%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWX182^1 : TPTP v9.3.1. Released v9.3.0.
% 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 08:40:45 AM UTC 2026
% Result : Theorem 29.05s 4.56s
% Output : Refutation 29.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX182^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n004.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:10:22 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.24 Running first-order model finding
% 0.08/0.24 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
% 7.61/1.61 % (1489682)Will run a generic schedule for satisfiability detection.
% 7.61/1.61 % (1489692)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=614519505:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 7.61/1.61 % (1489693)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2315943190:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 7.61/1.61 % (1489687)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3145773086_2999 on theBenchmark for (2999ds/0Mi)
% 7.61/1.61 % (1489688)% WARNING: option uhcvi not known.
% 7.61/1.61 % (1489688)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1130401995:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 7.61/1.61 % Exception at run slice level
% 7.61/1.61 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.61/1.61 % (1489691)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1906358053:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 7.61/1.61 % (1489690)dis+10_1_sil=32000:sp=arity:random_seed=2147090415:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 7.61/1.61 % (1489689)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3309958924:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 7.61/1.61 % (1489688)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.61/1.61 % (1489688)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.61/1.61 % (1489691)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.61/1.61 % (1489699)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=463533528:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 7.61/1.61 % (1489692)Instruction limit reached!
% 7.61/1.61 % (1489692)------------------------------
% 7.61/1.61 % (1489692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.61/1.61 % (1489692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.61/1.61 % (1489692)CaDiCaL version: 2.1.3
% 7.61/1.61 % (1489692)Termination reason: Instruction limit
% 7.61/1.61 % (1489692)Termination phase: Saturation
% 7.61/1.61 % (1489692)Time elapsed: 0.105 s
% 7.61/1.61 % (1489692)Peak memory usage: 12 MB
% 7.61/1.61 % (1489692)Instructions burned: 131 (million)
% 7.61/1.61 % Exception at run slice level
% 7.61/1.61 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.61/1.61 % (1489690)Instruction limit reached!
% 7.61/1.61 % (1489690)------------------------------
% 7.61/1.61 % (1489690)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.61/1.61 % (1489690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.61/1.61 % (1489690)CaDiCaL version: 2.1.3
% 7.61/1.61 % (1489690)Termination reason: Instruction limit
% 7.61/1.61 % (1489690)Termination phase: Saturation
% 7.61/1.61 % (1489690)Time elapsed: 0.098 s
% 7.61/1.61 % (1489690)Peak memory usage: 12 MB
% 7.61/1.61 % (1489690)Instructions burned: 103 (million)
% 7.61/1.61 % (1489704)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=1325849401:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 7.61/1.61 % (1489693)Instruction limit reached!
% 7.61/1.61 % (1489693)------------------------------
% 7.61/1.61 % (1489693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.61/1.61 % (1489693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.61/1.61 % (1489693)CaDiCaL version: 2.1.3
% 7.61/1.61 % (1489693)Termination reason: Instruction limit
% 7.61/1.61 % (1489693)Termination phase: Saturation
% 7.61/1.61 % (1489693)Time elapsed: 0.138 s
% 7.61/1.61 % (1489693)Peak memory usage: 13 MB
% 7.61/1.61 % (1489693)Instructions burned: 160 (million)
% 7.61/1.61 % (1489691)Instruction limit reached!
% 7.61/1.61 % (1489691)------------------------------
% 7.61/1.61 % (1489691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.61/1.61 % (1489691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.61/1.61 % (1489691)CaDiCaL version: 2.1.3
% 7.61/1.61 % (1489691)Termination reason: Instruction limit
% 7.61/1.61 % (1489691)Termination phase: Saturation
% 7.61/1.61 % (1489691)Time elapsed: 0.129 s
% 7.61/1.61 % (1489691)Peak memory usage: 13 MB
% 7.61/1.61 % (1489691)Instructions burned: 116 (million)
% 24.06/3.84 % (1489703)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=390842928:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 24.06/3.84 % (1489704)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 24.06/3.84 % (1489705)ott-21_1_sil=16000:fs=off:random_seed=2901751153:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 24.06/3.84 % (1489704)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 24.06/3.84 % (1489707)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=191838130:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 24.06/3.84 % (1489709)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=756714076:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 24.06/3.84 % Exception at run slice level
% 24.06/3.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 24.06/3.84 % (1489713)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4287890192:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 24.06/3.84 % (1489703)Instruction limit reached!
% 24.06/3.84 % (1489703)------------------------------
% 24.06/3.84 % (1489703)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.06/3.84 % (1489703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.06/3.84 % (1489703)CaDiCaL version: 2.1.3
% 24.06/3.84 % (1489703)Termination reason: Instruction limit
% 24.06/3.84 % (1489703)Termination phase: Saturation
% 24.06/3.84 % (1489703)Time elapsed: 0.113 s
% 24.06/3.84 % (1489703)Peak memory usage: 12 MB
% 24.06/3.84 % (1489703)Instructions burned: 131 (million)
% 24.06/3.84 % (1489705)Instruction limit reached!
% 24.06/3.84 % (1489705)------------------------------
% 24.06/3.84 % (1489705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.06/3.84 % (1489705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.06/3.84 % (1489705)CaDiCaL version: 2.1.3
% 24.06/3.84 % (1489705)Termination reason: Instruction limit
% 24.06/3.84 % (1489705)Termination phase: Saturation
% 24.06/3.84 % (1489705)Time elapsed: 0.144 s
% 24.06/3.84 % (1489705)Peak memory usage: 12 MB
% 24.06/3.84 % (1489705)Instructions burned: 181 (million)
% 24.06/3.84 % (1489715)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3920470474:i=889:ins=1_2996 on theBenchmark for (2996ds/889Mi)
% 24.06/3.84 % Exception at run slice level
% 24.06/3.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 24.06/3.84 % (1489717)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=630413051:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2996 on theBenchmark for (2996ds/692Mi)
% 24.06/3.84 % (1489717)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 24.06/3.84 % (1489718)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3312405977:i=879:kws=inv_precedence:fsr=off_2995 on theBenchmark for (2995ds/879Mi)
% 24.06/3.84 % (1489718)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 24.06/3.84 % (1489707)Instruction limit reached!
% 24.06/3.84 % (1489707)------------------------------
% 24.06/3.84 % (1489707)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.06/3.84 % (1489707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.06/3.84 % (1489707)CaDiCaL version: 2.1.3
% 24.06/3.84 % (1489707)Termination reason: Instruction limit
% 24.06/3.84 % (1489707)Termination phase: Saturation
% 24.06/3.84 % (1489707)Time elapsed: 0.414 s
% 24.06/3.84 % (1489707)Peak memory usage: 14 MB
% 24.06/3.84 % (1489707)Instructions burned: 477 (million)
% 24.06/3.84 % (1489721)fmb+10_1_sil=64000:random_seed=1868247387:i=22061:nm=2:gsp=on_2993 on theBenchmark for (2993ds/22061Mi)
% 24.06/3.84 % (1489721)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 24.06/3.84 % Exception at run slice level
% 24.06/3.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 24.06/3.84 % (1489723)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=954469349:i=9515:nm=5_2992 on theBenchmark for (2992ds/9515Mi)
% 24.06/3.84 % (1489704)Instruction limit reached!
% 24.06/3.84 % (1489704)------------------------------
% 24.06/3.84 % (1489704)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.05/4.56 % (1489704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.05/4.56 % (1489704)CaDiCaL version: 2.1.3
% 29.05/4.56 % (1489704)Termination reason: Instruction limit
% 29.05/4.56 % (1489704)Termination phase: Saturation
% 29.05/4.56 % (1489704)Time elapsed: 0.559 s
% 29.05/4.56 % (1489704)Peak memory usage: 16 MB
% 29.05/4.56 % (1489704)Instructions burned: 685 (million)
% 29.05/4.56 % (1489725)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=59293888:fmbsr=1.7:i=920_2992 on theBenchmark for (2992ds/920Mi)
% 29.05/4.56 % Exception at run slice level
% 29.05/4.56 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.05/4.56 % Exception at run slice level
% 29.05/4.56 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.05/4.56 % (1489727)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2910994270:i=5131_2991 on theBenchmark for (2991ds/5131Mi)
% 29.05/4.56 % (1489727)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 29.05/4.56 % (1489728)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=361758673:i=1472:ins=7:fdi=8:gsp=on_2991 on theBenchmark for (2991ds/1472Mi)
% 29.05/4.56 % (1489728)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 29.05/4.56 % (1489728)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 29.05/4.56 % (1489717)Instruction limit reached!
% 29.05/4.56 % (1489717)------------------------------
% 29.05/4.56 % (1489717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.05/4.56 % (1489717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.05/4.56 % (1489717)CaDiCaL version: 2.1.3
% 29.05/4.56 % (1489717)Termination reason: Instruction limit
% 29.05/4.56 % (1489717)Termination phase: Saturation
% 29.05/4.56 % (1489717)Time elapsed: 0.564 s
% 29.05/4.56 % (1489717)Peak memory usage: 15 MB
% 29.05/4.56 % (1489717)Instructions burned: 692 (million)
% 29.05/4.56 % (1489731)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=745785381:i=6324_2990 on theBenchmark for (2990ds/6324Mi)
% 29.05/4.56 % Exception at run slice level
% 29.05/4.56 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.05/4.56 % (1489733)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=4067255818:fmbsr=2.30978:i=2174_2989 on theBenchmark for (2989ds/2174Mi)
% 29.05/4.56 % Exception at run slice level
% 29.05/4.56 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.05/4.56 % (1489735)ott-2_1_sil=16000:newcnf=on:random_seed=1913980558:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2988 on theBenchmark for (2988ds/869Mi)
% 29.05/4.56 % (1489735)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 29.05/4.56 % (1489718)Instruction limit reached!
% 29.05/4.56 % (1489718)------------------------------
% 29.05/4.56 % (1489718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.05/4.56 % (1489718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.05/4.56 % (1489718)CaDiCaL version: 2.1.3
% 29.05/4.56 % (1489718)Termination reason: Instruction limit
% 29.05/4.56 % (1489718)Termination phase: Saturation
% 29.05/4.56 % (1489718)Time elapsed: 0.782 s
% 29.05/4.56 % (1489718)Peak memory usage: 17 MB
% 29.05/4.56 % (1489718)Instructions burned: 880 (million)
% 29.05/4.56 % (1489737)ott+10_1_sil=32000:tgt=ground:random_seed=2730210894:i=5114:av=off_2987 on theBenchmark for (2987ds/5114Mi)
% 29.05/4.56 % (1489713)Instruction limit reached!
% 29.05/4.56 % (1489713)------------------------------
% 29.05/4.56 % (1489713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.05/4.56 % (1489713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.05/4.56 % (1489713)CaDiCaL version: 2.1.3
% 29.05/4.56 % (1489713)Termination reason: Instruction limit
% 29.05/4.56 % (1489713)Termination phase: Saturation
% 29.05/4.56 % (1489713)Time elapsed: 0.960 s
% 29.05/4.56 % (1489713)Peak memory usage: 16 MB
% 29.05/4.56 % (1489713)Instructions burned: 1180 (million)
% 29.05/4.56 % (1489739)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3780203451:i=54282_2987 on theBenchmark for (2987ds/54282Mi)
% 29.05/4.56 % Exception at run slice level
% 29.05/4.56 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.05/4.56 % (1489741)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3799312961:i=3512:aac=none_2986 on theBenchmark for (2986ds/3512Mi)
% 29.05/4.56 % (1489741)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 29.05/4.56 % (1489735)Instruction limit reached!
% 29.05/4.56 % (1489735)------------------------------
% 29.05/4.56 % (1489735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.05/4.56 % (1489735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.05/4.56 % (1489735)CaDiCaL version: 2.1.3
% 29.05/4.56 % (1489735)Termination reason: Instruction limit
% 29.05/4.56 % (1489735)Termination phase: Saturation
% 29.05/4.56 % (1489735)Time elapsed: 0.716 s
% 29.05/4.56 % (1489735)Peak memory usage: 15 MB
% 29.05/4.56 % (1489735)Instructions burned: 870 (million)
% 29.05/4.56 % (1489743)dis+21_1_sil=32000:sas=cadical:random_seed=243673326:i=3773:amm=off_2981 on theBenchmark for (2981ds/3773Mi)
% 29.05/4.56 % (1489728)Instruction limit reached!
% 29.05/4.56 % (1489728)------------------------------
% 29.05/4.56 % (1489728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.05/4.56 % (1489728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.05/4.56 % (1489728)CaDiCaL version: 2.1.3
% 29.05/4.56 % (1489728)Termination reason: Instruction limit
% 29.05/4.56 % (1489728)Termination phase: Saturation
% 29.05/4.56 % (1489728)Time elapsed: 1.054 s
% 29.05/4.56 % (1489728)Peak memory usage: 19 MB
% 29.05/4.56 % (1489728)Instructions burned: 1473 (million)
% 29.05/4.56 % (1489745)ott+11_1_sil=16000:gs=on:random_seed=189157862:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2980 on theBenchmark for (2980ds/2251Mi)
% 29.05/4.56 % (1489745)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 29.05/4.56 % (1489745)Instruction limit reached!
% 29.05/4.56 % (1489745)------------------------------
% 29.05/4.56 % (1489745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.05/4.56 % (1489745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.05/4.56 % (1489745)CaDiCaL version: 2.1.3
% 29.05/4.56 % (1489745)Termination reason: Instruction limit
% 29.05/4.56 % (1489745)Termination phase: Saturation
% 29.05/4.56 % (1489745)Time elapsed: 1.015 s
% 29.05/4.56 % (1489745)Peak memory usage: 20 MB
% 29.05/4.56 % (1489745)Instructions burned: 2252 (million)
% 29.05/4.56 % (1489747)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=515686348:fmbsr=1.6:i=67534_2970 on theBenchmark for (2970ds/67534Mi)
% 29.05/4.56 % Exception at run slice level
% 29.05/4.56 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.05/4.56 % (1489749)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=1374541433:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2969 on theBenchmark for (2969ds/4591Mi)
% 29.05/4.56 % (1489727)Instruction limit reached!
% 29.05/4.56 % (1489727)------------------------------
% 29.05/4.56 % (1489727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.05/4.56 % (1489727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.05/4.56 % (1489727)CaDiCaL version: 2.1.3
% 29.05/4.56 % (1489727)Termination reason: Instruction limit
% 29.05/4.56 % (1489727)Termination phase: Saturation
% 29.05/4.56 % (1489727)Time elapsed: 2.693 s
% 29.05/4.56 % (1489727)Peak memory usage: 24 MB
% 29.05/4.56 % (1489727)Instructions burned: 5131 (million)
% 29.05/4.56 % (1489751)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=3489426179:i=29340_2964 on theBenchmark for (2964ds/29340Mi)
% 29.05/4.56 % (1489743)Instruction limit reached!
% 29.05/4.56 % (1489743)------------------------------
% 29.05/4.56 % (1489743)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.05/4.56 % (1489743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.05/4.56 % (1489743)CaDiCaL version: 2.1.3
% 29.05/4.56 % (1489743)Termination reason: Instruction limit
% 29.05/4.56 % (1489743)Termination phase: Saturation
% 29.05/4.56 % (1489743)Time elapsed: 1.669 s
% 29.05/4.56 % (1489743)Peak memory usage: 23 MB
% 29.05/4.56 % (1489743)Instructions burned: 3773 (million)
% 29.05/4.56 % (1489753)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=340837225:i=5211_2964 on theBenchmark for (2964ds/5211Mi)
% 29.05/4.56 % (1489737)Instruction limit reached!
% 29.05/4.56 % (1489737)------------------------------
% 29.05/4.56 % (1489737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.05/4.56 % (1489737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.05/4.56 % (1489737)CaDiCaL version: 2.1.3
% 29.05/4.56 % (1489737)Termination reason: Instruction limit
% 29.05/4.56 % (1489737)Termination phase: Saturation
% 29.05/4.56 % (1489737)Time elapsed: 2.463 s
% 29.05/4.56 % (1489737)Peak memory usage: 16 MB
% 29.05/4.56 % (1489737)Instructions burned: 5115 (million)
% 29.05/4.56 % (1489755)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=2815192680:i=5497:nm=2_2962 on theBenchmark for (2962ds/5497Mi)
% 29.05/4.56 % Exception at run slice level
% 29.05/4.56 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.05/4.56 % (1489757)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=706326723:fmbsr=2:i=46332_2962 on theBenchmark for (2962ds/46332Mi)
% 29.05/4.56 % Exception at run slice level
% 29.05/4.56 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.05/4.56 % (1489759)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=33860915:i=14071_2962 on theBenchmark for (2962ds/14071Mi)
% 29.05/4.56 % Exception at run slice level
% 29.05/4.56 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.05/4.56 % (1489761)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1194863988:i=22565:add=on:rawr=on_2961 on theBenchmark for (2961ds/22565Mi)
% 29.05/4.56 % (1489741)Instruction limit reached!
% 29.05/4.56 % (1489741)------------------------------
% 29.05/4.56 % (1489741)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.05/4.56 % (1489741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.05/4.56 % (1489741)CaDiCaL version: 2.1.3
% 29.05/4.56 % (1489741)Termination reason: Instruction limit
% 29.05/4.56 % (1489741)Termination phase: Saturation
% 29.05/4.56 % (1489741)Time elapsed: 2.826 s
% 29.05/4.56 % (1489741)Peak memory usage: 22 MB
% 29.05/4.56 % (1489741)Instructions burned: 3512 (million)
% 29.05/4.56 % (1489753) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1489682-1489753"...
% 29.05/4.56 % (1489763)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=981760077:i=8173:av=off_2957 on theBenchmark for (2957ds/8173Mi)
% 29.05/4.56 % (1489753)...printing done.
% 29.05/4.56 % (1489753)Refutation found. Thanks to Tanya!
% 29.05/4.56 % SZS status Theorem for theBenchmark
% 29.05/4.56 % SZS output start Proof for theBenchmark
% 29.05/4.56 thf(type_def_5, type, unsorted: $tType).
% 29.05/4.56 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 29.05/4.56 thf(type_def_7, type, d_unsorted: $tType).
% 29.05/4.56 thf(func_def_0, type, subrel: (($i > $i > $o) > ($i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_1, type, inv: (($i > $i > $o) > $i > $i > $o)).
% 29.05/4.56 thf(func_def_2, type, idem: ((($i > $i > $o) > $i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_3, type, infl: ((($i > $i > $o) > $i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_4, type, mono: ((($i > $i > $o) > $i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_5, type, refl: (($i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_6, type, irrefl: (($i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_7, type, rc: (($i > $i > $o) > $i > $i > $o)).
% 29.05/4.56 thf(func_def_8, type, symm: (($i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_9, type, antisymm: (($i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_10, type, asymm: (($i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_11, type, sc: (($i > $i > $o) > $i > $i > $o)).
% 29.05/4.56 thf(func_def_12, type, trans: (($i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_13, type, tc: (($i > $i > $o) > $i > $i > $o)).
% 29.05/4.56 thf(func_def_14, type, trc: (($i > $i > $o) > $i > $i > $o)).
% 29.05/4.56 thf(func_def_15, type, trsc: (($i > $i > $o) > $i > $i > $o)).
% 29.05/4.56 thf(func_def_16, type, po: (($i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_17, type, so: (($i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_18, type, total: (($i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_19, type, term: (($i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_20, type, ind: (($i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_21, type, innf: (($i > $i > $o) > $i > $o)).
% 29.05/4.56 thf(func_def_22, type, nfof: (($i > $i > $o) > $i > $i > $o)).
% 29.05/4.56 thf(func_def_23, type, norm: (($i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_24, type, join: (($i > $i > $o) > $i > $i > $o)).
% 29.05/4.56 thf(func_def_25, type, lconfl: (($i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_26, type, sconfl: (($i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_27, type, confl: (($i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_28, type, cr: (($i > $i > $o) > $o)).
% 29.05/4.56 thf(func_def_29, type, d2unsorted: (d_unsorted > $i)).
% 29.05/4.56 thf(func_def_30, type, d_unsorted_0: d_unsorted).
% 29.05/4.56 thf(func_def_32, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 29.05/4.56 thf(func_def_33, type, vOR: ($o > $o > $o)).
% 29.05/4.56 thf(func_def_34, type, vNOT: ($o > $o)).
% 29.05/4.56 thf(func_def_35, type, db3: !>[X0: $tType]:(X0)).
% 29.05/4.56 thf(func_def_36, type, db0: !>[X0: $tType]:(X0)).
% 29.05/4.56 thf(func_def_37, type, db1: !>[X0: $tType]:(X0)).
% 29.05/4.56 thf(func_def_38, type, db2: !>[X0: $tType]:(X0)).
% 29.05/4.56 thf(func_def_39, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 29.05/4.56 thf(func_def_40, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 29.05/4.56 thf(func_def_41, type, db4: !>[X0: $tType]:(X0)).
% 29.05/4.56 thf(func_def_42, type, db5: !>[X0: $tType]:(X0)).
% 29.05/4.56 thf(func_def_43, type, vAND: ($o > $o > $o)).
% 29.05/4.56 thf(func_def_44, type, db7: !>[X0: $tType]:(X0)).
% 29.05/4.56 thf(func_def_45, type, db6: !>[X0: $tType]:(X0)).
% 29.05/4.56 thf(func_def_46, type, db9: !>[X0: $tType]:(X0)).
% 29.05/4.56 thf(func_def_47, type, db8: !>[X0: $tType]:(X0)).
% 29.05/4.56 thf(func_def_48, type, vIMP: ($o > $o > $o)).
% 29.05/4.56 thf(func_def_49, type, sK0: ($i > d_unsorted)).
% 29.05/4.56 thf(func_def_53, type, sK2: ($i > $i > $o)).
% 29.05/4.56 thf(func_def_55, type, sK4: ($i > $o)).
% 29.05/4.56 thf(func_def_56, type, sK5: ($i > $o)).
% 29.05/4.56 thf(func_def_57, type, sK6: ($i > $i)).
% 29.05/4.56 thf(func_def_58, type, sK7: ($i > $i)).
% 29.05/4.56 thf(func_def_59, type, sK8: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_60, type, sK9: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_61, type, sK10: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_62, type, sK11: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_63, type, sK12: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_64, type, sK13: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_65, type, sK14: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_66, type, sK15: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_67, type, sK16: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_68, type, sK17: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_69, type, sK18: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_70, type, sK19: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_71, type, sK20: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_72, type, sK21: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_73, type, sK22: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_74, type, sK23: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_75, type, sK24: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_76, type, sK25: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_77, type, sK26: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_78, type, sK27: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_79, type, sK28: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_80, type, sK29: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_81, type, sK30: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_82, type, sK31: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_83, type, sK32: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_84, type, sK33: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_85, type, sK34: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_86, type, sK35: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_87, type, sK36: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_88, type, sK37: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_89, type, sK38: ($i > $i)).
% 29.05/4.56 thf(func_def_90, type, sK39: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_91, type, sK40: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_92, type, sK41: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_93, type, sK42: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_94, type, sK43: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_95, type, sK44: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_96, type, sK45: ($i > $i)).
% 29.05/4.56 thf(func_def_97, type, sK46: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_98, type, sK47: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_99, type, sK48: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_100, type, sK49: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_101, type, sK50: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_102, type, sK51: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_104, type, sK53: ($i > $i)).
% 29.05/4.56 thf(func_def_105, type, sK54: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_106, type, sK55: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_107, type, sK56: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_108, type, sK57: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_109, type, sK58: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_110, type, sK59: (($i > $i > $o) > $i)).
% 29.05/4.56 thf(func_def_111, type, sK60: (($i > $o) > $i)).
% 29.05/4.56 thf(func_def_112, type, sK61: (($i > $o) > $i)).
% 29.05/4.56 thf(func_def_113, type, sK62: ($i > ($i > $o) > $i > $i > $o)).
% 29.05/4.56 thf(func_def_114, type, sK63: (($i > $o) > $i > $i > $i > $o)).
% 29.05/4.56 thf(func_def_115, type, sK64: (($i > $o) > $i > $i > $i > $o)).
% 29.05/4.56 thf(func_def_116, type, sK65: (($i > $o) > $i > $i > $i > $o)).
% 29.05/4.56 thf(func_def_117, type, sK66: (($i > $o) > $i)).
% 29.05/4.56 thf(func_def_118, type, sK67: (($i > $o) > $i > $i > $i > $o)).
% 29.05/4.56 thf(f1,axiom,(
% 29.05/4.56 (cr = (^[X4 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i,X36 : ($i > $i > $o),X37 : ($i > $i > $o)] : ((X37 @ X6 @ X7) | ~ ! [X14 : $i,X15 : $i] : ((X37 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X26 : $i] : ((X37 @ X12 @ X26) | ~(X37 @ X13 @ X26) | ~(X37 @ X12 @ X13)) | (X36 @ X7 @ X6) | ~ ! [X14 : $i,X15 : $i] : ((X36 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X25 : $i] : ((X36 @ X12 @ X25) | ~(X36 @ X13 @ X25) | ~(X36 @ X12 @ X13)) | ~ ! [X27 : $i] : (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X27) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X26 : $i] : ((X5 @ X12 @ X26) | ~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13))) | ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X7 @ X27) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X25 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X13 @ X25) | ~(X5 @ X12 @ X13)))) | (X6 = X7) | (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X7) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X11 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13))) & ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X7 @ X6) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X11 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13))) & (X6 != X7)))))) & (confl = (^[X4 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i,X11 : $i,X33 : ($i > $i > $o),X34 : ($i > $i > $o)] : ((X34 @ X11 @ X7) | ~ ! [X14 : $i,X15 : $i] : ((X34 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X26 : $i] : ((X34 @ X12 @ X26) | ~(X34 @ X13 @ X26) | ~(X34 @ X12 @ X13)) | (X33 @ X7 @ X11) | ~ ! [X14 : $i,X15 : $i] : ((X33 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X25 : $i] : ((X33 @ X12 @ X25) | ~(X33 @ X13 @ X25) | ~(X33 @ X12 @ X13)) | ~ ! [X27 : $i] : (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X11 @ X27) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X26 : $i] : ((X5 @ X12 @ X26) | ~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13))) | ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X7 @ X27) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X25 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X13 @ X25) | ~(X5 @ X12 @ X13)))) | (X7 = X11) | (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X7) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X35 : $i] : ((X5 @ X12 @ X35) | ~(X5 @ X13 @ X35) | ~(X5 @ X12 @ X13))) & (X6 != X7)) | (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X11) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X26 : $i] : ((X5 @ X12 @ X26) | ~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13))) & (X6 != X11)))))) & (sconfl = (^[X4 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i,X11 : $i,X30 : ($i > $i > $o),X31 : ($i > $i > $o)] : ((X31 @ X11 @ X7) | ~ ! [X14 : $i,X15 : $i] : ((X31 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X26 : $i] : ((X31 @ X12 @ X26) | ~(X31 @ X13 @ X26) | ~(X31 @ X12 @ X13)) | (X30 @ X7 @ X11) | ~ ! [X14 : $i,X15 : $i] : ((X30 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X25 : $i] : ((X30 @ X12 @ X25) | ~(X30 @ X13 @ X25) | ~(X30 @ X12 @ X13)) | ~ ! [X27 : $i] : (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X11 @ X27) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X26 : $i] : ((X5 @ X12 @ X26) | ~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13))) | ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X7 @ X27) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X25 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X13 @ X25) | ~(X5 @ X12 @ X13)))) | (X7 = X11) | (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X7) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X32 : $i] : ((X5 @ X12 @ X32) | ~(X5 @ X13 @ X32) | ~(X5 @ X12 @ X13))) & (X6 != X7)) | ~(X4 @ X6 @ X11))))) & (lconfl = (^[X4 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i,X11 : $i,X28 : ($i > $i > $o),X29 : ($i > $i > $o)] : ((X29 @ X11 @ X7) | ~ ! [X14 : $i,X15 : $i] : ((X29 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X26 : $i] : ((X29 @ X12 @ X26) | ~(X29 @ X13 @ X26) | ~(X29 @ X12 @ X13)) | (X28 @ X7 @ X11) | ~ ! [X14 : $i,X15 : $i] : ((X28 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X25 : $i] : ((X28 @ X12 @ X25) | ~(X28 @ X13 @ X25) | ~(X28 @ X12 @ X13)) | ~ ! [X27 : $i] : (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X11 @ X27) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X26 : $i] : ((X5 @ X12 @ X26) | ~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13))) | ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X7 @ X27) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X25 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X13 @ X25) | ~(X5 @ X12 @ X13)))) | (X7 = X11) | ~(X4 @ X6 @ X7) | ~(X4 @ X6 @ X11))))) & (join = (^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : (~(! [X27 : $i] : (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X27) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X26 : $i] : ((X5 @ X12 @ X26) | ~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13))) | ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X7 @ X27) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X25 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X13 @ X25) | ~(X5 @ X12 @ X13)))) & ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X7) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X26 : $i] : ((X5 @ X12 @ X26) | ~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13))) & ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X7 @ X6) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X25 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X13 @ X25) | ~(X5 @ X12 @ X13))) & (X6 != X7))))) & (norm = (^[X4 : ($i > $i > $o)] : (! [X6 : $i,X23 : $i] : (~ ! [X24 : $i] : (~ ! [X22 : $i] : ~(X4 @ X24 @ X22) | ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X24) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X11 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13)))) | ~(X4 @ X6 @ X23))))) & (nfof = (^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : (! [X22 : $i] : ~(X4 @ X6 @ X22) & (! [X5 : ($i > $i > $o)] : ((X5 @ X7 @ X6) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X11 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13))) | (X6 = X7))))) & (innf = (^[X4 : ($i > $i > $o), X6 : $i] : (! [X7 : $i] : ~(X4 @ X6 @ X7)))) & (ind = (^[X4 : ($i > $i > $o)] : (! [X20 : ($i > $o),X21 : $i] : ((X20 @ X21) | ~ ! [X6 : $i] : ((X20 @ X6) | ~ ! [X7 : $i] : ((X20 @ X7) | ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X7) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X11 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13))))))))) & (term = (^[X4 : ($i > $i > $o)] : (! [X18 : ($i > $o),X19 : $i] : (~ ! [X6 : $i] : (~ ! [X7 : $i] : (~(X4 @ X6 @ X7) | ~(X18 @ X7)) | ~(X18 @ X6)) | ~(X18 @ X19))))) & (total = (^[X4 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i] : ((X4 @ X7 @ X6) | (X4 @ X6 @ X7) | (X6 = X7))))) & (so = (^[X4 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i,X11 : $i] : ((X4 @ X6 @ X11) | ~(X4 @ X7 @ X11) | ~(X4 @ X6 @ X7)) & ! [X6 : $i,X7 : $i] : (~(X4 @ X7 @ X6) | ~(X4 @ X6 @ X7))))) & (po = (^[X4 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i,X11 : $i] : ((X4 @ X6 @ X11) | ~(X4 @ X7 @ X11) | ~(X4 @ X6 @ X7)) & ! [X6 : $i,X7 : $i] : ((X6 = X7) | ~(X4 @ X7 @ X6) | ~(X4 @ X6 @ X7)) & ! [X6 : $i] : (X4 @ X6 @ X6)))) & (trsc = (^[X4 : ($i > $i > $o), X16 : $i, X17 : $i] : (! [X5 : ($i > $i > $o)] : ((X5 @ X16 @ X17) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X11 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13))) | ! [X5 : ($i > $i > $o)] : ((X5 @ X17 @ X16) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X11 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13))) | (X16 = X17)))) & (trc = (^[X4 : ($i > $i > $o), X16 : $i, X17 : $i] : (! [X5 : ($i > $i > $o)] : ((X5 @ X16 @ X17) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X11 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13))) | (X16 = X17)))) & (tc = (^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : (! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X7) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X11 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13)))))) & (trans = (^[X4 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i,X11 : $i] : ((X4 @ X6 @ X11) | ~(X4 @ X7 @ X11) | ~(X4 @ X6 @ X7))))) & (sc = (^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : ((X4 @ X6 @ X7) | (X4 @ X7 @ X6)))) & (asymm = (^[X4 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i] : (~(X4 @ X7 @ X6) | ~(X4 @ X6 @ X7))))) & (antisymm = (^[X4 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i] : ((X6 = X7) | ~(X4 @ X7 @ X6) | ~(X4 @ X6 @ X7))))) & (symm = (^[X4 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i] : ((X4 @ X7 @ X6) | ~(X4 @ X6 @ X7))))) & (rc = (^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : ((X4 @ X6 @ X7) | (X6 = X7)))) & (irrefl = (^[X4 : ($i > $i > $o)] : (! [X6 : $i] : ~(X4 @ X6 @ X6)))) & (refl = (^[X4 : ($i > $i > $o)] : (! [X6 : $i] : (X4 @ X6 @ X6)))) & (mono = (^[X8 : (($i > $i > $o) > $i > $i > $o)] : (! [X4 : ($i > $i > $o),X5 : ($i > $i > $o),X9 : $i,X10 : $i] : ((X8 @ X5 @ X9 @ X10) | ~(X8 @ X4 @ X9 @ X10) | ~ ! [X6 : $i,X7 : $i] : ((X5 @ X6 @ X7) | ~(X4 @ X6 @ X7)))))) & (infl = (^[X8 : (($i > $i > $o) > $i > $i > $o)] : (! [X4 : ($i > $i > $o),X6 : $i,X7 : $i] : ((X8 @ X4 @ X6 @ X7) | ~(X4 @ X6 @ X7))))) & (idem = (^[X8 : (($i > $i > $o) > $i > $i > $o)] : (! [X4 : ($i > $i > $o)] : (((X8 @ X4)) = ((X8 @ (X8 @ X4))))))) & (inv = (^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : ((X4 @ X7 @ X6)))) & (subrel = (^[X4 : ($i > $i > $o), X5 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i] : ((X5 @ X6 @ X7) | ~(X4 @ X6 @ X7))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X3))) => (X2 = X3)) & ! [X1 : d_unsorted] : (X1 = d_unsorted_0) & ! [X0 : $i] : ? [X1 : d_unsorted] : (X0 = ((d2unsorted @ X1)))),
% 29.05/4.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',sev441_1)).
% 29.05/4.56 thf(f2,conjecture,(
% 29.05/4.56 (ind = (^[X0 : ($i > $i > $o)] : (! [X1 : ($i > $o)] : (! [X2 : $i] : (! [X3 : $i] : ((tc @ X0 @ X2 @ X3) => (X1 @ X3)) => (X1 @ X2)) => ! [X2 : $i] : (X1 @ X2)))))),
% 29.05/4.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satisfying_the_induction_principle)).
% 29.05/4.56 thf(f3,negated_conjecture,(
% 29.05/4.56 ~ (ind = (^[X0 : ($i > $i > $o)] : (! [X1 : ($i > $o)] : (! [X2 : $i] : (! [X3 : $i] : ((tc @ X0 @ X2 @ X3) => (X1 @ X3)) => (X1 @ X2)) => ! [X2 : $i] : (X1 @ X2)))))),
% 29.05/4.56 inference(negated_conjecture,[status(cth)],[f2])).
% 29.05/4.56 thf(f4,plain,(
% 29.05/4.56 (cr = (^[X0 : ($i > $i > $o)] : (! [X1 : $i,X2 : $i,X3 : ($i > $i > $o),X4 : ($i > $i > $o)] : ((X4 @ X1 @ X2) | ~ ! [X5 : $i,X6 : $i] : ((X4 @ X5 @ X6) | ~(X0 @ X5 @ X6)) | ~ ! [X7 : $i,X8 : $i,X9 : $i] : ((X4 @ X7 @ X9) | ~(X4 @ X8 @ X9) | ~(X4 @ X7 @ X8)) | (X3 @ X2 @ X1) | ~ ! [X10 : $i,X11 : $i] : ((X3 @ X10 @ X11) | ~(X0 @ X10 @ X11)) | ~ ! [X12 : $i,X13 : $i,X14 : $i] : ((X3 @ X12 @ X14) | ~(X3 @ X13 @ X14) | ~(X3 @ X12 @ X13)) | ~ ! [X15 : $i] : (~ ! [X16 : ($i > $i > $o)] : ((X16 @ X1 @ X15) | ~ ! [X17 : $i,X18 : $i] : ((X16 @ X17 @ X18) | ~(X0 @ X17 @ X18)) | ~ ! [X19 : $i,X20 : $i,X21 : $i] : ((X16 @ X19 @ X21) | ~(X16 @ X20 @ X21) | ~(X16 @ X19 @ X20))) | ~ ! [X22 : ($i > $i > $o)] : ((X22 @ X2 @ X15) | ~ ! [X23 : $i,X24 : $i] : ((X22 @ X23 @ X24) | ~(X0 @ X23 @ X24)) | ~ ! [X25 : $i,X26 : $i,X27 : $i] : ((X22 @ X25 @ X27) | ~(X22 @ X26 @ X27) | ~(X22 @ X25 @ X26)))) | (X1 = X2) | (~ ! [X28 : ($i > $i > $o)] : ((X28 @ X1 @ X2) | ~ ! [X29 : $i,X30 : $i] : ((X28 @ X29 @ X30) | ~(X0 @ X29 @ X30)) | ~ ! [X31 : $i,X32 : $i,X33 : $i] : ((X28 @ X31 @ X33) | ~(X28 @ X32 @ X33) | ~(X28 @ X31 @ X32))) & ~ ! [X34 : ($i > $i > $o)] : ((X34 @ X2 @ X1) | ~ ! [X35 : $i,X36 : $i] : ((X34 @ X35 @ X36) | ~(X0 @ X35 @ X36)) | ~ ! [X37 : $i,X38 : $i,X39 : $i] : ((X34 @ X37 @ X39) | ~(X34 @ X38 @ X39) | ~(X34 @ X37 @ X38))) & (X1 != X2)))))) & (confl = (^[X40 : ($i > $i > $o)] : (! [X41 : $i,X42 : $i,X43 : $i,X44 : ($i > $i > $o),X45 : ($i > $i > $o)] : ((X45 @ X43 @ X42) | ~ ! [X46 : $i,X47 : $i] : ((X45 @ X46 @ X47) | ~(X40 @ X46 @ X47)) | ~ ! [X48 : $i,X49 : $i,X50 : $i] : ((X45 @ X48 @ X50) | ~(X45 @ X49 @ X50) | ~(X45 @ X48 @ X49)) | (X44 @ X42 @ X43) | ~ ! [X51 : $i,X52 : $i] : ((X44 @ X51 @ X52) | ~(X40 @ X51 @ X52)) | ~ ! [X53 : $i,X54 : $i,X55 : $i] : ((X44 @ X53 @ X55) | ~(X44 @ X54 @ X55) | ~(X44 @ X53 @ X54)) | ~ ! [X56 : $i] : (~ ! [X57 : ($i > $i > $o)] : ((X57 @ X43 @ X56) | ~ ! [X58 : $i,X59 : $i] : ((X57 @ X58 @ X59) | ~(X40 @ X58 @ X59)) | ~ ! [X60 : $i,X61 : $i,X62 : $i] : ((X57 @ X60 @ X62) | ~(X57 @ X61 @ X62) | ~(X57 @ X60 @ X61))) | ~ ! [X63 : ($i > $i > $o)] : ((X63 @ X42 @ X56) | ~ ! [X64 : $i,X65 : $i] : ((X63 @ X64 @ X65) | ~(X40 @ X64 @ X65)) | ~ ! [X66 : $i,X67 : $i,X68 : $i] : ((X63 @ X66 @ X68) | ~(X63 @ X67 @ X68) | ~(X63 @ X66 @ X67)))) | (X42 = X43) | (~ ! [X69 : ($i > $i > $o)] : ((X69 @ X41 @ X42) | ~ ! [X70 : $i,X71 : $i] : ((X69 @ X70 @ X71) | ~(X40 @ X70 @ X71)) | ~ ! [X72 : $i,X73 : $i,X74 : $i] : ((X69 @ X72 @ X74) | ~(X69 @ X73 @ X74) | ~(X69 @ X72 @ X73))) & (X41 != X42)) | (~ ! [X75 : ($i > $i > $o)] : ((X75 @ X41 @ X43) | ~ ! [X76 : $i,X77 : $i] : ((X75 @ X76 @ X77) | ~(X40 @ X76 @ X77)) | ~ ! [X78 : $i,X79 : $i,X80 : $i] : ((X75 @ X78 @ X80) | ~(X75 @ X79 @ X80) | ~(X75 @ X78 @ X79))) & (X41 != X43)))))) & (sconfl = (^[X81 : ($i > $i > $o)] : (! [X82 : $i,X83 : $i,X84 : $i,X85 : ($i > $i > $o),X86 : ($i > $i > $o)] : ((X86 @ X84 @ X83) | ~ ! [X87 : $i,X88 : $i] : ((X86 @ X87 @ X88) | ~(X81 @ X87 @ X88)) | ~ ! [X89 : $i,X90 : $i,X91 : $i] : ((X86 @ X89 @ X91) | ~(X86 @ X90 @ X91) | ~(X86 @ X89 @ X90)) | (X85 @ X83 @ X84) | ~ ! [X92 : $i,X93 : $i] : ((X85 @ X92 @ X93) | ~(X81 @ X92 @ X93)) | ~ ! [X94 : $i,X95 : $i,X96 : $i] : ((X85 @ X94 @ X96) | ~(X85 @ X95 @ X96) | ~(X85 @ X94 @ X95)) | ~ ! [X97 : $i] : (~ ! [X98 : ($i > $i > $o)] : ((X98 @ X84 @ X97) | ~ ! [X99 : $i,X100 : $i] : ((X98 @ X99 @ X100) | ~(X81 @ X99 @ X100)) | ~ ! [X101 : $i,X102 : $i,X103 : $i] : ((X98 @ X101 @ X103) | ~(X98 @ X102 @ X103) | ~(X98 @ X101 @ X102))) | ~ ! [X104 : ($i > $i > $o)] : ((X104 @ X83 @ X97) | ~ ! [X105 : $i,X106 : $i] : ((X104 @ X105 @ X106) | ~(X81 @ X105 @ X106)) | ~ ! [X107 : $i,X108 : $i,X109 : $i] : ((X104 @ X107 @ X109) | ~(X104 @ X108 @ X109) | ~(X104 @ X107 @ X108)))) | (X83 = X84) | (~ ! [X110 : ($i > $i > $o)] : ((X110 @ X82 @ X83) | ~ ! [X111 : $i,X112 : $i] : ((X110 @ X111 @ X112) | ~(X81 @ X111 @ X112)) | ~ ! [X113 : $i,X114 : $i,X115 : $i] : ((X110 @ X113 @ X115) | ~(X110 @ X114 @ X115) | ~(X110 @ X113 @ X114))) & (X82 != X83)) | ~(X81 @ X82 @ X84))))) & (lconfl = (^[X116 : ($i > $i > $o)] : (! [X117 : $i,X118 : $i,X119 : $i,X120 : ($i > $i > $o),X121 : ($i > $i > $o)] : ((X121 @ X119 @ X118) | ~ ! [X122 : $i,X123 : $i] : ((X121 @ X122 @ X123) | ~(X116 @ X122 @ X123)) | ~ ! [X124 : $i,X125 : $i,X126 : $i] : ((X121 @ X124 @ X126) | ~(X121 @ X125 @ X126) | ~(X121 @ X124 @ X125)) | (X120 @ X118 @ X119) | ~ ! [X127 : $i,X128 : $i] : ((X120 @ X127 @ X128) | ~(X116 @ X127 @ X128)) | ~ ! [X129 : $i,X130 : $i,X131 : $i] : ((X120 @ X129 @ X131) | ~(X120 @ X130 @ X131) | ~(X120 @ X129 @ X130)) | ~ ! [X132 : $i] : (~ ! [X133 : ($i > $i > $o)] : ((X133 @ X119 @ X132) | ~ ! [X134 : $i,X135 : $i] : ((X133 @ X134 @ X135) | ~(X116 @ X134 @ X135)) | ~ ! [X136 : $i,X137 : $i,X138 : $i] : ((X133 @ X136 @ X138) | ~(X133 @ X137 @ X138) | ~(X133 @ X136 @ X137))) | ~ ! [X139 : ($i > $i > $o)] : ((X139 @ X118 @ X132) | ~ ! [X140 : $i,X141 : $i] : ((X139 @ X140 @ X141) | ~(X116 @ X140 @ X141)) | ~ ! [X142 : $i,X143 : $i,X144 : $i] : ((X139 @ X142 @ X144) | ~(X139 @ X143 @ X144) | ~(X139 @ X142 @ X143)))) | (X118 = X119) | ~(X116 @ X117 @ X118) | ~(X116 @ X117 @ X119))))) & (join = (^[X145 : ($i > $i > $o), X146 : $i, X147 : $i] : (~(! [X148 : $i] : (~ ! [X149 : ($i > $i > $o)] : ((X149 @ X146 @ X148) | ~ ! [X150 : $i,X151 : $i] : ((X149 @ X150 @ X151) | ~(X145 @ X150 @ X151)) | ~ ! [X152 : $i,X153 : $i,X154 : $i] : ((X149 @ X152 @ X154) | ~(X149 @ X153 @ X154) | ~(X149 @ X152 @ X153))) | ~ ! [X155 : ($i > $i > $o)] : ((X155 @ X147 @ X148) | ~ ! [X156 : $i,X157 : $i] : ((X155 @ X156 @ X157) | ~(X145 @ X156 @ X157)) | ~ ! [X158 : $i,X159 : $i,X160 : $i] : ((X155 @ X158 @ X160) | ~(X155 @ X159 @ X160) | ~(X155 @ X158 @ X159)))) & ~ ! [X161 : ($i > $i > $o)] : ((X161 @ X146 @ X147) | ~ ! [X162 : $i,X163 : $i] : ((X161 @ X162 @ X163) | ~(X145 @ X162 @ X163)) | ~ ! [X164 : $i,X165 : $i,X166 : $i] : ((X161 @ X164 @ X166) | ~(X161 @ X165 @ X166) | ~(X161 @ X164 @ X165))) & ~ ! [X167 : ($i > $i > $o)] : ((X167 @ X147 @ X146) | ~ ! [X168 : $i,X169 : $i] : ((X167 @ X168 @ X169) | ~(X145 @ X168 @ X169)) | ~ ! [X170 : $i,X171 : $i,X172 : $i] : ((X167 @ X170 @ X172) | ~(X167 @ X171 @ X172) | ~(X167 @ X170 @ X171))) & (X146 != X147))))) & (norm = (^[X173 : ($i > $i > $o)] : (! [X174 : $i,X175 : $i] : (~ ! [X176 : $i] : (~ ! [X177 : $i] : ~(X173 @ X176 @ X177) | ~ ! [X178 : ($i > $i > $o)] : ((X178 @ X174 @ X176) | ~ ! [X179 : $i,X180 : $i] : ((X178 @ X179 @ X180) | ~(X173 @ X179 @ X180)) | ~ ! [X181 : $i,X182 : $i,X183 : $i] : ((X178 @ X181 @ X183) | ~(X178 @ X182 @ X183) | ~(X178 @ X181 @ X182)))) | ~(X173 @ X174 @ X175))))) & (nfof = (^[X184 : ($i > $i > $o), X185 : $i, X186 : $i] : (! [X187 : $i] : ~(X184 @ X185 @ X187) & (! [X188 : ($i > $i > $o)] : ((X188 @ X186 @ X185) | ~ ! [X189 : $i,X190 : $i] : ((X188 @ X189 @ X190) | ~(X184 @ X189 @ X190)) | ~ ! [X191 : $i,X192 : $i,X193 : $i] : ((X188 @ X191 @ X193) | ~(X188 @ X192 @ X193) | ~(X188 @ X191 @ X192))) | (X185 = X186))))) & (innf = (^[X194 : ($i > $i > $o), X195 : $i] : (! [X196 : $i] : ~(X194 @ X195 @ X196)))) & (ind = (^[X197 : ($i > $i > $o)] : (! [X198 : ($i > $o),X199 : $i] : ((X198 @ X199) | ~ ! [X200 : $i] : ((X198 @ X200) | ~ ! [X201 : $i] : ((X198 @ X201) | ~ ! [X202 : ($i > $i > $o)] : ((X202 @ X200 @ X201) | ~ ! [X203 : $i,X204 : $i] : ((X202 @ X203 @ X204) | ~(X197 @ X203 @ X204)) | ~ ! [X205 : $i,X206 : $i,X207 : $i] : ((X202 @ X205 @ X207) | ~(X202 @ X206 @ X207) | ~(X202 @ X205 @ X206))))))))) & (term = (^[X208 : ($i > $i > $o)] : (! [X209 : ($i > $o),X210 : $i] : (~ ! [X211 : $i] : (~ ! [X212 : $i] : (~(X208 @ X211 @ X212) | ~(X209 @ X212)) | ~(X209 @ X211)) | ~(X209 @ X210))))) & (total = (^[X213 : ($i > $i > $o)] : (! [X214 : $i,X215 : $i] : ((X213 @ X215 @ X214) | (X213 @ X214 @ X215) | (X214 = X215))))) & (so = (^[X216 : ($i > $i > $o)] : (! [X217 : $i,X218 : $i,X219 : $i] : ((X216 @ X217 @ X219) | ~(X216 @ X218 @ X219) | ~(X216 @ X217 @ X218)) & ! [X220 : $i,X221 : $i] : (~(X216 @ X221 @ X220) | ~(X216 @ X220 @ X221))))) & (po = (^[X222 : ($i > $i > $o)] : (! [X223 : $i,X224 : $i,X225 : $i] : ((X222 @ X223 @ X225) | ~(X222 @ X224 @ X225) | ~(X222 @ X223 @ X224)) & ! [X226 : $i,X227 : $i] : ((X226 = X227) | ~(X222 @ X227 @ X226) | ~(X222 @ X226 @ X227)) & ! [X228 : $i] : (X222 @ X228 @ X228)))) & (trsc = (^[X229 : ($i > $i > $o), X230 : $i, X231 : $i] : (! [X232 : ($i > $i > $o)] : ((X232 @ X230 @ X231) | ~ ! [X233 : $i,X234 : $i] : ((X232 @ X233 @ X234) | ~(X229 @ X233 @ X234)) | ~ ! [X235 : $i,X236 : $i,X237 : $i] : ((X232 @ X235 @ X237) | ~(X232 @ X236 @ X237) | ~(X232 @ X235 @ X236))) | ! [X238 : ($i > $i > $o)] : ((X238 @ X231 @ X230) | ~ ! [X239 : $i,X240 : $i] : ((X238 @ X239 @ X240) | ~(X229 @ X239 @ X240)) | ~ ! [X241 : $i,X242 : $i,X243 : $i] : ((X238 @ X241 @ X243) | ~(X238 @ X242 @ X243) | ~(X238 @ X241 @ X242))) | (X230 = X231)))) & (trc = (^[X244 : ($i > $i > $o), X245 : $i, X246 : $i] : (! [X247 : ($i > $i > $o)] : ((X247 @ X245 @ X246) | ~ ! [X248 : $i,X249 : $i] : ((X247 @ X248 @ X249) | ~(X244 @ X248 @ X249)) | ~ ! [X250 : $i,X251 : $i,X252 : $i] : ((X247 @ X250 @ X252) | ~(X247 @ X251 @ X252) | ~(X247 @ X250 @ X251))) | (X245 = X246)))) & (tc = (^[X253 : ($i > $i > $o), X254 : $i, X255 : $i] : (! [X256 : ($i > $i > $o)] : ((X256 @ X254 @ X255) | ~ ! [X257 : $i,X258 : $i] : ((X256 @ X257 @ X258) | ~(X253 @ X257 @ X258)) | ~ ! [X259 : $i,X260 : $i,X261 : $i] : ((X256 @ X259 @ X261) | ~(X256 @ X260 @ X261) | ~(X256 @ X259 @ X260)))))) & (trans = (^[X262 : ($i > $i > $o)] : (! [X263 : $i,X264 : $i,X265 : $i] : ((X262 @ X263 @ X265) | ~(X262 @ X264 @ X265) | ~(X262 @ X263 @ X264))))) & (sc = (^[X266 : ($i > $i > $o), X267 : $i, X268 : $i] : ((X266 @ X267 @ X268) | (X266 @ X268 @ X267)))) & (asymm = (^[X269 : ($i > $i > $o)] : (! [X270 : $i,X271 : $i] : (~(X269 @ X271 @ X270) | ~(X269 @ X270 @ X271))))) & (antisymm = (^[X272 : ($i > $i > $o)] : (! [X273 : $i,X274 : $i] : ((X273 = X274) | ~(X272 @ X274 @ X273) | ~(X272 @ X273 @ X274))))) & (symm = (^[X275 : ($i > $i > $o)] : (! [X276 : $i,X277 : $i] : ((X275 @ X277 @ X276) | ~(X275 @ X276 @ X277))))) & (rc = (^[X278 : ($i > $i > $o), X279 : $i, X280 : $i] : ((X278 @ X279 @ X280) | (X279 = X280)))) & (irrefl = (^[X281 : ($i > $i > $o)] : (! [X282 : $i] : ~(X281 @ X282 @ X282)))) & (refl = (^[X283 : ($i > $i > $o)] : (! [X284 : $i] : (X283 @ X284 @ X284)))) & (mono = (^[X285 : (($i > $i > $o) > $i > $i > $o)] : (! [X286 : ($i > $i > $o),X287 : ($i > $i > $o),X288 : $i,X289 : $i] : ((X285 @ X287 @ X288 @ X289) | ~(X285 @ X286 @ X288 @ X289) | ~ ! [X290 : $i,X291 : $i] : ((X287 @ X290 @ X291) | ~(X286 @ X290 @ X291)))))) & (infl = (^[X292 : (($i > $i > $o) > $i > $i > $o)] : (! [X293 : ($i > $i > $o),X294 : $i,X295 : $i] : ((X292 @ X293 @ X294 @ X295) | ~(X293 @ X294 @ X295))))) & (idem = (^[X296 : (($i > $i > $o) > $i > $i > $o)] : (! [X297 : ($i > $i > $o)] : (((X296 @ X297)) = ((X296 @ (X296 @ X297))))))) & (inv = (^[X298 : ($i > $i > $o), X299 : $i, X300 : $i] : ((X298 @ X300 @ X299)))) & (subrel = (^[X301 : ($i > $i > $o), X302 : ($i > $i > $o)] : (! [X303 : $i,X304 : $i] : ((X302 @ X303 @ X304) | ~(X301 @ X303 @ X304))))) & ! [X305 : d_unsorted,X306 : d_unsorted] : ((((d2unsorted @ X305)) = ((d2unsorted @ X306))) => (X305 = X306)) & ! [X307 : d_unsorted] : (d_unsorted_0 = X307) & ! [X308 : $i] : ? [X309 : d_unsorted] : (((d2unsorted @ X309)) = X308)),
% 29.05/4.56 inference(rectify,[],[f1])).
% 29.05/4.56 thf(f5,plain,(
% 29.05/4.56 (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((((((((((~ (Y4 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y3)))))) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y6)) | (~ (Y2 @ Y6 @ Y5))) | (Y2 @ Y7 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y2 @ Y6 @ Y5)))))))) | (Y2 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y6 @ Y5))) | (Y1 @ Y7 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y1 @ Y4 @ Y3)))))))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! 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@ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (Y7 @ Y4 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (Y7 @ Y3 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y7)) | (~ (Y2 @ Y7 @ Y6))) | (Y2 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6)))))))) | (Y2 @ Y4 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y7)) | (~ (Y1 @ Y7 @ Y6))) | (Y1 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y1 @ Y3 @ Y4)))))))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! 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@ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (Y7 @ Y3 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y7)) | (~ (Y2 @ Y7 @ Y6))) | (Y2 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6)))))))) | (Y2 @ Y4 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y7)) | (~ (Y1 @ Y7 @ Y6))) | (Y1 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y1 @ Y3 @ Y4)))))))))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y5 @ Y3)) | (~ (Y0 @ Y5 @ Y4))) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! 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@ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y1 @ Y3)))))))))))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1)))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4))))))))))))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (Y0 @ Y2 @ Y1)) | (Y0 @ Y1 @ Y2)))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1)))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1)))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y1 @ Y2)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! 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[X305 : d_unsorted,X306 : d_unsorted] : ((((d2unsorted @ X305)) = ((d2unsorted @ X306))) => (X305 = X306)) & ! [X307 : d_unsorted] : (d_unsorted_0 = X307) & ! [X308 : $i] : ? [X309 : d_unsorted] : (((d2unsorted @ X309)) = X308)),
% 29.05/4.56 inference(fool_elimination,[],[f4])).
% 29.05/4.56 thf(f6,plain,(
% 29.05/4.56 ~ (ind = (^[X0 : ($i > $i > $o)] : (! [X1 : ($i > $o)] : (! [X2 : $i] : (! [X3 : $i] : ((tc @ X0 @ X2 @ X3) => (X1 @ X3)) => (X1 @ X2)) => ! [X4 : $i] : (X1 @ X4)))))),
% 29.05/4.56 inference(rectify,[],[f3])).
% 29.05/4.56 thf(f7,plain,(
% 29.05/4.56 ~ (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((tc @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 29.05/4.56 inference(fool_elimination,[],[f6])).
% 29.05/4.56 thf(f8,plain,(
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@ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y4 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y5))))))) | (~ (Y0 @ Y4 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y2 @ Y1)))))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((~ (Y3 @ Y2 @ Y1)) | (Y0 @ Y3 @ Y2 @ Y1)))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : ((((d2unsorted @ X1)) = ((d2unsorted @ X0))) => (X0 = X1)) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3)),
% 29.05/4.56 inference(rectify,[],[f5])).
% 29.05/4.56 thf(f9,plain,(
% 29.05/4.56 (ind != (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((tc @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 29.05/4.56 inference(flattening,[],[f7])).
% 29.05/4.56 thf(f10,plain,(
% 29.05/4.56 (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((((((((((~ (Y4 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y3)))))) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y6)) | (~ (Y2 @ Y6 @ Y5))) | (Y2 @ Y7 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y2 @ Y6 @ Y5)))))))) | (Y2 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y6 @ Y5))) | (Y1 @ Y7 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y1 @ Y4 @ Y3)))))))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! 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@ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (Y7 @ Y4 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (Y7 @ Y3 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y7)) | (~ (Y2 @ Y7 @ Y6))) | (Y2 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6)))))))) | (Y2 @ Y4 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y7)) | (~ (Y1 @ Y7 @ Y6))) | (Y1 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y1 @ Y3 @ Y4)))))))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! 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@ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (Y7 @ Y3 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y7)) | (~ (Y2 @ Y7 @ Y6))) | (Y2 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6)))))))) | (Y2 @ Y4 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y7)) | (~ (Y1 @ Y7 @ Y6))) | (Y1 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y1 @ Y3 @ Y4)))))))))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y5 @ Y3)) | (~ (Y0 @ Y5 @ Y4))) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (Y7 @ Y4 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (Y7 @ Y3 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y7)) | (~ (Y2 @ Y7 @ Y6))) | (Y2 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6)))))))) | (Y2 @ Y4 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y7)) | (~ (Y1 @ Y7 @ Y6))) | (Y1 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y1 @ Y3 @ Y4)))))))))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! 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@ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y1 @ Y3)))))))))))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1)))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4))))))))))))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (Y0 @ Y2 @ Y1)) | (Y0 @ Y1 @ Y2)))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1)))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1)))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y1 @ Y2)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y4 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y5))))))) | (~ (Y0 @ Y4 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y2 @ Y1)))))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((~ (Y3 @ Y2 @ Y1)) | (Y0 @ Y3 @ Y2 @ Y1)))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : ((X0 = X1) | (((d2unsorted @ X1)) != ((d2unsorted @ X0)))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3)),
% 29.05/4.56 inference(ennf_transformation,[],[f8])).
% 29.05/4.56 thf(f11,plain,(
% 29.05/4.56 (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((((((((((~ (Y4 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y3)))))) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y6)) | (~ (Y2 @ Y6 @ Y5))) | (Y2 @ Y7 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y2 @ Y6 @ Y5)))))))) | (Y2 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y6 @ Y5))) | (Y1 @ Y7 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y1 @ Y4 @ Y3)))))))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((((((((~ (Y5 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y5 @ Y3)))))) | ((~ (Y5 = Y4)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y5 @ Y4))))))) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (Y7 @ Y4 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (Y7 @ Y3 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y7)) | (~ (Y2 @ Y7 @ Y6))) | (Y2 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6)))))))) | (Y2 @ Y4 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y7)) | (~ (Y1 @ Y7 @ Y6))) | (Y1 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y1 @ Y3 @ Y4)))))))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! 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@ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (Y7 @ Y3 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y7)) | (~ (Y2 @ Y7 @ Y6))) | (Y2 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6)))))))) | (Y2 @ Y4 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y7)) | (~ (Y1 @ Y7 @ Y6))) | (Y1 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y1 @ Y3 @ Y4)))))))))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y5 @ Y3)) | (~ (Y0 @ Y5 @ Y4))) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (Y7 @ Y4 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (Y7 @ Y3 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y7)) | (~ (Y2 @ Y7 @ Y6))) | (Y2 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6)))))))) | (Y2 @ Y4 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y7)) | (~ (Y1 @ Y7 @ Y6))) | (Y1 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y1 @ Y3 @ Y4)))))))))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y1 @ Y3)))))))))))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1)))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4))))))))))))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (Y0 @ Y2 @ Y1)) | (Y0 @ Y1 @ Y2)))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1)))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1)))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y1 @ Y2)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y4 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y5))))))) | (~ (Y0 @ Y4 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y2 @ Y1)))))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((~ (Y3 @ Y2 @ Y1)) | (Y0 @ Y3 @ Y2 @ Y1)))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : ((X0 = X1) | (((d2unsorted @ X1)) != ((d2unsorted @ X0)))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & ! [X3 : $i] : (((d2unsorted @ (sK0 @ X3))) = X3)),
% 29.05/4.56 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK0 @ X3)],[f10])).
% 29.05/4.56 thf(f12,plain,(
% 29.05/4.56 ( ! [X3 : $i] : ((((d2unsorted @ (sK0 @ X3))) = X3)) )),
% 29.05/4.56 inference(cnf_transformation,[],[f11])).
% 29.05/4.56 thf(f13,plain,(
% 29.05/4.56 ( ! [X2 : d_unsorted] : ((d_unsorted_0 = X2)) )),
% 29.05/4.56 inference(cnf_transformation,[],[f11])).
% 29.05/4.56 thf(f28,plain,(
% 29.05/4.56 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))))))))),
% 29.05/4.56 inference(cnf_transformation,[],[f11])).
% 29.05/4.56 thf(f35,plain,(
% 29.05/4.56 (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))))),
% 29.05/4.56 inference(cnf_transformation,[],[f11])).
% 29.05/4.56 thf(f44,plain,(
% 29.05/4.56 (ind != (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((tc @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 29.05/4.56 inference(cnf_transformation,[],[f9])).
% 29.05/4.56 thf(f46,definition,(
% 29.05/4.56 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 29.05/4.56 introduced(theory,[fool_exhaustiveness_axiom])).
% 29.05/4.56 thf(f47,plain,(
% 29.05/4.56 ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) != (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y4 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (Y7 @ Y5 @ Y6))))))))) @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 29.05/4.56 inference(definition_unfolding,[],[f44,f35,f28])).
% 29.05/4.56 thf(f48,plain,(
% 29.05/4.56 ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) != (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3)))) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ Y1))))))),
% 29.05/4.56 inference(beta-eta_normalization,[],[f47])).
% 29.05/4.56 thf(f85,plain,(
% 29.05/4.56 ( ! [X3 : $i] : ((((d2unsorted @ d_unsorted_0)) = X3)) )),
% 29.05/4.56 inference(forward_demodulation,[],[f12,f13])).
% 29.05/4.56 thf(f89,plain,(
% 29.05/4.56 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 29.05/4.56 inference(constrained_superposition,[],[f85,f85])).
% 29.05/4.56 thf(f94,plain,(
% 29.05/4.56 ((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) @ sK2)) != (((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3)))) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ Y1))))) @ sK2)))),
% 29.05/4.56 inference(negative_extensionality,[],[f48])).
% 29.05/4.56 thf(f95,plain,(
% 29.05/4.56 ($true = (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) @ sK2))) | ($true = (((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3)))) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ Y1))))) @ sK2)))),
% 29.05/4.56 inference(xor_proxy_clausification,[],[f94])).
% 29.05/4.56 thf(f96,plain,(
% 29.05/4.56 ($false = (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) @ sK2))) | ($false = (((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3)))) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ Y1))))) @ sK2)))),
% 29.05/4.56 inference(xor_proxy_clausification,[],[f94])).
% 29.05/4.56 thf(f97,plain,(
% 29.05/4.56 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK2 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3))))) | (Y1 @ Y3))))) | (Y1 @ Y2))))) | (Y1 @ Y0)))))))) | ($false = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK2 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))))))),
% 29.05/4.56 inference(beta-eta_normalization,[],[f96])).
% 29.05/4.56 thf(f98,plain,(
% 29.05/4.56 ($false = (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK2 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3))))) | (Y1 @ Y3))))) | (Y1 @ Y2))))) | (Y1 @ Y0))))) @ sK3))) | ($false = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK2 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))))))),
% 29.05/4.56 inference(sigma_proxy_clausification,[],[f97])).
% 29.05/4.56 thf(f99,plain,(
% 29.05/4.56 ($false = (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK2 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3))))) | (Y1 @ Y3))))) | (Y1 @ Y2))))) | (Y1 @ Y0))))) @ sK3))) | ($false = (((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK2 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))) @ sK4)))),
% 29.05/4.56 inference(sigma_proxy_clausification,[],[f98])).
% 29.05/4.56 thf(f100,plain,(
% 29.05/4.56 ($false = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK2 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))) | (Y0 @ Y2))))) | (Y0 @ Y1))))) | (Y0 @ sK3)))))) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1)))) => (sK4 @ Y1)))) => (sK4 @ Y0)))) => (!! @ $i @ sK4))))),
% 29.05/4.56 inference(beta-eta_normalization,[],[f99])).
% 29.05/4.56 thf(f101,plain,(
% 29.05/4.56 ($false = (((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK2 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))) | (Y0 @ Y2))))) | (Y0 @ Y1))))) | (Y0 @ sK3))) @ sK5))) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1)))) => (sK4 @ Y1)))) => (sK4 @ Y0)))) => (!! @ $i @ sK4))))),
% 29.05/4.56 inference(sigma_proxy_clausification,[],[f100])).
% 29.05/4.56 thf(f102,plain,(
% 29.05/4.56 ($false = (((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK2 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))) | (Y0 @ Y2))))) | (Y0 @ Y1))))) | (Y0 @ sK3))) @ sK5))) | ($false = ((!! @ $i @ sK4)))),
% 29.05/4.56 inference(imp_proxy_clausification,[],[f101])).
% 29.05/4.56 thf(f103,plain,(
% 29.05/4.56 ($false = (((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK2 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))) | (Y0 @ Y2))))) | (Y0 @ Y1))))) | (Y0 @ sK3))) @ sK5))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1)))) => (sK4 @ Y1)))) => (sK4 @ Y0))))))),
% 29.05/4.56 inference(imp_proxy_clausification,[],[f101])).
% 29.05/4.56 thf(f104,plain,(
% 29.05/4.56 ( ! [X1 : $i] : (($false = (((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK2 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))) | (Y0 @ Y2))))) | (Y0 @ Y1))))) | (Y0 @ sK3))) @ sK5))) | ($true = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1)))) => (sK4 @ Y1)))) => (sK4 @ Y0))) @ X1)))) )),
% 29.05/4.56 inference(pi_proxy_clausification,[],[f103])).
% 29.05/4.56 thf(f105,plain,(
% 29.05/4.56 ( ! [X1 : $i] : (($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))) | (sK5 @ Y1))))) | (sK5 @ Y0))))) | (sK5 @ sK3)))) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X1 @ Y0)))) => (sK4 @ Y0)))) => (sK4 @ X1))))) )),
% 29.05/4.56 inference(beta-eta_normalization,[],[f104])).
% 29.05/4.56 thf(f106,plain,(
% 29.05/4.56 ( ! [X1 : $i] : (($false = ((sK5 @ sK3))) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X1 @ Y0)))) => (sK4 @ Y0)))) => (sK4 @ X1))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f105])).
% 29.05/4.56 thf(f107,plain,(
% 29.05/4.56 ( ! [X1 : $i] : (($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))) | (sK5 @ Y1))))) | (sK5 @ Y0))))))) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X1 @ Y0)))) => (sK4 @ Y0)))) => (sK4 @ X1))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f105])).
% 29.05/4.56 thf(f108,plain,(
% 29.05/4.56 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))) | (sK5 @ Y1))))) | (sK5 @ Y0)))))) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X1 @ Y0)))) => (sK4 @ Y0)))) => (sK4 @ X1))))) )),
% 29.05/4.56 inference(not_proxy_clausification,[],[f107])).
% 29.05/4.56 thf(f109,plain,(
% 29.05/4.56 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))) | (sK5 @ Y1))))) | (sK5 @ Y0))) @ X2))) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X1 @ Y0)))) => (sK4 @ Y0)))) => (sK4 @ X1))))) )),
% 29.05/4.56 inference(pi_proxy_clausification,[],[f108])).
% 29.05/4.56 thf(f110,plain,(
% 29.05/4.56 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))) | (sK5 @ Y1))))) | (sK5 @ Y0))) @ X2))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X1 @ Y0)))) => (sK4 @ Y0)))))) | ($true = ((sK4 @ X1)))) )),
% 29.05/4.56 inference(imp_proxy_clausification,[],[f109])).
% 29.05/4.56 thf(f111,plain,(
% 29.05/4.56 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))) | (sK5 @ Y1))))) | (sK5 @ Y0))) @ X2))) | ($false = (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X1 @ Y0)))) => (sK4 @ Y0))) @ (sK6 @ X1)))) | ($true = ((sK4 @ X1)))) )),
% 29.05/4.56 inference(sigma_proxy_clausification,[],[f110])).
% 29.05/4.56 thf(f112,plain,(
% 29.05/4.56 ( ! [X2 : $i,X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X2 @ Y0))))) | (sK5 @ Y0))))) | (sK5 @ X2)))) | ($false = (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X1 @ (sK6 @ X1))))) => (sK4 @ (sK6 @ X1))))) | ($true = ((sK4 @ X1)))) )),
% 29.05/4.56 inference(beta-eta_normalization,[],[f111])).
% 29.05/4.56 thf(f113,plain,(
% 29.05/4.56 ( ! [X2 : $i,X1 : $i] : (($true = ((sK5 @ X2))) | ($false = (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X1 @ (sK6 @ X1))))) => (sK4 @ (sK6 @ X1))))) | ($true = ((sK4 @ X1))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X2 @ Y0))))) | (sK5 @ Y0)))))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f112])).
% 29.05/4.56 thf(f115,plain,(
% 29.05/4.56 ( ! [X2 : $i,X1 : $i] : (($true = ((sK5 @ X2))) | ($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X1 @ (sK6 @ X1))))))) | ($true = ((sK4 @ X1))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X2 @ Y0))))) | (sK5 @ Y0)))))))) )),
% 29.05/4.56 inference(imp_proxy_clausification,[],[f113])).
% 29.05/4.56 thf(f116,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((sK5 @ X2))) | ($true = (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X1 @ (sK6 @ X1)))) @ X3))) | ($true = ((sK4 @ X1))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X2 @ Y0))))) | (sK5 @ Y0)))))))) )),
% 29.05/4.56 inference(pi_proxy_clausification,[],[f115])).
% 29.05/4.56 thf(f117,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((sK5 @ X2))) | ($true = (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X1 @ (sK6 @ X1)))) @ X3))) | ($true = ((sK4 @ X1))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X2 @ Y0))))) | (sK5 @ Y0))))))) )),
% 29.05/4.56 inference(not_proxy_clausification,[],[f116])).
% 29.05/4.56 thf(f118,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((sK5 @ X2))) | ($true = (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X1 @ (sK6 @ X1)))) @ X3))) | ($true = ((sK4 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X2 @ Y0))))) | (sK5 @ Y0))) @ (sK7 @ X2))))) )),
% 29.05/4.56 inference(sigma_proxy_clausification,[],[f117])).
% 29.05/4.56 thf(f119,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((sK5 @ X2))) | ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X3 @ Y2 @ Y1)) | (~ (X3 @ Y1 @ Y0))) | (X3 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK2 @ Y1 @ Y0)) | (X3 @ Y1 @ Y0)))))))) | (X3 @ X1 @ (sK6 @ X1))))) | ($true = ((sK4 @ X1))) | ($false = (((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X2 @ (sK7 @ X2)))))) | (sK5 @ (sK7 @ X2)))))) )),
% 29.05/4.56 inference(beta-eta_normalization,[],[f118])).
% 29.05/4.56 thf(f120,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($false = (((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X2 @ (sK7 @ X2)))))) | (sK5 @ (sK7 @ X2))))) | ($true = (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X3 @ Y2 @ Y1)) | (~ (X3 @ Y1 @ Y0))) | (X3 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK2 @ Y1 @ Y0)) | (X3 @ Y1 @ Y0))))))))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f119])).
% 29.05/4.56 thf(f122,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($false = ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X2 @ (sK7 @ X2)))))))) | ($true = (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X3 @ Y2 @ Y1)) | (~ (X3 @ Y1 @ Y0))) | (X3 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK2 @ Y1 @ Y0)) | (X3 @ Y1 @ Y0))))))))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f120])).
% 29.05/4.56 thf(f123,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X2 @ (sK7 @ X2))))))) | ($true = (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X3 @ Y2 @ Y1)) | (~ (X3 @ Y1 @ Y0))) | (X3 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK2 @ Y1 @ Y0)) | (X3 @ Y1 @ Y0))))))))))) )),
% 29.05/4.56 inference(not_proxy_clausification,[],[f122])).
% 29.05/4.56 thf(f124,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X2 @ (sK7 @ X2)))) @ X4))) | ($true = (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X3 @ Y2 @ Y1)) | (~ (X3 @ Y1 @ Y0))) | (X3 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK2 @ Y1 @ Y0)) | (X3 @ Y1 @ Y0))))))))))) )),
% 29.05/4.56 inference(pi_proxy_clausification,[],[f123])).
% 29.05/4.56 thf(f125,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X2 @ (sK7 @ X2)))) @ X4))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK2 @ Y1 @ Y0)) | (X3 @ Y1 @ Y0))))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X3 @ Y2 @ Y1)) | (~ (X3 @ Y1 @ Y0))) | (X3 @ Y2 @ Y0)))))))))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f124])).
% 29.05/4.56 thf(f126,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X2 @ (sK7 @ X2)))) @ X4))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK2 @ Y1 @ Y0)) | (X3 @ Y1 @ Y0)))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X3 @ Y2 @ Y1)) | (~ (X3 @ Y1 @ Y0))) | (X3 @ Y2 @ Y0)))))))))))) )),
% 29.05/4.56 inference(not_proxy_clausification,[],[f125])).
% 29.05/4.56 thf(f127,plain,(
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% 29.05/4.56 inference(sigma_proxy_clausification,[],[f355])).
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% 29.05/4.56 inference(sigma_proxy_clausification,[],[f356])).
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% 29.05/4.56 inference(beta-eta_normalization,[],[f357])).
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% 29.05/4.56 inference(or_proxy_clausification,[],[f358])).
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% 29.05/4.56 inference(not_proxy_clausification,[],[f360])).
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% 29.05/4.56 inference(sigma_proxy_clausification,[],[f361])).
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% 29.05/4.56 inference(beta-eta_normalization,[],[f362])).
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% 29.05/4.56 inference(or_proxy_clausification,[],[f363])).
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% 29.05/4.56 inference(or_proxy_clausification,[],[f365])).
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% 29.05/4.56 inference(not_proxy_clausification,[],[f366])).
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% 29.05/4.56 inference(sigma_proxy_clausification,[],[f102])).
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% 29.05/4.56 inference(beta-eta_normalization,[],[f378])).
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% 29.05/4.56 inference(or_proxy_clausification,[],[f379])).
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% 29.05/4.56 inference(or_proxy_clausification,[],[f379])).
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% 29.05/4.56 inference(not_proxy_clausification,[],[f381])).
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% 29.05/4.56 inference(pi_proxy_clausification,[],[f382])).
% 29.05/4.56 thf(f384,plain,(
% 29.05/4.56 ( ! [X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ X1 @ Y0))))) | (sK5 @ Y0))))) | (sK5 @ X1)))) | ($false = ((sK4 @ sK52)))) )),
% 29.05/4.56 inference(beta-eta_normalization,[],[f383])).
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% 29.05/4.56 inference(or_proxy_clausification,[],[f384])).
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% 29.05/4.56 inference(not_proxy_clausification,[],[f385])).
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% 29.05/4.56 inference(sigma_proxy_clausification,[],[f386])).
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% 29.05/4.56 inference(beta-eta_normalization,[],[f387])).
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% 29.05/4.56 inference(or_proxy_clausification,[],[f388])).
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% 29.05/4.56 ( ! [X1 : $i] : (($true = ((sK5 @ X1))) | ($false = ((sK4 @ sK52))) | ($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X1 @ (sK53 @ X1)))))))) )),
% 29.05/4.56 inference(not_proxy_clausification,[],[f390])).
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% 29.05/4.56 inference(pi_proxy_clausification,[],[f391])).
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% 29.05/4.56 inference(beta-eta_normalization,[],[f392])).
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% 29.05/4.56 inference(or_proxy_clausification,[],[f393])).
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% 29.05/4.56 inference(or_proxy_clausification,[],[f394])).
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% 29.05/4.56 inference(sigma_proxy_clausification,[],[f396])).
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% 29.05/4.56 inference(not_proxy_clausification,[],[f397])).
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% 29.05/4.56 inference(sigma_proxy_clausification,[],[f398])).
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% 29.05/4.56 inference(beta-eta_normalization,[],[f399])).
% 29.05/4.56 thf(f401,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK5 @ X1))) | ($false = ((sK4 @ sK52))) | ($true = ((X2 @ X1 @ (sK53 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (sK2 @ Y0 @ (sK54 @ X2))) | (X2 @ Y0 @ (sK54 @ X2)))) @ (sK56 @ X2)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ Y1 @ Y0)) | (~ (X2 @ Y0 @ (sK55 @ X2)))) | (X2 @ Y1 @ (sK55 @ X2)))))))))) )),
% 29.05/4.56 inference(sigma_proxy_clausification,[],[f400])).
% 29.05/4.56 thf(f402,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK5 @ X1))) | ($false = ((sK4 @ sK52))) | ($true = ((X2 @ X1 @ (sK53 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (sK2 @ Y0 @ (sK54 @ X2))) | (X2 @ Y0 @ (sK54 @ X2)))) @ (sK56 @ X2)))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ Y1 @ Y0)) | (~ (X2 @ Y0 @ (sK55 @ X2)))) | (X2 @ Y1 @ (sK55 @ X2)))))) @ (sK57 @ X2))))) )),
% 29.05/4.56 inference(sigma_proxy_clausification,[],[f401])).
% 29.05/4.56 thf(f403,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK5 @ X1))) | ($false = ((sK4 @ sK52))) | ($true = ((X2 @ X1 @ (sK53 @ X1)))) | ($false = (((~ (sK2 @ (sK56 @ X2) @ (sK54 @ X2))) | (X2 @ (sK56 @ X2) @ (sK54 @ X2))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (((~ (X2 @ Y0 @ (sK57 @ X2))) | (~ (X2 @ (sK57 @ X2) @ (sK55 @ X2)))) | (X2 @ Y0 @ (sK55 @ X2)))))))) )),
% 29.05/4.56 inference(beta-eta_normalization,[],[f402])).
% 29.05/4.56 thf(f405,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK5 @ X1))) | ($false = ((sK4 @ sK52))) | ($true = ((X2 @ X1 @ (sK53 @ X1)))) | ($false = ((~ (sK2 @ (sK56 @ X2) @ (sK54 @ X2))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (((~ (X2 @ Y0 @ (sK57 @ X2))) | (~ (X2 @ (sK57 @ X2) @ (sK55 @ X2)))) | (X2 @ Y0 @ (sK55 @ X2)))))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f403])).
% 29.05/4.56 thf(f406,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK5 @ X1))) | ($false = ((sK4 @ sK52))) | ($true = ((X2 @ X1 @ (sK53 @ X1)))) | ($true = ((sK2 @ (sK56 @ X2) @ (sK54 @ X2)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (((~ (X2 @ Y0 @ (sK57 @ X2))) | (~ (X2 @ (sK57 @ X2) @ (sK55 @ X2)))) | (X2 @ Y0 @ (sK55 @ X2)))))))) )),
% 29.05/4.56 inference(not_proxy_clausification,[],[f405])).
% 29.05/4.56 thf(f407,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK5 @ X1))) | ($false = ((sK4 @ sK52))) | ($true = ((X2 @ X1 @ (sK53 @ X1)))) | ($true = ((sK2 @ (sK56 @ X2) @ (sK54 @ X2)))) | ($false = (((^[Y0 : $i]: (((~ (X2 @ Y0 @ (sK57 @ X2))) | (~ (X2 @ (sK57 @ X2) @ (sK55 @ X2)))) | (X2 @ Y0 @ (sK55 @ X2)))) @ (sK58 @ X2))))) )),
% 29.05/4.56 inference(sigma_proxy_clausification,[],[f406])).
% 29.05/4.56 thf(f408,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK5 @ X1))) | ($false = ((sK4 @ sK52))) | ($true = ((X2 @ X1 @ (sK53 @ X1)))) | ($true = ((sK2 @ (sK56 @ X2) @ (sK54 @ X2)))) | ($false = ((((~ (X2 @ (sK58 @ X2) @ (sK57 @ X2))) | (~ (X2 @ (sK57 @ X2) @ (sK55 @ X2)))) | (X2 @ (sK58 @ X2) @ (sK55 @ X2)))))) )),
% 29.05/4.56 inference(beta-eta_normalization,[],[f407])).
% 29.05/4.56 thf(f410,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK5 @ X1))) | ($false = ((sK4 @ sK52))) | ($true = ((X2 @ X1 @ (sK53 @ X1)))) | ($true = ((sK2 @ (sK56 @ X2) @ (sK54 @ X2)))) | ($false = (((~ (X2 @ (sK58 @ X2) @ (sK57 @ X2))) | (~ (X2 @ (sK57 @ X2) @ (sK55 @ X2))))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f408])).
% 29.05/4.56 thf(f411,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK5 @ X1))) | ($false = ((sK4 @ sK52))) | ($true = ((X2 @ X1 @ (sK53 @ X1)))) | ($true = ((sK2 @ (sK56 @ X2) @ (sK54 @ X2)))) | ($false = ((~ (X2 @ (sK57 @ X2) @ (sK55 @ X2)))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f410])).
% 29.05/4.56 thf(f414,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK5 @ X1))) | ($false = ((sK4 @ sK52))) | ($true = ((X2 @ X1 @ (sK53 @ X1)))) | ($true = ((sK2 @ (sK56 @ X2) @ (sK54 @ X2)))) | ($true = ((X2 @ (sK57 @ X2) @ (sK55 @ X2))))) )),
% 29.05/4.56 inference(not_proxy_clausification,[],[f411])).
% 29.05/4.56 thf(f423,plain,(
% 29.05/4.56 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK2 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3))))) | (Y1 @ Y3))))) | (Y1 @ Y2))))) | (Y1 @ Y0)))))))) | ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK2 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))))))),
% 29.05/4.56 inference(beta-eta_normalization,[],[f95])).
% 29.05/4.56 thf(f424,plain,(
% 29.05/4.56 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK2 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3))))) | (Y1 @ Y3))))) | (Y1 @ Y2))))) | (Y1 @ Y0))))) @ X1))) | ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK2 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))))))) )),
% 29.05/4.56 inference(pi_proxy_clausification,[],[f423])).
% 29.05/4.56 thf(f425,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK2 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y2 @ Y3))))) | (Y1 @ Y3))))) | (Y1 @ Y2))))) | (Y1 @ Y0))))) @ X1))) | ($true = (((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK2 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))) @ X2)))) )),
% 29.05/4.56 inference(pi_proxy_clausification,[],[f424])).
% 29.05/4.56 thf(f426,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK2 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))) | (Y0 @ Y2))))) | (Y0 @ Y1))))) | (Y0 @ X1)))))) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0)))) => (!! @ $i @ X2))))) )),
% 29.05/4.56 inference(beta-eta_normalization,[],[f425])).
% 29.05/4.56 thf(f427,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK2 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))) | (Y0 @ Y2))))) | (Y0 @ Y1))))) | (Y0 @ X1))) @ X3))) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0)))) => (!! @ $i @ X2))))) )),
% 29.05/4.56 inference(pi_proxy_clausification,[],[f426])).
% 29.05/4.56 thf(f428,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK2 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))) | (Y0 @ Y2))))) | (Y0 @ Y1))))) | (Y0 @ X1))) @ X3))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0)))))) | ($true = ((!! @ $i @ X2)))) )),
% 29.05/4.56 inference(imp_proxy_clausification,[],[f427])).
% 29.05/4.56 thf(f429,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK2 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))) | (Y0 @ Y2))))) | (Y0 @ Y1))))) | (Y0 @ X1))) @ X3))) | ($false = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0))) @ (sK60 @ X2)))) | ($true = ((!! @ $i @ X2)))) )),
% 29.05/4.56 inference(sigma_proxy_clausification,[],[f428])).
% 29.05/4.56 thf(f430,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK2 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2))))) | (Y0 @ Y2))))) | (Y0 @ Y1))))) | (Y0 @ X1))) @ X3))) | ($false = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0))) @ (sK60 @ X2)))) | ($true = ((X2 @ X4)))) )),
% 29.05/4.56 inference(pi_proxy_clausification,[],[f429])).
% 29.05/4.56 thf(f431,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))) | (X3 @ Y1))))) | (X3 @ Y0))))) | (X3 @ X1)))) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK60 @ X2) @ Y0)))) => (X2 @ Y0)))) => (X2 @ (sK60 @ X2))))) | ($true = ((X2 @ X4)))) )),
% 29.05/4.56 inference(beta-eta_normalization,[],[f430])).
% 29.05/4.56 thf(f432,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i] : (($true = ((X3 @ X1))) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK60 @ X2) @ Y0)))) => (X2 @ Y0)))) => (X2 @ (sK60 @ X2))))) | ($true = ((X2 @ X4))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))) | (X3 @ Y1))))) | (X3 @ Y0)))))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f431])).
% 29.05/4.56 thf(f433,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i] : (($true = ((X3 @ X1))) | ($false = ((X2 @ (sK60 @ X2)))) | ($true = ((X2 @ X4))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))) | (X3 @ Y1))))) | (X3 @ Y0)))))))) )),
% 29.05/4.56 inference(imp_proxy_clausification,[],[f432])).
% 29.05/4.56 thf(f434,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i] : (($true = ((X3 @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK60 @ X2) @ Y0)))) => (X2 @ Y0)))))) | ($true = ((X2 @ X4))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))) | (X3 @ Y1))))) | (X3 @ Y0)))))))) )),
% 29.05/4.56 inference(imp_proxy_clausification,[],[f432])).
% 29.05/4.56 thf(f435,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($true = (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK60 @ X2) @ Y0)))) => (X2 @ Y0))) @ X5))) | ($true = ((X2 @ X4))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))) | (X3 @ Y1))))) | (X3 @ Y0)))))))) )),
% 29.05/4.56 inference(pi_proxy_clausification,[],[f434])).
% 29.05/4.56 thf(f436,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($true = (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK60 @ X2) @ Y0)))) => (X2 @ Y0))) @ X5))) | ($true = ((X2 @ X4))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))) | (X3 @ Y1))))) | (X3 @ Y0))))))) )),
% 29.05/4.56 inference(not_proxy_clausification,[],[f435])).
% 29.05/4.56 thf(f437,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($true = (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK60 @ X2) @ Y0)))) => (X2 @ Y0))) @ X5))) | ($true = ((X2 @ X4))) | ($false = (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))) | (X3 @ Y1))))) | (X3 @ Y0))) @ (sK61 @ X3))))) )),
% 29.05/4.56 inference(sigma_proxy_clausification,[],[f436])).
% 29.05/4.56 thf(f438,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($true = (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK60 @ X2) @ X5)))) => (X2 @ X5)))) | ($true = ((X2 @ X4))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK61 @ X3) @ Y0))))) | (X3 @ Y0))))) | (X3 @ (sK61 @ X3)))))) )),
% 29.05/4.56 inference(beta-eta_normalization,[],[f437])).
% 29.05/4.56 thf(f439,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK60 @ X2) @ X5)))))) | ($true = ((X2 @ X4))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK61 @ X3) @ Y0))))) | (X3 @ Y0))))) | (X3 @ (sK61 @ X3))))) | ($true = ((X2 @ X5)))) )),
% 29.05/4.56 inference(imp_proxy_clausification,[],[f438])).
% 29.05/4.56 thf(f440,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK60 @ X2) @ X5))) @ (sK62 @ X5 @ X2)))) | ($true = ((X2 @ X4))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK61 @ X3) @ Y0))))) | (X3 @ Y0))))) | (X3 @ (sK61 @ X3))))) | ($true = ((X2 @ X5)))) )),
% 29.05/4.56 inference(sigma_proxy_clausification,[],[f439])).
% 29.05/4.56 thf(f442,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK60 @ X2) @ X5))) @ (sK62 @ X5 @ X2)))) | ($true = ((X2 @ X4))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK61 @ X3) @ Y0))))) | (X3 @ Y0))))))) | ($true = ((X2 @ X5)))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f440])).
% 29.05/4.56 thf(f443,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK60 @ X2) @ X5))) @ (sK62 @ X5 @ X2)))) | ($true = ((X2 @ X4))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK61 @ X3) @ Y0))))) | (X3 @ Y0)))))) | ($true = ((X2 @ X5)))) )),
% 29.05/4.56 inference(not_proxy_clausification,[],[f442])).
% 29.05/4.56 thf(f444,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK60 @ X2) @ X5))) @ (sK62 @ X5 @ X2)))) | ($true = ((X2 @ X4))) | ($true = (((^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK61 @ X3) @ Y0))))) | (X3 @ Y0))) @ X6))) | ($true = ((X2 @ X5)))) )),
% 29.05/4.56 inference(pi_proxy_clausification,[],[f443])).
% 29.05/4.56 thf(f445,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK62 @ X5 @ X2 @ Y2 @ Y1)) | (~ (sK62 @ X5 @ X2 @ Y1 @ Y0))) | (sK62 @ X5 @ X2 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK2 @ Y1 @ Y0)) | (sK62 @ X5 @ X2 @ Y1 @ Y0)))))))) | (sK62 @ X5 @ X2 @ (sK60 @ X2) @ X5)))) | ($true = ((X2 @ X4))) | ($true = (((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK61 @ X3) @ X6))))) | (X3 @ X6)))) | ($true = ((X2 @ X5)))) )),
% 29.05/4.56 inference(beta-eta_normalization,[],[f444])).
% 29.05/4.56 thf(f446,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = ((sK62 @ X5 @ X2 @ (sK60 @ X2) @ X5))) | ($true = ((X2 @ X4))) | ($true = (((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK61 @ X3) @ X6))))) | (X3 @ X6)))) | ($true = ((X2 @ X5)))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f445])).
% 29.05/4.56 thf(f447,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK62 @ X5 @ X2 @ Y2 @ Y1)) | (~ (sK62 @ X5 @ X2 @ Y1 @ Y0))) | (sK62 @ X5 @ X2 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK2 @ Y1 @ Y0)) | (sK62 @ X5 @ X2 @ Y1 @ Y0)))))))))) | ($true = ((X2 @ X4))) | ($true = (((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK61 @ X3) @ X6))))) | (X3 @ X6)))) | ($true = ((X2 @ X5)))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f445])).
% 29.05/4.56 thf(f448,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK2 @ Y1 @ Y0)) | (sK62 @ X5 @ X2 @ Y1 @ Y0))))))))) | ($true = ((X2 @ X4))) | ($true = (((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK61 @ X3) @ X6))))) | (X3 @ X6)))) | ($true = ((X2 @ X5)))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f447])).
% 29.05/4.56 thf(f496,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK2 @ Y1 @ Y0)) | (sK62 @ X5 @ X2 @ Y1 @ Y0)))))))) | ($true = ((X2 @ X4))) | ($true = (((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK2 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ (sK61 @ X3) @ X6))))) | (X3 @ X6)))) | ($true = ((X2 @ X5)))) )),
% 29.05/4.56 inference(not_proxy_clausification,[],[f448])).
% 29.05/4.56 thf(f497,plain,(
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% 29.05/4.56 inference(pi_proxy_clausification,[],[f496])).
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% 29.05/4.56 inference(or_proxy_clausification,[],[f497])).
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% 29.05/4.56 inference(not_proxy_clausification,[],[f498])).
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% 29.05/4.56 inference(sigma_proxy_clausification,[],[f499])).
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% 29.05/4.56 inference(beta-eta_normalization,[],[f500])).
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% 29.05/4.56 inference(pi_proxy_clausification,[],[f501])).
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% 29.05/4.56 inference(or_proxy_clausification,[],[f502])).
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% 29.05/4.56 inference(or_proxy_clausification,[],[f502])).
% 29.05/4.56 thf(f505,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($true = (((^[Y0 : $i]: ((~ (sK2 @ Y0 @ X7)) | (sK62 @ X5 @ X2 @ Y0 @ X7))) @ X8))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK2 @ Y1 @ Y0)) | (sK64 @ X3 @ X6 @ Y1 @ Y0)))))))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f504])).
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% 29.05/4.56 inference(not_proxy_clausification,[],[f505])).
% 29.05/4.56 thf(f521,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($true = (((^[Y0 : $i]: ((~ (sK2 @ Y0 @ X7)) | (sK62 @ X5 @ X2 @ Y0 @ X7))) @ X8))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK2 @ Y1 @ Y0)) | (sK64 @ X3 @ X6 @ Y1 @ Y0))))) @ X9)))) )),
% 29.05/4.56 inference(pi_proxy_clausification,[],[f520])).
% 29.05/4.56 thf(f522,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($true = (((~ (sK2 @ X8 @ X7)) | (sK62 @ X5 @ X2 @ X8 @ X7)))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK2 @ Y0 @ X9)) | (sK64 @ X3 @ X6 @ Y0 @ X9))))))) )),
% 29.05/4.56 inference(beta-eta_normalization,[],[f521])).
% 29.05/4.56 thf(f523,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($true = ((sK62 @ X5 @ X2 @ X8 @ X7))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK2 @ Y0 @ X9)) | (sK64 @ X3 @ X6 @ Y0 @ X9)))))) | ($true = ((~ (sK2 @ X8 @ X7))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f522])).
% 29.05/4.56 thf(f524,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X10 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($true = ((sK62 @ X5 @ X2 @ X8 @ X7))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($true = (((^[Y0 : $i]: ((~ (sK2 @ Y0 @ X9)) | (sK64 @ X3 @ X6 @ Y0 @ X9))) @ X10))) | ($true = ((~ (sK2 @ X8 @ X7))))) )),
% 29.05/4.56 inference(pi_proxy_clausification,[],[f523])).
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% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X10 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($true = ((sK62 @ X5 @ X2 @ X8 @ X7))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($true = (((^[Y0 : $i]: ((~ (sK2 @ Y0 @ X9)) | (sK64 @ X3 @ X6 @ Y0 @ X9))) @ X10))) | ($false = ((sK2 @ X8 @ X7)))) )),
% 29.05/4.56 inference(not_proxy_clausification,[],[f524])).
% 29.05/4.56 thf(f526,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X10 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($true = ((sK62 @ X5 @ X2 @ X8 @ X7))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($true = (((~ (sK2 @ X10 @ X9)) | (sK64 @ X3 @ X6 @ X10 @ X9)))) | ($false = ((sK2 @ X8 @ X7)))) )),
% 29.05/4.56 inference(beta-eta_normalization,[],[f525])).
% 29.05/4.56 thf(f527,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X10 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($true = ((sK62 @ X5 @ X2 @ X8 @ X7))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($true = ((sK64 @ X3 @ X6 @ X10 @ X9))) | ($false = ((sK2 @ X8 @ X7))) | ($true = ((~ (sK2 @ X10 @ X9))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f526])).
% 29.05/4.56 thf(f528,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X10 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($true = ((sK62 @ X5 @ X2 @ X8 @ X7))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($true = ((sK64 @ X3 @ X6 @ X10 @ X9))) | ($false = ((sK2 @ X8 @ X7))) | ($false = ((sK2 @ X10 @ X9)))) )),
% 29.05/4.56 inference(not_proxy_clausification,[],[f527])).
% 29.05/4.56 thf(f529,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($true = (((~ (sK2 @ X8 @ X7)) | (sK62 @ X5 @ X2 @ X8 @ X7)))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($false = ((sK64 @ X3 @ X6 @ (sK61 @ X3) @ X6)))) )),
% 29.05/4.56 inference(beta-eta_normalization,[],[f503])).
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% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($true = ((sK62 @ X5 @ X2 @ X8 @ X7))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($false = ((sK64 @ X3 @ X6 @ (sK61 @ X3) @ X6))) | ($true = ((~ (sK2 @ X8 @ X7))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f529])).
% 29.05/4.56 thf(f531,plain,(
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% 29.05/4.56 inference(not_proxy_clausification,[],[f530])).
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% 29.05/4.56 inference(or_proxy_clausification,[],[f446])).
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% 29.05/4.56 inference(not_proxy_clausification,[],[f532])).
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% 29.05/4.56 inference(sigma_proxy_clausification,[],[f533])).
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% 29.05/4.56 inference(beta-eta_normalization,[],[f534])).
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% 29.05/4.56 inference(or_proxy_clausification,[],[f535])).
% 29.05/4.56 thf(f537,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = ((sK62 @ X5 @ X2 @ (sK60 @ X2) @ X5))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK65 @ X3 @ X6 @ Y2 @ Y1)) | (~ (sK65 @ X3 @ X6 @ Y1 @ Y0))) | (sK65 @ X3 @ X6 @ Y2 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK2 @ Y1 @ Y0)) | (sK65 @ X3 @ X6 @ Y1 @ Y0))))))))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f535])).
% 29.05/4.56 thf(f538,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = ((sK62 @ X5 @ X2 @ (sK60 @ X2) @ X5))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK2 @ Y1 @ Y0)) | (sK65 @ X3 @ X6 @ Y1 @ Y0)))))))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f537])).
% 29.05/4.56 thf(f551,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = ((sK62 @ X5 @ X2 @ (sK60 @ X2) @ X5))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK2 @ Y1 @ Y0)) | (sK65 @ X3 @ X6 @ Y1 @ Y0))))))))) )),
% 29.05/4.56 inference(not_proxy_clausification,[],[f538])).
% 29.05/4.56 thf(f552,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = ((sK62 @ X5 @ X2 @ (sK60 @ X2) @ X5))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK2 @ Y1 @ Y0)) | (sK65 @ X3 @ X6 @ Y1 @ Y0))))) @ X7)))) )),
% 29.05/4.56 inference(pi_proxy_clausification,[],[f551])).
% 29.05/4.56 thf(f553,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = ((sK62 @ X5 @ X2 @ (sK60 @ X2) @ X5))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK2 @ Y0 @ X7)) | (sK65 @ X3 @ X6 @ Y0 @ X7))))))) )),
% 29.05/4.56 inference(beta-eta_normalization,[],[f552])).
% 29.05/4.56 thf(f554,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = ((sK62 @ X5 @ X2 @ (sK60 @ X2) @ X5))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($true = (((^[Y0 : $i]: ((~ (sK2 @ Y0 @ X7)) | (sK65 @ X3 @ X6 @ Y0 @ X7))) @ X8)))) )),
% 29.05/4.56 inference(pi_proxy_clausification,[],[f553])).
% 29.05/4.56 thf(f555,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = ((sK62 @ X5 @ X2 @ (sK60 @ X2) @ X5))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($true = (((~ (sK2 @ X8 @ X7)) | (sK65 @ X3 @ X6 @ X8 @ X7))))) )),
% 29.05/4.56 inference(beta-eta_normalization,[],[f554])).
% 29.05/4.56 thf(f556,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = ((sK62 @ X5 @ X2 @ (sK60 @ X2) @ X5))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($true = ((sK65 @ X3 @ X6 @ X8 @ X7))) | ($true = ((~ (sK2 @ X8 @ X7))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f555])).
% 29.05/4.56 thf(f557,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X3 @ X1))) | ($false = ((sK62 @ X5 @ X2 @ (sK60 @ X2) @ X5))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($true = ((sK65 @ X3 @ X6 @ X8 @ X7))) | ($false = ((sK2 @ X8 @ X7)))) )),
% 29.05/4.56 inference(not_proxy_clausification,[],[f556])).
% 29.05/4.56 thf(f581,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i] : (($true = ((X3 @ X1))) | ($false = ((X2 @ (sK60 @ X2)))) | ($true = ((X2 @ X4))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))) | (X3 @ Y1))))) | (X3 @ Y0))))))) )),
% 29.05/4.56 inference(not_proxy_clausification,[],[f433])).
% 29.05/4.56 thf(f582,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i] : (($true = ((X3 @ X1))) | ($false = ((X2 @ (sK60 @ X2)))) | ($true = ((X2 @ X4))) | ($false = (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK2 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y0 @ Y1))))) | (X3 @ Y1))))) | (X3 @ Y0))) @ (sK66 @ X3))))) )),
% 29.05/4.56 inference(sigma_proxy_clausification,[],[f581])).
% 29.05/4.56 thf(f583,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i] : (($true = ((X3 @ X1))) | ($false = ((X2 @ (sK60 @ X2)))) | ($true = ((X2 @ X4))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK2 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ (sK66 @ X3) @ Y0))))) | (X3 @ Y0))))) | (X3 @ (sK66 @ X3)))))) )),
% 29.05/4.56 inference(beta-eta_normalization,[],[f582])).
% 29.05/4.56 thf(f584,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i] : (($true = ((X3 @ X1))) | ($false = ((X2 @ (sK60 @ X2)))) | ($true = ((X2 @ X4))) | ($false = ((X3 @ (sK66 @ X3))))) )),
% 29.05/4.56 inference(or_proxy_clausification,[],[f583])).
% 29.05/4.56 thf(f622,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (sK8 @ X3)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2)))) | ($true = ((X3 @ (sK11 @ X3) @ (sK9 @ X3)))) | ($true = ((sK2 @ (sK15 @ X4) @ (sK12 @ X4)))) | ($true = ((X4 @ (sK16 @ X4) @ (sK13 @ X4))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f182,f85])).
% 29.05/4.56 thf(f626,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (sK8 @ X3)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2)))) | ($true = ((X3 @ (sK11 @ X3) @ (sK9 @ X3)))) | ($false = ((X4 @ (sK15 @ X4) @ (sK12 @ X4)))) | ($false = ((X4 @ (sK20 @ X4) @ (sK13 @ X4))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f185,f85])).
% 29.05/4.56 thf(f683,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (sK46 @ X2)))) | ($false = ((sK5 @ sK3))) | ($true = ((X2 @ X1 @ (sK45 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X2 @ (sK49 @ X2) @ (sK47 @ X2))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f369,f85])).
% 29.05/4.56 thf(f695,definition,(
% 29.05/4.56 spl1_13 <=> ($false = ((sK5 @ sK3)))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition])).
% 29.05/4.56 thf(f697,plain,(
% 29.05/4.56 ($false = ((sK5 @ sK3))) | ~spl1_13),
% 29.05/4.56 inference(avatar_component_clause,[],[f695])).
% 29.05/4.56 thf(f700,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (sK54 @ X2)))) | ($true = ((sK5 @ X1))) | ($false = ((sK4 @ sK52))) | ($true = ((X2 @ X1 @ (sK53 @ X1)))) | ($true = ((X2 @ (sK57 @ X2) @ (sK55 @ X2))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f414,f85])).
% 29.05/4.56 thf(f706,definition,(
% 29.05/4.56 spl1_14 <=> ($false = ((sK4 @ sK52)))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition])).
% 29.05/4.56 thf(f708,plain,(
% 29.05/4.56 ($false = ((sK4 @ sK52))) | ~spl1_14),
% 29.05/4.56 inference(avatar_component_clause,[],[f706])).
% 29.05/4.56 thf(f716,plain,(
% 29.05/4.56 spl1_14 | spl1_13),
% 29.05/4.56 inference(avatar_split_clause,[],[f380,f695,f706])).
% 29.05/4.56 thf(f718,definition,(
% 29.05/4.56 spl1_17 <=> ! [X4 : $i,X2 : ($i > $o)] : ($true = ((X2 @ X4)))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition])).
% 29.05/4.56 thf(f719,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X4 : $i] : (($true = ((X2 @ X4)))) ) | ~spl1_17),
% 29.05/4.56 inference(avatar_component_clause,[],[f718])).
% 29.05/4.56 thf(f748,definition,(
% 29.05/4.56 spl1_26 <=> ! [X4 : $i,X7 : $i,X8 : $i,X5 : $i,X2 : ($i > $o)] : (($true = ((sK62 @ X5 @ X2 @ X8 @ X7))) | ($false = ((sK2 @ X8 @ X7))) | ($true = ((X2 @ X5))) | ($true = ((X2 @ X4))))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_26])],[avatar_definition])).
% 29.05/4.56 thf(f749,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X8 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((sK62 @ X5 @ X2 @ X8 @ X7))) | ($false = ((sK2 @ X8 @ X7))) | ($true = ((X2 @ X5))) | ($true = ((X2 @ X4)))) ) | ~spl1_26),
% 29.05/4.56 inference(avatar_component_clause,[],[f748])).
% 29.05/4.56 thf(f761,definition,(
% 29.05/4.56 spl1_30 <=> ! [X3 : ($i > $o),X10 : $i,X6 : $i,X9 : $i,X1 : $i] : (($true = ((X3 @ X1))) | ($false = ((sK2 @ X10 @ X9))) | ($true = ((sK64 @ X3 @ X6 @ X10 @ X9))) | ($true = ((X3 @ X6))))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_30])],[avatar_definition])).
% 29.05/4.56 thf(f762,plain,(
% 29.05/4.56 ( ! [X3 : ($i > $o),X10 : $i,X1 : $i,X6 : $i,X9 : $i] : (($true = ((X3 @ X1))) | ($false = ((sK2 @ X10 @ X9))) | ($true = ((sK64 @ X3 @ X6 @ X10 @ X9))) | ($true = ((X3 @ X6)))) ) | ~spl1_30),
% 29.05/4.56 inference(avatar_component_clause,[],[f761])).
% 29.05/4.56 thf(f763,plain,(
% 29.05/4.56 spl1_26 | spl1_30),
% 29.05/4.56 inference(avatar_split_clause,[],[f528,f761,f748])).
% 29.05/4.56 thf(f764,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((sK64 @ X3 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6))) | ($true = ((X3 @ X1))) | ($true = ((sK62 @ X5 @ X2 @ X8 @ X7))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($false = ((sK2 @ X8 @ X7)))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f531,f85])).
% 29.05/4.56 thf(f766,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((sK62 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5))) | ($true = ((X3 @ X1))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($true = ((sK65 @ X3 @ X6 @ X8 @ X7))) | ($false = ((sK2 @ X8 @ X7)))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f557,f85])).
% 29.05/4.56 thf(f767,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($false = ((sK62 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5))) | ($true = ((X3 @ X1))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5))) | ($false = ((sK65 @ X3 @ X6 @ (sK61 @ X3) @ X6)))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f536,f85])).
% 29.05/4.56 thf(f774,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i] : (($false = ((X2 @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X3 @ X1))) | ($true = ((X2 @ X4))) | ($false = ((X3 @ (sK66 @ X3))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f584,f85])).
% 29.05/4.56 thf(f782,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2)))) | ($true = ((X3 @ (sK11 @ X3) @ (sK9 @ X3)))) | ($true = ((sK2 @ (sK15 @ X4) @ (sK12 @ X4)))) | ($true = ((X4 @ (sK16 @ X4) @ (sK13 @ X4))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f622,f85])).
% 29.05/4.56 thf(f786,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2)))) | ($true = ((X3 @ (sK11 @ X3) @ (sK9 @ X3)))) | ($false = ((X4 @ (sK15 @ X4) @ (sK12 @ X4)))) | ($false = ((X4 @ (sK20 @ X4) @ (sK13 @ X4))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f626,f85])).
% 29.05/4.56 thf(f824,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($false = ((sK5 @ sK3))) | ($true = ((X2 @ X1 @ (sK45 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X2 @ (sK49 @ X2) @ (sK47 @ X2))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f683,f85])).
% 29.05/4.56 thf(f830,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X1))) | ($false = ((sK4 @ sK52))) | ($true = ((X2 @ X1 @ (sK53 @ X1)))) | ($true = ((X2 @ (sK57 @ X2) @ (sK55 @ X2))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f700,f85])).
% 29.05/4.56 thf(f846,definition,(
% 29.05/4.56 spl1_34 <=> ! [X6 : $i,X1 : $i,X3 : ($i > $o)] : (($false = ((sK64 @ X3 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6))) | ($true = ((X3 @ X6))) | ($true = ((X3 @ X1))))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_34])],[avatar_definition])).
% 29.05/4.56 thf(f847,plain,(
% 29.05/4.56 ( ! [X3 : ($i > $o),X1 : $i,X6 : $i] : (($false = ((sK64 @ X3 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6))) | ($true = ((X3 @ X6))) | ($true = ((X3 @ X1)))) ) | ~spl1_34),
% 29.05/4.56 inference(avatar_component_clause,[],[f846])).
% 29.05/4.56 thf(f848,plain,(
% 29.05/4.56 spl1_26 | spl1_34),
% 29.05/4.56 inference(avatar_split_clause,[],[f764,f846,f748])).
% 29.05/4.56 thf(f862,definition,(
% 29.05/4.56 spl1_39 <=> ! [X2 : ($i > $o),X5 : $i,X4 : $i] : (($false = ((sK62 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5))) | ($true = ((X2 @ X5))) | ($true = ((X2 @ X4))))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_39])],[avatar_definition])).
% 29.05/4.56 thf(f863,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X4 : $i,X5 : $i] : (($false = ((sK62 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5))) | ($true = ((X2 @ X5))) | ($true = ((X2 @ X4)))) ) | ~spl1_39),
% 29.05/4.56 inference(avatar_component_clause,[],[f862])).
% 29.05/4.56 thf(f866,definition,(
% 29.05/4.56 spl1_40 <=> ! [X6 : $i,X7 : $i,X8 : $i,X3 : ($i > $o),X1 : $i] : (($true = ((X3 @ X1))) | ($false = ((sK2 @ X8 @ X7))) | ($true = ((sK65 @ X3 @ X6 @ X8 @ X7))) | ($true = ((X3 @ X6))))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_40])],[avatar_definition])).
% 29.05/4.56 thf(f867,plain,(
% 29.05/4.56 ( ! [X3 : ($i > $o),X1 : $i,X8 : $i,X6 : $i,X7 : $i] : (($true = ((X3 @ X1))) | ($false = ((sK2 @ X8 @ X7))) | ($true = ((sK65 @ X3 @ X6 @ X8 @ X7))) | ($true = ((X3 @ X6)))) ) | ~spl1_40),
% 29.05/4.56 inference(avatar_component_clause,[],[f866])).
% 29.05/4.56 thf(f868,plain,(
% 29.05/4.56 spl1_40 | spl1_39),
% 29.05/4.56 inference(avatar_split_clause,[],[f766,f862,f866])).
% 29.05/4.56 thf(f869,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($false = ((sK65 @ X3 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6))) | ($false = ((sK62 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5))) | ($true = ((X3 @ X1))) | ($true = ((X2 @ X4))) | ($true = ((X3 @ X6))) | ($true = ((X2 @ X5)))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f767,f85])).
% 29.05/4.56 thf(f874,definition,(
% 29.05/4.56 spl1_42 <=> ! [X1 : $i,X3 : ($i > $o)] : (($false = ((X3 @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X3 @ X1))))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_42])],[avatar_definition])).
% 29.05/4.56 thf(f875,plain,(
% 29.05/4.56 ( ! [X3 : ($i > $o),X1 : $i] : (($false = ((X3 @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X3 @ X1)))) ) | ~spl1_42),
% 29.05/4.56 inference(avatar_component_clause,[],[f874])).
% 29.05/4.56 thf(f894,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i,X4 : $i] : (($false = ((X3 @ (d2unsorted @ d_unsorted_0)))) | ($false = ((X2 @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X3 @ X1))) | ($true = ((X2 @ X4)))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f774,f85])).
% 29.05/4.56 thf(f902,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK9 @ X3)))) | ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2)))) | ($true = ((sK2 @ (sK15 @ X4) @ (sK12 @ X4)))) | ($true = ((X4 @ (sK16 @ X4) @ (sK13 @ X4))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f782,f85])).
% 29.05/4.56 thf(f906,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK9 @ X3)))) | ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2)))) | ($false = ((X4 @ (sK15 @ X4) @ (sK12 @ X4)))) | ($false = ((X4 @ (sK20 @ X4) @ (sK13 @ X4))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f786,f85])).
% 29.05/4.56 thf(f944,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (sK47 @ X2)))) | ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($false = ((sK5 @ sK3))) | ($true = ((X2 @ X1 @ (sK45 @ X1)))) | ($true = ((sK4 @ X1)))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f824,f85])).
% 29.05/4.56 thf(f950,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (sK55 @ X2)))) | ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X1))) | ($false = ((sK4 @ sK52))) | ($true = ((X2 @ X1 @ (sK53 @ X1))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f830,f85])).
% 29.05/4.56 thf(f959,definition,(
% 29.05/4.56 spl1_48 <=> ! [X6 : $i,X1 : $i,X3 : ($i > $o)] : (($false = ((sK65 @ X3 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6))) | ($true = ((X3 @ X6))) | ($true = ((X3 @ X1))))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_48])],[avatar_definition])).
% 29.05/4.56 thf(f960,plain,(
% 29.05/4.56 ( ! [X3 : ($i > $o),X1 : $i,X6 : $i] : (($false = ((sK65 @ X3 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6))) | ($true = ((X3 @ X6))) | ($true = ((X3 @ X1)))) ) | ~spl1_48),
% 29.05/4.56 inference(avatar_component_clause,[],[f959])).
% 29.05/4.56 thf(f961,plain,(
% 29.05/4.56 spl1_39 | spl1_48),
% 29.05/4.56 inference(avatar_split_clause,[],[f869,f959,f862])).
% 29.05/4.56 thf(f970,plain,(
% 29.05/4.56 spl1_42 | spl1_42),
% 29.05/4.56 inference(avatar_split_clause,[],[f894,f874,f874])).
% 29.05/4.56 thf(f978,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2)))) | ($true = ((sK2 @ (sK15 @ X4) @ (sK12 @ X4)))) | ($true = ((X4 @ (sK16 @ X4) @ (sK13 @ X4))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f902,f85])).
% 29.05/4.56 thf(f982,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2)))) | ($false = ((X4 @ (sK15 @ X4) @ (sK12 @ X4)))) | ($false = ((X4 @ (sK20 @ X4) @ (sK13 @ X4))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f906,f85])).
% 29.05/4.56 thf(f1028,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($false = ((sK5 @ sK3))) | ($true = ((X2 @ X1 @ (sK45 @ X1)))) | ($true = ((sK4 @ X1)))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f944,f85])).
% 29.05/4.56 thf(f1035,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X1))) | ($false = ((sK4 @ sK52))) | ($true = ((X2 @ X1 @ (sK53 @ X1))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f950,f85])).
% 29.05/4.56 thf(f1048,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (sK12 @ X4)))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2)))) | ($true = ((X4 @ (sK16 @ X4) @ (sK13 @ X4))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f978,f85])).
% 29.05/4.56 thf(f1052,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($false = ((X4 @ (d2unsorted @ d_unsorted_0) @ (sK12 @ X4)))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2)))) | ($false = ((X4 @ (sK20 @ X4) @ (sK13 @ X4))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f982,f85])).
% 29.05/4.56 thf(f1072,definition,(
% 29.05/4.56 spl1_53 <=> ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_53])],[avatar_definition])).
% 29.05/4.56 thf(f1074,plain,(
% 29.05/4.56 ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ~spl1_53),
% 29.05/4.56 inference(avatar_component_clause,[],[f1072])).
% 29.05/4.56 thf(f1082,definition,(
% 29.05/4.56 spl1_56 <=> ! [X1 : $i,X3 : ($i > $i > $o)] : (($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK4 @ X1))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_56])],[avatar_definition])).
% 29.05/4.56 thf(f1083,plain,(
% 29.05/4.56 ( ! [X3 : ($i > $i > $o),X1 : $i] : (($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK4 @ X1))) | ($true = ((X3 @ X1 @ (sK6 @ X1))))) ) | ~spl1_56),
% 29.05/4.56 inference(avatar_component_clause,[],[f1082])).
% 29.05/4.56 thf(f1111,definition,(
% 29.05/4.56 spl1_63 <=> ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK4 @ X1))) | ($true = ((X2 @ X1 @ (sK45 @ X1)))))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_63])],[avatar_definition])).
% 29.05/4.56 thf(f1112,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK4 @ X1))) | ($true = ((X2 @ X1 @ (sK45 @ X1))))) ) | ~spl1_63),
% 29.05/4.56 inference(avatar_component_clause,[],[f1111])).
% 29.05/4.56 thf(f1114,plain,(
% 29.05/4.56 spl1_13 | spl1_53 | spl1_63),
% 29.05/4.56 inference(avatar_split_clause,[],[f1028,f1111,f1072,f695])).
% 29.05/4.56 thf(f1124,definition,(
% 29.05/4.56 spl1_66 <=> ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X2 @ X1 @ (sK53 @ X1)))) | ($true = ((sK5 @ X1))))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_66])],[avatar_definition])).
% 29.05/4.56 thf(f1125,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X2 @ X1 @ (sK53 @ X1)))) | ($true = ((sK5 @ X1)))) ) | ~spl1_66),
% 29.05/4.56 inference(avatar_component_clause,[],[f1124])).
% 29.05/4.56 thf(f1127,plain,(
% 29.05/4.56 spl1_14 | spl1_53 | spl1_66),
% 29.05/4.56 inference(avatar_split_clause,[],[f1035,f1124,f1072,f706])).
% 29.05/4.56 thf(f1144,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2)))) | ($true = ((X4 @ (sK16 @ X4) @ (sK13 @ X4))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f1048,f85])).
% 29.05/4.56 thf(f1145,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2)))) | ($true = ((X4 @ (sK16 @ X4) @ (sK13 @ X4))))) )),
% 29.05/4.56 inference(duplicate_literal_removal,[],[f1144])).
% 29.05/4.56 thf(f1150,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($false = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2)))) | ($false = ((X4 @ (sK20 @ X4) @ (sK13 @ X4))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f1052,f85])).
% 29.05/4.56 thf(f1173,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (sK13 @ X4)))) | ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f1145,f85])).
% 29.05/4.56 thf(f1177,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($false = ((X4 @ (d2unsorted @ d_unsorted_0) @ (sK13 @ X4)))) | ($false = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f1150,f85])).
% 29.05/4.56 thf(f1198,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f1173,f85])).
% 29.05/4.56 thf(f1202,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($false = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($false = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2))))) )),
% 29.05/4.56 inference(forward_demodulation,[],[f1177,f85])).
% 29.05/4.56 thf(f1203,plain,(
% 29.05/4.56 ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($false = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK5 @ X2))) | ($true = ((X3 @ X1 @ (sK6 @ X1)))) | ($true = ((sK4 @ X1))) | ($true = ((X4 @ X2 @ (sK7 @ X2))))) )),
% 29.05/4.56 inference(duplicate_literal_removal,[],[f1202])).
% 29.05/4.56 thf(f1219,definition,(
% 29.05/4.56 spl1_68 <=> ! [X2 : $i,X4 : ($i > $i > $o)] : ($true = ((X4 @ X2 @ (sK7 @ X2))))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_68])],[avatar_definition])).
% 29.05/4.56 thf(f1220,plain,(
% 29.05/4.56 ( ! [X2 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ X2 @ (sK7 @ X2))))) ) | ~spl1_68),
% 29.05/4.56 inference(avatar_component_clause,[],[f1219])).
% 29.05/4.56 thf(f1222,definition,(
% 29.05/4.56 spl1_69 <=> ! [X4 : ($i > $i > $o),X2 : $i] : (($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X4 @ X2 @ (sK7 @ X2)))) | ($true = ((sK5 @ X2))))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_69])],[avatar_definition])).
% 29.05/4.56 thf(f1223,plain,(
% 29.05/4.56 ( ! [X2 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X4 @ X2 @ (sK7 @ X2)))) | ($true = ((sK5 @ X2)))) ) | ~spl1_69),
% 29.05/4.56 inference(avatar_component_clause,[],[f1222])).
% 29.05/4.56 thf(f1227,definition,(
% 29.05/4.56 spl1_70 <=> ! [X4 : ($i > $i > $o),X2 : $i] : (($false = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X4 @ X2 @ (sK7 @ X2)))) | ($true = ((sK5 @ X2))))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_70])],[avatar_definition])).
% 29.05/4.56 thf(f1228,plain,(
% 29.05/4.56 ( ! [X2 : $i,X4 : ($i > $i > $o)] : (($false = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X4 @ X2 @ (sK7 @ X2)))) | ($true = ((sK5 @ X2)))) ) | ~spl1_70),
% 29.05/4.56 inference(avatar_component_clause,[],[f1227])).
% 29.05/4.56 thf(f1232,plain,(
% 29.05/4.56 spl1_56 | spl1_53 | spl1_69),
% 29.05/4.56 inference(avatar_split_clause,[],[f1198,f1222,f1072,f1082])).
% 29.05/4.56 thf(f1234,plain,(
% 29.05/4.56 spl1_53 | spl1_56 | spl1_70),
% 29.05/4.56 inference(avatar_split_clause,[],[f1203,f1227,f1082,f1072])).
% 29.05/4.56 thf(f1243,plain,(
% 29.05/4.56 ( ! [X0 : $i] : (($false = ((sK5 @ X0)))) ) | ~spl1_13),
% 29.05/4.56 inference(constrained_superposition,[],[f697,f89])).
% 29.05/4.56 thf(f1247,plain,(
% 29.05/4.56 ( ! [X0 : $i] : (($false = ((sK4 @ X0)))) ) | ~spl1_14),
% 29.05/4.56 inference(constrained_superposition,[],[f708,f89])).
% 29.05/4.56 thf(f1300,plain,(
% 29.05/4.56 ( ! [X4 : $i] : (($true = (((^[Y0 : $i]: ($false)) @ X4)))) ) | ~spl1_17),
% 29.05/4.56 inference(primitive_instantiation,[],[f719])).
% 29.05/4.56 thf(f1343,plain,(
% 29.05/4.56 ($true = $false) | ~spl1_17),
% 29.05/4.56 inference(beta-eta_normalization,[],[f1300])).
% 29.05/4.56 thf(f1344,plain,(
% 29.05/4.56 $false | ~spl1_17),
% 29.05/4.56 inference(trivial_inequality_removal,[],[f1343])).
% 29.05/4.56 thf(f1345,plain,(
% 29.05/4.56 ~spl1_17),
% 29.05/4.56 inference(avatar_contradiction_clause,[],[f1344])).
% 29.05/4.56 thf(f1418,plain,(
% 29.05/4.56 ( ! [X2 : $i,X0 : $i,X1 : ($i > $o)] : (($false = ((X1 @ X0))) | (((X1 @ X2)) = $true)) ) | ~spl1_42),
% 29.05/4.56 inference(constrained_superposition,[],[f875,f85])).
% 29.05/4.56 thf(f1938,plain,(
% 29.05/4.56 ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : (($false != ((X0 @ X2))) | ($true = ((X0 @ X2))) | ($true != ((X0 @ X1)))) ) | ~spl1_42),
% 29.05/4.56 inference(equality_factoring,[],[f1418])).
% 29.05/4.56 thf(f2031,plain,(
% 29.05/4.56 ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : (($true != ((X0 @ X1))) | ($true = ((X0 @ X2)))) ) | ~spl1_42),
% 29.05/4.56 inference(forward_subsumption_resolution,[],[f1938,f46])).
% 29.05/4.56 thf(f2738,plain,(
% 29.05/4.56 ( ! [X2 : $i] : (($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))) @ X2 @ (sK7 @ X2))))) ) | ~spl1_68),
% 29.05/4.56 inference(primitive_instantiation,[],[f1220])).
% 29.05/4.56 thf(f2826,plain,(
% 29.05/4.56 ( ! [X2 : $i] : (($true = ((~ (X2 = (sK7 @ X2)))))) ) | ~spl1_68),
% 29.05/4.56 inference(beta-eta_normalization,[],[f2738])).
% 29.05/4.56 thf(f2827,plain,(
% 29.05/4.56 ( ! [X2 : $i] : (($false = ((X2 = (sK7 @ X2))))) ) | ~spl1_68),
% 29.05/4.56 inference(not_proxy_clausification,[],[f2826])).
% 29.05/4.56 thf(f2828,plain,(
% 29.05/4.56 ( ! [X2 : $i] : ((((sK7 @ X2)) != X2)) ) | ~spl1_68),
% 29.05/4.56 inference(equality_proxy_clausification,[],[f2827])).
% 29.05/4.56 thf(f2852,plain,(
% 29.05/4.56 $false | ~spl1_68),
% 29.05/4.56 inference(forward_subsumption_resolution,[],[f2828,f89])).
% 29.05/4.56 thf(f2853,plain,(
% 29.05/4.56 ~spl1_68),
% 29.05/4.56 inference(avatar_contradiction_clause,[],[f2852])).
% 29.05/4.56 thf(f2973,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = $false) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X2 @ X1 @ (sK53 @ X1))))) ) | (~spl1_13 | ~spl1_66)),
% 29.05/4.56 inference(forward_demodulation,[],[f1125,f1243])).
% 29.05/4.56 thf(f2974,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X2 @ X1 @ (sK53 @ X1))))) ) | (~spl1_13 | ~spl1_66)),
% 29.05/4.56 inference(trivial_inequality_removal,[],[f2973])).
% 29.05/4.56 thf(f4352,definition,(
% 29.05/4.56 spl1_96 <=> ! [X2 : ($i > $i > $o),X3 : $i] : (($true = ((X2 @ X3 @ (sK53 @ X3)))) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))))),
% 29.05/4.56 introduced(definition,[new_symbols(definition,[spl1_96])],[avatar_definition])).
% 29.05/4.56 thf(f4353,plain,(
% 29.05/4.56 ( ! [X2 : ($i > $i > $o),X3 : $i] : (($true = ((X2 @ X3 @ (sK53 @ X3)))) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) ) | ~spl1_96),
% 29.05/4.56 inference(avatar_component_clause,[],[f4352])).
% 29.05/4.56 thf(f6054,plain,(
% 29.05/4.56 spl1_96 | ~spl1_13 | ~spl1_66),
% 29.05/4.56 inference(avatar_split_clause,[],[f2974,f1124,f695,f4352])).
% 29.05/4.56 thf(f7227,plain,(
% 29.05/4.56 ( ! [X0 : ($i > $i),X1 : $i] : (($true = $false) | ($true = (((^[Y0 : $i]: (sK2 @ (X0 @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X1))) | (((d2unsorted @ d_unsorted_0)) != ((X0 @ (d2unsorted @ d_unsorted_0))))) ) | (~spl1_42 | ~spl1_53)),
% 29.05/4.57 inference(constrained_superposition,[],[f875,f1074])).
% 29.05/4.57 thf(f7322,plain,(
% 29.05/4.57 ( ! [X0 : ($i > $i),X1 : $i] : (($true = (((^[Y0 : $i]: (sK2 @ (X0 @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X1))) | (((d2unsorted @ d_unsorted_0)) != ((X0 @ (d2unsorted @ d_unsorted_0))))) ) | (~spl1_42 | ~spl1_53)),
% 29.05/4.57 inference(trivial_inequality_removal,[],[f7227])).
% 29.05/4.57 thf(f7323,plain,(
% 29.05/4.57 ( ! [X0 : ($i > $i),X1 : $i] : (($true = ((sK2 @ (X0 @ X1) @ X1))) | (((d2unsorted @ d_unsorted_0)) != ((X0 @ (d2unsorted @ d_unsorted_0))))) ) | (~spl1_42 | ~spl1_53)),
% 29.05/4.57 inference(beta-eta_normalization,[],[f7322])).
% 29.05/4.57 thf(f7388,plain,(
% 29.05/4.57 ( ! [X0 : ($i > $i),X1 : $i] : (($true = ((sK2 @ (X0 @ X1) @ X1)))) ) | (~spl1_42 | ~spl1_53)),
% 29.05/4.57 inference(forward_subsumption_resolution,[],[f7323,f85])).
% 29.05/4.57 thf(f7612,plain,(
% 29.05/4.57 ( ! [X2 : ($i > $o),X8 : $i,X7 : $i,X5 : $i] : (($true = ((sK62 @ X5 @ X2 @ X8 @ X7))) | ($false = ((sK2 @ X8 @ X7))) | ($true = ((X2 @ X5)))) ) | (~spl1_26 | ~spl1_42)),
% 29.05/4.57 inference(forward_subsumption_resolution,[],[f749,f2031])).
% 29.05/4.57 thf(f7617,plain,(
% 29.05/4.57 ( ! [X3 : ($i > $o),X10 : $i,X1 : $i,X6 : $i,X9 : $i] : (($true = ((X3 @ X1))) | ($false = ((sK2 @ X10 @ X9))) | ($true = ((sK64 @ X3 @ X6 @ X10 @ X9)))) ) | (~spl1_30 | ~spl1_42)),
% 29.05/4.57 inference(forward_subsumption_resolution,[],[f762,f2031])).
% 29.05/4.57 thf(f7618,plain,(
% 29.05/4.57 ( ! [X3 : ($i > $o),X6 : $i] : (($false = ((sK64 @ X3 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6))) | ($true = ((X3 @ X6)))) ) | (~spl1_34 | ~spl1_42)),
% 29.05/4.57 inference(forward_subsumption_resolution,[],[f847,f2031])).
% 29.05/4.57 thf(f8007,plain,(
% 29.05/4.57 ( ! [X2 : $i,X0 : $i] : (($true = ((sK2 @ X0 @ X2)))) ) | (~spl1_42 | ~spl1_53)),
% 29.05/4.57 inference(constrained_superposition,[],[f7388,f85])).
% 29.05/4.57 thf(f8243,plain,(
% 29.05/4.57 ( ! [X3 : ($i > $o),X10 : $i,X1 : $i,X6 : $i,X9 : $i] : (($true = $false) | ($true = ((X3 @ X1))) | ($true = ((sK64 @ X3 @ X6 @ X10 @ X9)))) ) | (~spl1_30 | ~spl1_42 | ~spl1_53)),
% 29.05/4.57 inference(forward_demodulation,[],[f7617,f8007])).
% 29.05/4.57 thf(f8244,plain,(
% 29.05/4.57 ( ! [X3 : ($i > $o),X10 : $i,X1 : $i,X6 : $i,X9 : $i] : (($true = ((X3 @ X1))) | ($true = ((sK64 @ X3 @ X6 @ X10 @ X9)))) ) | (~spl1_30 | ~spl1_42 | ~spl1_53)),
% 29.05/4.57 inference(trivial_inequality_removal,[],[f8243])).
% 29.05/4.57 thf(f8913,plain,(
% 29.05/4.57 ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : (($true = $false) | ($true = ((X0 @ X2))) | ($true = ((X0 @ X1)))) ) | (~spl1_30 | ~spl1_34 | ~spl1_42 | ~spl1_53)),
% 29.05/4.57 inference(constrained_superposition,[],[f8244,f7618])).
% 29.05/4.57 thf(f8930,plain,(
% 29.05/4.57 ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : (($true = ((X0 @ X2))) | ($true = ((X0 @ X1)))) ) | (~spl1_30 | ~spl1_34 | ~spl1_42 | ~spl1_53)),
% 29.05/4.57 inference(trivial_inequality_removal,[],[f8913])).
% 29.05/4.57 thf(f9029,plain,(
% 29.05/4.57 ( ! [X2 : $i,X0 : ($i > $o)] : (($true = ((X0 @ X2)))) ) | (~spl1_30 | ~spl1_34 | ~spl1_42 | ~spl1_53)),
% 29.05/4.57 inference(forward_subsumption_resolution,[],[f8930,f2031])).
% 29.05/4.57 thf(f9083,plain,(
% 29.05/4.57 spl1_17 | ~spl1_30 | ~spl1_34 | ~spl1_42 | ~spl1_53),
% 29.05/4.57 inference(avatar_split_clause,[],[f9029,f1072,f874,f846,f761,f718])).
% 29.05/4.57 thf(f9274,plain,(
% 29.05/4.57 ( ! [X2 : ($i > $o),X8 : $i,X7 : $i,X5 : $i] : (($true = $false) | ($true = ((sK62 @ X5 @ X2 @ X8 @ X7))) | ($true = ((X2 @ X5)))) ) | (~spl1_26 | ~spl1_42 | ~spl1_53)),
% 29.05/4.57 inference(forward_demodulation,[],[f7612,f8007])).
% 29.05/4.57 thf(f9275,plain,(
% 29.05/4.57 ( ! [X2 : ($i > $o),X8 : $i,X7 : $i,X5 : $i] : (($true = ((sK62 @ X5 @ X2 @ X8 @ X7))) | ($true = ((X2 @ X5)))) ) | (~spl1_26 | ~spl1_42 | ~spl1_53)),
% 29.05/4.57 inference(trivial_inequality_removal,[],[f9274])).
% 29.05/4.57 thf(f9473,plain,(
% 29.05/4.57 ( ! [X2 : ($i > $o),X5 : $i] : (($false = ((sK62 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5))) | ($true = ((X2 @ X5)))) ) | (~spl1_39 | ~spl1_42)),
% 29.05/4.57 inference(forward_subsumption_resolution,[],[f863,f2031])).
% 29.05/4.57 thf(f9494,plain,(
% 29.05/4.57 ( ! [X0 : $i,X1 : ($i > $o)] : (($true = $false) | ($true = ((X1 @ X0))) | ($true = ((X1 @ X0)))) ) | (~spl1_26 | ~spl1_39 | ~spl1_42 | ~spl1_53)),
% 29.05/4.57 inference(constrained_superposition,[],[f9275,f9473])).
% 29.05/4.57 thf(f9499,plain,(
% 29.05/4.57 ( ! [X0 : $i,X1 : ($i > $o)] : (($true = $false) | ($true = ((X1 @ X0)))) ) | (~spl1_26 | ~spl1_39 | ~spl1_42 | ~spl1_53)),
% 29.05/4.57 inference(duplicate_literal_removal,[],[f9494])).
% 29.05/4.57 thf(f9500,plain,(
% 29.05/4.57 ( ! [X0 : $i,X1 : ($i > $o)] : (($true = ((X1 @ X0)))) ) | (~spl1_26 | ~spl1_39 | ~spl1_42 | ~spl1_53)),
% 29.05/4.57 inference(trivial_inequality_removal,[],[f9499])).
% 29.05/4.57 thf(f9526,plain,(
% 29.05/4.57 spl1_17 | ~spl1_26 | ~spl1_39 | ~spl1_42 | ~spl1_53),
% 29.05/4.57 inference(avatar_split_clause,[],[f9500,f1072,f874,f862,f748,f718])).
% 29.05/4.57 thf(f10158,plain,(
% 29.05/4.57 ( ! [X3 : ($i > $o),X1 : $i,X8 : $i,X6 : $i,X7 : $i] : (($true = ((X3 @ X1))) | ($false = ((sK2 @ X8 @ X7))) | ($true = ((sK65 @ X3 @ X6 @ X8 @ X7)))) ) | (~spl1_40 | ~spl1_42)),
% 29.05/4.57 inference(forward_subsumption_resolution,[],[f867,f2031])).
% 29.05/4.57 thf(f10159,plain,(
% 29.05/4.57 ( ! [X3 : ($i > $o),X6 : $i] : (($false = ((sK65 @ X3 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6))) | ($true = ((X3 @ X6)))) ) | (~spl1_42 | ~spl1_48)),
% 29.05/4.57 inference(forward_subsumption_resolution,[],[f960,f2031])).
% 29.05/4.57 thf(f10221,definition,(
% 29.05/4.57 spl1_142 <=> ! [X4 : $i,X0 : ($i > $i > $o),X2 : $i,X1 : $i] : (($false = ((X0 @ X4 @ X4))) | ($true = ((X0 @ X1 @ X2))))),
% 29.05/4.57 introduced(definition,[new_symbols(definition,[spl1_142])],[avatar_definition])).
% 29.05/4.57 thf(f10222,plain,(
% 29.05/4.57 ( ! [X2 : $i,X0 : ($i > $i > $o),X1 : $i,X4 : $i] : (($false = ((X0 @ X4 @ X4))) | ($true = ((X0 @ X1 @ X2)))) ) | ~spl1_142),
% 29.05/4.57 inference(avatar_component_clause,[],[f10221])).
% 29.05/4.57 thf(f10281,plain,(
% 29.05/4.57 ( ! [X3 : ($i > $o),X1 : $i,X8 : $i,X6 : $i,X7 : $i] : (($true = $false) | ($true = ((X3 @ X1))) | ($true = ((sK65 @ X3 @ X6 @ X8 @ X7)))) ) | (~spl1_40 | ~spl1_42 | ~spl1_53)),
% 29.05/4.57 inference(forward_demodulation,[],[f10158,f8007])).
% 29.05/4.57 thf(f10282,plain,(
% 29.05/4.57 ( ! [X3 : ($i > $o),X1 : $i,X8 : $i,X6 : $i,X7 : $i] : (($true = ((X3 @ X1))) | ($true = ((sK65 @ X3 @ X6 @ X8 @ X7)))) ) | (~spl1_40 | ~spl1_42 | ~spl1_53)),
% 29.05/4.57 inference(trivial_inequality_removal,[],[f10281])).
% 29.05/4.57 thf(f11682,plain,(
% 29.05/4.57 ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : (($true = $false) | ($true = ((X0 @ X2))) | ($true = ((X0 @ X1)))) ) | (~spl1_40 | ~spl1_42 | ~spl1_48 | ~spl1_53)),
% 29.05/4.57 inference(constrained_superposition,[],[f10282,f10159])).
% 29.05/4.57 thf(f11693,plain,(
% 29.05/4.57 ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : (($true = ((X0 @ X2))) | ($true = ((X0 @ X1)))) ) | (~spl1_40 | ~spl1_42 | ~spl1_48 | ~spl1_53)),
% 29.05/4.57 inference(trivial_inequality_removal,[],[f11682])).
% 29.05/4.57 thf(f11750,plain,(
% 29.05/4.57 ( ! [X2 : $i,X0 : ($i > $o)] : (($true = ((X0 @ X2)))) ) | (~spl1_40 | ~spl1_42 | ~spl1_48 | ~spl1_53)),
% 29.05/4.57 inference(forward_subsumption_resolution,[],[f11693,f2031])).
% 29.05/4.57 thf(f11782,plain,(
% 29.05/4.57 spl1_17 | ~spl1_40 | ~spl1_42 | ~spl1_48 | ~spl1_53),
% 29.05/4.57 inference(avatar_split_clause,[],[f11750,f1072,f959,f874,f866,f718])).
% 29.05/4.57 thf(f12348,plain,(
% 29.05/4.57 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = $false) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X2 @ X1 @ (sK45 @ X1))))) ) | (~spl1_14 | ~spl1_63)),
% 29.05/4.57 inference(forward_demodulation,[],[f1112,f1247])).
% 29.05/4.57 thf(f12349,plain,(
% 29.05/4.57 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X2 @ X1 @ (sK45 @ X1))))) ) | (~spl1_14 | ~spl1_63)),
% 29.05/4.57 inference(trivial_inequality_removal,[],[f12348])).
% 29.05/4.57 thf(f13165,definition,(
% 29.05/4.57 spl1_173 <=> ! [X2 : ($i > $i > $o),X3 : $i] : (($true = ((X2 @ X3 @ (sK45 @ X3)))) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))))),
% 29.05/4.57 introduced(definition,[new_symbols(definition,[spl1_173])],[avatar_definition])).
% 29.05/4.57 thf(f13166,plain,(
% 29.05/4.57 ( ! [X2 : ($i > $i > $o),X3 : $i] : (($true = ((X2 @ X3 @ (sK45 @ X3)))) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) ) | ~spl1_173),
% 29.05/4.57 inference(avatar_component_clause,[],[f13165])).
% 29.05/4.57 thf(f13973,plain,(
% 29.05/4.57 spl1_173 | ~spl1_14 | ~spl1_63),
% 29.05/4.57 inference(avatar_split_clause,[],[f12349,f1111,f706,f13165])).
% 29.05/4.57 thf(f14067,plain,(
% 29.05/4.57 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i > $o),X1 : $i] : (($false != ((X0 @ X2 @ X3))) | ($true = ((X0 @ X2 @ X3))) | ($true != ((X0 @ X1 @ X1)))) ) | ~spl1_142),
% 29.05/4.57 inference(equality_factoring,[],[f10222])).
% 29.05/4.57 thf(f14315,plain,(
% 29.05/4.57 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i > $o),X1 : $i] : (($true != ((X0 @ X1 @ X1))) | ($true = ((X0 @ X2 @ X3)))) ) | ~spl1_142),
% 29.05/4.57 inference(forward_subsumption_resolution,[],[f14067,f46])).
% 29.05/4.57 thf(f16306,definition,(
% 29.05/4.57 spl1_180 <=> ! [X2 : ($i > $i > $o),X3 : $i] : (($true = ((X2 @ X3 @ (sK6 @ X3)))) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))))),
% 29.05/4.57 introduced(definition,[new_symbols(definition,[spl1_180])],[avatar_definition])).
% 29.05/4.57 thf(f16307,plain,(
% 29.05/4.57 ( ! [X2 : ($i > $i > $o),X3 : $i] : (($true = ((X2 @ X3 @ (sK6 @ X3)))) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) ) | ~spl1_180),
% 29.05/4.57 inference(avatar_component_clause,[],[f16306])).
% 29.05/4.57 thf(f18211,plain,(
% 29.05/4.57 ( ! [X2 : $i,X4 : ($i > $i > $o)] : (($true = $false) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X4 @ X2 @ (sK7 @ X2))))) ) | (~spl1_13 | ~spl1_69)),
% 29.05/4.57 inference(forward_demodulation,[],[f1223,f1243])).
% 29.05/4.57 thf(f18212,plain,(
% 29.05/4.57 ( ! [X2 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X4 @ X2 @ (sK7 @ X2))))) ) | (~spl1_13 | ~spl1_69)),
% 29.05/4.57 inference(trivial_inequality_removal,[],[f18211])).
% 29.05/4.57 thf(f18213,plain,(
% 29.05/4.57 ( ! [X2 : $i,X4 : ($i > $i > $o)] : (($true = $false) | ($false = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X4 @ X2 @ (sK7 @ X2))))) ) | (~spl1_13 | ~spl1_70)),
% 29.05/4.57 inference(forward_demodulation,[],[f1228,f1243])).
% 29.05/4.57 thf(f18214,plain,(
% 29.05/4.57 ( ! [X2 : $i,X4 : ($i > $i > $o)] : (($false = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X4 @ X2 @ (sK7 @ X2))))) ) | (~spl1_13 | ~spl1_70)),
% 29.05/4.57 inference(trivial_inequality_removal,[],[f18213])).
% 29.05/4.57 thf(f18215,plain,(
% 29.05/4.57 ( ! [X3 : ($i > $i > $o),X1 : $i] : (($true = $false) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X3 @ X1 @ (sK6 @ X1))))) ) | (~spl1_14 | ~spl1_56)),
% 29.05/4.57 inference(forward_demodulation,[],[f1083,f1247])).
% 29.05/4.57 thf(f18216,plain,(
% 29.05/4.57 ( ! [X3 : ($i > $i > $o),X1 : $i] : (($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X3 @ X1 @ (sK6 @ X1))))) ) | (~spl1_14 | ~spl1_56)),
% 29.05/4.57 inference(trivial_inequality_removal,[],[f18215])).
% 29.05/4.57 thf(f18217,plain,(
% 29.05/4.57 spl1_180 | ~spl1_14 | ~spl1_56),
% 29.05/4.57 inference(avatar_split_clause,[],[f18216,f1082,f706,f16306])).
% 29.05/4.57 thf(f18492,plain,(
% 29.05/4.57 ( ! [X3 : $i] : (($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))) @ X3 @ (sK53 @ X3)))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))) @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) ) | ~spl1_96),
% 29.05/4.57 inference(primitive_instantiation,[],[f4353])).
% 29.05/4.57 thf(f18794,plain,(
% 29.05/4.57 ( ! [X3 : $i] : (($true = ((~ (X3 = (sK53 @ X3))))) | ($true = ((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0)))))) ) | ~spl1_96),
% 29.05/4.57 inference(beta-eta_normalization,[],[f18492])).
% 29.05/4.57 thf(f18795,plain,(
% 29.05/4.57 ( ! [X3 : $i] : (($false = ((X3 = (sK53 @ X3)))) | ($true = ((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0)))))) ) | ~spl1_96),
% 29.05/4.57 inference(not_proxy_clausification,[],[f18794])).
% 29.05/4.57 thf(f18796,plain,(
% 29.05/4.57 ( ! [X3 : $i] : ((((sK53 @ X3)) != X3) | ($true = ((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0)))))) ) | ~spl1_96),
% 29.05/4.57 inference(equality_proxy_clausification,[],[f18795])).
% 29.05/4.57 thf(f18797,plain,(
% 29.05/4.57 ( ! [X3 : $i] : ((((sK53 @ X3)) != X3) | ($false = (((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0))))) ) | ~spl1_96),
% 29.05/4.57 inference(not_proxy_clausification,[],[f18796])).
% 29.05/4.57 thf(f18798,plain,(
% 29.05/4.57 ( ! [X3 : $i] : ((((sK53 @ X3)) != X3) | (((d2unsorted @ d_unsorted_0)) != ((d2unsorted @ d_unsorted_0)))) ) | ~spl1_96),
% 29.05/4.57 inference(equality_proxy_clausification,[],[f18797])).
% 29.05/4.57 thf(f18799,plain,(
% 29.05/4.57 ( ! [X3 : $i] : ((((sK53 @ X3)) != X3)) ) | ~spl1_96),
% 29.05/4.57 inference(trivial_inequality_removal,[],[f18798])).
% 29.05/4.57 thf(f18896,plain,(
% 29.05/4.57 $false | ~spl1_96),
% 29.05/4.57 inference(forward_subsumption_resolution,[],[f18799,f89])).
% 29.05/4.57 thf(f18897,plain,(
% 29.05/4.57 ~spl1_96),
% 29.05/4.57 inference(avatar_contradiction_clause,[],[f18896])).
% 29.05/4.57 thf(f19291,plain,(
% 29.05/4.57 ( ! [X3 : $i] : (($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))) @ X3 @ (sK45 @ X3)))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))) @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) ) | ~spl1_173),
% 29.05/4.57 inference(primitive_instantiation,[],[f13166])).
% 29.05/4.57 thf(f19587,plain,(
% 29.05/4.57 ( ! [X3 : $i] : (($true = ((~ (X3 = (sK45 @ X3))))) | ($true = ((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0)))))) ) | ~spl1_173),
% 29.05/4.57 inference(beta-eta_normalization,[],[f19291])).
% 29.05/4.57 thf(f19588,plain,(
% 29.05/4.57 ( ! [X3 : $i] : (($false = ((X3 = (sK45 @ X3)))) | ($true = ((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0)))))) ) | ~spl1_173),
% 29.05/4.57 inference(not_proxy_clausification,[],[f19587])).
% 29.05/4.57 thf(f19589,plain,(
% 29.05/4.57 ( ! [X3 : $i] : ((((sK45 @ X3)) != X3) | ($true = ((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0)))))) ) | ~spl1_173),
% 29.05/4.57 inference(equality_proxy_clausification,[],[f19588])).
% 29.05/4.57 thf(f19590,plain,(
% 29.05/4.57 ( ! [X3 : $i] : ((((sK45 @ X3)) != X3) | ($false = (((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0))))) ) | ~spl1_173),
% 29.05/4.57 inference(not_proxy_clausification,[],[f19589])).
% 29.05/4.57 thf(f19591,plain,(
% 29.05/4.57 ( ! [X3 : $i] : ((((sK45 @ X3)) != X3) | (((d2unsorted @ d_unsorted_0)) != ((d2unsorted @ d_unsorted_0)))) ) | ~spl1_173),
% 29.05/4.57 inference(equality_proxy_clausification,[],[f19590])).
% 29.05/4.57 thf(f19592,plain,(
% 29.05/4.57 ( ! [X3 : $i] : ((((sK45 @ X3)) != X3)) ) | ~spl1_173),
% 29.05/4.57 inference(trivial_inequality_removal,[],[f19591])).
% 29.05/4.57 thf(f19682,plain,(
% 29.05/4.57 $false | ~spl1_173),
% 29.05/4.57 inference(forward_subsumption_resolution,[],[f19592,f89])).
% 29.05/4.57 thf(f19683,plain,(
% 29.05/4.57 ~spl1_173),
% 29.05/4.57 inference(avatar_contradiction_clause,[],[f19682])).
% 29.05/4.57 thf(f19893,plain,(
% 29.05/4.57 ( ! [X3 : $i] : (($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))) @ X3 @ (sK6 @ X3)))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y0 = Y1))))) @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) ) | ~spl1_180),
% 29.05/4.57 inference(primitive_instantiation,[],[f16307])).
% 29.05/4.57 thf(f20189,plain,(
% 29.05/4.57 ( ! [X3 : $i] : (($true = ((~ (X3 = (sK6 @ X3))))) | ($true = ((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0)))))) ) | ~spl1_180),
% 29.05/4.57 inference(beta-eta_normalization,[],[f19893])).
% 29.05/4.57 thf(f20190,plain,(
% 29.05/4.57 ( ! [X3 : $i] : (($false = ((X3 = (sK6 @ X3)))) | ($true = ((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0)))))) ) | ~spl1_180),
% 29.05/4.57 inference(not_proxy_clausification,[],[f20189])).
% 29.05/4.57 thf(f20191,plain,(
% 29.05/4.57 ( ! [X3 : $i] : ((((sK6 @ X3)) != X3) | ($true = ((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0)))))) ) | ~spl1_180),
% 29.05/4.57 inference(equality_proxy_clausification,[],[f20190])).
% 29.05/4.57 thf(f20192,plain,(
% 29.05/4.57 ( ! [X3 : $i] : ((((sK6 @ X3)) != X3) | ($false = (((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0))))) ) | ~spl1_180),
% 29.05/4.57 inference(not_proxy_clausification,[],[f20191])).
% 29.05/4.57 thf(f20193,plain,(
% 29.05/4.57 ( ! [X3 : $i] : ((((sK6 @ X3)) != X3) | (((d2unsorted @ d_unsorted_0)) != ((d2unsorted @ d_unsorted_0)))) ) | ~spl1_180),
% 29.05/4.57 inference(equality_proxy_clausification,[],[f20192])).
% 29.05/4.57 thf(f20194,plain,(
% 29.05/4.57 ( ! [X3 : $i] : ((((sK6 @ X3)) != X3)) ) | ~spl1_180),
% 29.05/4.57 inference(trivial_inequality_removal,[],[f20193])).
% 29.05/4.57 thf(f20284,plain,(
% 29.05/4.57 $false | ~spl1_180),
% 29.05/4.57 inference(forward_subsumption_resolution,[],[f20194,f89])).
% 29.05/4.57 thf(f20285,plain,(
% 29.05/4.57 ~spl1_180),
% 29.05/4.57 inference(avatar_contradiction_clause,[],[f20284])).
% 29.05/4.57 thf(f21752,plain,(
% 29.05/4.57 ( ! [X2 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ X2 @ (sK7 @ X2))))) ) | (~spl1_13 | ~spl1_69 | ~spl1_142)),
% 29.05/4.57 inference(forward_subsumption_resolution,[],[f18212,f14315])).
% 29.05/4.57 thf(f21753,plain,(
% 29.05/4.57 spl1_68 | ~spl1_13 | ~spl1_69 | ~spl1_142),
% 29.05/4.57 inference(avatar_split_clause,[],[f21752,f10221,f1222,f695,f1219])).
% 29.05/4.57 thf(f21767,plain,(
% 29.05/4.57 ( ! [X2 : $i,X0 : $i,X1 : ($i > $i > $o)] : (($false = ((X1 @ X0 @ X0))) | ($true = ((X1 @ X2 @ (sK7 @ X2))))) ) | (~spl1_13 | ~spl1_70)),
% 29.05/4.57 inference(constrained_superposition,[],[f18214,f85])).
% 29.05/4.57 thf(f22293,plain,(
% 29.05/4.57 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $i > $o)] : (($true = ((X1 @ X2 @ X0))) | ($false = ((X1 @ X3 @ X3)))) ) | (~spl1_13 | ~spl1_70)),
% 29.05/4.57 inference(constrained_superposition,[],[f21767,f89])).
% 29.05/4.57 thf(f22556,plain,(
% 29.05/4.57 spl1_142 | ~spl1_13 | ~spl1_70),
% 29.05/4.57 inference(avatar_split_clause,[],[f22293,f1227,f695,f10221])).
% 29.05/4.57 cnf(s8, plain, spl1_13 | spl1_14, inference(sat_conversion,[],[f716])).
% 29.05/4.57 cnf(s12, plain, spl1_26 | spl1_30, inference(sat_conversion,[],[f763])).
% 29.05/4.57 cnf(s14, plain, spl1_26 | spl1_34, inference(sat_conversion,[],[f848])).
% 29.05/4.57 cnf(s16, plain, spl1_39 | spl1_40, inference(sat_conversion,[],[f868])).
% 29.05/4.57 cnf(s21, plain, spl1_39 | spl1_48, inference(sat_conversion,[],[f961])).
% 29.05/4.57 cnf(s24, plain, spl1_42 | spl1_42, inference(sat_conversion,[],[f970])).
% 29.05/4.57 cnf(s25, plain, spl1_42, inference(rat,[],[s24])).
% 29.05/4.57 cnf(s35, plain, spl1_13 | spl1_53 | spl1_63, inference(sat_conversion,[],[f1114])).
% 29.05/4.57 cnf(s39, plain, spl1_14 | spl1_53 | spl1_66, inference(sat_conversion,[],[f1127])).
% 29.05/4.57 cnf(s47, plain, spl1_53 | spl1_56 | spl1_69, inference(sat_conversion,[],[f1232])).
% 29.05/4.57 cnf(s49, plain, spl1_53 | spl1_56 | spl1_70, inference(sat_conversion,[],[f1234])).
% 29.05/4.57 cnf(s73, plain, ~spl1_17, inference(sat_conversion,[],[f1345])).
% 29.05/4.57 cnf(s246, plain, ~spl1_68, inference(sat_conversion,[],[f2853])).
% 29.05/4.57 cnf(s489, plain, ~spl1_13 | ~spl1_66 | spl1_96, inference(sat_conversion,[],[f6054])).
% 29.05/4.57 cnf(s549, plain, spl1_17 | ~spl1_30 | ~spl1_34 | ~spl1_42 | ~spl1_53, inference(sat_conversion,[],[f9083])).
% 29.05/4.57 cnf(s555, plain, spl1_17 | ~spl1_26 | ~spl1_39 | ~spl1_42 | ~spl1_53, inference(sat_conversion,[],[f9526])).
% 29.05/4.57 cnf(s655, plain, spl1_17 | ~spl1_40 | ~spl1_42 | ~spl1_48 | ~spl1_53, inference(sat_conversion,[],[f11782])).
% 29.05/4.57 cnf(s728, plain, ~spl1_14 | ~spl1_63 | spl1_173, inference(sat_conversion,[],[f13973])).
% 29.05/4.57 cnf(s837, plain, ~spl1_14 | ~spl1_56 | spl1_180, inference(sat_conversion,[],[f18217])).
% 29.05/4.57 cnf(s858, plain, ~spl1_96, inference(sat_conversion,[],[f18897])).
% 29.05/4.57 cnf(s960, plain, ~spl1_173, inference(sat_conversion,[],[f19683])).
% 29.05/4.57 cnf(s1025, plain, ~spl1_180, inference(sat_conversion,[],[f20285])).
% 29.05/4.57 cnf(s1101, plain, ~spl1_13 | spl1_68 | ~spl1_69 | ~spl1_142, inference(sat_conversion,[],[f21753])).
% 29.05/4.57 cnf(s1143, plain, ~spl1_13 | ~spl1_70 | spl1_142, inference(sat_conversion,[],[f22556])).
% 29.05/4.57 cnf(s1145, plain, ~spl1_14 | ~spl1_56, inference(rat,[],[s837,s1025])).
% 29.05/4.57 cnf(s1146, plain, ~spl1_14 | ~spl1_63, inference(rat,[],[s728,s960])).
% 29.05/4.57 cnf(s1147, plain, ~spl1_13 | ~spl1_66, inference(rat,[],[s489,s858])).
% 29.05/4.57 cnf(s1148, plain, spl1_26 | ~spl1_53, inference(rat,[],[s549,s12,s14,s73,s25])).
% 29.05/4.57 cnf(s1149, plain, ~spl1_26 | ~spl1_53, inference(rat,[],[s655,s16,s21,s555,s25,s73])).
% 29.05/4.57 cnf(s1150, plain, ~spl1_53, inference(rat,[],[s1149,s1148])).
% 29.05/4.57 cnf(s1152, plain, ~spl1_14, inference(rat,[],[s1101,s1143,s35,s47,s49,s1146,s1145,s246,s1150])).
% 29.05/4.57 cnf(s1153, plain, spl1_66, inference(rat,[],[s39,s1152,s1150])).
% 29.05/4.57 cnf(s1156, plain, spl1_13, inference(rat,[],[s8,s1152])).
% 29.05/4.57 cnf(s1158, plain, $false, inference(rat,[],[s1147,s1153,s1156])).
% 29.05/4.57 thf(f22559,plain,(
% 29.05/4.57 $false),
% 29.05/4.57 inference(avatar_sat_refutation,[],[s1158])).
% 29.05/4.57 % SZS output end Proof for theBenchmark
% 29.05/4.57 % (1489753)------------------------------
% 29.05/4.57 % (1489753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.05/4.57 % (1489753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.05/4.57 % (1489753)CaDiCaL version: 2.1.3
% 29.05/4.57 % (1489753)Termination reason: Refutation
% 29.05/4.57 % (1489753)Time elapsed: 0.706 s
% 29.05/4.57 % (1489753)Peak memory usage: 19 MB
% 29.05/4.57 % (1489753)Instructions burned: 1500 (million)
% 29.05/4.57 % (1489682)Success in time 4.308 s
% 29.05/4.57 % Vampire exiting
%------------------------------------------------------------------------------