% 121.38/17.50 thf(f11107,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | (~spl101_3 | ~spl101_11 | ~spl101_12 | ~spl101_13 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f11075,f7458])).
% 121.38/17.50 thf(f11109,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | (~spl101_3 | ~spl101_11 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_31)),
% 121.38/17.50 inference(forward_demodulation,[],[f11107,f9060])).
% 121.38/17.50 thf(f11110,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | (~spl101_3 | ~spl101_11 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_31)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11109])).
% 121.38/17.50 thf(f11113,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | (~spl101_3 | ~spl101_11 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_31 | ~spl101_32)),
% 121.38/17.50 inference(forward_demodulation,[],[f11110,f9064])).
% 121.38/17.50 thf(f11114,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | (~spl101_3 | ~spl101_11 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_31 | ~spl101_32)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11113])).
% 121.38/17.50 thf(f11119,plain,(
% 121.38/17.50 ($true = $false) | (~spl101_3 | ~spl101_11 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30 | ~spl101_31 | ~spl101_32)),
% 121.38/17.50 inference(constrained_superposition,[],[f11114,f9056])).
% 121.38/17.50 thf(f11125,plain,(
% 121.38/17.50 $false | (~spl101_3 | ~spl101_11 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30 | ~spl101_31 | ~spl101_32)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11119])).
% 121.38/17.50 thf(f11126,plain,(
% 121.38/17.50 ~spl101_3 | ~spl101_11 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30 | ~spl101_31 | ~spl101_32),
% 121.38/17.50 inference(avatar_contradiction_clause,[],[f11125])).
% 121.38/17.50 thf(f11127,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_3 | ~spl101_12 | ~spl101_13 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f9506,f7458])).
% 121.38/17.50 thf(f11131,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_3 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30)),
% 121.38/17.50 inference(forward_demodulation,[],[f11127,f9056])).
% 121.38/17.50 thf(f11132,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_3 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11131])).
% 121.38/17.50 thf(f11137,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | (~spl101_3 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30 | ~spl101_32)),
% 121.38/17.50 inference(forward_demodulation,[],[f11132,f9064])).
% 121.38/17.50 thf(f11138,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | (~spl101_3 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30 | ~spl101_32)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11137])).
% 121.38/17.50 thf(f11141,plain,(
% 121.38/17.50 spl101_31 | ~spl101_3 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30 | ~spl101_32),
% 121.38/17.50 inference(avatar_split_clause,[],[f11138,f9062,f9054,f7457,f7196,f7177,f7118,f9058])).
% 121.38/17.50 thf(f11143,definition,(
% 121.38/17.50 spl101_35 <=> ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2))))),
% 121.38/17.50 introduced(definition,[new_symbols(definition,[spl101_35])],[avatar_definition])).
% 121.38/17.50 thf(f11145,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ~spl101_35),
% 121.38/17.50 inference(avatar_component_clause,[],[f11143])).
% 121.38/17.50 thf(f11148,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_12 | ~spl101_13 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f9354,f7458])).
% 121.38/17.50 thf(f11159,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30)),
% 121.38/17.50 inference(forward_demodulation,[],[f11148,f9056])).
% 121.38/17.50 thf(f11160,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11159])).
% 121.38/17.50 thf(f11165,plain,(
% 121.38/17.50 spl101_32 | spl101_31 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30),
% 121.38/17.50 inference(avatar_split_clause,[],[f11160,f9054,f7457,f7196,f7177,f9058,f9062])).
% 121.38/17.50 thf(f11169,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | (~spl101_3 | ~spl101_11 | ~spl101_12 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f10872,f7458])).
% 121.38/17.50 thf(f11171,definition,(
% 121.38/17.50 spl101_36 <=> ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2))))),
% 121.38/17.50 introduced(definition,[new_symbols(definition,[spl101_36])],[avatar_definition])).
% 121.38/17.50 thf(f11173,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | ~spl101_36),
% 121.38/17.50 inference(avatar_component_clause,[],[f11171])).
% 121.38/17.50 thf(f11187,plain,(
% 121.38/17.50 spl101_35 | spl101_33 | spl101_30 | ~spl101_3 | ~spl101_11 | ~spl101_12 | spl101_20),
% 121.38/17.50 inference(avatar_split_clause,[],[f11169,f7457,f7177,f7158,f7118,f9054,f9176,f11143])).
% 121.38/17.50 thf(f11190,plain,(
% 121.38/17.50 ($true != $true) | ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | spl101_30),
% 121.38/17.50 inference(constrained_superposition,[],[f9055,f240])).
% 121.38/17.50 thf(f11191,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK3 @ sK2)))) | spl101_30),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11190])).
% 121.38/17.50 thf(f11192,plain,(
% 121.38/17.50 spl101_36 | spl101_30),
% 121.38/17.50 inference(avatar_split_clause,[],[f11191,f9054,f11171])).
% 121.38/17.50 thf(f11197,plain,(
% 121.38/17.50 ($true = $false) | (~spl101_31 | ~spl101_35)),
% 121.38/17.50 inference(constrained_superposition,[],[f11145,f9060])).
% 121.38/17.50 thf(f11203,plain,(
% 121.38/17.50 $false | (~spl101_31 | ~spl101_35)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11197])).
% 121.38/17.50 thf(f11204,plain,(
% 121.38/17.50 ~spl101_31 | ~spl101_35),
% 121.38/17.50 inference(avatar_contradiction_clause,[],[f11203])).
% 121.38/17.50 thf(f11219,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | ~spl101_2),
% 121.38/17.50 inference(constrained_superposition,[],[f4314,f7116])).
% 121.38/17.50 thf(f11220,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | ~spl101_2),
% 121.38/17.50 inference(constrained_superposition,[],[f4316,f7116])).
% 121.38/17.50 thf(f11221,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | ~spl101_2),
% 121.38/17.50 inference(constrained_superposition,[],[f4317,f7116])).
% 121.38/17.50 thf(f11222,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | ~spl101_2),
% 121.38/17.50 inference(constrained_superposition,[],[f4319,f7116])).
% 121.38/17.50 thf(f11223,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | ~spl101_2),
% 121.38/17.50 inference(constrained_superposition,[],[f4335,f7116])).
% 121.38/17.50 thf(f11224,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | ~spl101_2),
% 121.38/17.50 inference(constrained_superposition,[],[f4337,f7116])).
% 121.38/17.50 thf(f11229,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | ~spl101_2),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11224])).
% 121.38/17.50 thf(f11230,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | ~spl101_2),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11223])).
% 121.38/17.50 thf(f11231,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | ~spl101_2),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11222])).
% 121.38/17.50 thf(f11232,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | ~spl101_2),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11221])).
% 121.38/17.50 thf(f11233,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK8 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0)))) ) | ~spl101_2),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11220])).
% 121.38/17.50 thf(f11234,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | ~spl101_2),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11219])).
% 121.38/17.50 thf(f11251,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | ~spl101_14),
% 121.38/17.50 inference(constrained_superposition,[],[f4436,f7216])).
% 121.38/17.50 thf(f11252,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | ~spl101_14),
% 121.38/17.50 inference(constrained_superposition,[],[f4438,f7216])).
% 121.38/17.50 thf(f11255,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_4 | ~spl101_14)),
% 121.38/17.50 inference(constrained_superposition,[],[f7902,f7216])).
% 121.38/17.50 thf(f11256,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_4 | ~spl101_14)),
% 121.38/17.50 inference(constrained_superposition,[],[f8849,f7216])).
% 121.38/17.50 thf(f11257,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_4 | ~spl101_14)),
% 121.38/17.50 inference(constrained_superposition,[],[f9640,f7216])).
% 121.38/17.50 thf(f11258,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_4 | ~spl101_14)),
% 121.38/17.50 inference(constrained_superposition,[],[f9772,f7216])).
% 121.38/17.50 thf(f11259,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_4 | ~spl101_14)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11258])).
% 121.38/17.50 thf(f11260,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_4 | ~spl101_14)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11257])).
% 121.38/17.50 thf(f11261,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_4 | ~spl101_14)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11256])).
% 121.38/17.50 thf(f11262,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK17 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0)))) ) | (~spl101_4 | ~spl101_14)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11255])).
% 121.38/17.50 thf(f11265,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK17 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0))))) ) | ~spl101_14),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11252])).
% 121.38/17.50 thf(f11266,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | ~spl101_14),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11251])).
% 121.38/17.50 thf(f11317,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK7 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | (~spl101_2 | ~spl101_10)),
% 121.38/17.50 inference(constrained_superposition,[],[f7152,f11229])).
% 121.38/17.50 thf(f11318,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK8 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ X0))))) ) | (~spl101_2 | ~spl101_10)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11317])).
% 121.38/17.50 thf(f11349,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | (~spl101_2 | ~spl101_8)),
% 121.38/17.50 inference(constrained_superposition,[],[f7138,f11231])).
% 121.38/17.50 thf(f11350,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | (~spl101_2 | ~spl101_8)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11349])).
% 121.38/17.50 thf(f11355,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | (~spl101_2 | ~spl101_9)),
% 121.38/17.50 inference(constrained_superposition,[],[f7145,f11234])).
% 121.38/17.50 thf(f11356,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | (~spl101_2 | ~spl101_9)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11355])).
% 121.38/17.50 thf(f11389,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_2 | ~spl101_9)),
% 121.38/17.50 inference(constrained_superposition,[],[f11356,f11233])).
% 121.38/17.50 thf(f11419,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | (~spl101_2 | ~spl101_9)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f11389])).
% 121.38/17.50 thf(f11420,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | (~spl101_2 | ~spl101_9)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11419])).
% 121.38/17.50 thf(f11447,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_14 | ~spl101_15)),
% 121.38/17.50 inference(constrained_superposition,[],[f7283,f11266])).
% 121.38/17.50 thf(f11448,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK16 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_14 | ~spl101_15)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11447])).
% 121.38/17.50 thf(f11454,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | (~spl101_14 | ~spl101_15)),
% 121.38/17.50 inference(constrained_superposition,[],[f11448,f11265])).
% 121.38/17.50 thf(f11469,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | (~spl101_14 | ~spl101_15)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f11454])).
% 121.38/17.50 thf(f11470,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | (~spl101_14 | ~spl101_15)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11469])).
% 121.38/17.50 thf(f11491,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | (~spl101_2 | ~spl101_9)),
% 121.38/17.50 inference(constrained_superposition,[],[f7145,f11230])).
% 121.38/17.50 thf(f11492,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ (sK7 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | (~spl101_2 | ~spl101_9)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11491])).
% 121.38/17.50 thf(f11529,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | (~spl101_2 | ~spl101_8)),
% 121.38/17.50 inference(constrained_superposition,[],[f7138,f11232])).
% 121.38/17.50 thf(f11530,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | (~spl101_2 | ~spl101_8)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11529])).
% 121.38/17.50 thf(f11535,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK7 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | (~spl101_2 | ~spl101_9 | ~spl101_10)),
% 121.38/17.50 inference(constrained_superposition,[],[f7152,f11492])).
% 121.38/17.50 thf(f11536,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK9 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | (~spl101_2 | ~spl101_9 | ~spl101_10)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11535])).
% 121.38/17.50 thf(f11544,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_2 | ~spl101_9 | ~spl101_10)),
% 121.38/17.50 inference(constrained_superposition,[],[f11536,f11318])).
% 121.38/17.50 thf(f11577,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | (~spl101_2 | ~spl101_9 | ~spl101_10)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f11544])).
% 121.38/17.50 thf(f11578,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | (~spl101_2 | ~spl101_9 | ~spl101_10)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11577])).
% 121.38/17.50 thf(f11603,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | (~spl101_2 | ~spl101_8 | ~spl101_9)),
% 121.38/17.50 inference(constrained_superposition,[],[f7145,f11530])).
% 121.38/17.50 thf(f11604,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK10 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK7 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ X0))))) ) | (~spl101_2 | ~spl101_8 | ~spl101_9)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11603])).
% 121.38/17.50 thf(f11622,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | (~spl101_2 | ~spl101_8 | ~spl101_9)),
% 121.38/17.50 inference(constrained_superposition,[],[f11350,f11604])).
% 121.38/17.50 thf(f11626,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | (~spl101_2 | ~spl101_8 | ~spl101_9)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f11622])).
% 121.38/17.50 thf(f11627,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | (~spl101_2 | ~spl101_8 | ~spl101_9)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11626])).
% 121.38/17.50 thf(f11657,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | (~spl101_2 | ~spl101_8 | ~spl101_9 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f11627,f7458])).
% 121.38/17.50 thf(f11659,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | (~spl101_2 | ~spl101_8 | ~spl101_9 | spl101_17 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f11657,f7446])).
% 121.38/17.50 thf(f11661,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | (~spl101_2 | ~spl101_8 | ~spl101_9 | spl101_17 | ~spl101_18 | spl101_20)),
% 121.38/17.50 inference(forward_demodulation,[],[f11659,f7451])).
% 121.38/17.50 thf(f11662,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | (~spl101_2 | ~spl101_8 | ~spl101_9 | spl101_17 | ~spl101_18 | spl101_20)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11661])).
% 121.38/17.50 thf(f11667,plain,(
% 121.38/17.50 ($true = $false) | (~spl101_2 | ~spl101_8 | ~spl101_9 | spl101_17 | ~spl101_18 | ~spl101_19 | spl101_20)),
% 121.38/17.50 inference(constrained_superposition,[],[f11662,f7455])).
% 121.38/17.50 thf(f11673,plain,(
% 121.38/17.50 $false | (~spl101_2 | ~spl101_8 | ~spl101_9 | spl101_17 | ~spl101_18 | ~spl101_19 | spl101_20)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11667])).
% 121.38/17.50 thf(f11674,plain,(
% 121.38/17.50 ~spl101_2 | ~spl101_8 | ~spl101_9 | spl101_17 | ~spl101_18 | ~spl101_19 | spl101_20),
% 121.38/17.50 inference(avatar_contradiction_clause,[],[f11673])).
% 121.38/17.50 thf(f11692,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | (~spl101_2 | ~spl101_9 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f11420,f7458])).
% 121.38/17.50 thf(f11694,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK8 @ sK2)))) | (~spl101_2 | ~spl101_9 | ~spl101_10 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f11578,f7458])).
% 121.38/17.50 thf(f11704,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_2 | ~spl101_9 | ~spl101_19 | spl101_20)),
% 121.38/17.50 inference(forward_demodulation,[],[f11692,f7455])).
% 121.38/17.50 thf(f11705,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_2 | ~spl101_9 | ~spl101_19 | spl101_20)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11704])).
% 121.38/17.50 thf(f11708,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_2 | ~spl101_9 | ~spl101_10 | ~spl101_19 | spl101_20)),
% 121.38/17.50 inference(forward_demodulation,[],[f11694,f7455])).
% 121.38/17.50 thf(f11709,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK9 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | (~spl101_2 | ~spl101_9 | ~spl101_10 | ~spl101_19 | spl101_20)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11708])).
% 121.38/17.50 thf(f11712,plain,(
% 121.38/17.50 spl101_17 | spl101_18 | ~spl101_2 | ~spl101_9 | ~spl101_19 | spl101_20),
% 121.38/17.50 inference(avatar_split_clause,[],[f11705,f7457,f7453,f7144,f7115,f7449,f7445])).
% 121.38/17.50 thf(f11714,definition,(
% 121.38/17.50 spl101_38 <=> ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2))))),
% 121.38/17.50 introduced(definition,[new_symbols(definition,[spl101_38])],[avatar_definition])).
% 121.38/17.50 thf(f11716,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK7 @ sK2)))) | ~spl101_38),
% 121.38/17.50 inference(avatar_component_clause,[],[f11714])).
% 121.38/17.50 thf(f11718,plain,(
% 121.38/17.50 spl101_38 | spl101_18 | ~spl101_2 | ~spl101_9 | ~spl101_10 | ~spl101_19 | spl101_20),
% 121.38/17.50 inference(avatar_split_clause,[],[f11709,f7457,f7453,f7151,f7144,f7115,f7449,f11714])).
% 121.38/17.50 thf(f11725,plain,(
% 121.38/17.50 ($true = $false) | (~spl101_17 | ~spl101_38)),
% 121.38/17.50 inference(constrained_superposition,[],[f11716,f7447])).
% 121.38/17.50 thf(f11731,plain,(
% 121.38/17.50 $false | (~spl101_17 | ~spl101_38)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11725])).
% 121.38/17.50 thf(f11732,plain,(
% 121.38/17.50 ~spl101_17 | ~spl101_38),
% 121.38/17.50 inference(avatar_contradiction_clause,[],[f11731])).
% 121.38/17.50 thf(f11753,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ X0))))) ) | (~spl101_4 | ~spl101_16)),
% 121.38/17.50 inference(constrained_superposition,[],[f7932,f7350])).
% 121.38/17.50 thf(f11755,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ X0))))) ) | (~spl101_4 | ~spl101_15 | ~spl101_16)),
% 121.38/17.50 inference(constrained_superposition,[],[f9634,f7350])).
% 121.38/17.50 thf(f11758,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ X0))))) ) | (~spl101_4 | ~spl101_15 | ~spl101_16)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11755])).
% 121.38/17.50 thf(f11760,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK17 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ X0))))) ) | (~spl101_4 | ~spl101_16)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11753])).
% 121.38/17.50 thf(f11896,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_15 | ~spl101_16)),
% 121.38/17.50 inference(constrained_superposition,[],[f11760,f11758])).
% 121.38/17.50 thf(f11900,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_15 | ~spl101_16)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f11896])).
% 121.38/17.50 thf(f11901,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_15 | ~spl101_16)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11900])).
% 121.38/17.50 thf(f11945,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_15 | ~spl101_16 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f11901,f7458])).
% 121.38/17.50 thf(f11947,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_23)),
% 121.38/17.50 inference(forward_demodulation,[],[f11945,f7537])).
% 121.38/17.50 thf(f11948,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_23)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11947])).
% 121.38/17.50 thf(f11951,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | (~spl101_4 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_21 | ~spl101_23)),
% 121.38/17.50 inference(forward_demodulation,[],[f11948,f7529])).
% 121.38/17.50 thf(f11952,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | (~spl101_4 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_21 | ~spl101_23)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11951])).
% 121.38/17.50 thf(f11955,plain,(
% 121.38/17.50 spl101_22 | ~spl101_4 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_21 | ~spl101_23),
% 121.38/17.50 inference(avatar_split_clause,[],[f11952,f7535,f7527,f7457,f7349,f7282,f7121,f7531])).
% 121.38/17.50 thf(f11960,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK15 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_4 | ~spl101_14 | ~spl101_16)),
% 121.38/17.50 inference(constrained_superposition,[],[f7350,f11260])).
% 121.38/17.50 thf(f11961,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK17 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ X0))))) ) | (~spl101_4 | ~spl101_14 | ~spl101_16)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f11960])).
% 121.38/17.50 thf(f12004,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_4 | ~spl101_14 | ~spl101_15)),
% 121.38/17.50 inference(constrained_superposition,[],[f7283,f11261])).
% 121.38/17.50 thf(f12005,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($true = ((rel_s4 @ X0 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_4 | ~spl101_14 | ~spl101_15)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f12004])).
% 121.38/17.50 thf(f12021,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | (~spl101_4 | ~spl101_14 | ~spl101_15)),
% 121.38/17.50 inference(constrained_superposition,[],[f11262,f12005])).
% 121.38/17.50 thf(f12037,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_4 | ~spl101_14 | ~spl101_15)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f12021])).
% 121.38/17.50 thf(f12038,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_4 | ~spl101_14 | ~spl101_15)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f12037])).
% 121.38/17.50 thf(f13474,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_4 | ~spl101_14 | ~spl101_15)),
% 121.38/17.50 inference(constrained_superposition,[],[f7283,f11259])).
% 121.38/17.50 thf(f13475,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_4 | ~spl101_14 | ~spl101_15)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f13474])).
% 121.38/17.50 thf(f13480,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_4 | ~spl101_14 | ~spl101_15 | ~spl101_16)),
% 121.38/17.50 inference(constrained_superposition,[],[f7350,f13475])).
% 121.38/17.50 thf(f13481,plain,(
% 121.38/17.50 ( ! [X0 : $i] : (($false = ((rel_s4 @ sK2 @ (sK18 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ X0)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ X0)))) | ($false = ((rel_s4 @ sK2 @ X0))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ X0))))) ) | (~spl101_4 | ~spl101_14 | ~spl101_15 | ~spl101_16)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f13480])).
% 121.38/17.50 thf(f13500,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | (~spl101_4 | ~spl101_14 | ~spl101_15 | ~spl101_16)),
% 121.38/17.50 inference(constrained_superposition,[],[f11961,f13481])).
% 121.38/17.50 thf(f13501,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_14 | ~spl101_15 | ~spl101_16)),
% 121.38/17.50 inference(duplicate_literal_removal,[],[f13500])).
% 121.38/17.50 thf(f13502,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_14 | ~spl101_15 | ~spl101_16)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f13501])).
% 121.38/17.50 thf(f13534,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_14 | ~spl101_15 | ~spl101_16 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f13502,f7458])).
% 121.38/17.50 thf(f13536,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_14 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_22)),
% 121.38/17.50 inference(forward_demodulation,[],[f13534,f7533])).
% 121.38/17.50 thf(f13537,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_14 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_22)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f13536])).
% 121.38/17.50 thf(f13540,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_14 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_22 | ~spl101_23)),
% 121.38/17.50 inference(forward_demodulation,[],[f13537,f7537])).
% 121.38/17.50 thf(f13541,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_14 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_22 | ~spl101_23)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f13540])).
% 121.38/17.50 thf(f13553,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_14 | ~spl101_15 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f12038,f7458])).
% 121.38/17.50 thf(f13555,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_14 | ~spl101_15 | spl101_20 | ~spl101_22)),
% 121.38/17.50 inference(forward_demodulation,[],[f13553,f7533])).
% 121.38/17.50 thf(f13556,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_14 | ~spl101_15 | spl101_20 | ~spl101_22)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f13555])).
% 121.38/17.50 thf(f13559,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_14 | ~spl101_15 | spl101_20 | ~spl101_22 | ~spl101_23)),
% 121.38/17.50 inference(forward_demodulation,[],[f13556,f7537])).
% 121.38/17.50 thf(f13560,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_4 | ~spl101_14 | ~spl101_15 | spl101_20 | ~spl101_22 | ~spl101_23)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f13559])).
% 121.38/17.50 thf(f13563,plain,(
% 121.38/17.50 ($true = $false) | (~spl101_4 | ~spl101_14 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_22 | ~spl101_23)),
% 121.38/17.50 inference(forward_demodulation,[],[f13560,f13541])).
% 121.38/17.50 thf(f13564,plain,(
% 121.38/17.50 $false | (~spl101_4 | ~spl101_14 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_22 | ~spl101_23)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f13563])).
% 121.38/17.50 thf(f13565,plain,(
% 121.38/17.50 ~spl101_4 | ~spl101_14 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_22 | ~spl101_23),
% 121.38/17.50 inference(avatar_contradiction_clause,[],[f13564])).
% 121.38/17.50 thf(f13574,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK17 @ sK2)))) | (~spl101_14 | ~spl101_15 | spl101_20)),
% 121.38/17.50 inference(forward_subsumption_resolution,[],[f11470,f7458])).
% 121.38/17.50 thf(f13586,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_14 | ~spl101_15 | spl101_20 | ~spl101_22)),
% 121.38/17.50 inference(forward_demodulation,[],[f13574,f7533])).
% 121.38/17.50 thf(f13587,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK16 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK15 @ sK2)))) | (~spl101_14 | ~spl101_15 | spl101_20 | ~spl101_22)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f13586])).
% 121.38/17.50 thf(f13593,plain,(
% 121.38/17.50 spl101_21 | spl101_23 | ~spl101_14 | ~spl101_15 | spl101_20 | ~spl101_22),
% 121.38/17.50 inference(avatar_split_clause,[],[f13587,f7531,f7457,f7282,f7215,f7535,f7527])).
% 121.38/17.50 thf(f13600,plain,(
% 121.38/17.50 ($true = $false) | ~spl101_20),
% 121.38/17.50 inference(forward_demodulation,[],[f7459,f7110])).
% 121.38/17.50 thf(f13601,plain,(
% 121.38/17.50 $false | ~spl101_20),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f13600])).
% 121.38/17.50 thf(f13602,plain,(
% 121.38/17.50 ~spl101_20),
% 121.38/17.50 inference(avatar_contradiction_clause,[],[f13601])).
% 121.38/17.50 thf(f13603,plain,(
% 121.38/17.50 ($true = $false) | (~spl101_25 | ~spl101_34)),
% 121.38/17.50 inference(forward_demodulation,[],[f8432,f10618])).
% 121.38/17.50 thf(f13604,plain,(
% 121.38/17.50 $false | (~spl101_25 | ~spl101_34)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f13603])).
% 121.38/17.50 thf(f13605,plain,(
% 121.38/17.50 ~spl101_25 | ~spl101_34),
% 121.38/17.50 inference(avatar_contradiction_clause,[],[f13604])).
% 121.38/17.50 thf(f13611,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_1 | ~spl101_6 | ~spl101_34)),
% 121.38/17.50 inference(forward_demodulation,[],[f8525,f10618])).
% 121.38/17.50 thf(f13612,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl101_1 | ~spl101_6 | ~spl101_34)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f13611])).
% 121.38/17.50 thf(f13615,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ~spl101_6),
% 121.38/17.50 inference(forward_demodulation,[],[f8426,f7110])).
% 121.38/17.50 thf(f13616,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK11 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ~spl101_6),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f13615])).
% 121.38/17.50 thf(f13617,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_3 | ~spl101_12 | ~spl101_36)),
% 121.38/17.50 inference(forward_demodulation,[],[f9154,f11173])).
% 121.38/17.50 thf(f13618,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_3 | ~spl101_12 | ~spl101_36)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f13617])).
% 121.38/17.50 thf(f13623,plain,(
% 121.38/17.50 ($true = $false) | ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | (~spl101_1 | ~spl101_6 | ~spl101_34)),
% 121.38/17.50 inference(forward_demodulation,[],[f13612,f7110])).
% 121.38/17.50 thf(f13624,plain,(
% 121.38/17.50 ($false = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | (~spl101_1 | ~spl101_6 | ~spl101_34)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f13623])).
% 121.38/17.50 thf(f13627,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | (~spl101_6 | ~spl101_34)),
% 121.38/17.50 inference(forward_demodulation,[],[f13616,f10618])).
% 121.38/17.50 thf(f13628,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK13 @ sK2)))) | ($true = ((rel_s4 @ sK2 @ (sK12 @ sK2)))) | (~spl101_6 | ~spl101_34)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f13627])).
% 121.38/17.50 thf(f13629,plain,(
% 121.38/17.50 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_3 | ~spl101_12 | ~spl101_36)),
% 121.38/17.50 inference(forward_demodulation,[],[f13618,f7110])).
% 121.38/17.50 thf(f13630,plain,(
% 121.38/17.50 ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | ($false = ((rel_s4 @ sK2 @ (sK4 @ sK2)))) | (~spl101_3 | ~spl101_12 | ~spl101_36)),
% 121.38/17.50 inference(trivial_inequality_removal,[],[f13629])).
% 121.38/17.50 thf(f13634,plain,(
% 121.38/17.50 spl101_26 | spl101_29 | ~spl101_1 | ~spl101_6 | ~spl101_34),
% 121.38/17.51 inference(avatar_split_clause,[],[f13624,f10616,f7129,f7112,f8951,f8434])).
% 121.38/17.51 thf(f13636,plain,(
% 121.38/17.51 spl101_27 | spl101_26 | ~spl101_6 | ~spl101_34),
% 121.38/17.51 inference(avatar_split_clause,[],[f13628,f10616,f7129,f8434,f8438])).
% 121.38/17.51 thf(f13637,plain,(
% 121.38/17.51 ($true = $false) | ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | (~spl101_3 | ~spl101_12 | ~spl101_32 | ~spl101_36)),
% 121.38/17.51 inference(forward_demodulation,[],[f13630,f9064])).
% 121.38/17.51 thf(f13638,plain,(
% 121.38/17.51 ($true = ((rel_s4 @ sK2 @ (sK5 @ sK2)))) | (~spl101_3 | ~spl101_12 | ~spl101_32 | ~spl101_36)),
% 121.38/17.51 inference(trivial_inequality_removal,[],[f13637])).
% 121.38/17.51 thf(f13641,plain,(
% 121.38/17.51 spl101_31 | ~spl101_3 | ~spl101_12 | ~spl101_32 | ~spl101_36),
% 121.38/17.51 inference(avatar_split_clause,[],[f13638,f11171,f9062,f7177,f7118,f9058])).
% 121.38/17.51 cnf(s3, plain, spl101_1 | spl101_2 | spl101_3 | spl101_4, inference(sat_conversion,[],[f7123])).
% 121.38/17.51 cnf(s5, plain, spl101_2 | spl101_3 | spl101_4 | spl101_5, inference(sat_conversion,[],[f7127])).
% 121.38/17.51 cnf(s7, plain, spl101_2 | spl101_3 | spl101_4 | spl101_6, inference(sat_conversion,[],[f7131])).
% 121.38/17.51 cnf(s9, plain, spl101_2 | spl101_3 | spl101_4 | spl101_7, inference(sat_conversion,[],[f7135])).
% 121.38/17.51 cnf(s11, plain, spl101_1 | spl101_3 | spl101_4 | spl101_8, inference(sat_conversion,[],[f7139])).
% 121.38/17.51 cnf(s13, plain, spl101_3 | spl101_4 | spl101_5 | spl101_8, inference(sat_conversion,[],[f7140])).
% 121.38/17.51 cnf(s15, plain, spl101_3 | spl101_4 | spl101_6 | spl101_8, inference(sat_conversion,[],[f7141])).
% 121.38/17.51 cnf(s17, plain, spl101_3 | spl101_4 | spl101_7 | spl101_8, inference(sat_conversion,[],[f7142])).
% 121.38/17.51 cnf(s19, plain, spl101_1 | spl101_3 | spl101_4 | spl101_9, inference(sat_conversion,[],[f7146])).
% 121.38/17.51 cnf(s21, plain, spl101_3 | spl101_4 | spl101_5 | spl101_9, inference(sat_conversion,[],[f7147])).
% 121.38/17.51 cnf(s23, plain, spl101_3 | spl101_4 | spl101_6 | spl101_9, inference(sat_conversion,[],[f7148])).
% 121.38/17.51 cnf(s25, plain, spl101_3 | spl101_4 | spl101_7 | spl101_9, inference(sat_conversion,[],[f7149])).
% 121.38/17.51 cnf(s27, plain, spl101_1 | spl101_3 | spl101_4 | spl101_10, inference(sat_conversion,[],[f7153])).
% 121.38/17.51 cnf(s29, plain, spl101_3 | spl101_4 | spl101_5 | spl101_10, inference(sat_conversion,[],[f7154])).
% 121.38/17.51 cnf(s31, plain, spl101_3 | spl101_4 | spl101_6 | spl101_10, inference(sat_conversion,[],[f7155])).
% 121.38/17.51 cnf(s33, plain, spl101_3 | spl101_4 | spl101_7 | spl101_10, inference(sat_conversion,[],[f7156])).
% 121.38/17.51 cnf(s35, plain, spl101_1 | spl101_2 | spl101_4 | spl101_11, inference(sat_conversion,[],[f7160])).
% 121.38/17.51 cnf(s37, plain, spl101_2 | spl101_4 | spl101_5 | spl101_11, inference(sat_conversion,[],[f7161])).
% 121.38/17.51 cnf(s39, plain, spl101_2 | spl101_4 | spl101_6 | spl101_11, inference(sat_conversion,[],[f7162])).
% 121.38/17.51 cnf(s41, plain, spl101_2 | spl101_4 | spl101_7 | spl101_11, inference(sat_conversion,[],[f7163])).
% 121.38/17.51 cnf(s43, plain, spl101_1 | spl101_4 | spl101_8 | spl101_11, inference(sat_conversion,[],[f7164])).
% 121.38/17.51 cnf(s45, plain, spl101_4 | spl101_5 | spl101_8 | spl101_11, inference(sat_conversion,[],[f7165])).
% 121.38/17.51 cnf(s47, plain, spl101_4 | spl101_6 | spl101_8 | spl101_11, inference(sat_conversion,[],[f7166])).
% 121.38/17.51 cnf(s49, plain, spl101_4 | spl101_7 | spl101_8 | spl101_11, inference(sat_conversion,[],[f7167])).
% 121.38/17.51 cnf(s51, plain, spl101_1 | spl101_4 | spl101_9 | spl101_11, inference(sat_conversion,[],[f7168])).
% 121.38/17.51 cnf(s53, plain, spl101_4 | spl101_5 | spl101_9 | spl101_11, inference(sat_conversion,[],[f7169])).
% 121.38/17.51 cnf(s55, plain, spl101_4 | spl101_6 | spl101_9 | spl101_11, inference(sat_conversion,[],[f7170])).
% 121.38/17.51 cnf(s57, plain, spl101_4 | spl101_7 | spl101_9 | spl101_11, inference(sat_conversion,[],[f7171])).
% 121.38/17.51 cnf(s59, plain, spl101_1 | spl101_4 | spl101_10 | spl101_11, inference(sat_conversion,[],[f7172])).
% 121.38/17.51 cnf(s61, plain, spl101_4 | spl101_5 | spl101_10 | spl101_11, inference(sat_conversion,[],[f7173])).
% 121.38/17.51 cnf(s63, plain, spl101_4 | spl101_6 | spl101_10 | spl101_11, inference(sat_conversion,[],[f7174])).
% 121.38/17.51 cnf(s65, plain, spl101_4 | spl101_7 | spl101_10 | spl101_11, inference(sat_conversion,[],[f7175])).
% 121.38/17.51 cnf(s67, plain, spl101_1 | spl101_2 | spl101_4 | spl101_12, inference(sat_conversion,[],[f7179])).
% 121.38/17.51 cnf(s69, plain, spl101_2 | spl101_4 | spl101_5 | spl101_12, inference(sat_conversion,[],[f7180])).
% 121.38/17.51 cnf(s71, plain, spl101_2 | spl101_4 | spl101_6 | spl101_12, inference(sat_conversion,[],[f7181])).
% 121.38/17.51 cnf(s73, plain, spl101_2 | spl101_4 | spl101_7 | spl101_12, inference(sat_conversion,[],[f7182])).
% 121.38/17.51 cnf(s75, plain, spl101_1 | spl101_4 | spl101_8 | spl101_12, inference(sat_conversion,[],[f7183])).
% 121.38/17.51 cnf(s77, plain, spl101_4 | spl101_5 | spl101_8 | spl101_12, inference(sat_conversion,[],[f7184])).
% 121.38/17.51 cnf(s79, plain, spl101_4 | spl101_6 | spl101_8 | spl101_12, inference(sat_conversion,[],[f7185])).
% 121.38/17.51 cnf(s81, plain, spl101_4 | spl101_7 | spl101_8 | spl101_12, inference(sat_conversion,[],[f7186])).
% 121.38/17.51 cnf(s83, plain, spl101_1 | spl101_4 | spl101_9 | spl101_12, inference(sat_conversion,[],[f7187])).
% 121.38/17.51 cnf(s85, plain, spl101_4 | spl101_5 | spl101_9 | spl101_12, inference(sat_conversion,[],[f7188])).
% 121.38/17.51 cnf(s87, plain, spl101_4 | spl101_6 | spl101_9 | spl101_12, inference(sat_conversion,[],[f7189])).
% 121.38/17.51 cnf(s89, plain, spl101_4 | spl101_7 | spl101_9 | spl101_12, inference(sat_conversion,[],[f7190])).
% 121.38/17.51 cnf(s91, plain, spl101_1 | spl101_4 | spl101_10 | spl101_12, inference(sat_conversion,[],[f7191])).
% 121.38/17.51 cnf(s93, plain, spl101_4 | spl101_5 | spl101_10 | spl101_12, inference(sat_conversion,[],[f7192])).
% 121.38/17.51 cnf(s95, plain, spl101_4 | spl101_6 | spl101_10 | spl101_12, inference(sat_conversion,[],[f7193])).
% 121.38/17.51 cnf(s97, plain, spl101_4 | spl101_7 | spl101_10 | spl101_12, inference(sat_conversion,[],[f7194])).
% 121.38/17.51 cnf(s99, plain, spl101_1 | spl101_2 | spl101_4 | spl101_13, inference(sat_conversion,[],[f7198])).
% 121.38/17.51 cnf(s101, plain, spl101_2 | spl101_4 | spl101_5 | spl101_13, inference(sat_conversion,[],[f7199])).
% 121.38/17.51 cnf(s103, plain, spl101_2 | spl101_4 | spl101_6 | spl101_13, inference(sat_conversion,[],[f7200])).
% 121.38/17.51 cnf(s105, plain, spl101_2 | spl101_4 | spl101_7 | spl101_13, inference(sat_conversion,[],[f7201])).
% 121.38/17.51 cnf(s107, plain, spl101_1 | spl101_4 | spl101_8 | spl101_13, inference(sat_conversion,[],[f7202])).
% 121.38/17.51 cnf(s109, plain, spl101_4 | spl101_5 | spl101_8 | spl101_13, inference(sat_conversion,[],[f7203])).
% 121.38/17.51 cnf(s111, plain, spl101_4 | spl101_6 | spl101_8 | spl101_13, inference(sat_conversion,[],[f7204])).
% 121.38/17.51 cnf(s113, plain, spl101_4 | spl101_7 | spl101_8 | spl101_13, inference(sat_conversion,[],[f7205])).
% 121.38/17.51 cnf(s115, plain, spl101_1 | spl101_4 | spl101_9 | spl101_13, inference(sat_conversion,[],[f7206])).
% 121.38/17.51 cnf(s117, plain, spl101_4 | spl101_5 | spl101_9 | spl101_13, inference(sat_conversion,[],[f7207])).
% 121.38/17.51 cnf(s119, plain, spl101_4 | spl101_6 | spl101_9 | spl101_13, inference(sat_conversion,[],[f7208])).
% 121.38/17.51 cnf(s121, plain, spl101_4 | spl101_7 | spl101_9 | spl101_13, inference(sat_conversion,[],[f7209])).
% 121.38/17.51 cnf(s123, plain, spl101_1 | spl101_4 | spl101_10 | spl101_13, inference(sat_conversion,[],[f7210])).
% 121.38/17.51 cnf(s125, plain, spl101_4 | spl101_5 | spl101_10 | spl101_13, inference(sat_conversion,[],[f7211])).
% 121.38/17.51 cnf(s127, plain, spl101_4 | spl101_6 | spl101_10 | spl101_13, inference(sat_conversion,[],[f7212])).
% 121.38/17.51 cnf(s129, plain, spl101_4 | spl101_7 | spl101_10 | spl101_13, inference(sat_conversion,[],[f7213])).
% 121.38/17.51 cnf(s131, plain, spl101_1 | spl101_2 | spl101_3 | spl101_14, inference(sat_conversion,[],[f7217])).
% 121.38/17.51 cnf(s133, plain, spl101_2 | spl101_3 | spl101_5 | spl101_14, inference(sat_conversion,[],[f7218])).
% 121.38/17.51 cnf(s135, plain, spl101_2 | spl101_3 | spl101_6 | spl101_14, inference(sat_conversion,[],[f7219])).
% 121.38/17.51 cnf(s137, plain, spl101_2 | spl101_3 | spl101_7 | spl101_14, inference(sat_conversion,[],[f7220])).
% 121.38/17.51 cnf(s139, plain, spl101_1 | spl101_3 | spl101_8 | spl101_14, inference(sat_conversion,[],[f7221])).
% 121.38/17.51 cnf(s141, plain, spl101_3 | spl101_5 | spl101_8 | spl101_14, inference(sat_conversion,[],[f7222])).
% 121.38/17.51 cnf(s143, plain, spl101_3 | spl101_6 | spl101_8 | spl101_14, inference(sat_conversion,[],[f7223])).
% 121.38/17.51 cnf(s145, plain, spl101_3 | spl101_7 | spl101_8 | spl101_14, inference(sat_conversion,[],[f7224])).
% 121.38/17.51 cnf(s147, plain, spl101_1 | spl101_3 | spl101_9 | spl101_14, inference(sat_conversion,[],[f7225])).
% 121.38/17.51 cnf(s149, plain, spl101_3 | spl101_5 | spl101_9 | spl101_14, inference(sat_conversion,[],[f7226])).
% 121.38/17.51 cnf(s151, plain, spl101_3 | spl101_6 | spl101_9 | spl101_14, inference(sat_conversion,[],[f7227])).
% 121.38/17.51 cnf(s153, plain, spl101_3 | spl101_7 | spl101_9 | spl101_14, inference(sat_conversion,[],[f7228])).
% 121.38/17.51 cnf(s155, plain, spl101_1 | spl101_3 | spl101_10 | spl101_14, inference(sat_conversion,[],[f7229])).
% 121.38/17.51 cnf(s157, plain, spl101_3 | spl101_5 | spl101_10 | spl101_14, inference(sat_conversion,[],[f7230])).
% 121.38/17.51 cnf(s159, plain, spl101_3 | spl101_6 | spl101_10 | spl101_14, inference(sat_conversion,[],[f7231])).
% 121.38/17.51 cnf(s161, plain, spl101_3 | spl101_7 | spl101_10 | spl101_14, inference(sat_conversion,[],[f7232])).
% 121.38/17.51 cnf(s163, plain, spl101_1 | spl101_2 | spl101_11 | spl101_14, inference(sat_conversion,[],[f7233])).
% 121.38/17.51 cnf(s165, plain, spl101_2 | spl101_5 | spl101_11 | spl101_14, inference(sat_conversion,[],[f7234])).
% 121.38/17.51 cnf(s167, plain, spl101_2 | spl101_6 | spl101_11 | spl101_14, inference(sat_conversion,[],[f7235])).
% 121.38/17.51 cnf(s169, plain, spl101_2 | spl101_7 | spl101_11 | spl101_14, inference(sat_conversion,[],[f7236])).
% 121.38/17.51 cnf(s171, plain, spl101_1 | spl101_8 | spl101_11 | spl101_14, inference(sat_conversion,[],[f7237])).
% 121.38/17.51 cnf(s173, plain, spl101_5 | spl101_8 | spl101_11 | spl101_14, inference(sat_conversion,[],[f7238])).
% 121.38/17.51 cnf(s175, plain, spl101_6 | spl101_8 | spl101_11 | spl101_14, inference(sat_conversion,[],[f7239])).
% 121.38/17.51 cnf(s177, plain, spl101_7 | spl101_8 | spl101_11 | spl101_14, inference(sat_conversion,[],[f7240])).
% 121.38/17.51 cnf(s179, plain, spl101_1 | spl101_9 | spl101_11 | spl101_14, inference(sat_conversion,[],[f7241])).
% 121.38/17.51 cnf(s181, plain, spl101_5 | spl101_9 | spl101_11 | spl101_14, inference(sat_conversion,[],[f7242])).
% 121.38/17.51 cnf(s183, plain, spl101_6 | spl101_9 | spl101_11 | spl101_14, inference(sat_conversion,[],[f7243])).
% 121.38/17.51 cnf(s185, plain, spl101_7 | spl101_9 | spl101_11 | spl101_14, inference(sat_conversion,[],[f7244])).
% 121.38/17.51 cnf(s187, plain, spl101_1 | spl101_10 | spl101_11 | spl101_14, inference(sat_conversion,[],[f7245])).
% 121.38/17.51 cnf(s189, plain, spl101_5 | spl101_10 | spl101_11 | spl101_14, inference(sat_conversion,[],[f7246])).
% 121.38/17.51 cnf(s191, plain, spl101_6 | spl101_10 | spl101_11 | spl101_14, inference(sat_conversion,[],[f7247])).
% 121.38/17.51 cnf(s193, plain, spl101_7 | spl101_10 | spl101_11 | spl101_14, inference(sat_conversion,[],[f7248])).
% 121.38/17.51 cnf(s195, plain, spl101_1 | spl101_2 | spl101_12 | spl101_14, inference(sat_conversion,[],[f7249])).
% 121.38/17.51 cnf(s197, plain, spl101_2 | spl101_5 | spl101_12 | spl101_14, inference(sat_conversion,[],[f7250])).
% 121.38/17.51 cnf(s199, plain, spl101_2 | spl101_6 | spl101_12 | spl101_14, inference(sat_conversion,[],[f7251])).
% 121.38/17.51 cnf(s201, plain, spl101_2 | spl101_7 | spl101_12 | spl101_14, inference(sat_conversion,[],[f7252])).
% 121.38/17.51 cnf(s203, plain, spl101_1 | spl101_8 | spl101_12 | spl101_14, inference(sat_conversion,[],[f7253])).
% 121.38/17.51 cnf(s205, plain, spl101_5 | spl101_8 | spl101_12 | spl101_14, inference(sat_conversion,[],[f7254])).
% 121.38/17.51 cnf(s207, plain, spl101_6 | spl101_8 | spl101_12 | spl101_14, inference(sat_conversion,[],[f7255])).
% 121.38/17.51 cnf(s209, plain, spl101_7 | spl101_8 | spl101_12 | spl101_14, inference(sat_conversion,[],[f7256])).
% 121.38/17.51 cnf(s211, plain, spl101_1 | spl101_9 | spl101_12 | spl101_14, inference(sat_conversion,[],[f7257])).
% 121.38/17.51 cnf(s213, plain, spl101_5 | spl101_9 | spl101_12 | spl101_14, inference(sat_conversion,[],[f7258])).
% 121.38/17.51 cnf(s215, plain, spl101_6 | spl101_9 | spl101_12 | spl101_14, inference(sat_conversion,[],[f7259])).
% 121.38/17.51 cnf(s217, plain, spl101_7 | spl101_9 | spl101_12 | spl101_14, inference(sat_conversion,[],[f7260])).
% 121.38/17.51 cnf(s219, plain, spl101_1 | spl101_10 | spl101_12 | spl101_14, inference(sat_conversion,[],[f7261])).
% 121.38/17.51 cnf(s221, plain, spl101_5 | spl101_10 | spl101_12 | spl101_14, inference(sat_conversion,[],[f7262])).
% 121.38/17.51 cnf(s223, plain, spl101_6 | spl101_10 | spl101_12 | spl101_14, inference(sat_conversion,[],[f7263])).
% 121.38/17.51 cnf(s225, plain, spl101_7 | spl101_10 | spl101_12 | spl101_14, inference(sat_conversion,[],[f7264])).
% 121.38/17.51 cnf(s227, plain, spl101_1 | spl101_2 | spl101_13 | spl101_14, inference(sat_conversion,[],[f7265])).
% 121.38/17.51 cnf(s229, plain, spl101_2 | spl101_5 | spl101_13 | spl101_14, inference(sat_conversion,[],[f7266])).
% 121.38/17.51 cnf(s231, plain, spl101_2 | spl101_6 | spl101_13 | spl101_14, inference(sat_conversion,[],[f7267])).
% 121.38/17.51 cnf(s233, plain, spl101_2 | spl101_7 | spl101_13 | spl101_14, inference(sat_conversion,[],[f7268])).
% 121.38/17.51 cnf(s235, plain, spl101_1 | spl101_8 | spl101_13 | spl101_14, inference(sat_conversion,[],[f7269])).
% 121.38/17.51 cnf(s237, plain, spl101_5 | spl101_8 | spl101_13 | spl101_14, inference(sat_conversion,[],[f7270])).
% 121.38/17.51 cnf(s239, plain, spl101_6 | spl101_8 | spl101_13 | spl101_14, inference(sat_conversion,[],[f7271])).
% 121.38/17.51 cnf(s241, plain, spl101_7 | spl101_8 | spl101_13 | spl101_14, inference(sat_conversion,[],[f7272])).
% 121.38/17.51 cnf(s243, plain, spl101_1 | spl101_9 | spl101_13 | spl101_14, inference(sat_conversion,[],[f7273])).
% 121.38/17.51 cnf(s245, plain, spl101_5 | spl101_9 | spl101_13 | spl101_14, inference(sat_conversion,[],[f7274])).
% 121.38/17.51 cnf(s247, plain, spl101_6 | spl101_9 | spl101_13 | spl101_14, inference(sat_conversion,[],[f7275])).
% 121.38/17.51 cnf(s249, plain, spl101_7 | spl101_9 | spl101_13 | spl101_14, inference(sat_conversion,[],[f7276])).
% 121.38/17.51 cnf(s251, plain, spl101_1 | spl101_10 | spl101_13 | spl101_14, inference(sat_conversion,[],[f7277])).
% 121.38/17.51 cnf(s253, plain, spl101_5 | spl101_10 | spl101_13 | spl101_14, inference(sat_conversion,[],[f7278])).
% 121.38/17.51 cnf(s255, plain, spl101_6 | spl101_10 | spl101_13 | spl101_14, inference(sat_conversion,[],[f7279])).
% 121.38/17.51 cnf(s257, plain, spl101_7 | spl101_10 | spl101_13 | spl101_14, inference(sat_conversion,[],[f7280])).
% 121.38/17.51 cnf(s259, plain, spl101_1 | spl101_2 | spl101_3 | spl101_15, inference(sat_conversion,[],[f7284])).
% 121.38/17.51 cnf(s261, plain, spl101_2 | spl101_3 | spl101_5 | spl101_15, inference(sat_conversion,[],[f7285])).
% 121.38/17.51 cnf(s263, plain, spl101_2 | spl101_3 | spl101_6 | spl101_15, inference(sat_conversion,[],[f7286])).
% 121.38/17.51 cnf(s265, plain, spl101_2 | spl101_3 | spl101_7 | spl101_15, inference(sat_conversion,[],[f7287])).
% 121.38/17.51 cnf(s267, plain, spl101_1 | spl101_3 | spl101_8 | spl101_15, inference(sat_conversion,[],[f7288])).
% 121.38/17.51 cnf(s269, plain, spl101_3 | spl101_5 | spl101_8 | spl101_15, inference(sat_conversion,[],[f7289])).
% 121.38/17.51 cnf(s271, plain, spl101_3 | spl101_6 | spl101_8 | spl101_15, inference(sat_conversion,[],[f7290])).
% 121.38/17.51 cnf(s273, plain, spl101_3 | spl101_7 | spl101_8 | spl101_15, inference(sat_conversion,[],[f7291])).
% 121.38/17.51 cnf(s275, plain, spl101_1 | spl101_3 | spl101_9 | spl101_15, inference(sat_conversion,[],[f7292])).
% 121.38/17.51 cnf(s277, plain, spl101_3 | spl101_5 | spl101_9 | spl101_15, inference(sat_conversion,[],[f7293])).
% 121.38/17.51 cnf(s279, plain, spl101_3 | spl101_6 | spl101_9 | spl101_15, inference(sat_conversion,[],[f7294])).
% 121.38/17.51 cnf(s281, plain, spl101_3 | spl101_7 | spl101_9 | spl101_15, inference(sat_conversion,[],[f7295])).
% 121.38/17.51 cnf(s283, plain, spl101_1 | spl101_3 | spl101_10 | spl101_15, inference(sat_conversion,[],[f7296])).
% 121.38/17.51 cnf(s285, plain, spl101_3 | spl101_5 | spl101_10 | spl101_15, inference(sat_conversion,[],[f7297])).
% 121.38/17.51 cnf(s287, plain, spl101_3 | spl101_6 | spl101_10 | spl101_15, inference(sat_conversion,[],[f7298])).
% 121.38/17.51 cnf(s289, plain, spl101_3 | spl101_7 | spl101_10 | spl101_15, inference(sat_conversion,[],[f7299])).
% 121.38/17.51 cnf(s291, plain, spl101_1 | spl101_2 | spl101_11 | spl101_15, inference(sat_conversion,[],[f7300])).
% 121.38/17.51 cnf(s293, plain, spl101_2 | spl101_5 | spl101_11 | spl101_15, inference(sat_conversion,[],[f7301])).
% 121.38/17.51 cnf(s295, plain, spl101_2 | spl101_6 | spl101_11 | spl101_15, inference(sat_conversion,[],[f7302])).
% 121.38/17.51 cnf(s297, plain, spl101_2 | spl101_7 | spl101_11 | spl101_15, inference(sat_conversion,[],[f7303])).
% 121.38/17.51 cnf(s299, plain, spl101_1 | spl101_8 | spl101_11 | spl101_15, inference(sat_conversion,[],[f7304])).
% 121.38/17.51 cnf(s301, plain, spl101_5 | spl101_8 | spl101_11 | spl101_15, inference(sat_conversion,[],[f7305])).
% 121.38/17.51 cnf(s303, plain, spl101_6 | spl101_8 | spl101_11 | spl101_15, inference(sat_conversion,[],[f7306])).
% 121.38/17.51 cnf(s305, plain, spl101_7 | spl101_8 | spl101_11 | spl101_15, inference(sat_conversion,[],[f7307])).
% 121.38/17.51 cnf(s307, plain, spl101_1 | spl101_9 | spl101_11 | spl101_15, inference(sat_conversion,[],[f7308])).
% 121.38/17.51 cnf(s309, plain, spl101_5 | spl101_9 | spl101_11 | spl101_15, inference(sat_conversion,[],[f7309])).
% 121.38/17.51 cnf(s311, plain, spl101_6 | spl101_9 | spl101_11 | spl101_15, inference(sat_conversion,[],[f7310])).
% 121.38/17.51 cnf(s313, plain, spl101_7 | spl101_9 | spl101_11 | spl101_15, inference(sat_conversion,[],[f7311])).
% 121.38/17.51 cnf(s315, plain, spl101_1 | spl101_10 | spl101_11 | spl101_15, inference(sat_conversion,[],[f7312])).
% 121.38/17.51 cnf(s317, plain, spl101_5 | spl101_10 | spl101_11 | spl101_15, inference(sat_conversion,[],[f7313])).
% 121.38/17.51 cnf(s319, plain, spl101_6 | spl101_10 | spl101_11 | spl101_15, inference(sat_conversion,[],[f7314])).
% 121.38/17.51 cnf(s321, plain, spl101_7 | spl101_10 | spl101_11 | spl101_15, inference(sat_conversion,[],[f7315])).
% 121.38/17.51 cnf(s323, plain, spl101_1 | spl101_2 | spl101_12 | spl101_15, inference(sat_conversion,[],[f7316])).
% 121.38/17.51 cnf(s325, plain, spl101_2 | spl101_5 | spl101_12 | spl101_15, inference(sat_conversion,[],[f7317])).
% 121.38/17.51 cnf(s327, plain, spl101_2 | spl101_6 | spl101_12 | spl101_15, inference(sat_conversion,[],[f7318])).
% 121.38/17.51 cnf(s329, plain, spl101_2 | spl101_7 | spl101_12 | spl101_15, inference(sat_conversion,[],[f7319])).
% 121.38/17.51 cnf(s331, plain, spl101_1 | spl101_8 | spl101_12 | spl101_15, inference(sat_conversion,[],[f7320])).
% 121.38/17.51 cnf(s333, plain, spl101_5 | spl101_8 | spl101_12 | spl101_15, inference(sat_conversion,[],[f7321])).
% 121.38/17.51 cnf(s335, plain, spl101_6 | spl101_8 | spl101_12 | spl101_15, inference(sat_conversion,[],[f7322])).
% 121.38/17.51 cnf(s337, plain, spl101_7 | spl101_8 | spl101_12 | spl101_15, inference(sat_conversion,[],[f7323])).
% 121.38/17.51 cnf(s339, plain, spl101_1 | spl101_9 | spl101_12 | spl101_15, inference(sat_conversion,[],[f7324])).
% 121.38/17.51 cnf(s341, plain, spl101_5 | spl101_9 | spl101_12 | spl101_15, inference(sat_conversion,[],[f7325])).
% 121.38/17.51 cnf(s343, plain, spl101_6 | spl101_9 | spl101_12 | spl101_15, inference(sat_conversion,[],[f7326])).
% 121.38/17.51 cnf(s345, plain, spl101_7 | spl101_9 | spl101_12 | spl101_15, inference(sat_conversion,[],[f7327])).
% 121.38/17.51 cnf(s347, plain, spl101_1 | spl101_10 | spl101_12 | spl101_15, inference(sat_conversion,[],[f7328])).
% 121.38/17.51 cnf(s349, plain, spl101_5 | spl101_10 | spl101_12 | spl101_15, inference(sat_conversion,[],[f7329])).
% 121.38/17.51 cnf(s351, plain, spl101_6 | spl101_10 | spl101_12 | spl101_15, inference(sat_conversion,[],[f7330])).
% 121.38/17.51 cnf(s353, plain, spl101_7 | spl101_10 | spl101_12 | spl101_15, inference(sat_conversion,[],[f7331])).
% 121.38/17.51 cnf(s355, plain, spl101_1 | spl101_2 | spl101_13 | spl101_15, inference(sat_conversion,[],[f7332])).
% 121.38/17.51 cnf(s357, plain, spl101_2 | spl101_5 | spl101_13 | spl101_15, inference(sat_conversion,[],[f7333])).
% 121.38/17.51 cnf(s359, plain, spl101_2 | spl101_6 | spl101_13 | spl101_15, inference(sat_conversion,[],[f7334])).
% 121.38/17.51 cnf(s361, plain, spl101_2 | spl101_7 | spl101_13 | spl101_15, inference(sat_conversion,[],[f7335])).
% 121.38/17.51 cnf(s363, plain, spl101_1 | spl101_8 | spl101_13 | spl101_15, inference(sat_conversion,[],[f7336])).
% 121.38/17.51 cnf(s365, plain, spl101_5 | spl101_8 | spl101_13 | spl101_15, inference(sat_conversion,[],[f7337])).
% 121.38/17.51 cnf(s367, plain, spl101_6 | spl101_8 | spl101_13 | spl101_15, inference(sat_conversion,[],[f7338])).
% 121.38/17.51 cnf(s369, plain, spl101_7 | spl101_8 | spl101_13 | spl101_15, inference(sat_conversion,[],[f7339])).
% 121.38/17.51 cnf(s371, plain, spl101_1 | spl101_9 | spl101_13 | spl101_15, inference(sat_conversion,[],[f7340])).
% 121.38/17.51 cnf(s373, plain, spl101_5 | spl101_9 | spl101_13 | spl101_15, inference(sat_conversion,[],[f7341])).
% 121.38/17.51 cnf(s375, plain, spl101_6 | spl101_9 | spl101_13 | spl101_15, inference(sat_conversion,[],[f7342])).
% 121.38/17.51 cnf(s377, plain, spl101_7 | spl101_9 | spl101_13 | spl101_15, inference(sat_conversion,[],[f7343])).
% 121.38/17.51 cnf(s379, plain, spl101_1 | spl101_10 | spl101_13 | spl101_15, inference(sat_conversion,[],[f7344])).
% 121.38/17.51 cnf(s381, plain, spl101_5 | spl101_10 | spl101_13 | spl101_15, inference(sat_conversion,[],[f7345])).
% 121.38/17.51 cnf(s383, plain, spl101_6 | spl101_10 | spl101_13 | spl101_15, inference(sat_conversion,[],[f7346])).
% 121.38/17.51 cnf(s385, plain, spl101_7 | spl101_10 | spl101_13 | spl101_15, inference(sat_conversion,[],[f7347])).
% 121.38/17.51 cnf(s387, plain, spl101_1 | spl101_2 | spl101_3 | spl101_16, inference(sat_conversion,[],[f7351])).
% 121.38/17.51 cnf(s389, plain, spl101_2 | spl101_3 | spl101_5 | spl101_16, inference(sat_conversion,[],[f7352])).
% 121.38/17.51 cnf(s391, plain, spl101_2 | spl101_3 | spl101_6 | spl101_16, inference(sat_conversion,[],[f7353])).
% 121.38/17.51 cnf(s393, plain, spl101_2 | spl101_3 | spl101_7 | spl101_16, inference(sat_conversion,[],[f7354])).
% 121.38/17.51 cnf(s395, plain, spl101_1 | spl101_3 | spl101_8 | spl101_16, inference(sat_conversion,[],[f7355])).
% 121.38/17.51 cnf(s397, plain, spl101_3 | spl101_5 | spl101_8 | spl101_16, inference(sat_conversion,[],[f7356])).
% 121.38/17.51 cnf(s399, plain, spl101_3 | spl101_6 | spl101_8 | spl101_16, inference(sat_conversion,[],[f7357])).
% 121.38/17.51 cnf(s401, plain, spl101_3 | spl101_7 | spl101_8 | spl101_16, inference(sat_conversion,[],[f7358])).
% 121.38/17.51 cnf(s403, plain, spl101_1 | spl101_3 | spl101_9 | spl101_16, inference(sat_conversion,[],[f7359])).
% 121.38/17.51 cnf(s405, plain, spl101_3 | spl101_5 | spl101_9 | spl101_16, inference(sat_conversion,[],[f7360])).
% 121.38/17.51 cnf(s407, plain, spl101_3 | spl101_6 | spl101_9 | spl101_16, inference(sat_conversion,[],[f7361])).
% 121.38/17.51 cnf(s409, plain, spl101_3 | spl101_7 | spl101_9 | spl101_16, inference(sat_conversion,[],[f7362])).
% 121.38/17.51 cnf(s411, plain, spl101_1 | spl101_3 | spl101_10 | spl101_16, inference(sat_conversion,[],[f7363])).
% 121.38/17.51 cnf(s413, plain, spl101_3 | spl101_5 | spl101_10 | spl101_16, inference(sat_conversion,[],[f7364])).
% 121.38/17.51 cnf(s415, plain, spl101_3 | spl101_6 | spl101_10 | spl101_16, inference(sat_conversion,[],[f7365])).
% 121.38/17.51 cnf(s417, plain, spl101_3 | spl101_7 | spl101_10 | spl101_16, inference(sat_conversion,[],[f7366])).
% 121.38/17.51 cnf(s419, plain, spl101_1 | spl101_2 | spl101_11 | spl101_16, inference(sat_conversion,[],[f7367])).
% 121.38/17.51 cnf(s421, plain, spl101_2 | spl101_5 | spl101_11 | spl101_16, inference(sat_conversion,[],[f7368])).
% 121.38/17.51 cnf(s423, plain, spl101_2 | spl101_6 | spl101_11 | spl101_16, inference(sat_conversion,[],[f7369])).
% 121.38/17.51 cnf(s425, plain, spl101_2 | spl101_7 | spl101_11 | spl101_16, inference(sat_conversion,[],[f7370])).
% 121.38/17.51 cnf(s427, plain, spl101_1 | spl101_8 | spl101_11 | spl101_16, inference(sat_conversion,[],[f7371])).
% 121.38/17.51 cnf(s429, plain, spl101_5 | spl101_8 | spl101_11 | spl101_16, inference(sat_conversion,[],[f7372])).
% 121.38/17.51 cnf(s431, plain, spl101_6 | spl101_8 | spl101_11 | spl101_16, inference(sat_conversion,[],[f7373])).
% 121.38/17.51 cnf(s433, plain, spl101_7 | spl101_8 | spl101_11 | spl101_16, inference(sat_conversion,[],[f7374])).
% 121.38/17.51 cnf(s435, plain, spl101_1 | spl101_9 | spl101_11 | spl101_16, inference(sat_conversion,[],[f7375])).
% 121.38/17.51 cnf(s437, plain, spl101_5 | spl101_9 | spl101_11 | spl101_16, inference(sat_conversion,[],[f7376])).
% 121.38/17.51 cnf(s439, plain, spl101_6 | spl101_9 | spl101_11 | spl101_16, inference(sat_conversion,[],[f7377])).
% 121.38/17.51 cnf(s441, plain, spl101_7 | spl101_9 | spl101_11 | spl101_16, inference(sat_conversion,[],[f7378])).
% 121.38/17.51 cnf(s443, plain, spl101_1 | spl101_10 | spl101_11 | spl101_16, inference(sat_conversion,[],[f7379])).
% 121.38/17.51 cnf(s445, plain, spl101_5 | spl101_10 | spl101_11 | spl101_16, inference(sat_conversion,[],[f7380])).
% 121.38/17.51 cnf(s447, plain, spl101_6 | spl101_10 | spl101_11 | spl101_16, inference(sat_conversion,[],[f7381])).
% 121.38/17.51 cnf(s449, plain, spl101_7 | spl101_10 | spl101_11 | spl101_16, inference(sat_conversion,[],[f7382])).
% 121.38/17.51 cnf(s451, plain, spl101_1 | spl101_2 | spl101_12 | spl101_16, inference(sat_conversion,[],[f7383])).
% 121.38/17.51 cnf(s453, plain, spl101_2 | spl101_5 | spl101_12 | spl101_16, inference(sat_conversion,[],[f7384])).
% 121.38/17.51 cnf(s455, plain, spl101_2 | spl101_6 | spl101_12 | spl101_16, inference(sat_conversion,[],[f7385])).
% 121.38/17.51 cnf(s457, plain, spl101_2 | spl101_7 | spl101_12 | spl101_16, inference(sat_conversion,[],[f7386])).
% 121.38/17.51 cnf(s459, plain, spl101_1 | spl101_8 | spl101_12 | spl101_16, inference(sat_conversion,[],[f7387])).
% 121.38/17.51 cnf(s461, plain, spl101_5 | spl101_8 | spl101_12 | spl101_16, inference(sat_conversion,[],[f7388])).
% 121.38/17.51 cnf(s463, plain, spl101_6 | spl101_8 | spl101_12 | spl101_16, inference(sat_conversion,[],[f7389])).
% 121.38/17.51 cnf(s465, plain, spl101_7 | spl101_8 | spl101_12 | spl101_16, inference(sat_conversion,[],[f7390])).
% 121.38/17.51 cnf(s467, plain, spl101_1 | spl101_9 | spl101_12 | spl101_16, inference(sat_conversion,[],[f7391])).
% 121.38/17.51 cnf(s469, plain, spl101_5 | spl101_9 | spl101_12 | spl101_16, inference(sat_conversion,[],[f7392])).
% 121.38/17.51 cnf(s471, plain, spl101_6 | spl101_9 | spl101_12 | spl101_16, inference(sat_conversion,[],[f7393])).
% 121.38/17.51 cnf(s473, plain, spl101_7 | spl101_9 | spl101_12 | spl101_16, inference(sat_conversion,[],[f7394])).
% 121.38/17.51 cnf(s475, plain, spl101_1 | spl101_10 | spl101_12 | spl101_16, inference(sat_conversion,[],[f7395])).
% 121.38/17.51 cnf(s477, plain, spl101_5 | spl101_10 | spl101_12 | spl101_16, inference(sat_conversion,[],[f7396])).
% 121.38/17.51 cnf(s479, plain, spl101_6 | spl101_10 | spl101_12 | spl101_16, inference(sat_conversion,[],[f7397])).
% 121.38/17.51 cnf(s481, plain, spl101_7 | spl101_10 | spl101_12 | spl101_16, inference(sat_conversion,[],[f7398])).
% 121.38/17.51 cnf(s483, plain, spl101_1 | spl101_2 | spl101_13 | spl101_16, inference(sat_conversion,[],[f7399])).
% 121.38/17.51 cnf(s485, plain, spl101_2 | spl101_5 | spl101_13 | spl101_16, inference(sat_conversion,[],[f7400])).
% 121.38/17.51 cnf(s487, plain, spl101_2 | spl101_6 | spl101_13 | spl101_16, inference(sat_conversion,[],[f7401])).
% 121.38/17.51 cnf(s489, plain, spl101_2 | spl101_7 | spl101_13 | spl101_16, inference(sat_conversion,[],[f7402])).
% 121.38/17.51 cnf(s491, plain, spl101_1 | spl101_8 | spl101_13 | spl101_16, inference(sat_conversion,[],[f7403])).
% 121.38/17.51 cnf(s493, plain, spl101_5 | spl101_8 | spl101_13 | spl101_16, inference(sat_conversion,[],[f7404])).
% 121.38/17.51 cnf(s495, plain, spl101_6 | spl101_8 | spl101_13 | spl101_16, inference(sat_conversion,[],[f7405])).
% 121.38/17.51 cnf(s497, plain, spl101_7 | spl101_8 | spl101_13 | spl101_16, inference(sat_conversion,[],[f7406])).
% 121.38/17.51 cnf(s499, plain, spl101_1 | spl101_9 | spl101_13 | spl101_16, inference(sat_conversion,[],[f7407])).
% 121.38/17.51 cnf(s501, plain, spl101_5 | spl101_9 | spl101_13 | spl101_16, inference(sat_conversion,[],[f7408])).
% 121.38/17.51 cnf(s503, plain, spl101_6 | spl101_9 | spl101_13 | spl101_16, inference(sat_conversion,[],[f7409])).
% 121.38/17.51 cnf(s505, plain, spl101_7 | spl101_9 | spl101_13 | spl101_16, inference(sat_conversion,[],[f7410])).
% 121.38/17.51 cnf(s507, plain, spl101_1 | spl101_10 | spl101_13 | spl101_16, inference(sat_conversion,[],[f7411])).
% 121.38/17.51 cnf(s509, plain, spl101_5 | spl101_10 | spl101_13 | spl101_16, inference(sat_conversion,[],[f7412])).
% 121.38/17.51 cnf(s511, plain, spl101_6 | spl101_10 | spl101_13 | spl101_16, inference(sat_conversion,[],[f7413])).
% 121.38/17.51 cnf(s513, plain, spl101_7 | spl101_10 | spl101_13 | spl101_16, inference(sat_conversion,[],[f7414])).
% 121.38/17.51 cnf(s891, plain, ~spl101_9 | spl101_17 | spl101_18 | spl101_19 | spl101_20, inference(sat_conversion,[],[f7461])).
% 121.38/17.51 cnf(s1013, plain, ~spl101_9 | ~spl101_10 | ~spl101_17 | spl101_18 | spl101_19 | spl101_20, inference(sat_conversion,[],[f7800])).
% 121.38/17.51 cnf(s1103, plain, ~spl101_8 | ~spl101_9 | ~spl101_10 | ~spl101_17 | ~spl101_18 | spl101_19 | spl101_20, inference(sat_conversion,[],[f8103])).
% 121.38/17.51 cnf(s1129, plain, ~spl101_4 | ~spl101_15 | spl101_20 | spl101_21 | spl101_22 | ~spl101_23, inference(sat_conversion,[],[f8277])).
% 121.38/17.51 cnf(s1139, plain, ~spl101_15 | spl101_20 | spl101_21 | spl101_22 | spl101_23, inference(sat_conversion,[],[f8290])).
% 121.38/17.51 cnf(s1154, plain, ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_21 | spl101_22 | spl101_23, inference(sat_conversion,[],[f8358])).
% 121.38/17.51 cnf(s1285, plain, ~spl101_1 | ~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_25 | spl101_26 | ~spl101_27, inference(sat_conversion,[],[f8923])).
% 121.38/17.51 cnf(s1293, plain, ~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_25 | spl101_26 | spl101_27, inference(sat_conversion,[],[f8948])).
% 121.38/17.51 cnf(s1309, plain, ~spl101_26 | ~spl101_28, inference(sat_conversion,[],[f8966])).
% 121.38/17.51 cnf(s1353, plain, ~spl101_12 | spl101_20 | spl101_30 | spl101_31 | spl101_32, inference(sat_conversion,[],[f9066])).
% 121.38/17.51 cnf(s1406, plain, ~spl101_11 | ~spl101_12 | spl101_20 | spl101_30 | ~spl101_31 | spl101_32, inference(sat_conversion,[],[f9250])).
% 121.38/17.51 cnf(s1452, plain, ~spl101_8 | ~spl101_9 | spl101_17 | ~spl101_18 | spl101_19 | spl101_20, inference(sat_conversion,[],[f9472])).
% 121.38/17.51 cnf(s1538, plain, ~spl101_2 | ~spl101_8 | ~spl101_9 | ~spl101_10 | ~spl101_17 | ~spl101_18 | ~spl101_19 | spl101_20, inference(sat_conversion,[],[f9864])).
% 121.38/17.51 cnf(s1578, plain, ~spl101_14 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_21 | ~spl101_22 | spl101_23, inference(sat_conversion,[],[f10182])).
% 121.38/17.51 cnf(s1580, plain, ~spl101_27 | ~spl101_29, inference(sat_conversion,[],[f10185])).
% 121.38/17.51 cnf(s1650, plain, ~spl101_1 | ~spl101_5 | ~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_25 | ~spl101_27 | spl101_28, inference(sat_conversion,[],[f10611])).
% 121.38/17.51 cnf(s1663, plain, ~spl101_5 | ~spl101_6 | ~spl101_7 | spl101_20 | ~spl101_26 | spl101_27 | spl101_34, inference(sat_conversion,[],[f10640])).
% 121.38/17.51 cnf(s1665, plain, ~spl101_5 | ~spl101_6 | spl101_20 | spl101_25 | ~spl101_26 | spl101_27, inference(sat_conversion,[],[f10641])).
% 121.38/17.51 cnf(s1669, plain, ~spl101_1 | ~spl101_5 | ~spl101_6 | spl101_20 | spl101_25 | ~spl101_26 | spl101_29, inference(sat_conversion,[],[f10643])).
% 121.38/17.51 cnf(s1676, plain, spl101_25 | spl101_34, inference(sat_conversion,[],[f10646])).
% 121.38/17.51 cnf(s1741, plain, ~spl101_32 | ~spl101_33, inference(sat_conversion,[],[f11017])).
% 121.38/17.51 cnf(s1747, plain, ~spl101_11 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30 | ~spl101_31 | spl101_32, inference(sat_conversion,[],[f11033])).
% 121.38/17.51 cnf(s1768, plain, ~spl101_3 | ~spl101_11 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30 | ~spl101_31 | ~spl101_32, inference(sat_conversion,[],[f11126])).
% 121.38/17.51 cnf(s1772, plain, ~spl101_3 | ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30 | spl101_31 | ~spl101_32, inference(sat_conversion,[],[f11141])).
% 121.38/17.51 cnf(s1792, plain, ~spl101_12 | ~spl101_13 | spl101_20 | ~spl101_30 | spl101_31 | spl101_32, inference(sat_conversion,[],[f11165])).
% 121.38/17.51 cnf(s1821, plain, ~spl101_3 | ~spl101_11 | ~spl101_12 | spl101_20 | spl101_30 | spl101_33 | spl101_35, inference(sat_conversion,[],[f11187])).
% 121.38/17.51 cnf(s1830, plain, spl101_30 | spl101_36, inference(sat_conversion,[],[f11192])).
% 121.38/17.51 cnf(s1837, plain, ~spl101_31 | ~spl101_35, inference(sat_conversion,[],[f11204])).
% 121.38/17.51 cnf(s1930, plain, ~spl101_2 | ~spl101_8 | ~spl101_9 | spl101_17 | ~spl101_18 | ~spl101_19 | spl101_20, inference(sat_conversion,[],[f11674])).
% 121.38/17.51 cnf(s1946, plain, ~spl101_2 | ~spl101_9 | spl101_17 | spl101_18 | ~spl101_19 | spl101_20, inference(sat_conversion,[],[f11712])).
% 121.38/17.51 cnf(s1950, plain, ~spl101_2 | ~spl101_9 | ~spl101_10 | spl101_18 | ~spl101_19 | spl101_20 | spl101_38, inference(sat_conversion,[],[f11718])).
% 121.38/17.51 cnf(s1961, plain, ~spl101_17 | ~spl101_38, inference(sat_conversion,[],[f11732])).
% 121.38/17.51 cnf(s2005, plain, ~spl101_4 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_21 | spl101_22 | ~spl101_23, inference(sat_conversion,[],[f11955])).
% 121.38/17.51 cnf(s2724, plain, ~spl101_4 | ~spl101_14 | ~spl101_15 | ~spl101_16 | spl101_20 | ~spl101_22 | ~spl101_23, inference(sat_conversion,[],[f13565])).
% 121.38/17.51 cnf(s2744, plain, ~spl101_14 | ~spl101_15 | spl101_20 | spl101_21 | ~spl101_22 | spl101_23, inference(sat_conversion,[],[f13593])).
% 121.38/17.51 cnf(s2762, plain, ~spl101_20, inference(sat_conversion,[],[f13602])).
% 121.38/17.51 cnf(s2766, plain, ~spl101_25 | ~spl101_34, inference(sat_conversion,[],[f13605])).
% 121.38/17.51 cnf(s2775, plain, ~spl101_1 | ~spl101_6 | spl101_26 | spl101_29 | ~spl101_34, inference(sat_conversion,[],[f13634])).
% 121.38/17.51 cnf(s2779, plain, ~spl101_6 | spl101_26 | spl101_27 | ~spl101_34, inference(sat_conversion,[],[f13636])).
% 121.38/17.51 cnf(s2781, plain, ~spl101_3 | ~spl101_12 | spl101_31 | ~spl101_32 | ~spl101_36, inference(sat_conversion,[],[f13641])).
% 121.38/17.51 cnf(s2786, plain, ~spl101_14 | ~spl101_15 | spl101_21 | ~spl101_22 | spl101_23, inference(rat,[],[s2744,s2762])).
% 121.38/17.51 cnf(s2794, plain, ~spl101_4 | ~spl101_14 | ~spl101_15 | ~spl101_16 | ~spl101_22 | ~spl101_23, inference(rat,[],[s2724,s2762])).
% 121.38/17.51 cnf(s2797, plain, ~spl101_4 | ~spl101_15 | ~spl101_16 | ~spl101_21 | spl101_22 | ~spl101_23, inference(rat,[],[s2005,s2762])).
% 121.38/17.51 cnf(s2800, plain, ~spl101_2 | ~spl101_9 | ~spl101_10 | spl101_18 | ~spl101_19 | spl101_38, inference(rat,[],[s1950,s2762])).
% 121.38/17.51 cnf(s2802, plain, ~spl101_2 | ~spl101_9 | spl101_17 | spl101_18 | ~spl101_19, inference(rat,[],[s1946,s2762])).
% 121.38/17.51 cnf(s2807, plain, ~spl101_2 | ~spl101_8 | ~spl101_9 | spl101_17 | ~spl101_18 | ~spl101_19, inference(rat,[],[s1930,s2762])).
% 121.38/17.51 cnf(s2811, plain, ~spl101_3 | ~spl101_11 | ~spl101_12 | spl101_30 | spl101_33 | spl101_35, inference(rat,[],[s1821,s2762])).
% 121.38/17.51 cnf(s2823, plain, ~spl101_12 | ~spl101_13 | ~spl101_30 | spl101_31 | spl101_32, inference(rat,[],[s1792,s2762])).
% 121.38/17.51 cnf(s2831, plain, ~spl101_3 | ~spl101_12 | ~spl101_13 | ~spl101_30 | spl101_31 | ~spl101_32, inference(rat,[],[s1772,s2762])).
% 121.38/17.51 cnf(s2832, plain, ~spl101_3 | ~spl101_11 | ~spl101_12 | ~spl101_13 | ~spl101_30 | ~spl101_31 | ~spl101_32, inference(rat,[],[s1768,s2762])).
% 121.38/17.51 cnf(s2834, plain, ~spl101_11 | ~spl101_12 | ~spl101_13 | ~spl101_30 | ~spl101_31 | spl101_32, inference(rat,[],[s1747,s2762])).
% 121.38/17.51 cnf(s2837, plain, ~spl101_1 | ~spl101_5 | ~spl101_6 | spl101_25 | ~spl101_26 | spl101_29, inference(rat,[],[s1669,s2762])).
% 121.38/17.51 cnf(s2839, plain, ~spl101_5 | ~spl101_6 | spl101_25 | ~spl101_26 | spl101_27, inference(rat,[],[s1665,s2762])).
% 121.38/17.51 cnf(s2840, plain, ~spl101_5 | ~spl101_6 | ~spl101_7 | ~spl101_26 | spl101_27 | spl101_34, inference(rat,[],[s1663,s2762])).
% 121.38/17.51 cnf(s2845, plain, ~spl101_1 | ~spl101_5 | ~spl101_6 | ~spl101_7 | ~spl101_25 | ~spl101_27 | spl101_28, inference(rat,[],[s1650,s2762])).
% 121.38/17.51 cnf(s2846, plain, ~spl101_14 | ~spl101_15 | ~spl101_16 | ~spl101_21 | ~spl101_22 | spl101_23, inference(rat,[],[s1578,s2762])).
% 121.38/17.51 cnf(s2848, plain, ~spl101_2 | ~spl101_8 | ~spl101_9 | ~spl101_10 | ~spl101_17 | ~spl101_18 | ~spl101_19, inference(rat,[],[s1538,s2762])).
% 121.38/17.51 cnf(s2850, plain, ~spl101_8 | ~spl101_9 | spl101_17 | ~spl101_18 | spl101_19, inference(rat,[],[s1452,s2762])).
% 121.38/17.51 cnf(s2854, plain, ~spl101_11 | ~spl101_12 | spl101_30 | ~spl101_31 | spl101_32, inference(rat,[],[s1406,s2762])).
% 121.38/17.51 cnf(s2860, plain, ~spl101_12 | spl101_30 | spl101_31 | spl101_32, inference(rat,[],[s1353,s2762])).
% 121.38/17.51 cnf(s2865, plain, ~spl101_6 | ~spl101_7 | ~spl101_25 | spl101_26 | spl101_27, inference(rat,[],[s1293,s2762])).
% 121.38/17.51 cnf(s2868, plain, ~spl101_1 | ~spl101_6 | ~spl101_7 | ~spl101_25 | spl101_26 | ~spl101_27, inference(rat,[],[s1285,s2762])).
% 121.38/17.51 cnf(s2875, plain, ~spl101_15 | ~spl101_16 | ~spl101_21 | spl101_22 | spl101_23, inference(rat,[],[s1154,s2762])).
% 121.38/17.51 cnf(s2877, plain, ~spl101_15 | spl101_21 | spl101_22 | spl101_23, inference(rat,[],[s1139,s2762])).
% 121.38/17.51 cnf(s2881, plain, ~spl101_4 | ~spl101_15 | spl101_21 | spl101_22 | ~spl101_23, inference(rat,[],[s1129,s2762])).
% 121.38/17.51 cnf(s2883, plain, ~spl101_8 | ~spl101_9 | ~spl101_10 | ~spl101_17 | ~spl101_18 | spl101_19, inference(rat,[],[s1103,s2762])).
% 121.38/17.51 cnf(s2885, plain, ~spl101_9 | ~spl101_10 | ~spl101_17 | spl101_18 | spl101_19, inference(rat,[],[s1013,s2762])).
% 121.38/17.51 cnf(s2890, plain, ~spl101_9 | spl101_17 | spl101_18 | spl101_19, inference(rat,[],[s891,s2762])).
% 121.38/17.51 cnf(s2892, plain, spl101_22 | spl101_21 | ~spl101_4 | ~spl101_15, inference(rat,[],[s2877,s2881])).
% 121.38/17.51 cnf(s2893, plain, spl101_21 | ~spl101_4 | ~spl101_14 | ~spl101_15 | ~spl101_16, inference(rat,[],[s2786,s2794,s2892])).
% 121.38/17.51 cnf(s2894, plain, spl101_22 | ~spl101_21 | ~spl101_4 | ~spl101_15 | ~spl101_16, inference(rat,[],[s2797,s2875])).
% 121.38/17.51 cnf(s2895, plain, ~spl101_4 | ~spl101_16 | ~spl101_14 | ~spl101_15, inference(rat,[],[s2846,s2794,s2894,s2893])).
% 121.38/17.51 cnf(s2896, plain, spl101_3 | spl101_2 | spl101_1, inference(rat,[],[s2895,s3,s131,s259,s387])).
% 121.38/17.51 cnf(s2899, plain, spl101_31 | spl101_30 | ~spl101_12 | ~spl101_3, inference(rat,[],[s2860,s2781,s1830])).
% 121.38/17.51 cnf(s2900, plain, spl101_30 | ~spl101_11 | ~spl101_12 | ~spl101_3, inference(rat,[],[s1741,s2811,s2854,s1837,s2899])).
% 121.38/17.51 cnf(s2901, plain, spl101_31 | ~spl101_30 | ~spl101_3 | ~spl101_12 | ~spl101_13, inference(rat,[],[s2823,s2831])).
% 121.38/17.51 cnf(s2902, plain, spl101_16 | spl101_2 | spl101_1, inference(rat,[],[s2832,s2834,s2901,s2900,s419,s451,s483,s2896])).
% 121.38/17.51 cnf(s2903, plain, spl101_14 | spl101_2 | spl101_1, inference(rat,[],[s2832,s2834,s2901,s2900,s163,s195,s227,s2896])).
% 121.38/17.51 cnf(s2904, plain, spl101_15 | spl101_2 | spl101_1, inference(rat,[],[s2832,s2834,s2901,s2900,s291,s323,s355,s2896])).
% 121.38/17.51 cnf(s2905, plain, spl101_2 | spl101_1, inference(rat,[],[s2832,s2834,s2901,s2900,s35,s67,s99,s2895,s2904,s2903,s2902,s2896])).
% 121.38/17.51 cnf(s2906, plain, spl101_18 | spl101_17 | ~spl101_9 | ~spl101_2, inference(rat,[],[s2802,s2890])).
% 121.38/17.51 cnf(s2907, plain, ~spl101_18 | spl101_17 | ~spl101_9 | ~spl101_8 | ~spl101_2, inference(rat,[],[s2850,s2807])).
% 121.38/17.51 cnf(s2908, plain, spl101_17 | ~spl101_8 | ~spl101_9 | ~spl101_2, inference(rat,[],[s2907,s2906])).
% 121.38/17.51 cnf(s2909, plain, spl101_18 | ~spl101_17 | ~spl101_9 | ~spl101_10 | ~spl101_2, inference(rat,[],[s2800,s2885,s1961])).
% 121.38/17.51 cnf(s2910, plain, ~spl101_18 | ~spl101_17 | ~spl101_2 | ~spl101_8 | ~spl101_9 | ~spl101_10, inference(rat,[],[s2883,s2848])).
% 121.38/17.51 cnf(s2911, plain, spl101_11 | spl101_16 | spl101_1, inference(rat,[],[s2910,s2909,s2908,s427,s435,s443,s2905])).
% 121.38/17.51 cnf(s2912, plain, ~spl101_13 | ~spl101_12 | ~spl101_3 | ~spl101_11, inference(rat,[],[s2832,s2834,s2901,s2900])).
% 121.38/17.51 cnf(s2913, plain, spl101_13 | spl101_16 | spl101_1, inference(rat,[],[s2910,s2909,s2908,s491,s499,s507,s2905])).
% 121.38/17.51 cnf(s2914, plain, spl101_12 | spl101_16 | spl101_1, inference(rat,[],[s2910,s2909,s2908,s459,s467,s475,s2905])).
% 121.38/17.51 cnf(s2915, plain, spl101_16 | spl101_1, inference(rat,[],[s2910,s2909,s2908,s395,s403,s411,s2912,s2914,s2913,s2911,s2905])).
% 121.38/17.51 cnf(s2916, plain, spl101_13 | spl101_14 | spl101_1, inference(rat,[],[s2910,s2909,s2908,s235,s243,s251,s2905])).
% 121.38/17.51 cnf(s2917, plain, spl101_12 | spl101_14 | spl101_1, inference(rat,[],[s2910,s2909,s2908,s203,s211,s219,s2905])).
% 121.38/17.51 cnf(s2918, plain, spl101_11 | spl101_14 | spl101_1, inference(rat,[],[s2910,s2909,s2908,s171,s179,s187,s2905])).
% 121.38/17.51 cnf(s2919, plain, spl101_14 | spl101_1, inference(rat,[],[s2910,s2909,s2908,s139,s147,s155,s2912,s2918,s2917,s2916,s2905])).
% 121.38/17.51 cnf(s2920, plain, spl101_13 | spl101_15 | spl101_1, inference(rat,[],[s2910,s2909,s2908,s363,s371,s379,s2905])).
% 121.38/17.51 cnf(s2921, plain, spl101_12 | spl101_15 | spl101_1, inference(rat,[],[s2910,s2909,s2908,s331,s339,s347,s2905])).
% 121.38/17.51 cnf(s2922, plain, spl101_11 | spl101_15 | spl101_1, inference(rat,[],[s2910,s2909,s2908,s299,s307,s315,s2905])).
% 121.38/17.51 cnf(s2923, plain, spl101_15 | spl101_1, inference(rat,[],[s2910,s2909,s2908,s267,s275,s283,s2912,s2922,s2921,s2920,s2905])).
% 121.38/17.51 cnf(s2924, plain, spl101_13 | spl101_1, inference(rat,[],[s2910,s2909,s2908,s107,s115,s123,s2905,s2895,s2923,s2919,s2915])).
% 121.38/17.51 cnf(s2925, plain, spl101_12 | spl101_1, inference(rat,[],[s2910,s2909,s2908,s75,s83,s91,s2905,s2895,s2923,s2919,s2915])).
% 121.38/17.51 cnf(s2926, plain, spl101_11 | spl101_1, inference(rat,[],[s2910,s2909,s2908,s43,s51,s59,s2905,s2895,s2923,s2919,s2915])).
% 121.38/17.51 cnf(s2927, plain, spl101_1, inference(rat,[],[s2910,s2909,s2908,s11,s19,s27,s2912,s2926,s2925,s2924,s2895,s2923,s2919,s2915,s2905])).
% 121.38/17.51 cnf(s2928, plain, spl101_26 | ~spl101_34 | ~spl101_6, inference(rat,[],[s1580,s2775,s2779,s2927])).
% 121.38/17.51 cnf(s2929, plain, ~spl101_26 | spl101_25 | ~spl101_5 | ~spl101_6, inference(rat,[],[s1580,s2839,s2837,s2927])).
% 121.38/17.51 cnf(s2930, plain, spl101_25 | ~spl101_5 | ~spl101_6, inference(rat,[],[s2929,s2928,s1676])).
% 121.38/17.51 cnf(s2931, plain, spl101_26 | ~spl101_25 | ~spl101_6 | ~spl101_7, inference(rat,[],[s2868,s2865,s2927])).
% 121.38/17.51 cnf(s2932, plain, spl101_16 | spl101_13 | spl101_2, inference(rat,[],[s2845,s2840,s1309,s2931,s2766,s2930,s485,s489,s487,s2927])).
% 121.38/17.51 cnf(s2933, plain, spl101_14 | spl101_13 | spl101_2, inference(rat,[],[s2845,s2840,s1309,s2931,s2766,s2930,s229,s233,s231,s2927])).
% 121.38/17.51 cnf(s2934, plain, spl101_15 | spl101_13 | spl101_2, inference(rat,[],[s2845,s2840,s1309,s2931,s2766,s2930,s357,s361,s359,s2927])).
% 121.38/17.51 cnf(s2935, plain, spl101_13 | spl101_2 | ~spl101_4, inference(rat,[],[s2934,s2895,s2933,s2932])).
% 121.38/17.51 cnf(s2936, plain, spl101_16 | spl101_12 | spl101_2, inference(rat,[],[s2845,s2840,s1309,s2931,s2766,s2930,s455,s453,s457,s2927])).
% 121.38/17.51 cnf(s2937, plain, spl101_14 | spl101_12 | spl101_2, inference(rat,[],[s2845,s2840,s1309,s2931,s2766,s2930,s199,s197,s201,s2927])).
% 121.38/17.51 cnf(s2938, plain, spl101_15 | spl101_12 | spl101_2, inference(rat,[],[s2845,s2840,s1309,s2931,s2766,s2930,s327,s325,s329,s2927])).
% 121.38/17.51 cnf(s2939, plain, spl101_12 | spl101_2 | ~spl101_4, inference(rat,[],[s2938,s2895,s2937,s2936])).
% 121.38/17.51 cnf(s2940, plain, spl101_16 | spl101_11 | spl101_2, inference(rat,[],[s2845,s2840,s1309,s2931,s2766,s2930,s421,s425,s423,s2927])).
% 121.38/17.51 cnf(s2941, plain, spl101_14 | spl101_11 | spl101_2, inference(rat,[],[s2845,s2840,s1309,s2931,s2766,s2930,s165,s169,s167,s2927])).
% 121.38/17.51 cnf(s2942, plain, spl101_15 | spl101_11 | spl101_2, inference(rat,[],[s2845,s2840,s1309,s2931,s2766,s2930,s293,s297,s295,s2927])).
% 121.38/17.51 cnf(s2943, plain, spl101_11 | spl101_2 | ~spl101_4, inference(rat,[],[s2942,s2895,s2941,s2940])).
% 121.38/17.51 cnf(s2944, plain, spl101_16 | spl101_3 | spl101_2, inference(rat,[],[s2845,s2840,s1309,s2931,s2766,s2930,s389,s391,s393,s2927])).
% 121.38/17.51 cnf(s2945, plain, spl101_14 | spl101_3 | spl101_2, inference(rat,[],[s2845,s2840,s1309,s2931,s2766,s2930,s133,s137,s135,s2927])).
% 121.38/17.51 cnf(s2946, plain, spl101_15 | spl101_3 | spl101_2, inference(rat,[],[s2845,s2840,s1309,s2931,s2766,s2930,s261,s265,s263,s2927])).
% 121.38/17.51 cnf(s2947, plain, spl101_2 | ~spl101_4, inference(rat,[],[s2946,s2895,s2945,s2944,s2912,s2943,s2939,s2935])).
% 121.38/17.51 cnf(s2948, plain, spl101_5 | spl101_16 | spl101_13 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s493,s509,s501])).
% 121.38/17.51 cnf(s2949, plain, spl101_7 | spl101_16 | spl101_13 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s497,s513,s505])).
% 121.38/17.51 cnf(s2950, plain, ~spl101_6 | ~spl101_7 | ~spl101_5, inference(rat,[],[s2845,s2840,s1309,s2931,s2766,s2930,s2927])).
% 121.38/17.51 cnf(s2951, plain, spl101_16 | spl101_13 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s495,s511,s503,s2950,s2949,s2948])).
% 121.38/17.51 cnf(s2952, plain, spl101_7 | spl101_14 | spl101_13 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s241,s257,s249])).
% 121.38/17.51 cnf(s2953, plain, spl101_5 | spl101_14 | spl101_13 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s237,s253,s245])).
% 121.38/17.51 cnf(s2954, plain, spl101_14 | spl101_13 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s239,s247,s255,s2950,s2953,s2952])).
% 121.38/17.51 cnf(s2955, plain, spl101_7 | spl101_15 | spl101_13 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s369,s385,s377])).
% 121.38/17.51 cnf(s2956, plain, spl101_5 | spl101_15 | spl101_13 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s365,s381,s373])).
% 121.38/17.51 cnf(s2957, plain, spl101_15 | spl101_13 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s367,s375,s383,s2950,s2956,s2955])).
% 121.38/17.51 cnf(s2958, plain, spl101_13 | ~spl101_4, inference(rat,[],[s2957,s2895,s2954,s2951,s2947])).
% 121.38/17.51 cnf(s2959, plain, spl101_7 | spl101_16 | spl101_12 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s465,s473,s481])).
% 121.38/17.51 cnf(s2960, plain, spl101_5 | spl101_16 | spl101_12 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s461,s469,s477])).
% 121.38/17.51 cnf(s2961, plain, spl101_16 | spl101_12 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s463,s471,s479,s2950,s2960,s2959])).
% 121.38/17.51 cnf(s2962, plain, spl101_7 | spl101_14 | spl101_12 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s209,s217,s225])).
% 121.38/17.51 cnf(s2963, plain, spl101_5 | spl101_14 | spl101_12 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s205,s213,s221])).
% 121.38/17.51 cnf(s2964, plain, spl101_14 | spl101_12 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s207,s215,s223,s2950,s2963,s2962])).
% 121.38/17.51 cnf(s2965, plain, spl101_7 | spl101_15 | spl101_12 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s337,s345,s353])).
% 121.38/17.51 cnf(s2966, plain, spl101_5 | spl101_15 | spl101_12 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s333,s341,s349])).
% 121.38/17.51 cnf(s2967, plain, spl101_15 | spl101_12 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s335,s343,s351,s2950,s2966,s2965])).
% 121.38/17.51 cnf(s2968, plain, spl101_12 | ~spl101_4, inference(rat,[],[s2967,s2895,s2964,s2961,s2947])).
% 121.38/17.51 cnf(s2969, plain, spl101_16 | spl101_7 | spl101_11 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s433,s441,s449])).
% 121.38/17.51 cnf(s2970, plain, spl101_7 | ~spl101_15 | spl101_11 | ~spl101_4, inference(rat,[],[s2910,s2909,s2908,s177,s185,s193,s2895,s2969,s2947])).
% 121.38/17.51 cnf(s2971, plain, spl101_16 | spl101_5 | spl101_11 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s429,s437,s445])).
% 121.38/17.51 cnf(s2972, plain, ~spl101_15 | ~spl101_6 | spl101_11 | ~spl101_4, inference(rat,[],[s2910,s2909,s2908,s173,s181,s189,s2895,s2971,s2950,s2970,s2947])).
% 121.38/17.51 cnf(s2973, plain, spl101_7 | spl101_15 | spl101_11 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s305,s313,s321])).
% 121.38/17.51 cnf(s2974, plain, ~spl101_6 | spl101_11 | ~spl101_4, inference(rat,[],[s2910,s2909,s2908,s301,s309,s317,s2950,s2973,s2972,s2947])).
% 121.38/17.51 cnf(s2975, plain, spl101_9 | ~spl101_15 | spl101_11 | ~spl101_4, inference(rat,[],[s2895,s183,s439,s2974])).
% 121.38/17.51 cnf(s2976, plain, spl101_16 | ~spl101_9 | spl101_6 | spl101_11 | ~spl101_2, inference(rat,[],[s2910,s2909,s2908,s431,s447])).
% 121.38/17.51 cnf(s2977, plain, ~spl101_15 | spl101_11 | ~spl101_4, inference(rat,[],[s2910,s2909,s2908,s175,s191,s2895,s2976,s2975,s2947,s2974])).
% 121.38/17.51 cnf(s2978, plain, spl101_11 | ~spl101_4, inference(rat,[],[s2910,s2909,s2908,s303,s311,s319,s2977,s2974,s2947])).
% 121.38/17.51 cnf(s2979, plain, spl101_16 | spl101_9 | ~spl101_6 | spl101_3, inference(rat,[],[s2950,s405,s409])).
% 121.38/17.51 cnf(s2980, plain, spl101_9 | ~spl101_15 | ~spl101_6 | ~spl101_4, inference(rat,[],[s2950,s149,s153,s2895,s2979,s2912,s2978,s2968,s2958])).
% 121.38/17.51 cnf(s2981, plain, spl101_7 | spl101_16 | ~spl101_9 | ~spl101_4, inference(rat,[],[s2910,s2909,s2908,s401,s417,s2947,s2912,s2978,s2968,s2958])).
% 121.38/17.51 cnf(s2982, plain, spl101_16 | ~spl101_9 | ~spl101_6 | ~spl101_4, inference(rat,[],[s2910,s2909,s2908,s397,s413,s2950,s2981,s2947,s2912,s2978,s2968,s2958])).
% 121.38/17.51 cnf(s2983, plain, spl101_7 | spl101_14 | ~spl101_9 | ~spl101_4, inference(rat,[],[s2910,s2909,s2908,s145,s161,s2947,s2912,s2978,s2968,s2958])).
% 121.38/17.51 cnf(s2984, plain, ~spl101_15 | ~spl101_6 | ~spl101_4, inference(rat,[],[s2910,s2909,s2908,s141,s157,s2950,s2983,s2895,s2982,s2980,s2947,s2912,s2978,s2968,s2958])).
% 121.38/17.51 cnf(s2985, plain, spl101_9 | spl101_15 | ~spl101_6 | spl101_3, inference(rat,[],[s2950,s277,s281])).
% 121.38/17.51 cnf(s2986, plain, spl101_7 | ~spl101_6 | ~spl101_4, inference(rat,[],[s2910,s2909,s2908,s273,s289,s2947,s2985,s2984,s2912,s2978,s2968,s2958])).
% 121.38/17.51 cnf(s2987, plain, ~spl101_6 | ~spl101_4, inference(rat,[],[s2910,s2909,s2908,s269,s285,s2950,s2986,s2985,s2984,s2947,s2912,s2978,s2968,s2958])).
% 121.38/17.51 cnf(s2988, plain, spl101_9 | ~spl101_15 | ~spl101_4, inference(rat,[],[s2895,s151,s407,s2912,s2978,s2968,s2958,s2987])).
% 121.38/17.51 cnf(s2989, plain, spl101_16 | ~spl101_9 | ~spl101_4, inference(rat,[],[s2910,s2909,s2908,s399,s415,s2947,s2912,s2978,s2968,s2958,s2987])).
% 121.38/17.51 cnf(s2990, plain, ~spl101_15 | ~spl101_4, inference(rat,[],[s2910,s2909,s2908,s143,s159,s2895,s2989,s2988,s2947,s2912,s2978,s2968,s2958,s2987])).
% 121.38/17.51 cnf(s2991, plain, ~spl101_4, inference(rat,[],[s2910,s2909,s2908,s271,s279,s287,s2990,s2987,s2912,s2978,s2968,s2958,s2947])).
% 121.38/17.51 cnf(s2993, plain, spl101_7 | spl101_10 | ~spl101_3, inference(rat,[],[s2912,s65,s97,s129,s2991])).
% 121.38/17.51 cnf(s2994, plain, spl101_10 | ~spl101_6 | ~spl101_3, inference(rat,[],[s2912,s61,s93,s125,s2950,s2993,s2991])).
% 121.38/17.51 cnf(s2995, plain, spl101_7 | spl101_9 | ~spl101_3, inference(rat,[],[s2912,s57,s89,s121,s2991])).
% 121.38/17.51 cnf(s2996, plain, spl101_9 | ~spl101_6 | ~spl101_3, inference(rat,[],[s2912,s53,s85,s117,s2950,s2995,s2991])).
% 121.38/17.51 cnf(s2997, plain, spl101_2 | spl101_7 | ~spl101_3, inference(rat,[],[s2912,s41,s73,s105,s2991])).
% 121.38/17.51 cnf(s2998, plain, ~spl101_8 | ~spl101_2 | ~spl101_9 | ~spl101_10, inference(rat,[],[s2910,s2909,s2908])).
% 121.38/17.51 cnf(s2999, plain, spl101_7 | ~spl101_6 | ~spl101_3, inference(rat,[],[s81,s2912,s49,s113,s2998,s2997,s2994,s2996,s2991])).
% 121.38/17.51 cnf(s3000, plain, spl101_2 | spl101_5 | ~spl101_3, inference(rat,[],[s2912,s37,s69,s101,s2991])).
% 121.38/17.51 cnf(s3001, plain, ~spl101_6 | ~spl101_3, inference(rat,[],[s2912,s45,s77,s109,s2998,s3000,s2950,s2999,s2996,s2994,s2991])).
% 121.38/17.51 cnf(s3002, plain, spl101_2 | ~spl101_3, inference(rat,[],[s2912,s39,s71,s103,s3001,s2991])).
% 121.38/17.51 cnf(s3003, plain, spl101_13 | ~spl101_3, inference(rat,[],[s2998,s111,s119,s127,s3001,s3002,s2991])).
% 121.38/17.51 cnf(s3004, plain, spl101_9 | ~spl101_3, inference(rat,[],[s2912,s55,s87,s3001,s3003,s2991])).
% 121.38/17.51 cnf(s3005, plain, spl101_11 | ~spl101_3, inference(rat,[],[s2998,s47,s63,s3001,s3002,s3004,s2991])).
% 121.38/17.51 cnf(s3006, plain, ~spl101_3, inference(rat,[],[s2998,s79,s95,s2912,s3005,s3004,s3003,s3002,s3001,s2991])).
% 121.38/17.51 cnf(s3008, plain, spl101_9 | ~spl101_6, inference(rat,[],[s2950,s21,s25,s2991,s3006])).
% 121.38/17.51 cnf(s3011, plain, spl101_2 | ~spl101_6, inference(rat,[],[s2950,s5,s9,s3006,s2991])).
% 121.38/17.51 cnf(s3012, plain, spl101_7 | ~spl101_6, inference(rat,[],[s2998,s17,s33,s3008,s3011,s2991,s3006])).
% 121.38/17.51 cnf(s3013, plain, ~spl101_6, inference(rat,[],[s2998,s13,s29,s2950,s3012,s3011,s3008,s2991,s3006])).
% 121.38/17.51 cnf(s3014, plain, spl101_10, inference(rat,[],[s31,s3006,s2991,s3013])).
% 121.38/17.51 cnf(s3015, plain, spl101_9, inference(rat,[],[s23,s3006,s2991,s3013])).
% 121.38/17.51 cnf(s3016, plain, spl101_8, inference(rat,[],[s15,s3006,s2991,s3013])).
% 121.38/17.51 cnf(s3017, plain, spl101_2, inference(rat,[],[s7,s2991,s3006,s3013])).
% 121.38/17.51 cnf(s3018, plain, $false, inference(rat,[],[s2998,s3015,s3017,s3014,s3016])).
% 121.38/17.51 thf(f13642,plain,(
% 121.38/17.51 $false),
% 121.38/17.51 inference(avatar_sat_refutation,[],[s3018])).
% 121.38/17.51 % SZS output end Proof for theBenchmark
% 121.38/17.51 % (1608069)------------------------------
% 121.38/17.51 % (1608069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 121.38/17.51 % (1608069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 121.38/17.51 % (1608069)CaDiCaL version: 2.1.3
% 121.38/17.51 % (1608069)Termination reason: Refutation
% 121.38/17.51 % (1608069)Time elapsed: 2.184 s
% 121.38/17.51 % (1608069)Peak memory usage: 21 MB
% 121.38/17.51 % (1608069)Instructions burned: 5150 (million)
% 121.38/17.51 % (1607940)Success in time 17.255 s
% 121.38/17.51 % Vampire exiting
%------------------------------------------------------------------------------