%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV009^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 08:38:51 AM UTC 2026
% Result : Theorem 3.82s 0.80s
% Output : Refutation 3.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV009^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n018.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 15:02:05 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.82/0.80 % (191897)Will run a generic schedule for satisfiability detection.
% 3.82/0.80 % (191902)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1468298666_2999 on theBenchmark for (2999ds/0Mi)
% 3.82/0.80 % Exception at run slice level
% 3.82/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.82/0.80 % (191903)% WARNING: option uhcvi not known.
% 3.82/0.80 % (191903)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4094423136:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.82/0.80 % (191906)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1520792322:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.82/0.80 % (191904)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=232403501:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.82/0.80 % (191903)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.82/0.80 % (191905)dis+10_1_sil=32000:sp=arity:random_seed=3377786076:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.82/0.80 % (191906)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.82/0.80 % (191908)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1992307554:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.82/0.80 % (191907)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4002646509:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.82/0.80 % (191903)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.82/0.80 % (191910)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2981517912:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.82/0.80 % Exception at run slice level
% 3.82/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.82/0.80 % (191918)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3618799802:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.82/0.80 % (191918)Instruction limit reached!
% 3.82/0.80 % (191918)------------------------------
% 3.82/0.80 % (191918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.82/0.80 % (191918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/0.80 % (191918)CaDiCaL version: 2.1.3
% 3.82/0.80 % (191918)Termination reason: Instruction limit
% 3.82/0.80 % (191918)Termination phase: Saturation
% 3.82/0.80 % (191918)Time elapsed: 0.037 s
% 3.82/0.80 % (191918)Peak memory usage: 13 MB
% 3.82/0.80 % (191918)Instructions burned: 132 (million)
% 3.82/0.80 % (191905)Instruction limit reached!
% 3.82/0.80 % (191905)------------------------------
% 3.82/0.80 % (191905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.82/0.80 % (191905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/0.80 % (191905)CaDiCaL version: 2.1.3
% 3.82/0.80 % (191905)Termination reason: Instruction limit
% 3.82/0.80 % (191905)Termination phase: Saturation
% 3.82/0.80 % (191905)Time elapsed: 0.052 s
% 3.82/0.80 % (191905)Peak memory usage: 12 MB
% 3.82/0.80 % (191905)Instructions burned: 103 (million)
% 3.82/0.80 % (191906)Instruction limit reached!
% 3.82/0.80 % (191906)------------------------------
% 3.82/0.80 % (191906)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.82/0.80 % (191906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/0.80 % (191906)CaDiCaL version: 2.1.3
% 3.82/0.80 % (191906)Termination reason: Instruction limit
% 3.82/0.80 % (191906)Termination phase: Saturation
% 3.82/0.80 % (191906)Time elapsed: 0.058 s
% 3.82/0.80 % (191906)Peak memory usage: 12 MB
% 3.82/0.80 % (191906)Instructions burned: 117 (million)
% 3.82/0.80 % (191920)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=4167405403:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.82/0.80 % (191920)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.82/0.80 % (191920)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.82/0.80 % (191907)Instruction limit reached!
% 3.82/0.80 % (191907)------------------------------
% 3.82/0.80 % (191907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.82/0.80 % (191907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/0.80 % (191907)CaDiCaL version: 2.1.3
% 3.82/0.80 % (191907)Termination reason: Instruction limit
% 3.82/0.80 % (191907)Termination phase: Saturation
% 3.82/0.80 % (191907)Time elapsed: 0.065 s
% 3.82/0.80 % (191907)Peak memory usage: 12 MB
% 3.82/0.80 % (191907)Instructions burned: 132 (million)
% 3.82/0.80 % (191921)ott-21_1_sil=16000:fs=off:random_seed=2497143159:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 3.82/0.80 % (191922)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1530233825:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 3.82/0.80 % (191908)Instruction limit reached!
% 3.82/0.80 % (191908)------------------------------
% 3.82/0.80 % (191908)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.82/0.80 % (191908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/0.80 % (191908)CaDiCaL version: 2.1.3
% 3.82/0.80 % (191908)Termination reason: Instruction limit
% 3.82/0.80 % (191908)Termination phase: Saturation
% 3.82/0.80 % (191908)Time elapsed: 0.077 s
% 3.82/0.80 % (191908)Peak memory usage: 12 MB
% 3.82/0.80 % (191908)Instructions burned: 159 (million)
% 3.82/0.80 % (191924)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=701889358:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.82/0.80 % Exception at run slice level
% 3.82/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.82/0.80 % (191927)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=958477817:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.82/0.80 % (191929)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1126980664:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.82/0.80 % Exception at run slice level
% 3.82/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.82/0.80 % (191932)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=1849042155:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 3.82/0.80 % (191932)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.82/0.80 % (191921)Instruction limit reached!
% 3.82/0.80 % (191921)------------------------------
% 3.82/0.80 % (191921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.82/0.80 % (191921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/0.80 % (191921)CaDiCaL version: 2.1.3
% 3.82/0.80 % (191921)Termination reason: Instruction limit
% 3.82/0.80 % (191921)Termination phase: Saturation
% 3.82/0.80 % (191921)Time elapsed: 0.087 s
% 3.82/0.80 % (191921)Peak memory usage: 12 MB
% 3.82/0.80 % (191921)Instructions burned: 182 (million)
% 3.82/0.80 % (191934)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2051898154:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 3.82/0.80 % (191934)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.82/0.80 % (191920)Instruction limit reached!
% 3.82/0.80 % (191920)------------------------------
% 3.82/0.80 % (191920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.82/0.80 % (191920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/0.80 % (191920)CaDiCaL version: 2.1.3
% 3.82/0.80 % (191920)Termination reason: Instruction limit
% 3.82/0.80 % (191920)Termination phase: Saturation
% 3.82/0.80 % (191920)Time elapsed: 0.170 s
% 3.82/0.80 % (191920)Peak memory usage: 14 MB
% 3.82/0.80 % (191920)Instructions burned: 687 (million)
% 3.82/0.80 % (191936)fmb+10_1_sil=64000:random_seed=4068246450:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 3.82/0.80 % (191936)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.82/0.80 % Exception at run slice level
% 3.82/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.82/0.80 % (191938)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2714973758:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 3.82/0.80 % Exception at run slice level
% 3.82/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.82/0.80 % (191940)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=358104662:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 3.82/0.80 % Exception at run slice level
% 3.82/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.82/0.80 % (191942)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1916486601:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 3.82/0.80 % (191942)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.82/0.80 % (191922)Instruction limit reached!
% 3.82/0.80 % (191922)------------------------------
% 3.82/0.80 % (191922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.82/0.80 % (191922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/0.80 % (191922)CaDiCaL version: 2.1.3
% 3.82/0.80 % (191922)Termination reason: Instruction limit
% 3.82/0.80 % (191922)Termination phase: Saturation
% 3.82/0.80 % (191922)Time elapsed: 0.245 s
% 3.82/0.80 % (191922)Peak memory usage: 13 MB
% 3.82/0.80 % (191922)Instructions burned: 477 (million)
% 3.82/0.80 % (191944)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3379416131:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 3.82/0.80 % (191944)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.82/0.80 % (191944)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.82/0.80 % (191932)Instruction limit reached!
% 3.82/0.80 % (191932)------------------------------
% 3.82/0.80 % (191932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.82/0.80 % (191932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/0.80 % (191932)CaDiCaL version: 2.1.3
% 3.82/0.80 % (191932)Termination reason: Instruction limit
% 3.82/0.80 % (191932)Termination phase: Saturation
% 3.82/0.80 % (191932)Time elapsed: 0.324 s
% 3.82/0.80 % (191932)Peak memory usage: 16 MB
% 3.82/0.80 % (191932)Instructions burned: 693 (million)
% 3.82/0.80 % (191946)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=814324272:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 3.82/0.80 % Exception at run slice level
% 3.82/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.82/0.80 % (191948)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2026422421:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 3.82/0.80 % Exception at run slice level
% 3.82/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.82/0.80 % (191950)ott-2_1_sil=16000:newcnf=on:random_seed=2668124738:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 3.82/0.80 % (191950)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.82/0.80 % (191942) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-191897-191942"...
% 3.82/0.80 % (191942)...printing done.
% 3.82/0.80 % (191942)Refutation found. Thanks to Tanya!
% 3.82/0.80 % SZS status Theorem for theBenchmark
% 3.82/0.80 % SZS output start Proof for theBenchmark
% 3.82/0.80 thf(type_def_5, type, a: $tType).
% 3.82/0.80 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 3.82/0.80 thf(func_def_3, type, sP0: (((a > $o) > $o) > $o)).
% 3.82/0.80 thf(func_def_4, type, sK1: (((a > $o) > $o) > a)).
% 3.82/0.80 thf(func_def_5, type, sK2: (((a > $o) > $o) > a)).
% 3.82/0.80 thf(func_def_6, type, sK3: (((a > $o) > $o) > a)).
% 3.82/0.80 thf(func_def_7, type, sK4: (((a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_8, type, sK5: (((a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_9, type, sK6: ((a > $o) > $o)).
% 3.82/0.80 thf(func_def_10, type, sK7: a).
% 3.82/0.80 thf(func_def_11, type, sK8: a).
% 3.82/0.80 thf(func_def_12, type, sK9: (a > $o)).
% 3.82/0.80 thf(func_def_13, type, sK10: a).
% 3.82/0.80 thf(func_def_14, type, sK11: (a > a > $o)).
% 3.82/0.80 thf(func_def_15, type, vNOT: ($o > $o)).
% 3.82/0.80 thf(func_def_17, type, db0: !>[X0: $tType]:(X0)).
% 3.82/0.80 thf(func_def_18, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.82/0.80 thf(func_def_19, type, db1: !>[X0: $tType]:(X0)).
% 3.82/0.80 thf(func_def_20, type, sK13: (a > (a > (a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_21, type, db2: !>[X0: $tType]:(X0)).
% 3.82/0.80 thf(func_def_22, type, db3: !>[X0: $tType]:(X0)).
% 3.82/0.80 thf(func_def_23, type, sK14: (a > (a > (a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_24, type, sK15: (a > (a > (a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_25, type, sK16: (a > (a > (a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_26, type, sK17: (a > (a > (a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_27, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.82/0.80 thf(func_def_28, type, sK18: (a > (a > (a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_29, type, sK19: (a > (a > (a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_30, type, sK20: (a > (a > (a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_31, type, sK21: (a > (a > (a > $o) > a > $o) > a > $o)).
% 3.82/0.80 thf(func_def_32, type, db4: !>[X0: $tType]:(X0)).
% 3.82/0.80 thf(func_def_33, type, sK22: ((a > a > a) > a > a)).
% 3.82/0.80 thf(func_def_34, type, sK23: ((a > (a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_35, type, sK24: ((a > (a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_36, type, sK25: ((a > (a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_37, type, sK26: ((a > (a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_38, type, sK27: ((a > a > a) > a)).
% 3.82/0.80 thf(func_def_39, type, sK28: (((a > $o) > $o) > (a > (a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_40, type, sK29: ((a > (a > $o) > $o) > ((a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_41, type, sK30: ((a > (a > $o) > $o) > ((a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_42, type, sK31: ((a > (a > $o) > $o) > ((a > $o) > $o) > a > $o)).
% 3.82/0.80 thf(func_def_43, type, sK32: ((a > a > a) > ((a > $o) > $o) > a)).
% 3.82/0.80 thf(func_def_44, type, sK33: ((a > a > (a > $o) > $o) > a > a)).
% 3.82/0.80 thf(func_def_45, type, db5: !>[X0: $tType]:(X0)).
% 3.82/0.80 thf(func_def_46, type, sK34: ((a > a > (a > $o) > $o) > a > a)).
% 3.82/0.80 thf(func_def_47, type, sK35: ((a > a > (a > $o) > $o) > a)).
% 3.82/0.80 thf(f1,conjecture,(
% 3.82/0.80 ! [X0 : ((a > $o) > $o)] : (! [X1 : a] : ? [X2 : (a > $o)] : (! [X3 : (a > $o)] : (((X3 @ X1) & (X0 @ X3)) => (X3 = X2)) & (X2 @ X1) & (X0 @ X2)) => (! [X1 : a,X5 : a,X6 : a] : ((? [X4 : (a > $o)] : ((X4 @ X6) & (X4 @ X5) & (X0 @ X4)) & ? [X4 : (a > $o)] : ((X4 @ X5) & (X4 @ X1) & (X0 @ X4))) => ? [X4 : (a > $o)] : ((X4 @ X6) & (X4 @ X1) & (X0 @ X4))) & ! [X1 : a,X5 : a] : (? [X4 : (a > $o)] : ((X4 @ X5) & (X4 @ X1) & (X0 @ X4)) => ? [X4 : (a > $o)] : ((X4 @ X1) & (X4 @ X5) & (X0 @ X4))) & ! [X1 : a] : ? [X4 : (a > $o)] : ((X4 @ X1) & (X4 @ X1) & (X0 @ X4))))),
% 3.82/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM261_B_pme)).
% 3.82/0.80 thf(f2,negated_conjecture,(
% 3.82/0.80 ~ ! [X0 : ((a > $o) > $o)] : (! [X1 : a] : ? [X2 : (a > $o)] : (! [X3 : (a > $o)] : (((X3 @ X1) & (X0 @ X3)) => (X3 = X2)) & (X2 @ X1) & (X0 @ X2)) => (! [X1 : a,X5 : a,X6 : a] : ((? [X4 : (a > $o)] : ((X4 @ X6) & (X4 @ X5) & (X0 @ X4)) & ? [X4 : (a > $o)] : ((X4 @ X5) & (X4 @ X1) & (X0 @ X4))) => ? [X4 : (a > $o)] : ((X4 @ X6) & (X4 @ X1) & (X0 @ X4))) & ! [X1 : a,X5 : a] : (? [X4 : (a > $o)] : ((X4 @ X5) & (X4 @ X1) & (X0 @ X4)) => ? [X4 : (a > $o)] : ((X4 @ X1) & (X4 @ X5) & (X0 @ X4))) & ! [X1 : a] : ? [X4 : (a > $o)] : ((X4 @ X1) & (X4 @ X1) & (X0 @ X4))))),
% 3.82/0.80 inference(negated_conjecture,[status(cth)],[f1])).
% 3.82/0.80 thf(f3,plain,(
% 3.82/0.80 ~ ! [X0 : ((a > $o) > $o)] : (! [X1 : a] : ? [X2 : (a > $o)] : (! [X3 : (a > $o)] : (((X3 @ X1) & (X0 @ X3)) => (X3 = X2)) & (X2 @ X1) & (X0 @ X2)) => (! [X4 : a,X5 : a,X6 : a] : ((? [X7 : (a > $o)] : ((X7 @ X6) & (X7 @ X5) & (X0 @ X7)) & ? [X8 : (a > $o)] : ((X8 @ X5) & (X8 @ X4) & (X0 @ X8))) => ? [X9 : (a > $o)] : ((X9 @ X6) & (X9 @ X4) & (X0 @ X9))) & ! [X10 : a,X11 : a] : (? [X12 : (a > $o)] : ((X12 @ X11) & (X12 @ X10) & (X0 @ X12)) => ? [X13 : (a > $o)] : ((X13 @ X10) & (X13 @ X11) & (X0 @ X13))) & ! [X14 : a] : ? [X15 : (a > $o)] : ((X15 @ X14) & (X15 @ X14) & (X0 @ X15))))),
% 3.82/0.80 inference(rectify,[],[f2])).
% 3.82/0.80 thf(f4,plain,(
% 3.82/0.80 ~ ! [X0 : ((a > $o) > $o)] : (! [X1 : a] : ? [X2 : (a > $o)] : (! [X3 : (a > $o)] : (((((X3 @ X1)) = $true) & (((X0 @ X3)) = $true)) => (X2 = X3)) & (((X2 @ X1)) = $true) & (((X0 @ X2)) = $true)) => (! [X4 : a,X5 : a,X6 : a] : ((? [X7 : (a > $o)] : ((((X7 @ X6)) = $true) & (((X7 @ X5)) = $true) & (((X0 @ X7)) = $true)) & ? [X8 : (a > $o)] : ((((X8 @ X5)) = $true) & (((X8 @ X4)) = $true) & (((X0 @ X8)) = $true))) => ? [X9 : (a > $o)] : ((((X9 @ X6)) = $true) & (((X9 @ X4)) = $true) & (((X0 @ X9)) = $true))) & ! [X10 : a,X11 : a] : (? [X12 : (a > $o)] : ((((X12 @ X11)) = $true) & (((X12 @ X10)) = $true) & (((X0 @ X12)) = $true)) => ? [X13 : (a > $o)] : ((((X13 @ X10)) = $true) & (((X13 @ X11)) = $true) & (((X0 @ X13)) = $true))) & ! [X14 : a] : ? [X15 : (a > $o)] : ((((X15 @ X14)) = $true) & (((X15 @ X14)) = $true) & (((X0 @ X15)) = $true))))),
% 3.82/0.80 inference(fool_elimination,[],[f3])).
% 3.82/0.80 thf(f5,plain,(
% 3.82/0.80 ? [X0 : ((a > $o) > $o)] : ((? [X4 : a,X5 : a,X6 : a] : (! [X9 : (a > $o)] : ((((X9 @ X6)) != $true) | (((X9 @ X4)) != $true) | (((X0 @ X9)) != $true)) & (? [X7 : (a > $o)] : ((((X7 @ X6)) = $true) & (((X7 @ X5)) = $true) & (((X0 @ X7)) = $true)) & ? [X8 : (a > $o)] : ((((X8 @ X5)) = $true) & (((X8 @ X4)) = $true) & (((X0 @ X8)) = $true)))) | ? [X10 : a,X11 : a] : (! [X13 : (a > $o)] : ((((X13 @ X10)) != $true) | (((X13 @ X11)) != $true) | (((X0 @ X13)) != $true)) & ? [X12 : (a > $o)] : ((((X12 @ X11)) = $true) & (((X12 @ X10)) = $true) & (((X0 @ X12)) = $true))) | ? [X14 : a] : ! [X15 : (a > $o)] : ((((X15 @ X14)) != $true) | (((X15 @ X14)) != $true) | (((X0 @ X15)) != $true))) & ! [X1 : a] : ? [X2 : (a > $o)] : (! [X3 : (a > $o)] : ((X2 = X3) | ((((X3 @ X1)) != $true) | (((X0 @ X3)) != $true))) & (((X2 @ X1)) = $true) & (((X0 @ X2)) = $true)))),
% 3.82/0.80 inference(ennf_transformation,[],[f4])).
% 3.82/0.80 thf(f6,plain,(
% 3.82/0.80 ? [X0 : ((a > $o) > $o)] : ((? [X4 : a,X5 : a,X6 : a] : (! [X9 : (a > $o)] : ((((X9 @ X6)) != $true) | (((X9 @ X4)) != $true) | (((X0 @ X9)) != $true)) & ? [X7 : (a > $o)] : ((((X7 @ X6)) = $true) & (((X7 @ X5)) = $true) & (((X0 @ X7)) = $true)) & ? [X8 : (a > $o)] : ((((X8 @ X5)) = $true) & (((X8 @ X4)) = $true) & (((X0 @ X8)) = $true))) | ? [X10 : a,X11 : a] : (! [X13 : (a > $o)] : ((((X13 @ X10)) != $true) | (((X13 @ X11)) != $true) | (((X0 @ X13)) != $true)) & ? [X12 : (a > $o)] : ((((X12 @ X11)) = $true) & (((X12 @ X10)) = $true) & (((X0 @ X12)) = $true))) | ? [X14 : a] : ! [X15 : (a > $o)] : ((((X15 @ X14)) != $true) | (((X15 @ X14)) != $true) | (((X0 @ X15)) != $true))) & ! [X1 : a] : ? [X2 : (a > $o)] : (! [X3 : (a > $o)] : ((X2 = X3) | (((X3 @ X1)) != $true) | (((X0 @ X3)) != $true)) & (((X2 @ X1)) = $true) & (((X0 @ X2)) = $true)))),
% 3.82/0.80 inference(flattening,[],[f5])).
% 3.82/0.80 thf(f7,definition,(
% 3.82/0.80 ! [X0 : ((a > $o) > $o)] : (? [X4 : a,X5 : a,X6 : a] : (! [X9 : (a > $o)] : ((((X9 @ X6)) != $true) | (((X9 @ X4)) != $true) | (((X0 @ X9)) != $true)) & ? [X7 : (a > $o)] : ((((X7 @ X6)) = $true) & (((X7 @ X5)) = $true) & (((X0 @ X7)) = $true)) & ? [X8 : (a > $o)] : ((((X8 @ X5)) = $true) & (((X8 @ X4)) = $true) & (((X0 @ X8)) = $true))) | ~ ($true = ((sP0 @ X0))))),
% 3.82/0.80 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.82/0.80 thf(f8,plain,(
% 3.82/0.80 ? [X0 : ((a > $o) > $o)] : ((($true = ((sP0 @ X0))) | ? [X10 : a,X11 : a] : (! [X13 : (a > $o)] : ((((X13 @ X10)) != $true) | (((X13 @ X11)) != $true) | (((X0 @ X13)) != $true)) & ? [X12 : (a > $o)] : ((((X12 @ X11)) = $true) & (((X12 @ X10)) = $true) & (((X0 @ X12)) = $true))) | ? [X14 : a] : ! [X15 : (a > $o)] : ((((X15 @ X14)) != $true) | (((X15 @ X14)) != $true) | (((X0 @ X15)) != $true))) & ! [X1 : a] : ? [X2 : (a > $o)] : (! [X3 : (a > $o)] : ((X2 = X3) | (((X3 @ X1)) != $true) | (((X0 @ X3)) != $true)) & (((X2 @ X1)) = $true) & (((X0 @ X2)) = $true)))),
% 3.82/0.80 inference(definition_folding,[],[f6,f7])).
% 3.82/0.80 thf(f9,plain,(
% 3.82/0.80 ! [X0 : ((a > $o) > $o)] : (? [X4 : a,X5 : a,X6 : a] : (! [X9 : (a > $o)] : ((((X9 @ X6)) != $true) | (((X9 @ X4)) != $true) | (((X0 @ X9)) != $true)) & ? [X7 : (a > $o)] : ((((X7 @ X6)) = $true) & (((X7 @ X5)) = $true) & (((X0 @ X7)) = $true)) & ? [X8 : (a > $o)] : ((((X8 @ X5)) = $true) & (((X8 @ X4)) = $true) & (((X0 @ X8)) = $true))) | ($true != ((sP0 @ X0))))),
% 3.82/0.80 inference(nnf_transformation,[],[f7])).
% 3.82/0.80 thf(f10,plain,(
% 3.82/0.80 ! [X0 : ((a > $o) > $o)] : (? [X1 : a,X2 : a,X3 : a] : (! [X4 : (a > $o)] : (($true != ((X4 @ X3))) | (((X4 @ X1)) != $true) | (((X0 @ X4)) != $true)) & ? [X5 : (a > $o)] : (($true = ((X5 @ X3))) & ($true = ((X5 @ X2))) & ($true = ((X0 @ X5)))) & ? [X6 : (a > $o)] : (($true = ((X6 @ X2))) & ($true = ((X6 @ X1))) & ($true = ((X0 @ X6))))) | ($true != ((sP0 @ X0))))),
% 3.82/0.80 inference(rectify,[],[f9])).
% 3.82/0.80 thf(f11,plain,(
% 3.82/0.80 ! [X0 : ((a > $o) > $o)] : ((! [X4 : (a > $o)] : (($true != ((X4 @ (sK3 @ X0)))) | ($true != ((X4 @ (sK1 @ X0)))) | (((X0 @ X4)) != $true)) & (($true = ((sK4 @ X0 @ (sK3 @ X0)))) & ($true = ((sK4 @ X0 @ (sK2 @ X0)))) & ($true = ((X0 @ (sK4 @ X0))))) & (($true = ((sK5 @ X0 @ (sK2 @ X0)))) & ($true = ((sK5 @ X0 @ (sK1 @ X0)))) & ($true = ((X0 @ (sK5 @ X0)))))) | ($true != ((sP0 @ X0))))),
% 3.82/0.80 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X6,sK5 @ X0),skolemize(X6,sK5 @ X0),skolemize(X6,sK5 @ X0),skolemize(X6,sK5 @ X0),skolemize(X6,sK5 @ X0)],[f10])).
% 3.82/0.80 thf(f12,plain,(
% 3.82/0.80 ? [X0 : ((a > $o) > $o)] : ((($true = ((sP0 @ X0))) | ? [X1 : a,X2 : a] : (! [X3 : (a > $o)] : ((((X3 @ X1)) != $true) | ($true != ((X3 @ X2))) | (((X0 @ X3)) != $true)) & ? [X4 : (a > $o)] : (($true = ((X4 @ X2))) & (((X4 @ X1)) = $true) & (((X0 @ X4)) = $true))) | ? [X5 : a] : ! [X6 : (a > $o)] : (($true != ((X6 @ X5))) | ($true != ((X6 @ X5))) | ($true != ((X0 @ X6))))) & ! [X7 : a] : ? [X8 : (a > $o)] : (! [X9 : (a > $o)] : ((X8 = X9) | ($true != ((X9 @ X7))) | (((X0 @ X9)) != $true)) & ($true = ((X8 @ X7))) & (((X0 @ X8)) = $true)))),
% 3.82/0.80 inference(rectify,[],[f8])).
% 3.82/0.80 thf(f13,plain,(
% 3.82/0.80 (($true = ((sP0 @ sK6))) | (! [X3 : (a > $o)] : (($true != ((X3 @ sK7))) | ($true != ((X3 @ sK8))) | ($true != ((sK6 @ X3)))) & (($true = ((sK9 @ sK8))) & ($true = ((sK9 @ sK7))) & ($true = ((sK6 @ sK9))))) | ! [X6 : (a > $o)] : (($true != ((X6 @ sK10))) | ($true != ((X6 @ sK10))) | ($true != ((sK6 @ X6))))) & ! [X7 : a] : (! [X9 : (a > $o)] : ((((sK11 @ X7)) = X9) | ($true != ((X9 @ X7))) | ($true != ((sK6 @ X9)))) & ($true = ((sK11 @ X7 @ X7))) & ($true = ((sK6 @ (sK11 @ X7)))))),
% 3.82/0.80 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,vAPP]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X4,sK9),skolemize(X5,sK10),skolemize(X6,sK5 @ X0)],[f12])).
% 3.82/0.80 thf(f14,plain,(
% 3.82/0.80 ( ! [X0 : ((a > $o) > $o)] : (($true != ((sP0 @ X0))) | ($true = ((X0 @ (sK5 @ X0))))) )),
% 3.82/0.80 inference(cnf_transformation,[],[f11])).
% 3.82/0.80 thf(f15,plain,(
% 3.82/0.80 ( ! [X0 : ((a > $o) > $o)] : (($true != ((sP0 @ X0))) | ($true = ((sK5 @ X0 @ (sK1 @ X0))))) )),
% 3.82/0.80 inference(cnf_transformation,[],[f11])).
% 3.82/0.80 thf(f16,plain,(
% 3.82/0.80 ( ! [X0 : ((a > $o) > $o)] : (($true != ((sP0 @ X0))) | ($true = ((sK5 @ X0 @ (sK2 @ X0))))) )),
% 3.82/0.80 inference(cnf_transformation,[],[f11])).
% 3.82/0.80 thf(f17,plain,(
% 3.82/0.80 ( ! [X0 : ((a > $o) > $o)] : (($true != ((sP0 @ X0))) | ($true = ((X0 @ (sK4 @ X0))))) )),
% 3.82/0.80 inference(cnf_transformation,[],[f11])).
% 3.82/0.80 thf(f18,plain,(
% 3.82/0.80 ( ! [X0 : ((a > $o) > $o)] : (($true != ((sP0 @ X0))) | ($true = ((sK4 @ X0 @ (sK2 @ X0))))) )),
% 3.82/0.80 inference(cnf_transformation,[],[f11])).
% 3.82/0.80 thf(f19,plain,(
% 3.82/0.80 ( ! [X0 : ((a > $o) > $o)] : (($true != ((sP0 @ X0))) | ($true = ((sK4 @ X0 @ (sK3 @ X0))))) )),
% 3.82/0.80 inference(cnf_transformation,[],[f11])).
% 3.82/0.80 thf(f20,plain,(
% 3.82/0.80 ( ! [X0 : ((a > $o) > $o),X4 : (a > $o)] : (($true != ((sP0 @ X0))) | ($true != ((X4 @ (sK1 @ X0)))) | (((X0 @ X4)) != $true) | ($true != ((X4 @ (sK3 @ X0))))) )),
% 3.82/0.80 inference(cnf_transformation,[],[f11])).
% 3.82/0.80 thf(f21,plain,(
% 3.82/0.80 ( ! [X7 : a] : (($true = ((sK6 @ (sK11 @ X7))))) )),
% 3.82/0.80 inference(cnf_transformation,[],[f13])).
% 3.82/0.80 thf(f22,plain,(
% 3.82/0.80 ( ! [X7 : a] : (($true = ((sK11 @ X7 @ X7)))) )),
% 3.82/0.80 inference(cnf_transformation,[],[f13])).
% 3.82/0.80 thf(f23,plain,(
% 3.82/0.80 ( ! [X9 : (a > $o),X7 : a] : (($true != ((sK6 @ X9))) | ($true != ((X9 @ X7))) | (((sK11 @ X7)) = X9)) )),
% 3.82/0.80 inference(cnf_transformation,[],[f13])).
% 3.82/0.80 thf(f24,plain,(
% 3.82/0.80 ( ! [X6 : (a > $o)] : (($true = ((sP0 @ sK6))) | ($true = ((sK6 @ sK9))) | ($true != ((X6 @ sK10))) | ($true != ((X6 @ sK10))) | ($true != ((sK6 @ X6)))) )),
% 3.82/0.80 inference(cnf_transformation,[],[f13])).
% 3.82/0.80 thf(f25,plain,(
% 3.82/0.80 ( ! [X6 : (a > $o)] : (($true = ((sP0 @ sK6))) | ($true = ((sK9 @ sK7))) | ($true != ((X6 @ sK10))) | ($true != ((X6 @ sK10))) | ($true != ((sK6 @ X6)))) )),
% 3.82/0.80 inference(cnf_transformation,[],[f13])).
% 3.82/0.80 thf(f26,plain,(
% 3.82/0.80 ( ! [X6 : (a > $o)] : (($true = ((sP0 @ sK6))) | ($true = ((sK9 @ sK8))) | ($true != ((X6 @ sK10))) | ($true != ((X6 @ sK10))) | ($true != ((sK6 @ X6)))) )),
% 3.82/0.80 inference(cnf_transformation,[],[f13])).
% 3.82/0.80 thf(f27,plain,(
% 3.82/0.80 ( ! [X3 : (a > $o),X6 : (a > $o)] : (($true = ((sP0 @ sK6))) | ($true != ((X3 @ sK7))) | ($true != ((X3 @ sK8))) | ($true != ((sK6 @ X3))) | ($true != ((X6 @ sK10))) | ($true != ((X6 @ sK10))) | ($true != ((sK6 @ X6)))) )),
% 3.82/0.80 inference(cnf_transformation,[],[f13])).
% 3.82/0.80 thf(f29,definition,(
% 3.82/0.80 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 3.82/0.80 introduced(theory,[fool_exhaustiveness_axiom])).
% 3.82/0.80 thf(f30,plain,(
% 3.82/0.80 ( ! [X6 : (a > $o)] : (($true = ((sP0 @ sK6))) | ($true = ((sK6 @ sK9))) | ($true != ((X6 @ sK10))) | ($true != ((sK6 @ X6)))) )),
% 3.82/0.80 inference(duplicate_literal_removal,[],[f24])).
% 3.82/0.80 thf(f31,plain,(
% 3.82/0.80 ( ! [X6 : (a > $o)] : (($true = ((sP0 @ sK6))) | ($true = ((sK9 @ sK7))) | ($true != ((X6 @ sK10))) | ($true != ((sK6 @ X6)))) )),
% 3.82/0.80 inference(duplicate_literal_removal,[],[f25])).
% 3.82/0.80 thf(f32,plain,(
% 3.82/0.80 ( ! [X6 : (a > $o)] : (($true = ((sP0 @ sK6))) | ($true = ((sK9 @ sK8))) | ($true != ((X6 @ sK10))) | ($true != ((sK6 @ X6)))) )),
% 3.82/0.80 inference(duplicate_literal_removal,[],[f26])).
% 3.82/0.80 thf(f33,plain,(
% 3.82/0.80 ( ! [X3 : (a > $o),X6 : (a > $o)] : (($true = ((sP0 @ sK6))) | ($true != ((X3 @ sK7))) | ($true != ((X3 @ sK8))) | ($true != ((sK6 @ X3))) | ($true != ((X6 @ sK10))) | ($true != ((sK6 @ X6)))) )),
% 3.82/0.80 inference(duplicate_literal_removal,[],[f27])).
% 3.82/0.80 thf(f37,definition,(
% 3.82/0.80 spl12_1 <=> ! [X6 : (a > $o)] : (($true != ((X6 @ sK10))) | ($true != ((sK6 @ X6))))),
% 3.82/0.80 introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition])).
% 3.82/0.80 thf(f38,plain,(
% 3.82/0.80 ( ! [X6 : (a > $o)] : (($true != ((sK6 @ X6))) | ($true != ((X6 @ sK10)))) ) | ~spl12_1),
% 3.82/0.80 inference(avatar_component_clause,[],[f37])).
% 3.82/0.80 thf(f40,definition,(
% 3.82/0.80 spl12_2 <=> ($true = ((sK9 @ sK7)))),
% 3.82/0.80 introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition])).
% 3.82/0.80 thf(f42,plain,(
% 3.82/0.80 ($true = ((sK9 @ sK7))) | ~spl12_2),
% 3.82/0.80 inference(avatar_component_clause,[],[f40])).
% 3.82/0.80 thf(f44,definition,(
% 3.82/0.80 spl12_3 <=> ($true = ((sP0 @ sK6)))),
% 3.82/0.80 introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition])).
% 3.82/0.80 thf(f45,plain,(
% 3.82/0.80 ($true != ((sP0 @ sK6))) | spl12_3),
% 3.82/0.80 inference(avatar_component_clause,[],[f44])).
% 3.82/0.80 thf(f46,plain,(
% 3.82/0.80 ($true = ((sP0 @ sK6))) | ~spl12_3),
% 3.82/0.80 inference(avatar_component_clause,[],[f44])).
% 3.82/0.80 thf(f47,plain,(
% 3.82/0.80 spl12_1 | spl12_2 | spl12_3),
% 3.82/0.80 inference(avatar_split_clause,[],[f31,f44,f40,f37])).
% 3.82/0.80 thf(f49,definition,(
% 3.82/0.80 spl12_4 <=> ($true = ((sK9 @ sK8)))),
% 3.82/0.80 introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition])).
% 3.82/0.80 thf(f51,plain,(
% 3.82/0.80 ($true = ((sK9 @ sK8))) | ~spl12_4),
% 3.82/0.80 inference(avatar_component_clause,[],[f49])).
% 3.82/0.80 thf(f52,plain,(
% 3.82/0.80 spl12_1 | spl12_4 | spl12_3),
% 3.82/0.80 inference(avatar_split_clause,[],[f32,f44,f49,f37])).
% 3.82/0.80 thf(f91,plain,(
% 3.82/0.80 ($true != $true) | ($true = ((sK6 @ (sK5 @ sK6)))) | ~spl12_3),
% 3.82/0.80 inference(constrained_superposition,[],[f14,f46])).
% 3.82/0.80 thf(f94,plain,(
% 3.82/0.80 ($true = ((sK6 @ (sK5 @ sK6)))) | ~spl12_3),
% 3.82/0.80 inference(trivial_inequality_removal,[],[f91])).
% 3.82/0.80 thf(f96,plain,(
% 3.82/0.80 ( ! [X0 : a] : (($true != $true) | ($true != ((sK5 @ sK6 @ X0))) | (((sK11 @ X0)) = ((sK5 @ sK6)))) ) | ~spl12_3),
% 3.82/0.80 inference(constrained_superposition,[],[f23,f94])).
% 3.82/0.80 thf(f97,plain,(
% 3.82/0.81 ( ! [X0 : a] : (($true != ((sK5 @ sK6 @ X0))) | (((sK11 @ X0)) = ((sK5 @ sK6)))) ) | ~spl12_3),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f96])).
% 3.82/0.81 thf(f100,plain,(
% 3.82/0.81 ($true != $true) | ($true = ((sK6 @ (sK4 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(constrained_superposition,[],[f17,f46])).
% 3.82/0.81 thf(f103,plain,(
% 3.82/0.81 ($true = ((sK6 @ (sK4 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f100])).
% 3.82/0.81 thf(f105,plain,(
% 3.82/0.81 ( ! [X0 : a] : (($true != $true) | ($true != ((sK4 @ sK6 @ X0))) | (((sK11 @ X0)) = ((sK4 @ sK6)))) ) | ~spl12_3),
% 3.82/0.81 inference(constrained_superposition,[],[f23,f103])).
% 3.82/0.81 thf(f106,plain,(
% 3.82/0.81 ( ! [X0 : a] : (($true != ((sK4 @ sK6 @ X0))) | (((sK11 @ X0)) = ((sK4 @ sK6)))) ) | ~spl12_3),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f105])).
% 3.82/0.81 thf(f109,plain,(
% 3.82/0.81 ($true != $true) | ($true = ((sK5 @ sK6 @ (sK1 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(constrained_superposition,[],[f15,f46])).
% 3.82/0.81 thf(f112,plain,(
% 3.82/0.81 ($true = ((sK5 @ sK6 @ (sK1 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f109])).
% 3.82/0.81 thf(f130,plain,(
% 3.82/0.81 ($true != $true) | ($true = ((sK5 @ sK6 @ (sK2 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(constrained_superposition,[],[f16,f46])).
% 3.82/0.81 thf(f133,plain,(
% 3.82/0.81 ($true = ((sK5 @ sK6 @ (sK2 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f130])).
% 3.82/0.81 thf(f140,plain,(
% 3.82/0.81 ($true != $true) | ($true = ((sK4 @ sK6 @ (sK2 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(constrained_superposition,[],[f18,f46])).
% 3.82/0.81 thf(f143,plain,(
% 3.82/0.81 ($true = ((sK4 @ sK6 @ (sK2 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f140])).
% 3.82/0.81 thf(f150,plain,(
% 3.82/0.81 ($true != $true) | ($true = ((sK4 @ sK6 @ (sK3 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(constrained_superposition,[],[f19,f46])).
% 3.82/0.81 thf(f153,plain,(
% 3.82/0.81 ($true = ((sK4 @ sK6 @ (sK3 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f150])).
% 3.82/0.81 thf(f160,plain,(
% 3.82/0.81 ( ! [X0 : (a > $o)] : (($true != $true) | ($true != ((X0 @ (sK1 @ sK6)))) | ($true != ((sK6 @ X0))) | ($true != ((X0 @ (sK3 @ sK6))))) ) | ~spl12_3),
% 3.82/0.81 inference(constrained_superposition,[],[f20,f46])).
% 3.82/0.81 thf(f163,plain,(
% 3.82/0.81 ( ! [X0 : (a > $o)] : (($true != ((X0 @ (sK3 @ sK6)))) | ($true != ((sK6 @ X0))) | ($true != ((X0 @ (sK1 @ sK6))))) ) | ~spl12_3),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f160])).
% 3.82/0.81 thf(f185,plain,(
% 3.82/0.81 ( ! [X0 : (a > $o)] : (($true != $true) | ($true != ((sK6 @ X0))) | ($true != ((X0 @ (sK1 @ sK6)))) | ($false = ((X0 @ (sK3 @ sK6))))) ) | ~spl12_3),
% 3.82/0.81 inference(constrained_superposition,[],[f163,f29])).
% 3.82/0.81 thf(f189,plain,(
% 3.82/0.81 ( ! [X0 : (a > $o)] : (($true != ((X0 @ (sK1 @ sK6)))) | ($true != ((sK6 @ X0))) | ($false = ((X0 @ (sK3 @ sK6))))) ) | ~spl12_3),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f185])).
% 3.82/0.81 thf(f791,plain,(
% 3.82/0.81 ($true != $true) | (((sK5 @ sK6)) = ((sK11 @ (sK2 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(constrained_superposition,[],[f97,f133])).
% 3.82/0.81 thf(f806,plain,(
% 3.82/0.81 (((sK5 @ sK6)) = ((sK11 @ (sK2 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f791])).
% 3.82/0.81 thf(f812,plain,(
% 3.82/0.81 ($true != $true) | (((sK4 @ sK6)) = ((sK11 @ (sK2 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(constrained_superposition,[],[f106,f143])).
% 3.82/0.81 thf(f829,plain,(
% 3.82/0.81 (((sK4 @ sK6)) = ((sK11 @ (sK2 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f812])).
% 3.82/0.81 thf(f868,plain,(
% 3.82/0.81 ( ! [X0 : (a > $o)] : (($true != $true) | ($true != ((sK6 @ X0))) | ($false = ((X0 @ (sK3 @ sK6)))) | ($false = ((X0 @ (sK1 @ sK6))))) ) | ~spl12_3),
% 3.82/0.81 inference(constrained_superposition,[],[f189,f29])).
% 3.82/0.81 thf(f872,plain,(
% 3.82/0.81 ( ! [X0 : (a > $o)] : (($true != ((sK6 @ X0))) | ($false = ((X0 @ (sK3 @ sK6)))) | ($false = ((X0 @ (sK1 @ sK6))))) ) | ~spl12_3),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f868])).
% 3.82/0.81 thf(f1366,plain,(
% 3.82/0.81 (((sK5 @ sK6)) = ((sK4 @ sK6))) | ~spl12_3),
% 3.82/0.81 inference(constrained_superposition,[],[f829,f806])).
% 3.82/0.81 thf(f1494,plain,(
% 3.82/0.81 ( ! [X1 : a] : ((((sK5 @ sK6 @ X1)) = ((sK4 @ sK6 @ X1)))) ) | ~spl12_3),
% 3.82/0.81 inference(argument_congruence,[],[f1366])).
% 3.82/0.81 thf(f1498,plain,(
% 3.82/0.81 ( ! [X1 : a] : (($false = ((sK5 @ sK6 @ X1))) | ($true = ((sK4 @ sK6 @ X1)))) ) | ~spl12_3),
% 3.82/0.81 inference(iff_proxy_clausification,[],[f1494])).
% 3.82/0.81 thf(f1709,plain,(
% 3.82/0.81 ($true = $false) | ($true = ((sK4 @ sK6 @ (sK1 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(constrained_superposition,[],[f112,f1498])).
% 3.82/0.81 thf(f1730,plain,(
% 3.82/0.81 ($true = ((sK4 @ sK6 @ (sK1 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f1709])).
% 3.82/0.81 thf(f7625,plain,(
% 3.82/0.81 ($true != $true) | ($false = ((sK4 @ sK6 @ (sK3 @ sK6)))) | ($false = ((sK4 @ sK6 @ (sK1 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(constrained_superposition,[],[f872,f103])).
% 3.82/0.81 thf(f7650,plain,(
% 3.82/0.81 ($false = ((sK4 @ sK6 @ (sK3 @ sK6)))) | ($false = ((sK4 @ sK6 @ (sK1 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f7625])).
% 3.82/0.81 thf(f7662,plain,(
% 3.82/0.81 ($true = $false) | ($false = ((sK4 @ sK6 @ (sK3 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(forward_demodulation,[],[f7650,f1730])).
% 3.82/0.81 thf(f7663,plain,(
% 3.82/0.81 ($false = ((sK4 @ sK6 @ (sK3 @ sK6)))) | ~spl12_3),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f7662])).
% 3.82/0.81 thf(f7670,plain,(
% 3.82/0.81 ($true = $false) | ~spl12_3),
% 3.82/0.81 inference(constrained_superposition,[],[f7663,f153])).
% 3.82/0.81 thf(f7767,plain,(
% 3.82/0.81 $false | ~spl12_3),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f7670])).
% 3.82/0.81 thf(f7768,plain,(
% 3.82/0.81 ~spl12_3),
% 3.82/0.81 inference(avatar_contradiction_clause,[],[f7767])).
% 3.82/0.81 thf(f7865,plain,(
% 3.82/0.81 ( ! [X0 : a] : (($true != $true) | ($true != ((sK11 @ X0 @ sK10)))) ) | ~spl12_1),
% 3.82/0.81 inference(constrained_superposition,[],[f38,f21])).
% 3.82/0.81 thf(f7888,plain,(
% 3.82/0.81 ( ! [X0 : a] : (($true != ((sK11 @ X0 @ sK10)))) ) | ~spl12_1),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f7865])).
% 3.82/0.81 thf(f7896,plain,(
% 3.82/0.81 ($true != $true) | ~spl12_1),
% 3.82/0.81 inference(constrained_superposition,[],[f7888,f22])).
% 3.82/0.81 thf(f7945,plain,(
% 3.82/0.81 $false | ~spl12_1),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f7896])).
% 3.82/0.81 thf(f7946,plain,(
% 3.82/0.81 ~spl12_1),
% 3.82/0.81 inference(avatar_contradiction_clause,[],[f7945])).
% 3.82/0.81 thf(f8211,plain,(
% 3.82/0.81 ( ! [X6 : (a > $o)] : (($true = ((sK6 @ sK9))) | ($true != ((X6 @ sK10))) | ($true != ((sK6 @ X6)))) ) | spl12_3),
% 3.82/0.81 inference(forward_subsumption_resolution,[],[f30,f45])).
% 3.82/0.81 thf(f8213,definition,(
% 3.82/0.81 spl12_8 <=> ($true = ((sK6 @ sK9)))),
% 3.82/0.81 introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition])).
% 3.82/0.81 thf(f8215,plain,(
% 3.82/0.81 ($true = ((sK6 @ sK9))) | ~spl12_8),
% 3.82/0.81 inference(avatar_component_clause,[],[f8213])).
% 3.82/0.81 thf(f8216,plain,(
% 3.82/0.81 spl12_1 | spl12_8 | spl12_3),
% 3.82/0.81 inference(avatar_split_clause,[],[f8211,f44,f8213,f37])).
% 3.82/0.81 thf(f8293,plain,(
% 3.82/0.81 ( ! [X3 : (a > $o),X6 : (a > $o)] : (($true != ((X3 @ sK7))) | ($true != ((X3 @ sK8))) | ($true != ((sK6 @ X3))) | ($true != ((X6 @ sK10))) | ($true != ((sK6 @ X6)))) ) | spl12_3),
% 3.82/0.81 inference(forward_subsumption_resolution,[],[f33,f45])).
% 3.82/0.81 thf(f8329,definition,(
% 3.82/0.81 spl12_9 <=> ! [X3 : (a > $o)] : (($true != ((X3 @ sK7))) | ($true != ((sK6 @ X3))) | ($true != ((X3 @ sK8))))),
% 3.82/0.81 introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition])).
% 3.82/0.81 thf(f8330,plain,(
% 3.82/0.81 ( ! [X3 : (a > $o)] : (($true != ((sK6 @ X3))) | ($true != ((X3 @ sK7))) | ($true != ((X3 @ sK8)))) ) | ~spl12_9),
% 3.82/0.81 inference(avatar_component_clause,[],[f8329])).
% 3.82/0.81 thf(f8331,plain,(
% 3.82/0.81 spl12_1 | spl12_9 | spl12_3),
% 3.82/0.81 inference(avatar_split_clause,[],[f8293,f44,f8329,f37])).
% 3.82/0.81 thf(f8348,plain,(
% 3.82/0.81 ($true != $true) | ($true != ((sK9 @ sK7))) | ($true != ((sK9 @ sK8))) | (~spl12_8 | ~spl12_9)),
% 3.82/0.81 inference(constrained_superposition,[],[f8330,f8215])).
% 3.82/0.81 thf(f8369,plain,(
% 3.82/0.81 ($true != ((sK9 @ sK7))) | ($true != ((sK9 @ sK8))) | (~spl12_8 | ~spl12_9)),
% 3.82/0.81 inference(trivial_inequality_removal,[],[f8348])).
% 3.82/0.81 thf(f8380,plain,(
% 3.82/0.81 ($true != ((sK9 @ sK8))) | (~spl12_2 | ~spl12_8 | ~spl12_9)),
% 3.82/0.81 inference(forward_subsumption_resolution,[],[f8369,f42])).
% 3.82/0.81 thf(f8381,plain,(
% 3.82/0.81 $false | (~spl12_2 | ~spl12_4 | ~spl12_8 | ~spl12_9)),
% 3.82/0.81 inference(forward_subsumption_resolution,[],[f8380,f51])).
% 3.82/0.81 thf(f8382,plain,(
% 3.82/0.81 ~spl12_2 | ~spl12_4 | ~spl12_8 | ~spl12_9),
% 3.82/0.81 inference(avatar_contradiction_clause,[],[f8381])).
% 3.82/0.81 cnf(s1, plain, spl12_1 | spl12_2 | spl12_3, inference(sat_conversion,[],[f47])).
% 3.82/0.81 cnf(s2, plain, spl12_1 | spl12_3 | spl12_4, inference(sat_conversion,[],[f52])).
% 3.82/0.81 cnf(s6, plain, ~spl12_3, inference(sat_conversion,[],[f7768])).
% 3.82/0.81 cnf(s7, plain, ~spl12_1, inference(sat_conversion,[],[f7946])).
% 3.82/0.81 cnf(s9, plain, spl12_1 | spl12_3 | spl12_8, inference(sat_conversion,[],[f8216])).
% 3.82/0.81 cnf(s10, plain, spl12_1 | spl12_3 | spl12_9, inference(sat_conversion,[],[f8331])).
% 3.82/0.81 cnf(s11, plain, ~spl12_2 | ~spl12_4 | ~spl12_8 | ~spl12_9, inference(sat_conversion,[],[f8382])).
% 3.82/0.81 cnf(s12, plain, spl12_9, inference(rat,[],[s10,s7,s6])).
% 3.82/0.81 cnf(s13, plain, spl12_8, inference(rat,[],[s9,s7,s6])).
% 3.82/0.81 cnf(s17, plain, spl12_4, inference(rat,[],[s2,s6,s7])).
% 3.82/0.81 cnf(s18, plain, ~spl12_2, inference(rat,[],[s11,s12,s13,s17])).
% 3.82/0.81 cnf(s20, plain, $false, inference(rat,[],[s1,s6,s18,s7])).
% 3.82/0.81 thf(f8383,plain,(
% 3.82/0.81 $false),
% 3.82/0.81 inference(avatar_sat_refutation,[],[s20])).
% 3.82/0.81 % SZS output end Proof for theBenchmark
% 3.82/0.81 % (191942)------------------------------
% 3.82/0.81 % (191942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.82/0.81 % (191942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/0.81 % (191942)CaDiCaL version: 2.1.3
% 3.82/0.81 % (191942)Termination reason: Refutation
% 3.82/0.81 % (191942)Time elapsed: 0.265 s
% 3.82/0.81 % (191942)Peak memory usage: 16 MB
% 3.82/0.81 % (191942)Instructions burned: 1061 (million)
% 3.82/0.81 % (191897)Success in time 0.582 s
% 3.82/0.81 % Vampire exiting
%------------------------------------------------------------------------------