%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV040^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 08:38:54 AM UTC 2026
% Result : Theorem 9.02s 2.00s
% Output : Refutation 9.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV040^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.27 % Computer : n008.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Tue Sep 29 15:05:31 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.32 Running first-order model finding
% 0.26/0.32 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
% 6.81/1.41 % (3275163)Will run a generic schedule for satisfiability detection.
% 6.81/1.41 % (3275171)dis+10_1_sil=32000:sp=arity:random_seed=4120302673:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.81/1.41 % (3275169)% WARNING: option uhcvi not known.
% 6.81/1.41 % (3275170)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=338893643:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.81/1.41 % (3275168)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3570951973_2999 on theBenchmark for (2999ds/0Mi)
% 6.81/1.41 % (3275169)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1196841276:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.81/1.41 % (3275172)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1501484776:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.81/1.41 % (3275174)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1048990204:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.81/1.41 % (3275173)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2918788503:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.81/1.41 % (3275169)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.81/1.41 % (3275172)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.81/1.41 % Exception at run slice level
% 6.81/1.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.81/1.41 % (3275169)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.81/1.41 % (3275171)Instruction limit reached!
% 6.81/1.41 % (3275171)------------------------------
% 6.81/1.41 % (3275171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.81/1.41 % (3275171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.41 % (3275171)CaDiCaL version: 2.1.3
% 6.81/1.41 % (3275171)Termination reason: Instruction limit
% 6.81/1.41 % (3275171)Termination phase: Saturation
% 6.81/1.41 % (3275171)Time elapsed: 0.046 s
% 6.81/1.41 % (3275171)Peak memory usage: 12 MB
% 6.81/1.41 % (3275171)Instructions burned: 104 (million)
% 6.81/1.41 % (3275182)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2506932368:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.81/1.41 % Exception at run slice level
% 6.81/1.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.81/1.41 % (3275183)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3415131226:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.81/1.41 % (3275185)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=3655729329:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 6.81/1.41 % (3275185)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.81/1.41 % (3275185)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.81/1.41 % (3275172)Instruction limit reached!
% 6.81/1.41 % (3275172)------------------------------
% 6.81/1.41 % (3275172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.81/1.41 % (3275172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.41 % (3275172)CaDiCaL version: 2.1.3
% 6.81/1.41 % (3275172)Termination reason: Instruction limit
% 6.81/1.41 % (3275172)Termination phase: Saturation
% 6.81/1.41 % (3275172)Time elapsed: 0.094 s
% 6.81/1.41 % (3275172)Peak memory usage: 12 MB
% 6.81/1.41 % (3275172)Instructions burned: 117 (million)
% 6.81/1.41 % (3275173)Instruction limit reached!
% 6.81/1.41 % (3275173)------------------------------
% 6.81/1.41 % (3275173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.81/1.41 % (3275173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.41 % (3275173)CaDiCaL version: 2.1.3
% 6.81/1.41 % (3275173)Termination reason: Instruction limit
% 6.81/1.41 % (3275173)Termination phase: Saturation
% 6.81/1.41 % (3275173)Time elapsed: 0.109 s
% 6.81/1.41 % (3275173)Peak memory usage: 13 MB
% 6.81/1.41 % (3275173)Instructions burned: 131 (million)
% 6.81/1.41 % (3275183)Instruction limit reached!
% 6.81/1.41 % (3275183)------------------------------
% 6.81/1.41 % (3275183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.02/2.00 % (3275183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.02/2.00 % (3275183)CaDiCaL version: 2.1.3
% 9.02/2.00 % (3275183)Termination reason: Instruction limit
% 9.02/2.00 % (3275183)Termination phase: Saturation
% 9.02/2.00 % (3275183)Time elapsed: 0.059 s
% 9.02/2.00 % (3275183)Peak memory usage: 13 MB
% 9.02/2.00 % (3275183)Instructions burned: 131 (million)
% 9.02/2.00 % (3275188)ott-21_1_sil=16000:fs=off:random_seed=3854206901:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 9.02/2.00 % (3275190)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3826077724:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 9.02/2.00 % Exception at run slice level
% 9.02/2.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.02/2.00 % (3275174)Instruction limit reached!
% 9.02/2.00 % (3275174)------------------------------
% 9.02/2.00 % (3275174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.02/2.00 % (3275174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.02/2.00 % (3275174)CaDiCaL version: 2.1.3
% 9.02/2.00 % (3275174)Termination reason: Instruction limit
% 9.02/2.00 % (3275174)Termination phase: Saturation
% 9.02/2.00 % (3275174)Time elapsed: 0.133 s
% 9.02/2.00 % (3275174)Peak memory usage: 12 MB
% 9.02/2.00 % (3275174)Instructions burned: 161 (million)
% 9.02/2.00 % (3275189)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3801727778:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 9.02/2.00 % (3275193)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3176414750:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 9.02/2.00 % (3275194)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=848744888:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 9.02/2.00 % Exception at run slice level
% 9.02/2.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.02/2.00 % (3275198)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=2767557186:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 9.02/2.00 % (3275198)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 9.02/2.00 % (3275188)Instruction limit reached!
% 9.02/2.00 % (3275188)------------------------------
% 9.02/2.00 % (3275188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.02/2.00 % (3275188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.02/2.00 % (3275188)CaDiCaL version: 2.1.3
% 9.02/2.00 % (3275188)Termination reason: Instruction limit
% 9.02/2.00 % (3275188)Termination phase: Saturation
% 9.02/2.00 % (3275188)Time elapsed: 0.143 s
% 9.02/2.00 % (3275188)Peak memory usage: 12 MB
% 9.02/2.00 % (3275188)Instructions burned: 180 (million)
% 9.02/2.00 % (3275200)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3241392230:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 9.02/2.00 % (3275200)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 9.02/2.00 % (3275189)Instruction limit reached!
% 9.02/2.00 % (3275189)------------------------------
% 9.02/2.00 % (3275189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.02/2.00 % (3275189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.02/2.00 % (3275189)CaDiCaL version: 2.1.3
% 9.02/2.00 % (3275189)Termination reason: Instruction limit
% 9.02/2.00 % (3275189)Termination phase: Saturation
% 9.02/2.00 % (3275189)Time elapsed: 0.400 s
% 9.02/2.00 % (3275189)Peak memory usage: 14 MB
% 9.02/2.00 % (3275189)Instructions burned: 478 (million)
% 9.02/2.00 % (3275202)fmb+10_1_sil=64000:random_seed=2732735387:i=22061:nm=2:gsp=on_2994 on theBenchmark for (2994ds/22061Mi)
% 9.02/2.00 % (3275202)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 9.02/2.00 % Exception at run slice level
% 9.02/2.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.02/2.00 % (3275204)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1079638021:i=9515:nm=5_2993 on theBenchmark for (2993ds/9515Mi)
% 9.02/2.00 % (3275185)Instruction limit reached!
% 9.02/2.00 % (3275185)------------------------------
% 9.02/2.00 % (3275185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.02/2.00 % (3275185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.02/2.00 % (3275185)CaDiCaL version: 2.1.3
% 9.02/2.00 % (3275185)Termination reason: Instruction limit
% 9.02/2.00 % (3275185)Termination phase: Saturation
% 9.02/2.00 % (3275185)Time elapsed: 0.550 s
% 9.02/2.00 % (3275185)Peak memory usage: 15 MB
% 9.02/2.00 % (3275185)Instructions burned: 685 (million)
% 9.02/2.00 % Exception at run slice level
% 9.02/2.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.02/2.00 % (3275206)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3796965060:fmbsr=1.7:i=920_2993 on theBenchmark for (2993ds/920Mi)
% 9.02/2.00 % Exception at run slice level
% 9.02/2.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.02/2.00 % (3275193)Instruction limit reached!
% 9.02/2.00 % (3275193)------------------------------
% 9.02/2.00 % (3275193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.02/2.00 % (3275193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.02/2.00 % (3275193)CaDiCaL version: 2.1.3
% 9.02/2.00 % (3275193)Termination reason: Instruction limit
% 9.02/2.00 % (3275193)Termination phase: Saturation
% 9.02/2.00 % (3275193)Time elapsed: 0.495 s
% 9.02/2.00 % (3275193)Peak memory usage: 18 MB
% 9.02/2.00 % (3275193)Instructions burned: 1180 (million)
% 9.02/2.00 % (3275207)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2173479280:i=5131_2993 on theBenchmark for (2993ds/5131Mi)
% 9.02/2.00 % (3275207)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 9.02/2.00 % (3275210)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3286618129:i=6324_2993 on theBenchmark for (2993ds/6324Mi)
% 9.02/2.00 % Exception at run slice level
% 9.02/2.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.02/2.00 % (3275209)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2213826929:i=1472:ins=7:fdi=8:gsp=on_2993 on theBenchmark for (2993ds/1472Mi)
% 9.02/2.00 % (3275209)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 9.02/2.00 % (3275209)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 9.02/2.00 % (3275213)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2107170309:fmbsr=2.30978:i=2174_2992 on theBenchmark for (2992ds/2174Mi)
% 9.02/2.00 % Exception at run slice level
% 9.02/2.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.02/2.00 % (3275216)ott-2_1_sil=16000:newcnf=on:random_seed=375621239:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2992 on theBenchmark for (2992ds/869Mi)
% 9.02/2.00 % (3275216)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 9.02/2.00 % (3275198)Instruction limit reached!
% 9.02/2.00 % (3275198)------------------------------
% 9.02/2.00 % (3275198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.02/2.00 % (3275198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.02/2.00 % (3275198)CaDiCaL version: 2.1.3
% 9.02/2.00 % (3275198)Termination reason: Instruction limit
% 9.02/2.00 % (3275198)Termination phase: Saturation
% 9.02/2.00 % (3275198)Time elapsed: 0.558 s
% 9.02/2.00 % (3275198)Peak memory usage: 16 MB
% 9.02/2.00 % (3275198)Instructions burned: 693 (million)
% 9.02/2.00 % (3275218)ott+10_1_sil=32000:tgt=ground:random_seed=3235540908:i=5114:av=off_2991 on theBenchmark for (2991ds/5114Mi)
% 9.02/2.00 % (3275200)Instruction limit reached!
% 9.02/2.00 % (3275200)------------------------------
% 9.02/2.00 % (3275200)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.02/2.00 % (3275200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.02/2.00 % (3275200)CaDiCaL version: 2.1.3
% 9.02/2.00 % (3275200)Termination reason: Instruction limit
% 9.02/2.00 % (3275200)Termination phase: Saturation
% 9.02/2.00 % (3275200)Time elapsed: 0.713 s
% 9.02/2.00 % (3275200)Peak memory usage: 15 MB
% 9.02/2.00 % (3275200)Instructions burned: 879 (million)
% 9.02/2.00 % (3275220)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=432513171:i=54282_2989 on theBenchmark for (2989ds/54282Mi)
% 9.02/2.00 % Exception at run slice level
% 9.02/2.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 9.02/2.00 % (3275222)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2699245213:i=3512:aac=none_2989 on theBenchmark for (2989ds/3512Mi)
% 9.02/2.00 % (3275222)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 9.02/2.00 % (3275216)Instruction limit reached!
% 9.02/2.00 % (3275216)------------------------------
% 9.02/2.00 % (3275216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.02/2.00 % (3275216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.02/2.00 % (3275216)CaDiCaL version: 2.1.3
% 9.02/2.00 % (3275216)Termination reason: Instruction limit
% 9.02/2.00 % (3275216)Termination phase: Saturation
% 9.02/2.00 % (3275216)Time elapsed: 0.631 s
% 9.02/2.00 % (3275216)Peak memory usage: 17 MB
% 9.02/2.00 % (3275216)Instructions burned: 869 (million)
% 9.02/2.00 % (3275226)dis+21_1_sil=32000:sas=cadical:random_seed=2776534685:i=3773:amm=off_2986 on theBenchmark for (2986ds/3773Mi)
% 9.02/2.00 % (3275207) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3275163-3275207"...
% 9.02/2.00 % (3275207)...printing done.
% 9.02/2.00 % (3275207)Refutation found. Thanks to Tanya!
% 9.02/2.00 % SZS status Theorem for theBenchmark
% 9.02/2.00 % SZS output start Proof for theBenchmark
% 9.02/2.00 thf(type_def_5, type, a: $tType).
% 9.02/2.00 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 9.02/2.00 thf(func_def_3, type, vAND: ($o > $o > $o)).
% 9.02/2.00 thf(func_def_4, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 9.02/2.00 thf(func_def_5, type, vIMP: ($o > $o > $o)).
% 9.02/2.00 thf(func_def_6, type, db3: !>[X0: $tType]:(X0)).
% 9.02/2.00 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 9.02/2.00 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 9.02/2.00 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 9.02/2.00 thf(func_def_10, type, db4: !>[X0: $tType]:(X0)).
% 9.02/2.00 thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
% 9.02/2.00 thf(func_def_12, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 9.02/2.00 thf(func_def_13, type, sP0: ((a > a > $o) > (a > a > $o) > $o)).
% 9.02/2.00 thf(func_def_14, type, sP1: ((a > a > $o) > (a > a > $o) > $o)).
% 9.02/2.00 thf(func_def_15, type, sP2: $o).
% 9.02/2.00 thf(func_def_16, type, sK3: (a > a > $o)).
% 9.02/2.00 thf(func_def_17, type, sK4: (a > a > $o)).
% 9.02/2.00 thf(func_def_18, type, sK5: (a > a > $o)).
% 9.02/2.00 thf(func_def_19, type, sK6: ((a > a > $o) > a)).
% 9.02/2.00 thf(func_def_20, type, sK7: ((a > a > $o) > a)).
% 9.02/2.00 thf(func_def_21, type, sK8: ((a > a > $o) > a)).
% 9.02/2.00 thf(func_def_22, type, sK9: ((a > a > $o) > a)).
% 9.02/2.00 thf(func_def_23, type, sK10: ((a > a > $o) > a)).
% 9.02/2.00 thf(func_def_24, type, sK11: ((a > a > $o) > a)).
% 9.02/2.00 thf(func_def_25, type, sK12: ((a > a > $o) > a)).
% 9.02/2.00 thf(func_def_26, type, sK13: ((a > a > $o) > a)).
% 9.02/2.00 thf(func_def_27, type, sK14: ((a > a > $o) > a)).
% 9.02/2.00 thf(func_def_28, type, sK15: ((a > a > $o) > a)).
% 9.02/2.00 thf(func_def_29, type, sK16: (a > a > $o)).
% 9.02/2.00 thf(func_def_30, type, sK17: (a > a > $o)).
% 9.02/2.00 thf(func_def_31, type, vNOT: ($o > $o)).
% 9.02/2.00 thf(f1,conjecture,(
% 9.02/2.00 ((^[X6 : (a > a > $o), X7 : (a > a > $o)] : ((X6 = X7) & ! [X0 : a,X1 : a,X4 : a] : (((X6 @ X1 @ X4) & (X6 @ X0 @ X1)) => (X6 @ X0 @ X4)) & ! [X0 : a,X1 : a] : ((X6 @ X0 @ X1) => (X6 @ X1 @ X0)))) = (^[X6 : (a > a > $o), X7 : (a > a > $o)] : ((X6 = X7) & ! [X0 : a,X1 : a,X4 : a] : (((X6 @ X1 @ X4) & (X6 @ X0 @ X1)) => (X6 @ X0 @ X4)) & ! [X0 : a,X1 : a] : ((X6 @ X0 @ X1) => (X6 @ X1 @ X0))))) & ! [X0 : (a > a > $o),X1 : (a > a > $o),X4 : (a > a > $o)] : (((X1 = X4) & ! [X2 : a,X3 : a,X5 : a] : (((X1 @ X3 @ X5) & (X1 @ X2 @ X3)) => (X1 @ X2 @ X5)) & ! [X2 : a,X3 : a] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)) & (X0 = X1) & ! [X2 : a,X3 : a,X5 : a] : (((X0 @ X3 @ X5) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X5)) & ! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) => (X0 @ X3 @ X2))) => ((X0 = X4) & ! [X2 : a,X3 : a,X5 : a] : (((X0 @ X3 @ X5) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X5)) & ! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) => (X0 @ X3 @ X2)))) & ! [X0 : (a > a > $o),X1 : (a > a > $o)] : (((X0 = X1) & ! [X2 : a,X3 : a,X4 : a] : (((X0 @ X3 @ X4) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X4)) & ! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) => (X0 @ X3 @ X2))) => ((X1 = X0) & ! [X2 : a,X3 : a,X4 : a] : (((X1 @ X3 @ X4) & (X1 @ X2 @ X3)) => (X1 @ X2 @ X4)) & ! [X2 : a,X3 : a] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2))))),
% 9.02/2.00 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM515_pme)).
% 9.02/2.00 thf(f2,negated_conjecture,(
% 9.02/2.00 ~(((^[X6 : (a > a > $o), X7 : (a > a > $o)] : ((X6 = X7) & ! [X0 : a,X1 : a,X4 : a] : (((X6 @ X1 @ X4) & (X6 @ X0 @ X1)) => (X6 @ X0 @ X4)) & ! [X0 : a,X1 : a] : ((X6 @ X0 @ X1) => (X6 @ X1 @ X0)))) = (^[X6 : (a > a > $o), X7 : (a > a > $o)] : ((X6 = X7) & ! [X0 : a,X1 : a,X4 : a] : (((X6 @ X1 @ X4) & (X6 @ X0 @ X1)) => (X6 @ X0 @ X4)) & ! [X0 : a,X1 : a] : ((X6 @ X0 @ X1) => (X6 @ X1 @ X0))))) & ! [X0 : (a > a > $o),X1 : (a > a > $o),X4 : (a > a > $o)] : (((X1 = X4) & ! [X2 : a,X3 : a,X5 : a] : (((X1 @ X3 @ X5) & (X1 @ X2 @ X3)) => (X1 @ X2 @ X5)) & ! [X2 : a,X3 : a] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)) & (X0 = X1) & ! [X2 : a,X3 : a,X5 : a] : (((X0 @ X3 @ X5) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X5)) & ! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) => (X0 @ X3 @ X2))) => ((X0 = X4) & ! [X2 : a,X3 : a,X5 : a] : (((X0 @ X3 @ X5) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X5)) & ! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) => (X0 @ X3 @ X2)))) & ! [X0 : (a > a > $o),X1 : (a > a > $o)] : (((X0 = X1) & ! [X2 : a,X3 : a,X4 : a] : (((X0 @ X3 @ X4) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X4)) & ! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) => (X0 @ X3 @ X2))) => ((X1 = X0) & ! [X2 : a,X3 : a,X4 : a] : (((X1 @ X3 @ X4) & (X1 @ X2 @ X3)) => (X1 @ X2 @ X4)) & ! [X2 : a,X3 : a] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)))))),
% 9.02/2.00 inference(negated_conjecture,[status(cth)],[f1])).
% 9.02/2.00 thf(f3,plain,(
% 9.02/2.00 ~(((^[X0 : (a > a > $o), X1 : (a > a > $o)] : ((X0 = X1) & ! [X2 : a,X3 : a,X4 : a] : (((X0 @ X3 @ X4) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X4)) & ! [X5 : a,X6 : a] : ((X0 @ X5 @ X6) => (X0 @ X6 @ X5)))) = (^[X7 : (a > a > $o), X8 : (a > a > $o)] : ((X7 = X8) & ! [X9 : a,X10 : a,X11 : a] : (((X7 @ X10 @ X11) & (X7 @ X9 @ X10)) => (X7 @ X9 @ X11)) & ! [X12 : a,X13 : a] : ((X7 @ X12 @ X13) => (X7 @ X13 @ X12))))) & ! [X14 : (a > a > $o),X15 : (a > a > $o),X16 : (a > a > $o)] : (((X15 = X16) & ! [X17 : a,X18 : a,X19 : a] : (((X15 @ X18 @ X19) & (X15 @ X17 @ X18)) => (X15 @ X17 @ X19)) & ! [X20 : a,X21 : a] : ((X15 @ X20 @ X21) => (X15 @ X21 @ X20)) & (X14 = X15) & ! [X22 : a,X23 : a,X24 : a] : (((X14 @ X23 @ X24) & (X14 @ X22 @ X23)) => (X14 @ X22 @ X24)) & ! [X25 : a,X26 : a] : ((X14 @ X25 @ X26) => (X14 @ X26 @ X25))) => ((X14 = X16) & ! [X27 : a,X28 : a,X29 : a] : (((X14 @ X28 @ X29) & (X14 @ X27 @ X28)) => (X14 @ X27 @ X29)) & ! [X30 : a,X31 : a] : ((X14 @ X30 @ X31) => (X14 @ X31 @ X30)))) & ! [X32 : (a > a > $o),X33 : (a > a > $o)] : (((X32 = X33) & ! [X34 : a,X35 : a,X36 : a] : (((X32 @ X35 @ X36) & (X32 @ X34 @ X35)) => (X32 @ X34 @ X36)) & ! [X37 : a,X38 : a] : ((X32 @ X37 @ X38) => (X32 @ X38 @ X37))) => ((X32 = X33) & ! [X39 : a,X40 : a,X41 : a] : (((X33 @ X40 @ X41) & (X33 @ X39 @ X40)) => (X33 @ X39 @ X41)) & ! [X42 : a,X43 : a] : ((X33 @ X42 @ X43) => (X33 @ X43 @ X42)))))),
% 9.02/2.00 inference(rectify,[],[f2])).
% 9.02/2.00 thf(f4,plain,(
% 9.02/2.00 ~(((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1))))) = (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1)))))) & ! [X14 : (a > a > $o),X15 : (a > a > $o),X16 : (a > a > $o)] : (((X15 = X16) & ! [X17 : a,X18 : a,X19 : a] : (((((X15 @ X18 @ X19)) = $true) & (((X15 @ X17 @ X18)) = $true)) => (((X15 @ X17 @ X19)) = $true)) & ! [X20 : a,X21 : a] : ((((X15 @ X20 @ X21)) = $true) => (((X15 @ X21 @ X20)) = $true)) & (X14 = X15) & ! [X22 : a,X23 : a,X24 : a] : (((((X14 @ X23 @ X24)) = $true) & (((X14 @ X22 @ X23)) = $true)) => (((X14 @ X22 @ X24)) = $true)) & ! [X25 : a,X26 : a] : ((((X14 @ X25 @ X26)) = $true) => (((X14 @ X26 @ X25)) = $true))) => ((X14 = X16) & ! [X27 : a,X28 : a,X29 : a] : (((((X14 @ X28 @ X29)) = $true) & (((X14 @ X27 @ X28)) = $true)) => (((X14 @ X27 @ X29)) = $true)) & ! [X30 : a,X31 : a] : ((((X14 @ X30 @ X31)) = $true) => (((X14 @ X31 @ X30)) = $true)))) & ! [X32 : (a > a > $o),X33 : (a > a > $o)] : (((X32 = X33) & ! [X34 : a,X35 : a,X36 : a] : (((((X32 @ X35 @ X36)) = $true) & (((X32 @ X34 @ X35)) = $true)) => (((X32 @ X34 @ X36)) = $true)) & ! [X37 : a,X38 : a] : ((((X32 @ X37 @ X38)) = $true) => (((X32 @ X38 @ X37)) = $true))) => ((X32 = X33) & ! [X39 : a,X40 : a,X41 : a] : (((((X33 @ X40 @ X41)) = $true) & (((X33 @ X39 @ X40)) = $true)) => (((X33 @ X39 @ X41)) = $true)) & ! [X42 : a,X43 : a] : ((((X33 @ X42 @ X43)) = $true) => (((X33 @ X43 @ X42)) = $true)))))),
% 9.02/2.00 inference(fool_elimination,[],[f3])).
% 9.02/2.00 thf(f5,plain,(
% 9.02/2.00 ~(((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1))))) = (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1)))))) & ! [X0 : (a > a > $o),X1 : (a > a > $o),X2 : (a > a > $o)] : (((X1 = X2) & ! [X3 : a,X4 : a,X5 : a] : ((($true = ((X1 @ X4 @ X5))) & (((X1 @ X3 @ X4)) = $true)) => (((X1 @ X3 @ X5)) = $true)) & ! [X6 : a,X7 : a] : (($true = ((X1 @ X6 @ X7))) => ($true = ((X1 @ X7 @ X6)))) & (X0 = X1) & ! [X8 : a,X9 : a,X10 : a] : ((($true = ((X0 @ X9 @ X10))) & ($true = ((X0 @ X8 @ X9)))) => ($true = ((X0 @ X8 @ X10)))) & ! [X11 : a,X12 : a] : (($true = ((X0 @ X11 @ X12))) => ($true = ((X0 @ X12 @ X11))))) => ((X0 = X2) & ! [X13 : a,X14 : a,X15 : a] : ((($true = ((X0 @ X14 @ X15))) & ($true = ((X0 @ X13 @ X14)))) => ($true = ((X0 @ X13 @ X15)))) & ! [X16 : a,X17 : a] : (($true = ((X0 @ X16 @ X17))) => ($true = ((X0 @ X17 @ X16)))))) & ! [X18 : (a > a > $o),X19 : (a > a > $o)] : (((X18 = X19) & ! [X20 : a,X21 : a,X22 : a] : ((($true = ((X18 @ X21 @ X22))) & ($true = ((X18 @ X20 @ X21)))) => ($true = ((X18 @ X20 @ X22)))) & ! [X23 : a,X24 : a] : (($true = ((X18 @ X23 @ X24))) => ($true = ((X18 @ X24 @ X23))))) => ((X18 = X19) & ! [X25 : a,X26 : a,X27 : a] : ((($true = ((X19 @ X26 @ X27))) & ($true = ((X19 @ X25 @ X26)))) => ($true = ((X19 @ X25 @ X27)))) & ! [X28 : a,X29 : a] : (($true = ((X19 @ X28 @ X29))) => ($true = ((X19 @ X29 @ X28)))))))),
% 9.02/2.00 inference(rectify,[],[f4])).
% 9.02/2.00 thf(f6,plain,(
% 9.02/2.00 ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1))))) != (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1)))))) | ? [X0 : (a > a > $o),X1 : (a > a > $o),X2 : (a > a > $o)] : (((X0 != X2) | ? [X13 : a,X14 : a,X15 : a] : (($true != ((X0 @ X13 @ X15))) & (($true = ((X0 @ X14 @ X15))) & ($true = ((X0 @ X13 @ X14))))) | ? [X16 : a,X17 : a] : (($true != ((X0 @ X17 @ X16))) & ($true = ((X0 @ X16 @ X17))))) & ((X1 = X2) & ! [X3 : a,X4 : a,X5 : a] : ((((X1 @ X3 @ X5)) = $true) | (($true != ((X1 @ X4 @ X5))) | (((X1 @ X3 @ X4)) != $true))) & ! [X6 : a,X7 : a] : (($true = ((X1 @ X7 @ X6))) | ($true != ((X1 @ X6 @ X7)))) & (X0 = X1) & ! [X8 : a,X9 : a,X10 : a] : (($true = ((X0 @ X8 @ X10))) | (($true != ((X0 @ X9 @ X10))) | ($true != ((X0 @ X8 @ X9))))) & ! [X11 : a,X12 : a] : (($true = ((X0 @ X12 @ X11))) | ($true != ((X0 @ X11 @ X12)))))) | ? [X18 : (a > a > $o),X19 : (a > a > $o)] : (((X18 != X19) | ? [X25 : a,X26 : a,X27 : a] : (($true != ((X19 @ X25 @ X27))) & (($true = ((X19 @ X26 @ X27))) & ($true = ((X19 @ X25 @ X26))))) | ? [X28 : a,X29 : a] : (($true != ((X19 @ X29 @ X28))) & ($true = ((X19 @ X28 @ X29))))) & ((X18 = X19) & ! [X20 : a,X21 : a,X22 : a] : (($true = ((X18 @ X20 @ X22))) | (($true != ((X18 @ X21 @ X22))) | ($true != ((X18 @ X20 @ X21))))) & ! [X23 : a,X24 : a] : (($true = ((X18 @ X24 @ X23))) | ($true != ((X18 @ X23 @ X24))))))),
% 9.02/2.00 inference(ennf_transformation,[],[f5])).
% 9.02/2.00 thf(f7,plain,(
% 9.02/2.00 ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1))))) != (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1)))))) | ? [X0 : (a > a > $o),X1 : (a > a > $o),X2 : (a > a > $o)] : (((X0 != X2) | ? [X13 : a,X14 : a,X15 : a] : (($true != ((X0 @ X13 @ X15))) & ($true = ((X0 @ X14 @ X15))) & ($true = ((X0 @ X13 @ X14)))) | ? [X16 : a,X17 : a] : (($true != ((X0 @ X17 @ X16))) & ($true = ((X0 @ X16 @ X17))))) & (X1 = X2) & ! [X3 : a,X4 : a,X5 : a] : ((((X1 @ X3 @ X5)) = $true) | ($true != ((X1 @ X4 @ X5))) | (((X1 @ X3 @ X4)) != $true)) & ! [X6 : a,X7 : a] : (($true = ((X1 @ X7 @ X6))) | ($true != ((X1 @ X6 @ X7)))) & (X0 = X1) & ! [X8 : a,X9 : a,X10 : a] : (($true = ((X0 @ X8 @ X10))) | ($true != ((X0 @ X9 @ X10))) | ($true != ((X0 @ X8 @ X9)))) & ! [X11 : a,X12 : a] : (($true = ((X0 @ X12 @ X11))) | ($true != ((X0 @ X11 @ X12))))) | ? [X18 : (a > a > $o),X19 : (a > a > $o)] : (((X18 != X19) | ? [X25 : a,X26 : a,X27 : a] : (($true != ((X19 @ X25 @ X27))) & ($true = ((X19 @ X26 @ X27))) & ($true = ((X19 @ X25 @ X26)))) | ? [X28 : a,X29 : a] : (($true != ((X19 @ X29 @ X28))) & ($true = ((X19 @ X28 @ X29))))) & (X18 = X19) & ! [X20 : a,X21 : a,X22 : a] : (($true = ((X18 @ X20 @ X22))) | ($true != ((X18 @ X21 @ X22))) | ($true != ((X18 @ X20 @ X21)))) & ! [X23 : a,X24 : a] : (($true = ((X18 @ X24 @ X23))) | ($true != ((X18 @ X23 @ X24)))))),
% 9.02/2.00 inference(flattening,[],[f6])).
% 9.02/2.00 thf(f8,definition,(
% 9.02/2.00 ! [X19 : (a > a > $o),X18 : (a > a > $o)] : ((X18 != X19) | ? [X25 : a,X26 : a,X27 : a] : (($true != ((X19 @ X25 @ X27))) & ($true = ((X19 @ X26 @ X27))) & ($true = ((X19 @ X25 @ X26)))) | ? [X28 : a,X29 : a] : (($true != ((X19 @ X29 @ X28))) & ($true = ((X19 @ X28 @ X29)))) | ~ ($true = ((sP0 @ X18 @ X19))))),
% 9.02/2.00 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 9.02/2.00 thf(f9,definition,(
% 9.02/2.00 ! [X2 : (a > a > $o),X0 : (a > a > $o)] : ((X0 != X2) | ? [X13 : a,X14 : a,X15 : a] : (($true != ((X0 @ X13 @ X15))) & ($true = ((X0 @ X14 @ X15))) & ($true = ((X0 @ X13 @ X14)))) | ? [X16 : a,X17 : a] : (($true != ((X0 @ X17 @ X16))) & ($true = ((X0 @ X16 @ X17)))) | ~ ($true = ((sP1 @ X0 @ X2))))),
% 9.02/2.00 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 9.02/2.00 thf(f10,definition,(
% 9.02/2.00 ? [X0 : (a > a > $o),X1 : (a > a > $o),X2 : (a > a > $o)] : (($true = ((sP1 @ X0 @ X2))) & (X1 = X2) & ! [X3 : a,X4 : a,X5 : a] : ((((X1 @ X3 @ X5)) = $true) | ($true != ((X1 @ X4 @ X5))) | (((X1 @ X3 @ X4)) != $true)) & ! [X6 : a,X7 : a] : (($true = ((X1 @ X7 @ X6))) | ($true != ((X1 @ X6 @ X7)))) & (X0 = X1) & ! [X8 : a,X9 : a,X10 : a] : (($true = ((X0 @ X8 @ X10))) | ($true != ((X0 @ X9 @ X10))) | ($true != ((X0 @ X8 @ X9)))) & ! [X11 : a,X12 : a] : (($true = ((X0 @ X12 @ X11))) | ($true != ((X0 @ X11 @ X12))))) | ~ ($true = sP2)),
% 9.02/2.00 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 9.02/2.00 thf(f11,plain,(
% 9.02/2.00 ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1))))) != (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1)))))) | ($true = sP2) | ? [X18 : (a > a > $o),X19 : (a > a > $o)] : (($true = ((sP0 @ X18 @ X19))) & (X18 = X19) & ! [X20 : a,X21 : a,X22 : a] : (($true = ((X18 @ X20 @ X22))) | ($true != ((X18 @ X21 @ X22))) | ($true != ((X18 @ X20 @ X21)))) & ! [X23 : a,X24 : a] : (($true = ((X18 @ X24 @ X23))) | ($true != ((X18 @ X23 @ X24)))))),
% 9.02/2.00 inference(definition_folding,[],[f7,f10,f9,f8])).
% 9.02/2.00 thf(f12,plain,(
% 9.02/2.00 ? [X0 : (a > a > $o),X1 : (a > a > $o),X2 : (a > a > $o)] : (($true = ((sP1 @ X0 @ X2))) & (X1 = X2) & ! [X3 : a,X4 : a,X5 : a] : ((((X1 @ X3 @ X5)) = $true) | ($true != ((X1 @ X4 @ X5))) | (((X1 @ X3 @ X4)) != $true)) & ! [X6 : a,X7 : a] : (($true = ((X1 @ X7 @ X6))) | ($true != ((X1 @ X6 @ X7)))) & (X0 = X1) & ! [X8 : a,X9 : a,X10 : a] : (($true = ((X0 @ X8 @ X10))) | ($true != ((X0 @ X9 @ X10))) | ($true != ((X0 @ X8 @ X9)))) & ! [X11 : a,X12 : a] : (($true = ((X0 @ X12 @ X11))) | ($true != ((X0 @ X11 @ X12))))) | ($true != sP2)),
% 9.02/2.00 inference(nnf_transformation,[],[f10])).
% 9.02/2.00 thf(f13,plain,(
% 9.02/2.00 (($true = ((sP1 @ sK3 @ sK5))) & (sK4 = sK5) & ! [X3 : a,X4 : a,X5 : a] : (($true = ((sK4 @ X3 @ X5))) | ($true != ((sK4 @ X4 @ X5))) | ($true != ((sK4 @ X3 @ X4)))) & ! [X6 : a,X7 : a] : (($true = ((sK4 @ X7 @ X6))) | ($true != ((sK4 @ X6 @ X7)))) & (sK3 = sK4) & ! [X8 : a,X9 : a,X10 : a] : (($true = ((sK3 @ X8 @ X10))) | ($true != ((sK3 @ X9 @ X10))) | ($true != ((sK3 @ X8 @ X9)))) & ! [X11 : a,X12 : a] : (($true = ((sK3 @ X12 @ X11))) | ($true != ((sK3 @ X11 @ X12))))) | ($true != sP2)),
% 9.02/2.00 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f12])).
% 9.02/2.00 thf(f14,plain,(
% 9.02/2.00 ! [X2 : (a > a > $o),X0 : (a > a > $o)] : ((X0 != X2) | ? [X13 : a,X14 : a,X15 : a] : (($true != ((X0 @ X13 @ X15))) & ($true = ((X0 @ X14 @ X15))) & ($true = ((X0 @ X13 @ X14)))) | ? [X16 : a,X17 : a] : (($true != ((X0 @ X17 @ X16))) & ($true = ((X0 @ X16 @ X17)))) | ($true != ((sP1 @ X0 @ X2))))),
% 9.02/2.00 inference(nnf_transformation,[],[f9])).
% 9.02/2.00 thf(f15,plain,(
% 9.02/2.00 ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((X0 != X1) | ? [X2 : a,X3 : a,X4 : a] : ((((X1 @ X2 @ X4)) != $true) & (((X1 @ X3 @ X4)) = $true) & (((X1 @ X2 @ X3)) = $true)) | ? [X5 : a,X6 : a] : (($true != ((X1 @ X6 @ X5))) & ($true = ((X1 @ X5 @ X6)))) | ($true != ((sP1 @ X1 @ X0))))),
% 9.02/2.00 inference(rectify,[],[f14])).
% 9.02/2.00 thf(f16,plain,(
% 9.02/2.00 ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((X0 != X1) | (($true != ((X1 @ (sK6 @ X1) @ (sK8 @ X1)))) & ($true = ((X1 @ (sK7 @ X1) @ (sK8 @ X1)))) & ($true = ((X1 @ (sK6 @ X1) @ (sK7 @ X1))))) | (($true != ((X1 @ (sK10 @ X1) @ (sK9 @ X1)))) & ($true = ((X1 @ (sK9 @ X1) @ (sK10 @ X1))))) | ($true != ((sP1 @ X1 @ X0))))),
% 9.02/2.00 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X6,sK10 @ X1),skolemize(X6,sK10 @ X1),skolemize(X6,sK10 @ X1),skolemize(X6,sK10 @ X1),skolemize(X6,sK10 @ X1)],[f15])).
% 9.02/2.00 thf(f17,plain,(
% 9.02/2.00 ! [X19 : (a > a > $o),X18 : (a > a > $o)] : ((X18 != X19) | ? [X25 : a,X26 : a,X27 : a] : (($true != ((X19 @ X25 @ X27))) & ($true = ((X19 @ X26 @ X27))) & ($true = ((X19 @ X25 @ X26)))) | ? [X28 : a,X29 : a] : (($true != ((X19 @ X29 @ X28))) & ($true = ((X19 @ X28 @ X29)))) | ($true != ((sP0 @ X18 @ X19))))),
% 9.02/2.00 inference(nnf_transformation,[],[f8])).
% 9.02/2.00 thf(f18,plain,(
% 9.02/2.00 ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((X0 != X1) | ? [X2 : a,X3 : a,X4 : a] : ((((X0 @ X2 @ X4)) != $true) & (((X0 @ X3 @ X4)) = $true) & (((X0 @ X2 @ X3)) = $true)) | ? [X5 : a,X6 : a] : ((((X0 @ X6 @ X5)) != $true) & (((X0 @ X5 @ X6)) = $true)) | ($true != ((sP0 @ X1 @ X0))))),
% 9.02/2.00 inference(rectify,[],[f17])).
% 9.02/2.00 thf(f19,plain,(
% 9.02/2.00 ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((X0 != X1) | (($true != ((X0 @ (sK11 @ X0) @ (sK13 @ X0)))) & ($true = ((X0 @ (sK12 @ X0) @ (sK13 @ X0)))) & ($true = ((X0 @ (sK11 @ X0) @ (sK12 @ X0))))) | (($true != ((X0 @ (sK15 @ X0) @ (sK14 @ X0)))) & ($true = ((X0 @ (sK14 @ X0) @ (sK15 @ X0))))) | ($true != ((sP0 @ X1 @ X0))))),
% 9.02/2.00 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X6,sK10 @ X1),skolemize(X6,sK10 @ X1),skolemize(X6,sK10 @ X1),skolemize(X6,sK10 @ X1),skolemize(X6,sK10 @ X1)],[f18])).
% 9.02/2.00 thf(f20,plain,(
% 9.02/2.00 ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1))))) != (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1)))))) | ($true = sP2) | ? [X0 : (a > a > $o),X1 : (a > a > $o)] : (($true = ((sP0 @ X0 @ X1))) & (X0 = X1) & ! [X2 : a,X3 : a,X4 : a] : ((((X0 @ X2 @ X4)) = $true) | (((X0 @ X3 @ X4)) != $true) | (((X0 @ X2 @ X3)) != $true)) & ! [X5 : a,X6 : a] : ((((X0 @ X6 @ X5)) = $true) | (((X0 @ X5 @ X6)) != $true)))),
% 9.02/2.00 inference(rectify,[],[f11])).
% 9.02/2.00 thf(f21,plain,(
% 9.02/2.00 ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1))))) != (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1)))))) | ($true = sP2) | (($true = ((sP0 @ sK16 @ sK17))) & (sK16 = sK17) & ! [X2 : a,X3 : a,X4 : a] : (($true = ((sK16 @ X2 @ X4))) | ($true != ((sK16 @ X3 @ X4))) | ($true != ((sK16 @ X2 @ X3)))) & ! [X5 : a,X6 : a] : (($true = ((sK16 @ X6 @ X5))) | ($true != ((sK16 @ X5 @ X6)))))),
% 9.02/2.00 inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17]),skolemize(X0,sK16),skolemize(X1,sK17)],[f20])).
% 9.02/2.00 thf(f22,plain,(
% 9.02/2.00 ( ! [X11 : a,X12 : a] : (($true = ((sK3 @ X12 @ X11))) | ($true != ((sK3 @ X11 @ X12))) | ($true != sP2)) )),
% 9.02/2.00 inference(cnf_transformation,[],[f13])).
% 9.02/2.00 thf(f23,plain,(
% 9.02/2.00 ( ! [X10 : a,X8 : a,X9 : a] : (($true = ((sK3 @ X8 @ X10))) | ($true != ((sK3 @ X9 @ X10))) | ($true != ((sK3 @ X8 @ X9))) | ($true != sP2)) )),
% 9.02/2.00 inference(cnf_transformation,[],[f13])).
% 9.02/2.00 thf(f24,plain,(
% 9.02/2.00 (sK3 = sK4) | ($true != sP2)),
% 9.02/2.00 inference(cnf_transformation,[],[f13])).
% 9.02/2.00 thf(f27,plain,(
% 9.02/2.00 (sK4 = sK5) | ($true != sP2)),
% 9.02/2.00 inference(cnf_transformation,[],[f13])).
% 9.02/2.00 thf(f28,plain,(
% 9.02/2.00 ($true = ((sP1 @ sK3 @ sK5))) | ($true != sP2)),
% 9.02/2.00 inference(cnf_transformation,[],[f13])).
% 9.02/2.00 thf(f29,plain,(
% 9.02/2.00 ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((X0 != X1) | ($true = ((X1 @ (sK6 @ X1) @ (sK7 @ X1)))) | ($true = ((X1 @ (sK9 @ X1) @ (sK10 @ X1)))) | ($true != ((sP1 @ X1 @ X0)))) )),
% 9.02/2.00 inference(cnf_transformation,[],[f16])).
% 9.02/2.00 thf(f30,plain,(
% 9.02/2.00 ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((X0 != X1) | ($true = ((X1 @ (sK6 @ X1) @ (sK7 @ X1)))) | ($true != ((X1 @ (sK10 @ X1) @ (sK9 @ X1)))) | ($true != ((sP1 @ X1 @ X0)))) )),
% 9.02/2.00 inference(cnf_transformation,[],[f16])).
% 9.02/2.00 thf(f31,plain,(
% 9.02/2.00 ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((X0 != X1) | ($true = ((X1 @ (sK7 @ X1) @ (sK8 @ X1)))) | ($true = ((X1 @ (sK9 @ X1) @ (sK10 @ X1)))) | ($true != ((sP1 @ X1 @ X0)))) )),
% 9.02/2.00 inference(cnf_transformation,[],[f16])).
% 9.02/2.00 thf(f32,plain,(
% 9.02/2.00 ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((X0 != X1) | ($true = ((X1 @ (sK7 @ X1) @ (sK8 @ X1)))) | ($true != ((X1 @ (sK10 @ X1) @ (sK9 @ X1)))) | ($true != ((sP1 @ X1 @ X0)))) )),
% 9.02/2.00 inference(cnf_transformation,[],[f16])).
% 9.02/2.00 thf(f33,plain,(
% 9.02/2.00 ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((X0 != X1) | ($true != ((X1 @ (sK6 @ X1) @ (sK8 @ X1)))) | ($true = ((X1 @ (sK9 @ X1) @ (sK10 @ X1)))) | ($true != ((sP1 @ X1 @ X0)))) )),
% 9.02/2.00 inference(cnf_transformation,[],[f16])).
% 9.02/2.00 thf(f34,plain,(
% 9.02/2.00 ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((X0 != X1) | ($true != ((X1 @ (sK6 @ X1) @ (sK8 @ X1)))) | ($true != ((X1 @ (sK10 @ X1) @ (sK9 @ X1)))) | ($true != ((sP1 @ X1 @ X0)))) )),
% 9.02/2.00 inference(cnf_transformation,[],[f16])).
% 9.02/2.00 thf(f35,plain,(
% 9.02/2.00 ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((X0 != X1) | ($true = ((X0 @ (sK11 @ X0) @ (sK12 @ X0)))) | ($true = ((X0 @ (sK14 @ X0) @ (sK15 @ X0)))) | ($true != ((sP0 @ X1 @ X0)))) )),
% 9.02/2.00 inference(cnf_transformation,[],[f19])).
% 9.02/2.00 thf(f36,plain,(
% 9.02/2.00 ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((X0 != X1) | ($true = ((X0 @ (sK11 @ X0) @ (sK12 @ X0)))) | ($true != ((X0 @ (sK15 @ X0) @ (sK14 @ X0)))) | ($true != ((sP0 @ X1 @ X0)))) )),
% 9.02/2.00 inference(cnf_transformation,[],[f19])).
% 9.02/2.00 thf(f37,plain,(
% 9.02/2.00 ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((X0 != X1) | ($true = ((X0 @ (sK12 @ X0) @ (sK13 @ X0)))) | ($true = ((X0 @ (sK14 @ X0) @ (sK15 @ X0)))) | ($true != ((sP0 @ X1 @ X0)))) )),
% 9.02/2.00 inference(cnf_transformation,[],[f19])).
% 9.02/2.00 thf(f38,plain,(
% 9.02/2.00 ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((X0 != X1) | ($true = ((X0 @ (sK12 @ X0) @ (sK13 @ X0)))) | ($true != ((X0 @ (sK15 @ X0) @ (sK14 @ X0)))) | ($true != ((sP0 @ X1 @ X0)))) )),
% 9.02/2.00 inference(cnf_transformation,[],[f19])).
% 9.02/2.00 thf(f39,plain,(
% 9.02/2.00 ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((X0 != X1) | ($true != ((X0 @ (sK11 @ X0) @ (sK13 @ X0)))) | ($true = ((X0 @ (sK14 @ X0) @ (sK15 @ X0)))) | ($true != ((sP0 @ X1 @ X0)))) )),
% 9.02/2.00 inference(cnf_transformation,[],[f19])).
% 9.02/2.00 thf(f40,plain,(
% 9.02/2.00 ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((X0 != X1) | ($true != ((X0 @ (sK11 @ X0) @ (sK13 @ X0)))) | ($true != ((X0 @ (sK15 @ X0) @ (sK14 @ X0)))) | ($true != ((sP0 @ X1 @ X0)))) )),
% 9.02/2.00 inference(cnf_transformation,[],[f19])).
% 9.02/2.00 thf(f41,plain,(
% 9.02/2.00 ( ! [X6 : a,X5 : a] : (((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1))))) != (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1)))))) | ($true = sP2) | ($true = ((sK16 @ X6 @ X5))) | ($true != ((sK16 @ X5 @ X6)))) )),
% 9.02/2.00 inference(cnf_transformation,[],[f21])).
% 9.02/2.00 thf(f42,plain,(
% 9.02/2.00 ( ! [X2 : a,X3 : a,X4 : a] : (((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1))))) != (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1)))))) | ($true = sP2) | ($true = ((sK16 @ X2 @ X4))) | ($true != ((sK16 @ X3 @ X4))) | ($true != ((sK16 @ X2 @ X3)))) )),
% 9.02/2.00 inference(cnf_transformation,[],[f21])).
% 9.02/2.00 thf(f43,plain,(
% 9.02/2.00 ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1))))) != (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1)))))) | ($true = sP2) | (sK16 = sK17)),
% 9.02/2.00 inference(cnf_transformation,[],[f21])).
% 9.02/2.00 thf(f44,plain,(
% 9.02/2.00 ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1))))) != (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y4 @ Y2))))))))) & (Y0 = Y1)))))) | ($true = sP2) | ($true = ((sP0 @ sK16 @ sK17)))),
% 9.02/2.00 inference(cnf_transformation,[],[f21])).
% 9.02/2.00 thf(f46,definition,(
% 9.02/2.00 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 9.02/2.00 introduced(theory,[fool_exhaustiveness_axiom])).
% 9.02/2.00 thf(f47,plain,(
% 9.02/2.00 ( ! [X1 : (a > a > $o)] : (($true != ((sP1 @ X1 @ X1))) | ($true != ((X1 @ (sK10 @ X1) @ (sK9 @ X1)))) | ($true != ((X1 @ (sK6 @ X1) @ (sK8 @ X1))))) )),
% 9.02/2.00 inference(equality_resolution,[],[f34])).
% 9.02/2.00 thf(f48,plain,(
% 9.02/2.00 ( ! [X1 : (a > a > $o)] : (($true != ((sP1 @ X1 @ X1))) | ($true = ((X1 @ (sK9 @ X1) @ (sK10 @ X1)))) | ($true != ((X1 @ (sK6 @ X1) @ (sK8 @ X1))))) )),
% 9.02/2.00 inference(equality_resolution,[],[f33])).
% 9.02/2.00 thf(f49,plain,(
% 9.02/2.00 ( ! [X1 : (a > a > $o)] : (($true != ((sP1 @ X1 @ X1))) | ($true != ((X1 @ (sK10 @ X1) @ (sK9 @ X1)))) | ($true = ((X1 @ (sK7 @ X1) @ (sK8 @ X1))))) )),
% 9.02/2.00 inference(equality_resolution,[],[f32])).
% 9.02/2.00 thf(f50,plain,(
% 9.02/2.00 ( ! [X1 : (a > a > $o)] : (($true != ((sP1 @ X1 @ X1))) | ($true = ((X1 @ (sK9 @ X1) @ (sK10 @ X1)))) | ($true = ((X1 @ (sK7 @ X1) @ (sK8 @ X1))))) )),
% 9.02/2.00 inference(equality_resolution,[],[f31])).
% 9.02/2.00 thf(f51,plain,(
% 9.02/2.00 ( ! [X1 : (a > a > $o)] : (($true != ((sP1 @ X1 @ X1))) | ($true != ((X1 @ (sK10 @ X1) @ (sK9 @ X1)))) | ($true = ((X1 @ (sK6 @ X1) @ (sK7 @ X1))))) )),
% 9.02/2.00 inference(equality_resolution,[],[f30])).
% 9.02/2.00 thf(f52,plain,(
% 9.02/2.00 ( ! [X1 : (a > a > $o)] : (($true != ((sP1 @ X1 @ X1))) | ($true = ((X1 @ (sK9 @ X1) @ (sK10 @ X1)))) | ($true = ((X1 @ (sK6 @ X1) @ (sK7 @ X1))))) )),
% 9.02/2.00 inference(equality_resolution,[],[f29])).
% 9.02/2.00 thf(f53,plain,(
% 9.02/2.00 ( ! [X1 : (a > a > $o)] : (($true != ((sP0 @ X1 @ X1))) | ($true != ((X1 @ (sK15 @ X1) @ (sK14 @ X1)))) | ($true != ((X1 @ (sK11 @ X1) @ (sK13 @ X1))))) )),
% 9.02/2.00 inference(equality_resolution,[],[f40])).
% 9.02/2.00 thf(f54,plain,(
% 9.02/2.00 ( ! [X1 : (a > a > $o)] : (($true != ((sP0 @ X1 @ X1))) | ($true = ((X1 @ (sK14 @ X1) @ (sK15 @ X1)))) | ($true != ((X1 @ (sK11 @ X1) @ (sK13 @ X1))))) )),
% 9.02/2.00 inference(equality_resolution,[],[f39])).
% 9.02/2.00 thf(f55,plain,(
% 9.02/2.00 ( ! [X1 : (a > a > $o)] : (($true != ((sP0 @ X1 @ X1))) | ($true != ((X1 @ (sK15 @ X1) @ (sK14 @ X1)))) | ($true = ((X1 @ (sK12 @ X1) @ (sK13 @ X1))))) )),
% 9.02/2.00 inference(equality_resolution,[],[f38])).
% 9.02/2.00 thf(f56,plain,(
% 9.02/2.00 ( ! [X1 : (a > a > $o)] : (($true != ((sP0 @ X1 @ X1))) | ($true = ((X1 @ (sK14 @ X1) @ (sK15 @ X1)))) | ($true = ((X1 @ (sK12 @ X1) @ (sK13 @ X1))))) )),
% 9.02/2.00 inference(equality_resolution,[],[f37])).
% 9.02/2.00 thf(f57,plain,(
% 9.02/2.00 ( ! [X1 : (a > a > $o)] : (($true != ((sP0 @ X1 @ X1))) | ($true != ((X1 @ (sK15 @ X1) @ (sK14 @ X1)))) | ($true = ((X1 @ (sK11 @ X1) @ (sK12 @ X1))))) )),
% 9.02/2.00 inference(equality_resolution,[],[f36])).
% 9.02/2.00 thf(f58,plain,(
% 9.02/2.00 ( ! [X1 : (a > a > $o)] : (($true != ((sP0 @ X1 @ X1))) | ($true = ((X1 @ (sK14 @ X1) @ (sK15 @ X1)))) | ($true = ((X1 @ (sK11 @ X1) @ (sK12 @ X1))))) )),
% 9.02/2.00 inference(equality_resolution,[],[f35])).
% 9.02/2.00 thf(f59,plain,(
% 9.02/2.00 ( ! [X6 : a,X5 : a] : (($true = sP2) | ($true = ((sK16 @ X6 @ X5))) | ($true != ((sK16 @ X5 @ X6)))) )),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f41])).
% 9.02/2.00 thf(f60,plain,(
% 9.02/2.00 ( ! [X2 : a,X3 : a,X4 : a] : (($true = sP2) | ($true = ((sK16 @ X2 @ X4))) | ($true != ((sK16 @ X3 @ X4))) | ($true != ((sK16 @ X2 @ X3)))) )),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f42])).
% 9.02/2.00 thf(f61,plain,(
% 9.02/2.00 ($true = sP2) | (sK16 = sK17)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f43])).
% 9.02/2.00 thf(f62,plain,(
% 9.02/2.00 ($true = sP2) | ($true = ((sP0 @ sK16 @ sK17)))),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f44])).
% 9.02/2.00 thf(f64,definition,(
% 9.02/2.00 spl18_1 <=> (sK16 = sK17)),
% 9.02/2.00 introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition])).
% 9.02/2.00 thf(f66,plain,(
% 9.02/2.00 (sK16 = sK17) | ~spl18_1),
% 9.02/2.00 inference(avatar_component_clause,[],[f64])).
% 9.02/2.00 thf(f68,definition,(
% 9.02/2.00 spl18_2 <=> ($true = sP2)),
% 9.02/2.00 introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition])).
% 9.02/2.00 thf(f69,plain,(
% 9.02/2.00 ($true != sP2) | spl18_2),
% 9.02/2.00 inference(avatar_component_clause,[],[f68])).
% 9.02/2.00 thf(f70,plain,(
% 9.02/2.00 ($true = sP2) | ~spl18_2),
% 9.02/2.00 inference(avatar_component_clause,[],[f68])).
% 9.02/2.00 thf(f71,plain,(
% 9.02/2.00 spl18_1 | spl18_2),
% 9.02/2.00 inference(avatar_split_clause,[],[f61,f68,f64])).
% 9.02/2.00 thf(f79,plain,(
% 9.02/2.00 (sK3 = sK4) | ~spl18_2),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f24,f70])).
% 9.02/2.00 thf(f81,plain,(
% 9.02/2.00 (sK4 = sK5) | ~spl18_2),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f27,f70])).
% 9.02/2.00 thf(f82,plain,(
% 9.02/2.00 (sK3 = sK5) | ~spl18_2),
% 9.02/2.00 inference(forward_demodulation,[],[f81,f79])).
% 9.02/2.00 thf(f84,plain,(
% 9.02/2.00 ($true = ((sP1 @ sK3 @ sK5))) | ~spl18_2),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f28,f70])).
% 9.02/2.00 thf(f85,plain,(
% 9.02/2.00 ($true = ((sP1 @ sK3 @ sK3))) | ~spl18_2),
% 9.02/2.00 inference(forward_demodulation,[],[f84,f82])).
% 9.02/2.00 thf(f92,plain,(
% 9.02/2.00 ( ! [X11 : a,X12 : a] : (($true != ((sK3 @ X11 @ X12))) | ($true = ((sK3 @ X12 @ X11)))) ) | ~spl18_2),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f22,f70])).
% 9.02/2.00 thf(f93,plain,(
% 9.02/2.00 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true = ((sK3 @ X1 @ X0))) | ($false = ((sK3 @ X0 @ X1)))) ) | ~spl18_2),
% 9.02/2.00 inference(constrained_superposition,[],[f92,f46])).
% 9.02/2.00 thf(f94,plain,(
% 9.02/2.00 ( ! [X0 : a,X1 : a] : (($true = ((sK3 @ X1 @ X0))) | ($false = ((sK3 @ X0 @ X1)))) ) | ~spl18_2),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f93])).
% 9.02/2.00 thf(f153,plain,(
% 9.02/2.00 ($true != $true) | ($true != ((sK3 @ (sK10 @ sK3) @ (sK9 @ sK3)))) | ($true != ((sK3 @ (sK6 @ sK3) @ (sK8 @ sK3)))) | ~spl18_2),
% 9.02/2.00 inference(constrained_superposition,[],[f47,f85])).
% 9.02/2.00 thf(f154,plain,(
% 9.02/2.00 ($true != ((sK3 @ (sK10 @ sK3) @ (sK9 @ sK3)))) | ($true != ((sK3 @ (sK6 @ sK3) @ (sK8 @ sK3)))) | ~spl18_2),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f153])).
% 9.02/2.00 thf(f167,plain,(
% 9.02/2.00 ($true != $true) | ($true != ((sK3 @ (sK10 @ sK3) @ (sK9 @ sK3)))) | ($true = ((sK3 @ (sK7 @ sK3) @ (sK8 @ sK3)))) | ~spl18_2),
% 9.02/2.00 inference(constrained_superposition,[],[f49,f85])).
% 9.02/2.00 thf(f168,plain,(
% 9.02/2.00 ($true != ((sK3 @ (sK10 @ sK3) @ (sK9 @ sK3)))) | ($true = ((sK3 @ (sK7 @ sK3) @ (sK8 @ sK3)))) | ~spl18_2),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f167])).
% 9.02/2.00 thf(f191,plain,(
% 9.02/2.00 ($true != $true) | ($true = ((sK3 @ (sK9 @ sK3) @ (sK10 @ sK3)))) | ($true = ((sK3 @ (sK7 @ sK3) @ (sK8 @ sK3)))) | ~spl18_2),
% 9.02/2.00 inference(constrained_superposition,[],[f50,f85])).
% 9.02/2.00 thf(f192,plain,(
% 9.02/2.00 ($true = ((sK3 @ (sK9 @ sK3) @ (sK10 @ sK3)))) | ($true = ((sK3 @ (sK7 @ sK3) @ (sK8 @ sK3)))) | ~spl18_2),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f191])).
% 9.02/2.00 thf(f227,plain,(
% 9.02/2.00 ($true != $true) | ($true = ((sK3 @ (sK9 @ sK3) @ (sK10 @ sK3)))) | ($true = ((sK3 @ (sK6 @ sK3) @ (sK7 @ sK3)))) | ~spl18_2),
% 9.02/2.00 inference(constrained_superposition,[],[f52,f85])).
% 9.02/2.00 thf(f228,plain,(
% 9.02/2.00 ($true = ((sK3 @ (sK9 @ sK3) @ (sK10 @ sK3)))) | ($true = ((sK3 @ (sK6 @ sK3) @ (sK7 @ sK3)))) | ~spl18_2),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f227])).
% 9.02/2.00 thf(f340,definition,(
% 9.02/2.00 spl18_3 <=> ($true = ((sK3 @ (sK6 @ sK3) @ (sK8 @ sK3))))),
% 9.02/2.00 introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition])).
% 9.02/2.00 thf(f341,plain,(
% 9.02/2.00 ($true = ((sK3 @ (sK6 @ sK3) @ (sK8 @ sK3)))) | ~spl18_3),
% 9.02/2.00 inference(avatar_component_clause,[],[f340])).
% 9.02/2.00 thf(f342,plain,(
% 9.02/2.00 ($true != ((sK3 @ (sK6 @ sK3) @ (sK8 @ sK3)))) | spl18_3),
% 9.02/2.00 inference(avatar_component_clause,[],[f340])).
% 9.02/2.00 thf(f344,definition,(
% 9.02/2.00 spl18_4 <=> ($true = ((sK3 @ (sK10 @ sK3) @ (sK9 @ sK3))))),
% 9.02/2.00 introduced(definition,[new_symbols(definition,[spl18_4])],[avatar_definition])).
% 9.02/2.00 thf(f345,plain,(
% 9.02/2.00 ($true = ((sK3 @ (sK10 @ sK3) @ (sK9 @ sK3)))) | ~spl18_4),
% 9.02/2.00 inference(avatar_component_clause,[],[f344])).
% 9.02/2.00 thf(f346,plain,(
% 9.02/2.00 ($true != ((sK3 @ (sK10 @ sK3) @ (sK9 @ sK3)))) | spl18_4),
% 9.02/2.00 inference(avatar_component_clause,[],[f344])).
% 9.02/2.00 thf(f347,plain,(
% 9.02/2.00 ~spl18_3 | ~spl18_4 | ~spl18_2),
% 9.02/2.00 inference(avatar_split_clause,[],[f154,f68,f344,f340])).
% 9.02/2.00 thf(f420,definition,(
% 9.02/2.00 spl18_5 <=> ($true = ((sK3 @ (sK7 @ sK3) @ (sK8 @ sK3))))),
% 9.02/2.00 introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition])).
% 9.02/2.00 thf(f422,plain,(
% 9.02/2.00 ($true = ((sK3 @ (sK7 @ sK3) @ (sK8 @ sK3)))) | ~spl18_5),
% 9.02/2.00 inference(avatar_component_clause,[],[f420])).
% 9.02/2.00 thf(f423,plain,(
% 9.02/2.00 spl18_5 | ~spl18_4 | ~spl18_2),
% 9.02/2.00 inference(avatar_split_clause,[],[f168,f68,f344,f420])).
% 9.02/2.00 thf(f425,plain,(
% 9.02/2.00 ($true != $true) | ($false = ((sK3 @ (sK9 @ sK3) @ (sK10 @ sK3)))) | (~spl18_2 | spl18_4)),
% 9.02/2.00 inference(constrained_superposition,[],[f346,f94])).
% 9.02/2.00 thf(f432,plain,(
% 9.02/2.00 ($false = ((sK3 @ (sK9 @ sK3) @ (sK10 @ sK3)))) | (~spl18_2 | spl18_4)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f425])).
% 9.02/2.00 thf(f466,definition,(
% 9.02/2.00 spl18_6 <=> ($true = ((sK3 @ (sK9 @ sK3) @ (sK10 @ sK3))))),
% 9.02/2.00 introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition])).
% 9.02/2.00 thf(f467,plain,(
% 9.02/2.00 ($true != ((sK3 @ (sK9 @ sK3) @ (sK10 @ sK3)))) | spl18_6),
% 9.02/2.00 inference(avatar_component_clause,[],[f466])).
% 9.02/2.00 thf(f468,plain,(
% 9.02/2.00 ($true = ((sK3 @ (sK9 @ sK3) @ (sK10 @ sK3)))) | ~spl18_6),
% 9.02/2.00 inference(avatar_component_clause,[],[f466])).
% 9.02/2.00 thf(f469,plain,(
% 9.02/2.00 spl18_5 | spl18_6 | ~spl18_2),
% 9.02/2.00 inference(avatar_split_clause,[],[f192,f68,f466,f420])).
% 9.02/2.00 thf(f522,definition,(
% 9.02/2.00 spl18_7 <=> ($true = ((sK3 @ (sK6 @ sK3) @ (sK7 @ sK3))))),
% 9.02/2.00 introduced(definition,[new_symbols(definition,[spl18_7])],[avatar_definition])).
% 9.02/2.00 thf(f524,plain,(
% 9.02/2.00 ($true = ((sK3 @ (sK6 @ sK3) @ (sK7 @ sK3)))) | ~spl18_7),
% 9.02/2.00 inference(avatar_component_clause,[],[f522])).
% 9.02/2.00 thf(f525,plain,(
% 9.02/2.00 spl18_7 | spl18_6 | ~spl18_2),
% 9.02/2.00 inference(avatar_split_clause,[],[f228,f68,f466,f522])).
% 9.02/2.00 thf(f532,plain,(
% 9.02/2.00 ($true = ((sP0 @ sK16 @ sK17))) | spl18_2),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f62,f69])).
% 9.02/2.00 thf(f533,plain,(
% 9.02/2.00 ($true = ((sP0 @ sK16 @ sK16))) | (~spl18_1 | spl18_2)),
% 9.02/2.00 inference(forward_demodulation,[],[f532,f66])).
% 9.02/2.00 thf(f537,plain,(
% 9.02/2.00 ($true != $true) | ($true = ((sK16 @ (sK14 @ sK16) @ (sK15 @ sK16)))) | ($true = ((sK16 @ (sK11 @ sK16) @ (sK12 @ sK16)))) | (~spl18_1 | spl18_2)),
% 9.02/2.00 inference(constrained_superposition,[],[f58,f533])).
% 9.02/2.00 thf(f538,plain,(
% 9.02/2.00 ($true != $true) | ($true != ((sK16 @ (sK15 @ sK16) @ (sK14 @ sK16)))) | ($true = ((sK16 @ (sK11 @ sK16) @ (sK12 @ sK16)))) | (~spl18_1 | spl18_2)),
% 9.02/2.00 inference(constrained_superposition,[],[f57,f533])).
% 9.02/2.00 thf(f539,plain,(
% 9.02/2.00 ($true != $true) | ($true = ((sK16 @ (sK14 @ sK16) @ (sK15 @ sK16)))) | ($true = ((sK16 @ (sK12 @ sK16) @ (sK13 @ sK16)))) | (~spl18_1 | spl18_2)),
% 9.02/2.00 inference(constrained_superposition,[],[f56,f533])).
% 9.02/2.00 thf(f540,plain,(
% 9.02/2.00 ($true != $true) | ($true != ((sK16 @ (sK15 @ sK16) @ (sK14 @ sK16)))) | ($true = ((sK16 @ (sK12 @ sK16) @ (sK13 @ sK16)))) | (~spl18_1 | spl18_2)),
% 9.02/2.00 inference(constrained_superposition,[],[f55,f533])).
% 9.02/2.00 thf(f541,plain,(
% 9.02/2.00 ($true != $true) | ($true = ((sK16 @ (sK14 @ sK16) @ (sK15 @ sK16)))) | ($true != ((sK16 @ (sK11 @ sK16) @ (sK13 @ sK16)))) | (~spl18_1 | spl18_2)),
% 9.02/2.00 inference(constrained_superposition,[],[f54,f533])).
% 9.02/2.00 thf(f542,plain,(
% 9.02/2.00 ($true != $true) | ($true != ((sK16 @ (sK15 @ sK16) @ (sK14 @ sK16)))) | ($true != ((sK16 @ (sK11 @ sK16) @ (sK13 @ sK16)))) | (~spl18_1 | spl18_2)),
% 9.02/2.00 inference(constrained_superposition,[],[f53,f533])).
% 9.02/2.00 thf(f543,plain,(
% 9.02/2.00 ($true != ((sK16 @ (sK15 @ sK16) @ (sK14 @ sK16)))) | ($true != ((sK16 @ (sK11 @ sK16) @ (sK13 @ sK16)))) | (~spl18_1 | spl18_2)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f542])).
% 9.02/2.00 thf(f544,plain,(
% 9.02/2.00 ($true = ((sK16 @ (sK14 @ sK16) @ (sK15 @ sK16)))) | ($true != ((sK16 @ (sK11 @ sK16) @ (sK13 @ sK16)))) | (~spl18_1 | spl18_2)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f541])).
% 9.02/2.00 thf(f545,plain,(
% 9.02/2.00 ($true != ((sK16 @ (sK15 @ sK16) @ (sK14 @ sK16)))) | ($true = ((sK16 @ (sK12 @ sK16) @ (sK13 @ sK16)))) | (~spl18_1 | spl18_2)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f540])).
% 9.02/2.00 thf(f546,plain,(
% 9.02/2.00 ($true = ((sK16 @ (sK14 @ sK16) @ (sK15 @ sK16)))) | ($true = ((sK16 @ (sK12 @ sK16) @ (sK13 @ sK16)))) | (~spl18_1 | spl18_2)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f539])).
% 9.02/2.00 thf(f547,plain,(
% 9.02/2.00 ($true != ((sK16 @ (sK15 @ sK16) @ (sK14 @ sK16)))) | ($true = ((sK16 @ (sK11 @ sK16) @ (sK12 @ sK16)))) | (~spl18_1 | spl18_2)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f538])).
% 9.02/2.00 thf(f548,plain,(
% 9.02/2.00 ($true = ((sK16 @ (sK14 @ sK16) @ (sK15 @ sK16)))) | ($true = ((sK16 @ (sK11 @ sK16) @ (sK12 @ sK16)))) | (~spl18_1 | spl18_2)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f537])).
% 9.02/2.00 thf(f551,plain,(
% 9.02/2.00 ( ! [X6 : a,X5 : a] : (($true != ((sK16 @ X5 @ X6))) | ($true = ((sK16 @ X6 @ X5)))) ) | spl18_2),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f59,f69])).
% 9.02/2.00 thf(f552,plain,(
% 9.02/2.00 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true = ((sK16 @ X1 @ X0))) | ($false = ((sK16 @ X0 @ X1)))) ) | spl18_2),
% 9.02/2.00 inference(constrained_superposition,[],[f551,f46])).
% 9.02/2.00 thf(f553,plain,(
% 9.02/2.00 ( ! [X0 : a,X1 : a] : (($true = ((sK16 @ X1 @ X0))) | ($false = ((sK16 @ X0 @ X1)))) ) | spl18_2),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f552])).
% 9.02/2.00 thf(f554,plain,(
% 9.02/2.00 ( ! [X2 : a,X3 : a,X4 : a] : (($true != ((sK16 @ X3 @ X4))) | ($true = ((sK16 @ X2 @ X4))) | ($true != ((sK16 @ X2 @ X3)))) ) | spl18_2),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f60,f69])).
% 9.02/2.00 thf(f667,definition,(
% 9.02/2.00 spl18_8 <=> ($true = ((sK16 @ (sK11 @ sK16) @ (sK13 @ sK16))))),
% 9.02/2.00 introduced(definition,[new_symbols(definition,[spl18_8])],[avatar_definition])).
% 9.02/2.00 thf(f668,plain,(
% 9.02/2.00 ($true = ((sK16 @ (sK11 @ sK16) @ (sK13 @ sK16)))) | ~spl18_8),
% 9.02/2.00 inference(avatar_component_clause,[],[f667])).
% 9.02/2.00 thf(f669,plain,(
% 9.02/2.00 ($true != ((sK16 @ (sK11 @ sK16) @ (sK13 @ sK16)))) | spl18_8),
% 9.02/2.00 inference(avatar_component_clause,[],[f667])).
% 9.02/2.00 thf(f671,definition,(
% 9.02/2.00 spl18_9 <=> ($true = ((sK16 @ (sK15 @ sK16) @ (sK14 @ sK16))))),
% 9.02/2.00 introduced(definition,[new_symbols(definition,[spl18_9])],[avatar_definition])).
% 9.02/2.00 thf(f672,plain,(
% 9.02/2.00 ($true = ((sK16 @ (sK15 @ sK16) @ (sK14 @ sK16)))) | ~spl18_9),
% 9.02/2.00 inference(avatar_component_clause,[],[f671])).
% 9.02/2.00 thf(f673,plain,(
% 9.02/2.00 ($true != ((sK16 @ (sK15 @ sK16) @ (sK14 @ sK16)))) | spl18_9),
% 9.02/2.00 inference(avatar_component_clause,[],[f671])).
% 9.02/2.00 thf(f674,plain,(
% 9.02/2.00 ~spl18_8 | ~spl18_9 | ~spl18_1 | spl18_2),
% 9.02/2.00 inference(avatar_split_clause,[],[f543,f68,f64,f671,f667])).
% 9.02/2.00 thf(f722,definition,(
% 9.02/2.00 spl18_10 <=> ($true = ((sK16 @ (sK12 @ sK16) @ (sK13 @ sK16))))),
% 9.02/2.00 introduced(definition,[new_symbols(definition,[spl18_10])],[avatar_definition])).
% 9.02/2.00 thf(f724,plain,(
% 9.02/2.00 ($true = ((sK16 @ (sK12 @ sK16) @ (sK13 @ sK16)))) | ~spl18_10),
% 9.02/2.00 inference(avatar_component_clause,[],[f722])).
% 9.02/2.00 thf(f725,plain,(
% 9.02/2.00 spl18_10 | ~spl18_9 | ~spl18_1 | spl18_2),
% 9.02/2.00 inference(avatar_split_clause,[],[f545,f68,f64,f671,f722])).
% 9.02/2.00 thf(f727,plain,(
% 9.02/2.00 ($true != $true) | ($false = ((sK16 @ (sK14 @ sK16) @ (sK15 @ sK16)))) | (spl18_2 | spl18_9)),
% 9.02/2.00 inference(constrained_superposition,[],[f673,f553])).
% 9.02/2.00 thf(f734,plain,(
% 9.02/2.00 ($false = ((sK16 @ (sK14 @ sK16) @ (sK15 @ sK16)))) | (spl18_2 | spl18_9)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f727])).
% 9.02/2.00 thf(f737,definition,(
% 9.02/2.00 spl18_11 <=> ($true = ((sK16 @ (sK14 @ sK16) @ (sK15 @ sK16))))),
% 9.02/2.00 introduced(definition,[new_symbols(definition,[spl18_11])],[avatar_definition])).
% 9.02/2.00 thf(f739,plain,(
% 9.02/2.00 ($true = ((sK16 @ (sK14 @ sK16) @ (sK15 @ sK16)))) | ~spl18_11),
% 9.02/2.00 inference(avatar_component_clause,[],[f737])).
% 9.02/2.00 thf(f740,plain,(
% 9.02/2.00 spl18_10 | spl18_11 | ~spl18_1 | spl18_2),
% 9.02/2.00 inference(avatar_split_clause,[],[f546,f68,f64,f737,f722])).
% 9.02/2.00 thf(f745,plain,(
% 9.02/2.00 ( ! [X0 : a] : (($true != $true) | ($true = ((sK16 @ X0 @ (sK13 @ sK16)))) | ($true != ((sK16 @ X0 @ (sK12 @ sK16))))) ) | (spl18_2 | ~spl18_10)),
% 9.02/2.00 inference(constrained_superposition,[],[f554,f724])).
% 9.02/2.00 thf(f756,plain,(
% 9.02/2.00 ( ! [X0 : a] : (($true != ((sK16 @ X0 @ (sK12 @ sK16)))) | ($true = ((sK16 @ X0 @ (sK13 @ sK16))))) ) | (spl18_2 | ~spl18_10)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f745])).
% 9.02/2.00 thf(f771,plain,(
% 9.02/2.00 ($true = $false) | ($true = ((sK16 @ (sK11 @ sK16) @ (sK12 @ sK16)))) | (~spl18_1 | spl18_2 | spl18_9)),
% 9.02/2.00 inference(forward_demodulation,[],[f548,f734])).
% 9.02/2.00 thf(f772,plain,(
% 9.02/2.00 ($true = ((sK16 @ (sK11 @ sK16) @ (sK12 @ sK16)))) | (~spl18_1 | spl18_2 | spl18_9)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f771])).
% 9.02/2.00 thf(f3523,plain,(
% 9.02/2.00 ($true != $true) | ($true = ((sK16 @ (sK11 @ sK16) @ (sK13 @ sK16)))) | (~spl18_1 | spl18_2 | spl18_9 | ~spl18_10)),
% 9.02/2.00 inference(constrained_superposition,[],[f756,f772])).
% 9.02/2.00 thf(f3529,plain,(
% 9.02/2.00 ($true = ((sK16 @ (sK11 @ sK16) @ (sK13 @ sK16)))) | (~spl18_1 | spl18_2 | spl18_9 | ~spl18_10)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f3523])).
% 9.02/2.00 thf(f3548,plain,(
% 9.02/2.00 $false | (~spl18_1 | spl18_2 | spl18_8 | spl18_9 | ~spl18_10)),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f3529,f669])).
% 9.02/2.00 thf(f3549,plain,(
% 9.02/2.00 ~spl18_1 | spl18_2 | spl18_8 | spl18_9 | ~spl18_10),
% 9.02/2.00 inference(avatar_contradiction_clause,[],[f3548])).
% 9.02/2.00 thf(f3550,plain,(
% 9.02/2.00 ($true = $false) | ($true != ((sK16 @ (sK11 @ sK16) @ (sK13 @ sK16)))) | (~spl18_1 | spl18_2 | spl18_9)),
% 9.02/2.00 inference(forward_demodulation,[],[f544,f734])).
% 9.02/2.00 thf(f3551,plain,(
% 9.02/2.00 ($true != ((sK16 @ (sK11 @ sK16) @ (sK13 @ sK16)))) | (~spl18_1 | spl18_2 | spl18_9)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f3550])).
% 9.02/2.00 thf(f3623,plain,(
% 9.02/2.00 $false | (~spl18_1 | spl18_2 | ~spl18_8 | spl18_9)),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f3551,f668])).
% 9.02/2.00 thf(f3624,plain,(
% 9.02/2.00 ~spl18_1 | spl18_2 | ~spl18_8 | spl18_9),
% 9.02/2.00 inference(avatar_contradiction_clause,[],[f3623])).
% 9.02/2.00 thf(f3811,plain,(
% 9.02/2.00 ($true = ((sK16 @ (sK11 @ sK16) @ (sK12 @ sK16)))) | (~spl18_1 | spl18_2 | ~spl18_9)),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f547,f672])).
% 9.02/2.00 thf(f3842,plain,(
% 9.02/2.00 ($true != $true) | ($true = ((sK16 @ (sK11 @ sK16) @ (sK13 @ sK16)))) | (~spl18_1 | spl18_2 | ~spl18_9 | ~spl18_10)),
% 9.02/2.00 inference(constrained_superposition,[],[f756,f3811])).
% 9.02/2.00 thf(f3843,plain,(
% 9.02/2.00 ($true = ((sK16 @ (sK11 @ sK16) @ (sK13 @ sK16)))) | (~spl18_1 | spl18_2 | ~spl18_9 | ~spl18_10)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f3842])).
% 9.02/2.00 thf(f3882,plain,(
% 9.02/2.00 $false | (~spl18_1 | spl18_2 | spl18_8 | ~spl18_9 | ~spl18_10)),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f3843,f669])).
% 9.02/2.00 thf(f3883,plain,(
% 9.02/2.00 ~spl18_1 | spl18_2 | spl18_8 | ~spl18_9 | ~spl18_10),
% 9.02/2.00 inference(avatar_contradiction_clause,[],[f3882])).
% 9.02/2.00 thf(f3940,plain,(
% 9.02/2.00 ($true = $false) | (~spl18_2 | spl18_4 | ~spl18_6)),
% 9.02/2.00 inference(constrained_superposition,[],[f432,f468])).
% 9.02/2.00 thf(f3972,plain,(
% 9.02/2.00 $false | (~spl18_2 | spl18_4 | ~spl18_6)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f3940])).
% 9.02/2.00 thf(f3973,plain,(
% 9.02/2.00 ~spl18_2 | spl18_4 | ~spl18_6),
% 9.02/2.00 inference(avatar_contradiction_clause,[],[f3972])).
% 9.02/2.00 thf(f3983,plain,(
% 9.02/2.00 (sK3 = sK4) | ~spl18_2),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f24,f70])).
% 9.02/2.00 thf(f3985,plain,(
% 9.02/2.00 (sK4 = sK5) | ~spl18_2),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f27,f70])).
% 9.02/2.00 thf(f3986,plain,(
% 9.02/2.00 (sK3 = sK5) | ~spl18_2),
% 9.02/2.00 inference(forward_demodulation,[],[f3985,f3983])).
% 9.02/2.00 thf(f3988,plain,(
% 9.02/2.00 ($true = ((sP1 @ sK3 @ sK5))) | ~spl18_2),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f28,f70])).
% 9.02/2.00 thf(f3989,plain,(
% 9.02/2.00 ($true = ((sP1 @ sK3 @ sK3))) | ~spl18_2),
% 9.02/2.00 inference(forward_demodulation,[],[f3988,f3986])).
% 9.02/2.00 thf(f3994,plain,(
% 9.02/2.00 ($true != $true) | ($true != ((sK3 @ (sK10 @ sK3) @ (sK9 @ sK3)))) | ($true = ((sK3 @ (sK6 @ sK3) @ (sK7 @ sK3)))) | ~spl18_2),
% 9.02/2.00 inference(constrained_superposition,[],[f51,f3989])).
% 9.02/2.00 thf(f3997,plain,(
% 9.02/2.00 ($true != $true) | ($true = ((sK3 @ (sK9 @ sK3) @ (sK10 @ sK3)))) | ($true != ((sK3 @ (sK6 @ sK3) @ (sK8 @ sK3)))) | ~spl18_2),
% 9.02/2.00 inference(constrained_superposition,[],[f48,f3989])).
% 9.02/2.00 thf(f4024,plain,(
% 9.02/2.00 ($true = ((sK3 @ (sK9 @ sK3) @ (sK10 @ sK3)))) | ($true != ((sK3 @ (sK6 @ sK3) @ (sK8 @ sK3)))) | ~spl18_2),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f3997])).
% 9.02/2.00 thf(f4027,plain,(
% 9.02/2.00 ($true != ((sK3 @ (sK10 @ sK3) @ (sK9 @ sK3)))) | ($true = ((sK3 @ (sK6 @ sK3) @ (sK7 @ sK3)))) | ~spl18_2),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f3994])).
% 9.02/2.00 thf(f4067,plain,(
% 9.02/2.00 ( ! [X10 : a,X8 : a,X9 : a] : (($true != ((sK3 @ X9 @ X10))) | ($true = ((sK3 @ X8 @ X10))) | ($true != ((sK3 @ X8 @ X9)))) ) | ~spl18_2),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f23,f70])).
% 9.02/2.00 thf(f4148,plain,(
% 9.02/2.00 ( ! [X0 : a] : (($true != $true) | ($true = ((sK3 @ X0 @ (sK8 @ sK3)))) | ($true != ((sK3 @ X0 @ (sK7 @ sK3))))) ) | (~spl18_2 | ~spl18_5)),
% 9.02/2.00 inference(constrained_superposition,[],[f4067,f422])).
% 9.02/2.00 thf(f4155,plain,(
% 9.02/2.00 ( ! [X0 : a] : (($true != ((sK3 @ X0 @ (sK7 @ sK3)))) | ($true = ((sK3 @ X0 @ (sK8 @ sK3))))) ) | (~spl18_2 | ~spl18_5)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f4148])).
% 9.02/2.00 thf(f4584,plain,(
% 9.02/2.00 ($true = ((sK3 @ (sK6 @ sK3) @ (sK7 @ sK3)))) | (~spl18_2 | ~spl18_4)),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f4027,f345])).
% 9.02/2.00 thf(f4585,plain,(
% 9.02/2.00 spl18_7 | ~spl18_2 | ~spl18_4),
% 9.02/2.00 inference(avatar_split_clause,[],[f4584,f344,f68,f522])).
% 9.02/2.00 thf(f6207,plain,(
% 9.02/2.00 ($true != $true) | ($true = ((sK3 @ (sK6 @ sK3) @ (sK8 @ sK3)))) | (~spl18_2 | ~spl18_5 | ~spl18_7)),
% 9.02/2.00 inference(constrained_superposition,[],[f4155,f524])).
% 9.02/2.00 thf(f6232,plain,(
% 9.02/2.00 ($true = ((sK3 @ (sK6 @ sK3) @ (sK8 @ sK3)))) | (~spl18_2 | ~spl18_5 | ~spl18_7)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f6207])).
% 9.02/2.00 thf(f6244,plain,(
% 9.02/2.00 $false | (~spl18_2 | spl18_3 | ~spl18_5 | ~spl18_7)),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f6232,f342])).
% 9.02/2.00 thf(f6245,plain,(
% 9.02/2.00 ~spl18_2 | spl18_3 | ~spl18_5 | ~spl18_7),
% 9.02/2.00 inference(avatar_contradiction_clause,[],[f6244])).
% 9.02/2.00 thf(f6711,plain,(
% 9.02/2.00 ($true != ((sK3 @ (sK6 @ sK3) @ (sK8 @ sK3)))) | (~spl18_2 | spl18_6)),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f4024,f467])).
% 9.02/2.00 thf(f6712,plain,(
% 9.02/2.00 $false | (~spl18_2 | ~spl18_3 | spl18_6)),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f6711,f341])).
% 9.02/2.00 thf(f6713,plain,(
% 9.02/2.00 ~spl18_2 | ~spl18_3 | spl18_6),
% 9.02/2.00 inference(avatar_contradiction_clause,[],[f6712])).
% 9.02/2.00 thf(f6820,plain,(
% 9.02/2.00 ( ! [X6 : a,X5 : a] : (($true != ((sK16 @ X5 @ X6))) | ($true = ((sK16 @ X6 @ X5)))) ) | spl18_2),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f59,f69])).
% 9.02/2.00 thf(f6973,plain,(
% 9.02/2.00 ($true != $true) | ($true = ((sK16 @ (sK15 @ sK16) @ (sK14 @ sK16)))) | (spl18_2 | ~spl18_11)),
% 9.02/2.00 inference(constrained_superposition,[],[f6820,f739])).
% 9.02/2.00 thf(f6974,plain,(
% 9.02/2.00 ($true = ((sK16 @ (sK15 @ sK16) @ (sK14 @ sK16)))) | (spl18_2 | ~spl18_11)),
% 9.02/2.00 inference(trivial_inequality_removal,[],[f6973])).
% 9.02/2.00 thf(f6992,plain,(
% 9.02/2.00 $false | (spl18_2 | spl18_9 | ~spl18_11)),
% 9.02/2.00 inference(forward_subsumption_resolution,[],[f6974,f673])).
% 9.02/2.00 thf(f6993,plain,(
% 9.02/2.00 spl18_2 | spl18_9 | ~spl18_11),
% 9.02/2.00 inference(avatar_contradiction_clause,[],[f6992])).
% 9.02/2.00 cnf(s1, plain, spl18_1 | spl18_2, inference(sat_conversion,[],[f71])).
% 9.02/2.00 cnf(s2, plain, ~spl18_2 | ~spl18_3 | ~spl18_4, inference(sat_conversion,[],[f347])).
% 9.02/2.00 cnf(s3, plain, ~spl18_2 | ~spl18_4 | spl18_5, inference(sat_conversion,[],[f423])).
% 9.02/2.00 cnf(s4, plain, ~spl18_2 | spl18_5 | spl18_6, inference(sat_conversion,[],[f469])).
% 9.02/2.00 cnf(s5, plain, ~spl18_2 | spl18_6 | spl18_7, inference(sat_conversion,[],[f525])).
% 9.02/2.00 cnf(s6, plain, ~spl18_1 | spl18_2 | ~spl18_8 | ~spl18_9, inference(sat_conversion,[],[f674])).
% 9.02/2.00 cnf(s7, plain, ~spl18_1 | spl18_2 | ~spl18_9 | spl18_10, inference(sat_conversion,[],[f725])).
% 9.02/2.00 cnf(s8, plain, ~spl18_1 | spl18_2 | spl18_10 | spl18_11, inference(sat_conversion,[],[f740])).
% 9.02/2.00 cnf(s9, plain, ~spl18_1 | spl18_2 | spl18_8 | spl18_9 | ~spl18_10, inference(sat_conversion,[],[f3549])).
% 9.02/2.00 cnf(s10, plain, ~spl18_1 | spl18_2 | ~spl18_8 | spl18_9, inference(sat_conversion,[],[f3624])).
% 9.02/2.00 cnf(s11, plain, ~spl18_1 | spl18_2 | spl18_8 | ~spl18_9 | ~spl18_10, inference(sat_conversion,[],[f3883])).
% 9.02/2.00 cnf(s13, plain, ~spl18_2 | spl18_4 | ~spl18_6, inference(sat_conversion,[],[f3973])).
% 9.02/2.00 cnf(s14, plain, ~spl18_2 | ~spl18_4 | spl18_7, inference(sat_conversion,[],[f4585])).
% 9.02/2.00 cnf(s15, plain, ~spl18_2 | spl18_3 | ~spl18_5 | ~spl18_7, inference(sat_conversion,[],[f6245])).
% 9.02/2.00 cnf(s16, plain, ~spl18_2 | ~spl18_3 | spl18_6, inference(sat_conversion,[],[f6713])).
% 9.02/2.00 cnf(s17, plain, spl18_2 | spl18_9 | ~spl18_11, inference(sat_conversion,[],[f6993])).
% 9.02/2.00 cnf(s18, plain, spl18_6 | spl18_3 | ~spl18_2, inference(rat,[],[s15,s5,s4])).
% 9.02/2.00 cnf(s19, plain, spl18_3 | ~spl18_2, inference(rat,[],[s15,s3,s14,s13,s18])).
% 9.02/2.00 cnf(s20, plain, ~spl18_3 | ~spl18_2, inference(rat,[],[s13,s2,s16])).
% 9.02/2.00 cnf(s21, plain, ~spl18_2, inference(rat,[],[s20,s19])).
% 9.02/2.00 cnf(s22, plain, spl18_1, inference(rat,[],[s1,s21])).
% 9.02/2.00 cnf(s23, plain, spl18_9 | spl18_8, inference(rat,[],[s8,s9,s17,s21,s22])).
% 9.02/2.00 cnf(s24, plain, ~spl18_9 | spl18_8, inference(rat,[],[s7,s11,s21,s22])).
% 9.02/2.00 cnf(s25, plain, spl18_8, inference(rat,[],[s24,s23])).
% 9.02/2.00 cnf(s26, plain, ~spl18_9, inference(rat,[],[s6,s22,s21,s25])).
% 9.02/2.00 cnf(s27, plain, $false, inference(rat,[],[s10,s21,s22,s25,s26])).
% 9.02/2.00 thf(f6994,plain,(
% 9.02/2.00 $false),
% 9.02/2.00 inference(avatar_sat_refutation,[],[s27])).
% 9.02/2.00 % SZS output end Proof for theBenchmark
% 9.02/2.00 % (3275207)------------------------------
% 9.02/2.00 % (3275207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.02/2.00 % (3275207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.02/2.00 % (3275207)CaDiCaL version: 2.1.3
% 9.02/2.00 % (3275207)Termination reason: Refutation
% 9.02/2.00 % (3275207)Time elapsed: 0.978 s
% 9.02/2.00 % (3275207)Peak memory usage: 15 MB
% 9.02/2.00 % (3275207)Instructions burned: 1225 (million)
% 9.02/2.00 % (3275163)Success in time 1.675 s
% 9.02/2.00 % Vampire exiting
%------------------------------------------------------------------------------