%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO388^5 : 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 : n020.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 08:49:50 AM UTC 2026
% Result : Theorem 6.47s 1.14s
% Output : Refutation 6.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO388^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n020.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:51:05 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 4.14/0.92 % (1300587)Will run a generic schedule for satisfiability detection.
% 4.14/0.92 % (1300593)% WARNING: option uhcvi not known.
% 4.14/0.92 % (1300593)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3757024110:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.14/0.92 % (1300593)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.14/0.92 % (1300593)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.14/0.92 % (1300595)dis+10_1_sil=32000:sp=arity:random_seed=2314609386:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.14/0.92 % (1300592)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1818327587_2999 on theBenchmark for (2999ds/0Mi)
% 4.14/0.92 % (1300596)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3570959310:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.14/0.92 % (1300594)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3158445828:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.14/0.92 % (1300597)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3885990698:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.14/0.92 % (1300598)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1905516450:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.14/0.92 % (1300596)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.14/0.92 % Exception at run slice level
% 4.14/0.92 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.14/0.92 % (1300606)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=36889805:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.14/0.92 % Exception at run slice level
% 4.14/0.92 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.14/0.92 % (1300608)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2441110679:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.14/0.92 % (1300595)Instruction limit reached!
% 4.14/0.92 % (1300595)------------------------------
% 4.14/0.92 % (1300595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.14/0.92 % (1300595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.14/0.92 % (1300595)CaDiCaL version: 2.1.3
% 4.14/0.92 % (1300595)Termination reason: Instruction limit
% 4.14/0.92 % (1300595)Termination phase: Saturation
% 4.14/0.92 % (1300595)Time elapsed: 0.051 s
% 4.14/0.92 % (1300595)Peak memory usage: 12 MB
% 4.14/0.92 % (1300595)Instructions burned: 103 (million)
% 4.14/0.92 % (1300596)Instruction limit reached!
% 4.14/0.92 % (1300596)------------------------------
% 4.14/0.92 % (1300596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.14/0.92 % (1300596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.14/0.92 % (1300596)CaDiCaL version: 2.1.3
% 4.14/0.92 % (1300596)Termination reason: Instruction limit
% 4.14/0.92 % (1300596)Termination phase: Saturation
% 4.14/0.92 % (1300596)Time elapsed: 0.055 s
% 4.14/0.92 % (1300596)Peak memory usage: 12 MB
% 4.14/0.92 % (1300596)Instructions burned: 117 (million)
% 4.14/0.92 % (1300597)Instruction limit reached!
% 4.14/0.92 % (1300597)------------------------------
% 4.14/0.92 % (1300597)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.14/0.92 % (1300597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.14/0.92 % (1300597)CaDiCaL version: 2.1.3
% 4.14/0.92 % (1300597)Termination reason: Instruction limit
% 4.14/0.92 % (1300597)Termination phase: Saturation
% 4.14/0.92 % (1300597)Time elapsed: 0.065 s
% 4.14/0.92 % (1300597)Peak memory usage: 12 MB
% 4.14/0.92 % (1300597)Instructions burned: 133 (million)
% 4.14/0.92 % (1300610)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=2522310573:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.14/0.92 % (1300610)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.14/0.92 % (1300610)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.14/0.92 % (1300611)ott-21_1_sil=16000:fs=off:random_seed=2384645724:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 4.14/0.92 % (1300598)Instruction limit reached!
% 6.47/1.14 % (1300598)------------------------------
% 6.47/1.14 % (1300598)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.47/1.14 % (1300598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.47/1.14 % (1300598)CaDiCaL version: 2.1.3
% 6.47/1.14 % (1300598)Termination reason: Instruction limit
% 6.47/1.14 % (1300598)Termination phase: Saturation
% 6.47/1.14 % (1300598)Time elapsed: 0.075 s
% 6.47/1.14 % (1300598)Peak memory usage: 12 MB
% 6.47/1.14 % (1300598)Instructions burned: 163 (million)
% 6.47/1.14 % (1300612)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3368073179:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 6.47/1.14 % (1300615)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=775935033:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 6.47/1.14 % Exception at run slice level
% 6.47/1.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.47/1.14 % (1300608)Instruction limit reached!
% 6.47/1.14 % (1300608)------------------------------
% 6.47/1.14 % (1300608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.47/1.14 % (1300608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.47/1.14 % (1300608)CaDiCaL version: 2.1.3
% 6.47/1.14 % (1300608)Termination reason: Instruction limit
% 6.47/1.14 % (1300608)Termination phase: Saturation
% 6.47/1.14 % (1300608)Time elapsed: 0.069 s
% 6.47/1.14 % (1300608)Peak memory usage: 12 MB
% 6.47/1.14 % (1300608)Instructions burned: 132 (million)
% 6.47/1.14 % (1300618)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=208969071:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 6.47/1.14 % (1300619)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=840512997:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 6.47/1.14 % Exception at run slice level
% 6.47/1.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.47/1.14 % (1300611)Instruction limit reached!
% 6.47/1.14 % (1300611)------------------------------
% 6.47/1.14 % (1300611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.47/1.14 % (1300611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.47/1.14 % (1300611)CaDiCaL version: 2.1.3
% 6.47/1.14 % (1300611)Termination reason: Instruction limit
% 6.47/1.14 % (1300611)Termination phase: Saturation
% 6.47/1.14 % (1300611)Time elapsed: 0.078 s
% 6.47/1.14 % (1300611)Peak memory usage: 12 MB
% 6.47/1.14 % (1300611)Instructions burned: 181 (million)
% 6.47/1.14 % (1300622)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=296448789: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)
% 6.47/1.14 % (1300622)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.47/1.14 % (1300623)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2215116942:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 6.47/1.14 % (1300623)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.47/1.14 % (1300612)Instruction limit reached!
% 6.47/1.14 % (1300612)------------------------------
% 6.47/1.14 % (1300612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.47/1.14 % (1300612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.47/1.14 % (1300612)CaDiCaL version: 2.1.3
% 6.47/1.14 % (1300612)Termination reason: Instruction limit
% 6.47/1.14 % (1300612)Termination phase: Saturation
% 6.47/1.14 % (1300612)Time elapsed: 0.238 s
% 6.47/1.14 % (1300612)Peak memory usage: 12 MB
% 6.47/1.14 % (1300612)Instructions burned: 478 (million)
% 6.47/1.14 % (1300626)fmb+10_1_sil=64000:random_seed=3654018888:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 6.47/1.14 % (1300626)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.47/1.14 % Exception at run slice level
% 6.47/1.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.47/1.14 % (1300628)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=836009498:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 6.47/1.14 % Exception at run slice level
% 6.47/1.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.47/1.14 % (1300610)Instruction limit reached!
% 6.47/1.14 % (1300610)------------------------------
% 6.47/1.14 % (1300610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.47/1.14 % (1300610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.47/1.14 % (1300610)CaDiCaL version: 2.1.3
% 6.47/1.14 % (1300610)Termination reason: Instruction limit
% 6.47/1.14 % (1300610)Termination phase: Saturation
% 6.47/1.14 % (1300610)Time elapsed: 0.302 s
% 6.47/1.14 % (1300610)Peak memory usage: 13 MB
% 6.47/1.14 % (1300610)Instructions burned: 686 (million)
% 6.47/1.14 % (1300630)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3857935276:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 6.47/1.14 % Exception at run slice level
% 6.47/1.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.47/1.14 % (1300631)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=908980818:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 6.47/1.14 % (1300631)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.47/1.14 % (1300633)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2608619608:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 6.47/1.14 % (1300633)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.47/1.14 % (1300633)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.47/1.14 % (1300622)Instruction limit reached!
% 6.47/1.14 % (1300622)------------------------------
% 6.47/1.14 % (1300622)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.47/1.14 % (1300622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.47/1.14 % (1300622)CaDiCaL version: 2.1.3
% 6.47/1.14 % (1300622)Termination reason: Instruction limit
% 6.47/1.14 % (1300622)Termination phase: Saturation
% 6.47/1.14 % (1300622)Time elapsed: 0.305 s
% 6.47/1.14 % (1300622)Peak memory usage: 15 MB
% 6.47/1.14 % (1300622)Instructions burned: 693 (million)
% 6.47/1.14 % (1300636)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=483622948:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 6.47/1.14 % Exception at run slice level
% 6.47/1.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.47/1.14 % (1300638)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=502615044:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 6.47/1.14 % Exception at run slice level
% 6.47/1.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.47/1.14 % (1300640)ott-2_1_sil=16000:newcnf=on:random_seed=1589882053:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 6.47/1.14 % (1300640)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.47/1.14 % (1300623)Instruction limit reached!
% 6.47/1.14 % (1300623)------------------------------
% 6.47/1.14 % (1300623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.47/1.14 % (1300623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.47/1.14 % (1300623)CaDiCaL version: 2.1.3
% 6.47/1.14 % (1300623)Termination reason: Instruction limit
% 6.47/1.14 % (1300623)Termination phase: Saturation
% 6.47/1.14 % (1300623)Time elapsed: 0.418 s
% 6.47/1.14 % (1300623)Peak memory usage: 14 MB
% 6.47/1.14 % (1300623)Instructions burned: 880 (million)
% 6.47/1.14 % (1300642)ott+10_1_sil=32000:tgt=ground:random_seed=3502785699:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 6.47/1.14 % (1300618)Instruction limit reached!
% 6.47/1.14 % (1300618)------------------------------
% 6.47/1.14 % (1300618)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.47/1.14 % (1300618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.47/1.14 % (1300618)CaDiCaL version: 2.1.3
% 6.47/1.14 % (1300618)Termination reason: Instruction limit
% 6.47/1.14 % (1300618)Termination phase: Saturation
% 6.47/1.14 % (1300618)Time elapsed: 0.523 s
% 6.47/1.14 % (1300618)Peak memory usage: 14 MB
% 6.47/1.14 % (1300618)Instructions burned: 1179 (million)
% 6.47/1.14 % (1300644)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1175183260:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 6.47/1.14 % Exception at run slice level
% 6.47/1.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.47/1.14 % (1300646)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2729057988:i=3512:aac=none_2993 on theBenchmark for (2993ds/3512Mi)
% 6.47/1.14 % (1300646)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.47/1.14 % (1300593) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1300587-1300593"...
% 6.47/1.14 % (1300593)...printing done.
% 6.47/1.14 % (1300593)Refutation found. Thanks to Tanya!
% 6.47/1.14 % SZS status Theorem for theBenchmark
% 6.47/1.14 % SZS output start Proof for theBenchmark
% 6.47/1.14 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 6.47/1.14 thf(func_def_0, type, cQ_6: ($i > $i > $i > $o)).
% 6.47/1.14 thf(func_def_1, type, f: ($i > $i)).
% 6.47/1.14 thf(func_def_2, type, cP_5: ($i > $i > $o)).
% 6.47/1.14 thf(func_def_3, type, cQ_5: ($i > $i > $i > $o)).
% 6.47/1.14 thf(func_def_8, type, cP_4: ($i > $i > $o)).
% 6.47/1.14 thf(func_def_9, type, cQ_4: ($i > $i > $i > $o)).
% 6.47/1.14 thf(func_def_10, type, cP_3: ($i > $i > $o)).
% 6.47/1.14 thf(func_def_11, type, cQ_3: ($i > $i > $i > $o)).
% 6.47/1.14 thf(func_def_12, type, cP_2: ($i > $i > $o)).
% 6.47/1.14 thf(func_def_13, type, cQ_2: ($i > $i > $i > $o)).
% 6.47/1.14 thf(func_def_14, type, cP_1: ($i > $i > $o)).
% 6.47/1.14 thf(func_def_15, type, cQ_1: ($i > $i > $i > $o)).
% 6.47/1.14 thf(f1,conjecture,(
% 6.47/1.14 ~(! [X0 : $i,X1 : $i,X2 : $i] : ~(cQ_6 @ X0 @ X1 @ X2) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_6 @ X3 @ X4 @ X5) | ~(cP_5 @ (f @ X2) @ X5) | ~(cP_5 @ (f @ X1) @ X4) | ~(cP_5 @ (f @ X0) @ X3) | ~(cQ_5 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_5 @ (f @ X0) @ X1) | ~(cP_5 @ X0 @ X1)) & ! [X0 : $i] : (cP_5 @ d @ X0) & (cP_5 @ c @ c) & (cP_5 @ b @ b) & (cP_5 @ a @ a) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_5 @ X3 @ X4 @ X5) | ~(cP_4 @ (f @ X2) @ X5) | ~(cP_4 @ (f @ X1) @ X4) | ~(cP_4 @ (f @ X0) @ X3) | ~(cQ_4 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_4 @ (f @ X0) @ X1) | ~(cP_4 @ X0 @ X1)) & ! [X0 : $i] : (cP_4 @ d @ X0) & (cP_4 @ c @ c) & (cP_4 @ b @ b) & (cP_4 @ a @ a) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_4 @ X3 @ X4 @ X5) | ~(cP_3 @ (f @ X2) @ X5) | ~(cP_3 @ (f @ X1) @ X4) | ~(cP_3 @ (f @ X0) @ X3) | ~(cQ_3 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_3 @ (f @ X0) @ X1) | ~(cP_3 @ X0 @ X1)) & ! [X0 : $i] : (cP_3 @ d @ X0) & (cP_3 @ c @ c) & (cP_3 @ b @ b) & (cP_3 @ a @ a) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_3 @ X3 @ X4 @ X5) | ~(cP_2 @ (f @ X2) @ X5) | ~(cP_2 @ (f @ X1) @ X4) | ~(cP_2 @ (f @ X0) @ X3) | ~(cQ_2 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_2 @ (f @ X0) @ X1) | ~(cP_2 @ X0 @ X1)) & ! [X0 : $i] : (cP_2 @ d @ X0) & (cP_2 @ c @ c) & (cP_2 @ b @ b) & (cP_2 @ a @ a) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_2 @ X3 @ X4 @ X5) | ~(cP_1 @ (f @ X2) @ X5) | ~(cP_1 @ (f @ X1) @ X4) | ~(cP_1 @ (f @ X0) @ X3) | ~(cQ_1 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_1 @ (f @ X0) @ X1) | ~(cP_1 @ X0 @ X1)) & ! [X0 : $i] : (cP_1 @ d @ X0) & (cP_1 @ c @ c) & (cP_1 @ b @ b) & (cP_1 @ a @ a) & (cQ_1 @ a @ b @ c))),
% 6.47/1.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM409_5)).
% 6.47/1.14 thf(f2,negated_conjecture,(
% 6.47/1.14 ~ ~(! [X0 : $i,X1 : $i,X2 : $i] : ~(cQ_6 @ X0 @ X1 @ X2) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_6 @ X3 @ X4 @ X5) | ~(cP_5 @ (f @ X2) @ X5) | ~(cP_5 @ (f @ X1) @ X4) | ~(cP_5 @ (f @ X0) @ X3) | ~(cQ_5 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_5 @ (f @ X0) @ X1) | ~(cP_5 @ X0 @ X1)) & ! [X0 : $i] : (cP_5 @ d @ X0) & (cP_5 @ c @ c) & (cP_5 @ b @ b) & (cP_5 @ a @ a) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_5 @ X3 @ X4 @ X5) | ~(cP_4 @ (f @ X2) @ X5) | ~(cP_4 @ (f @ X1) @ X4) | ~(cP_4 @ (f @ X0) @ X3) | ~(cQ_4 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_4 @ (f @ X0) @ X1) | ~(cP_4 @ X0 @ X1)) & ! [X0 : $i] : (cP_4 @ d @ X0) & (cP_4 @ c @ c) & (cP_4 @ b @ b) & (cP_4 @ a @ a) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_4 @ X3 @ X4 @ X5) | ~(cP_3 @ (f @ X2) @ X5) | ~(cP_3 @ (f @ X1) @ X4) | ~(cP_3 @ (f @ X0) @ X3) | ~(cQ_3 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_3 @ (f @ X0) @ X1) | ~(cP_3 @ X0 @ X1)) & ! [X0 : $i] : (cP_3 @ d @ X0) & (cP_3 @ c @ c) & (cP_3 @ b @ b) & (cP_3 @ a @ a) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_3 @ X3 @ X4 @ X5) | ~(cP_2 @ (f @ X2) @ X5) | ~(cP_2 @ (f @ X1) @ X4) | ~(cP_2 @ (f @ X0) @ X3) | ~(cQ_2 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_2 @ (f @ X0) @ X1) | ~(cP_2 @ X0 @ X1)) & ! [X0 : $i] : (cP_2 @ d @ X0) & (cP_2 @ c @ c) & (cP_2 @ b @ b) & (cP_2 @ a @ a) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_2 @ X3 @ X4 @ X5) | ~(cP_1 @ (f @ X2) @ X5) | ~(cP_1 @ (f @ X1) @ X4) | ~(cP_1 @ (f @ X0) @ X3) | ~(cQ_1 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_1 @ (f @ X0) @ X1) | ~(cP_1 @ X0 @ X1)) & ! [X0 : $i] : (cP_1 @ d @ X0) & (cP_1 @ c @ c) & (cP_1 @ b @ b) & (cP_1 @ a @ a) & (cQ_1 @ a @ b @ c))),
% 6.47/1.14 inference(negated_conjecture,[status(cth)],[f1])).
% 6.47/1.14 thf(f3,plain,(
% 6.47/1.14 ~ ~(! [X0 : $i,X1 : $i,X2 : $i] : ~(cQ_6 @ X0 @ X1 @ X2) & ! [X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i,X8 : $i] : ((cQ_6 @ X6 @ X7 @ X8) | ~(cP_5 @ (f @ X5) @ X8) | ~(cP_5 @ (f @ X4) @ X7) | ~(cP_5 @ (f @ X3) @ X6) | ~(cQ_5 @ X3 @ X4 @ X5)) & ! [X9 : $i,X10 : $i] : ((cP_5 @ (f @ X9) @ X10) | ~(cP_5 @ X9 @ X10)) & ! [X11 : $i] : (cP_5 @ d @ X11) & (cP_5 @ c @ c) & (cP_5 @ b @ b) & (cP_5 @ a @ a) & ! [X12 : $i,X13 : $i,X14 : $i,X15 : $i,X16 : $i,X17 : $i] : ((cQ_5 @ X15 @ X16 @ X17) | ~(cP_4 @ (f @ X14) @ X17) | ~(cP_4 @ (f @ X13) @ X16) | ~(cP_4 @ (f @ X12) @ X15) | ~(cQ_4 @ X12 @ X13 @ X14)) & ! [X18 : $i,X19 : $i] : ((cP_4 @ (f @ X18) @ X19) | ~(cP_4 @ X18 @ X19)) & ! [X20 : $i] : (cP_4 @ d @ X20) & (cP_4 @ c @ c) & (cP_4 @ b @ b) & (cP_4 @ a @ a) & ! [X21 : $i,X22 : $i,X23 : $i,X24 : $i,X25 : $i,X26 : $i] : ((cQ_4 @ X24 @ X25 @ X26) | ~(cP_3 @ (f @ X23) @ X26) | ~(cP_3 @ (f @ X22) @ X25) | ~(cP_3 @ (f @ X21) @ X24) | ~(cQ_3 @ X21 @ X22 @ X23)) & ! [X27 : $i,X28 : $i] : ((cP_3 @ (f @ X27) @ X28) | ~(cP_3 @ X27 @ X28)) & ! [X29 : $i] : (cP_3 @ d @ X29) & (cP_3 @ c @ c) & (cP_3 @ b @ b) & (cP_3 @ a @ a) & ! [X30 : $i,X31 : $i,X32 : $i,X33 : $i,X34 : $i,X35 : $i] : ((cQ_3 @ X33 @ X34 @ X35) | ~(cP_2 @ (f @ X32) @ X35) | ~(cP_2 @ (f @ X31) @ X34) | ~(cP_2 @ (f @ X30) @ X33) | ~(cQ_2 @ X30 @ X31 @ X32)) & ! [X36 : $i,X37 : $i] : ((cP_2 @ (f @ X36) @ X37) | ~(cP_2 @ X36 @ X37)) & ! [X38 : $i] : (cP_2 @ d @ X38) & (cP_2 @ c @ c) & (cP_2 @ b @ b) & (cP_2 @ a @ a) & ! [X39 : $i,X40 : $i,X41 : $i,X42 : $i,X43 : $i,X44 : $i] : ((cQ_2 @ X42 @ X43 @ X44) | ~(cP_1 @ (f @ X41) @ X44) | ~(cP_1 @ (f @ X40) @ X43) | ~(cP_1 @ (f @ X39) @ X42) | ~(cQ_1 @ X39 @ X40 @ X41)) & ! [X45 : $i,X46 : $i] : ((cP_1 @ (f @ X45) @ X46) | ~(cP_1 @ X45 @ X46)) & ! [X47 : $i] : (cP_1 @ d @ X47) & (cP_1 @ c @ c) & (cP_1 @ b @ b) & (cP_1 @ a @ a) & (cQ_1 @ a @ b @ c))),
% 6.47/1.14 inference(rectify,[],[f2])).
% 6.47/1.14 thf(f4,plain,(
% 6.47/1.14 ~ ~(! [X0 : $i,X1 : $i,X2 : $i] : ~ (((cQ_6 @ X0 @ X1 @ X2)) = $true) & ! [X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i,X8 : $i] : ((((cQ_6 @ X6 @ X7 @ X8)) = $true) | ~ (((cP_5 @ (f @ X5) @ X8)) = $true) | ~ (((cP_5 @ (f @ X4) @ X7)) = $true) | ~ (((cP_5 @ (f @ X3) @ X6)) = $true) | ~ (((cQ_5 @ X3 @ X4 @ X5)) = $true)) & ! [X9 : $i,X10 : $i] : ((((cP_5 @ (f @ X9) @ X10)) = $true) | ~ (((cP_5 @ X9 @ X10)) = $true)) & ! [X11 : $i] : (((cP_5 @ d @ X11)) = $true) & (((cP_5 @ c @ c)) = $true) & (((cP_5 @ b @ b)) = $true) & (((cP_5 @ a @ a)) = $true) & ! [X12 : $i,X13 : $i,X14 : $i,X15 : $i,X16 : $i,X17 : $i] : ((((cQ_5 @ X15 @ X16 @ X17)) = $true) | ~ (((cP_4 @ (f @ X14) @ X17)) = $true) | ~ (((cP_4 @ (f @ X13) @ X16)) = $true) | ~ (((cP_4 @ (f @ X12) @ X15)) = $true) | ~ (((cQ_4 @ X12 @ X13 @ X14)) = $true)) & ! [X18 : $i,X19 : $i] : ((((cP_4 @ (f @ X18) @ X19)) = $true) | ~ (((cP_4 @ X18 @ X19)) = $true)) & ! [X20 : $i] : (((cP_4 @ d @ X20)) = $true) & (((cP_4 @ c @ c)) = $true) & (((cP_4 @ b @ b)) = $true) & (((cP_4 @ a @ a)) = $true) & ! [X21 : $i,X22 : $i,X23 : $i,X24 : $i,X25 : $i,X26 : $i] : ((((cQ_4 @ X24 @ X25 @ X26)) = $true) | ~ (((cP_3 @ (f @ X23) @ X26)) = $true) | ~ (((cP_3 @ (f @ X22) @ X25)) = $true) | ~ (((cP_3 @ (f @ X21) @ X24)) = $true) | ~ (((cQ_3 @ X21 @ X22 @ X23)) = $true)) & ! [X27 : $i,X28 : $i] : ((((cP_3 @ (f @ X27) @ X28)) = $true) | ~ (((cP_3 @ X27 @ X28)) = $true)) & ! [X29 : $i] : (((cP_3 @ d @ X29)) = $true) & (((cP_3 @ c @ c)) = $true) & (((cP_3 @ b @ b)) = $true) & (((cP_3 @ a @ a)) = $true) & ! [X30 : $i,X31 : $i,X32 : $i,X33 : $i,X34 : $i,X35 : $i] : ((((cQ_3 @ X33 @ X34 @ X35)) = $true) | ~ (((cP_2 @ (f @ X32) @ X35)) = $true) | ~ (((cP_2 @ (f @ X31) @ X34)) = $true) | ~ (((cP_2 @ (f @ X30) @ X33)) = $true) | ~ (((cQ_2 @ X30 @ X31 @ X32)) = $true)) & ! [X36 : $i,X37 : $i] : ((((cP_2 @ (f @ X36) @ X37)) = $true) | ~ (((cP_2 @ X36 @ X37)) = $true)) & ! [X38 : $i] : (((cP_2 @ d @ X38)) = $true) & (((cP_2 @ c @ c)) = $true) & (((cP_2 @ b @ b)) = $true) & (((cP_2 @ a @ a)) = $true) & ! [X39 : $i,X40 : $i,X41 : $i,X42 : $i,X43 : $i,X44 : $i] : ((((cQ_2 @ X42 @ X43 @ X44)) = $true) | ~ (((cP_1 @ (f @ X41) @ X44)) = $true) | ~ (((cP_1 @ (f @ X40) @ X43)) = $true) | ~ (((cP_1 @ (f @ X39) @ X42)) = $true) | ~ (((cQ_1 @ X39 @ X40 @ X41)) = $true)) & ! [X45 : $i,X46 : $i] : ((((cP_1 @ (f @ X45) @ X46)) = $true) | ~ (((cP_1 @ X45 @ X46)) = $true)) & ! [X47 : $i] : (((cP_1 @ d @ X47)) = $true) & (((cP_1 @ c @ c)) = $true) & (((cP_1 @ b @ b)) = $true) & (((cP_1 @ a @ a)) = $true) & (((cQ_1 @ a @ b @ c)) = $true))),
% 6.47/1.14 inference(fool_elimination,[],[f3])).
% 6.47/1.14 thf(f5,plain,(
% 6.47/1.14 ! [X0 : $i,X1 : $i,X2 : $i] : (((cQ_6 @ X0 @ X1 @ X2)) != $true) & ! [X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i,X8 : $i] : ((((cQ_6 @ X6 @ X7 @ X8)) = $true) | (((cP_5 @ (f @ X5) @ X8)) != $true) | (((cP_5 @ (f @ X4) @ X7)) != $true) | (((cP_5 @ (f @ X3) @ X6)) != $true) | (((cQ_5 @ X3 @ X4 @ X5)) != $true)) & ! [X9 : $i,X10 : $i] : ((((cP_5 @ (f @ X9) @ X10)) = $true) | (((cP_5 @ X9 @ X10)) != $true)) & ! [X11 : $i] : (((cP_5 @ d @ X11)) = $true) & (((cP_5 @ c @ c)) = $true) & (((cP_5 @ b @ b)) = $true) & (((cP_5 @ a @ a)) = $true) & ! [X12 : $i,X13 : $i,X14 : $i,X15 : $i,X16 : $i,X17 : $i] : ((((cQ_5 @ X15 @ X16 @ X17)) = $true) | (((cP_4 @ (f @ X14) @ X17)) != $true) | (((cP_4 @ (f @ X13) @ X16)) != $true) | (((cP_4 @ (f @ X12) @ X15)) != $true) | (((cQ_4 @ X12 @ X13 @ X14)) != $true)) & ! [X18 : $i,X19 : $i] : ((((cP_4 @ (f @ X18) @ X19)) = $true) | (((cP_4 @ X18 @ X19)) != $true)) & ! [X20 : $i] : (((cP_4 @ d @ X20)) = $true) & (((cP_4 @ c @ c)) = $true) & (((cP_4 @ b @ b)) = $true) & (((cP_4 @ a @ a)) = $true) & ! [X21 : $i,X22 : $i,X23 : $i,X24 : $i,X25 : $i,X26 : $i] : ((((cQ_4 @ X24 @ X25 @ X26)) = $true) | (((cP_3 @ (f @ X23) @ X26)) != $true) | (((cP_3 @ (f @ X22) @ X25)) != $true) | (((cP_3 @ (f @ X21) @ X24)) != $true) | (((cQ_3 @ X21 @ X22 @ X23)) != $true)) & ! [X27 : $i,X28 : $i] : ((((cP_3 @ (f @ X27) @ X28)) = $true) | (((cP_3 @ X27 @ X28)) != $true)) & ! [X29 : $i] : (((cP_3 @ d @ X29)) = $true) & (((cP_3 @ c @ c)) = $true) & (((cP_3 @ b @ b)) = $true) & (((cP_3 @ a @ a)) = $true) & ! [X30 : $i,X31 : $i,X32 : $i,X33 : $i,X34 : $i,X35 : $i] : ((((cQ_3 @ X33 @ X34 @ X35)) = $true) | (((cP_2 @ (f @ X32) @ X35)) != $true) | (((cP_2 @ (f @ X31) @ X34)) != $true) | (((cP_2 @ (f @ X30) @ X33)) != $true) | (((cQ_2 @ X30 @ X31 @ X32)) != $true)) & ! [X36 : $i,X37 : $i] : ((((cP_2 @ (f @ X36) @ X37)) = $true) | (((cP_2 @ X36 @ X37)) != $true)) & ! [X38 : $i] : (((cP_2 @ d @ X38)) = $true) & (((cP_2 @ c @ c)) = $true) & (((cP_2 @ b @ b)) = $true) & (((cP_2 @ a @ a)) = $true) & ! [X39 : $i,X40 : $i,X41 : $i,X42 : $i,X43 : $i,X44 : $i] : ((((cQ_2 @ X42 @ X43 @ X44)) = $true) | (((cP_1 @ (f @ X41) @ X44)) != $true) | (((cP_1 @ (f @ X40) @ X43)) != $true) | (((cP_1 @ (f @ X39) @ X42)) != $true) | (((cQ_1 @ X39 @ X40 @ X41)) != $true)) & ! [X45 : $i,X46 : $i] : ((((cP_1 @ (f @ X45) @ X46)) = $true) | (((cP_1 @ X45 @ X46)) != $true)) & ! [X47 : $i] : (((cP_1 @ d @ X47)) = $true) & (((cP_1 @ c @ c)) = $true) & (((cP_1 @ b @ b)) = $true) & (((cP_1 @ a @ a)) = $true) & (((cQ_1 @ a @ b @ c)) = $true)),
% 6.47/1.14 inference(flattening,[],[f4])).
% 6.47/1.14 thf(f6,plain,(
% 6.47/1.14 (((cQ_1 @ a @ b @ c)) = $true)),
% 6.47/1.14 inference(cnf_transformation,[],[f5])).
% 6.47/1.14 thf(f7,plain,(
% 6.47/1.14 (((cP_1 @ a @ a)) = $true)),
% 6.47/1.14 inference(cnf_transformation,[],[f5])).
% 6.47/1.14 thf(f8,plain,(
% 6.47/1.14 (((cP_1 @ b @ b)) = $true)),
% 6.47/1.14 inference(cnf_transformation,[],[f5])).
% 6.47/1.14 thf(f9,plain,(
% 6.47/1.14 (((cP_1 @ c @ c)) = $true)),
% 6.47/1.14 inference(cnf_transformation,[],[f5])).
% 6.47/1.14 thf(f11,plain,(
% 6.47/1.14 ( ! [X46 : $i,X45 : $i] : ((((cP_1 @ X45 @ X46)) != $true) | (((cP_1 @ (f @ X45) @ X46)) = $true)) )),
% 6.47/1.14 inference(cnf_transformation,[],[f5])).
% 6.47/1.14 thf(f12,plain,(
% 6.47/1.14 ( ! [X40 : $i,X41 : $i,X39 : $i,X44 : $i,X42 : $i,X43 : $i] : ((((cQ_1 @ X39 @ X40 @ X41)) != $true) | (((cP_1 @ (f @ X41) @ X44)) != $true) | (((cP_1 @ (f @ X40) @ X43)) != $true) | (((cP_1 @ (f @ X39) @ X42)) != $true) | (((cQ_2 @ X42 @ X43 @ X44)) = $true)) )),
% 6.47/1.14 inference(cnf_transformation,[],[f5])).
% 6.47/1.14 thf(f13,plain,(
% 6.47/1.14 (((cP_2 @ a @ a)) = $true)),
% 6.47/1.14 inference(cnf_transformation,[],[f5])).
% 6.47/1.14 thf(f14,plain,(
% 6.47/1.14 (((cP_2 @ b @ b)) = $true)),
% 6.47/1.14 inference(cnf_transformation,[],[f5])).
% 6.47/1.14 thf(f15,plain,(
% 6.47/1.14 (((cP_2 @ c @ c)) = $true)),
% 6.47/1.14 inference(cnf_transformation,[],[f5])).
% 6.47/1.14 thf(f17,plain,(
% 6.47/1.14 ( ! [X36 : $i,X37 : $i] : ((((cP_2 @ X36 @ X37)) != $true) | (((cP_2 @ (f @ X36) @ X37)) = $true)) )),
% 6.47/1.14 inference(cnf_transformation,[],[f5])).
% 6.47/1.14 thf(f18,plain,(
% 6.47/1.14 ( ! [X31 : $i,X34 : $i,X35 : $i,X32 : $i,X30 : $i,X33 : $i] : ((((cQ_2 @ X30 @ X31 @ X32)) != $true) | (((cP_2 @ (f @ X32) @ X35)) != $true) | (((cP_2 @ (f @ X31) @ X34)) != $true) | (((cP_2 @ (f @ X30) @ X33)) != $true) | (((cQ_3 @ X33 @ X34 @ X35)) = $true)) )),
% 6.47/1.14 inference(cnf_transformation,[],[f5])).
% 6.47/1.14 thf(f19,plain,(
% 6.47/1.14 (((cP_3 @ a @ a)) = $true)),
% 6.47/1.14 inference(cnf_transformation,[],[f5])).
% 6.47/1.14 thf(f20,plain,(
% 6.47/1.14 (((cP_3 @ b @ b)) = $true)),
% 6.47/1.14 inference(cnf_transformation,[],[f5])).
% 6.47/1.14 thf(f21,plain,(
% 6.47/1.14 (((cP_3 @ c @ c)) = $true)),
% 6.47/1.14 inference(cnf_transformation,[],[f5])).
% 6.47/1.14 thf(f23,plain,(
% 6.47/1.14 ( ! [X28 : $i,X27 : $i] : ((((cP_3 @ X27 @ X28)) != $true) | (((cP_3 @ (f @ X27) @ X28)) = $true)) )),
% 6.47/1.14 inference(cnf_transformation,[],[f5])).
% 6.47/1.14 thf(f24,plain,(
% 6.47/1.14 ( ! [X21 : $i,X26 : $i,X24 : $i,X22 : $i,X25 : $i,X23 : $i] : ((((cQ_3 @ X21 @ X22 @ X23)) != $true) | (((cP_3 @ (f @ X23) @ X26)) != $true) | (((cP_3 @ (f @ X22) @ X25)) != $true) | (((cP_3 @ (f @ X21) @ X24)) != $true) | (((cQ_4 @ X24 @ X25 @ X26)) = $true)) )),
% 6.47/1.14 inference(cnf_transformation,[],[f5])).
% 6.47/1.14 thf(f25,plain,(
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% 6.47/1.14 inference(cnf_transformation,[],[f5])).
% 6.47/1.14 thf(f26,plain,(
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% 6.47/1.14 inference(cnf_transformation,[],[f5])).
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% 6.47/1.14 inference(cnf_transformation,[],[f5])).
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% 6.47/1.14 inference(cnf_transformation,[],[f5])).
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% 6.47/1.14 thf(f39,definition,(
% 6.47/1.14 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 6.47/1.14 introduced(theory,[fool_exhaustiveness_axiom])).
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% 6.47/1.14 inference(trivial_inequality_removal,[],[f42])).
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% 6.47/1.14 inference(trivial_inequality_removal,[],[f41])).
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% 6.47/1.14 inference(trivial_inequality_removal,[],[f52])).
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% 6.47/1.14 inference(trivial_inequality_removal,[],[f62])).
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% 6.47/1.14 inference(trivial_inequality_removal,[],[f61])).
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% 6.47/1.14 inference(constrained_superposition,[],[f29,f26])).
% 6.47/1.14 thf(f71,plain,(
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% 6.47/1.14 inference(trivial_inequality_removal,[],[f70])).
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% 6.47/1.14 inference(trivial_inequality_removal,[],[f69])).
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% 6.47/1.14 inference(constrained_superposition,[],[f35,f32])).
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% 6.47/1.14 inference(trivial_inequality_removal,[],[f79])).
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% 6.47/1.14 inference(constrained_superposition,[],[f12,f6])).
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% 6.47/1.14 inference(trivial_inequality_removal,[],[f107])).
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% 6.47/1.14 inference(constrained_superposition,[],[f18,f39])).
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% 6.47/1.14 inference(constrained_superposition,[],[f232,f64])).
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% 6.47/1.14 inference(trivial_inequality_removal,[],[f848])).
% 6.47/1.14 thf(f958,plain,(
% 6.47/1.14 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((cP_4 @ (f @ X0) @ X1)) != $true) | ($true = ((cQ_5 @ a @ X1 @ c))) | ($false = ((cQ_4 @ a @ X0 @ c)))) )),
% 6.47/1.14 inference(constrained_superposition,[],[f244,f72])).
% 6.47/1.14 thf(f965,plain,(
% 6.47/1.14 ( ! [X0 : $i,X1 : $i] : ((((cP_4 @ (f @ X0) @ X1)) != $true) | ($true = ((cQ_5 @ a @ X1 @ c))) | ($false = ((cQ_4 @ a @ X0 @ c)))) )),
% 6.47/1.14 inference(trivial_inequality_removal,[],[f958])).
% 6.47/1.14 thf(f1410,plain,(
% 6.47/1.14 ($true != $true) | ($true = ((cQ_2 @ a @ b @ c)))),
% 6.47/1.14 inference(constrained_superposition,[],[f359,f46])).
% 6.47/1.14 thf(f1413,plain,(
% 6.47/1.14 ($true = ((cQ_2 @ a @ b @ c)))),
% 6.47/1.14 inference(trivial_inequality_removal,[],[f1410])).
% 6.47/1.14 thf(f1621,plain,(
% 6.47/1.14 ($true != $true) | ($false = ((cQ_5 @ a @ b @ c)))),
% 6.47/1.14 inference(constrained_superposition,[],[f412,f82])).
% 6.47/1.14 thf(f1628,plain,(
% 6.47/1.14 ($false = ((cQ_5 @ a @ b @ c)))),
% 6.47/1.14 inference(trivial_inequality_removal,[],[f1621])).
% 6.47/1.14 thf(f6128,plain,(
% 6.47/1.14 ($true != $true) | ($true = ((cQ_3 @ a @ b @ c))) | ($false = ((cQ_2 @ a @ b @ c)))),
% 6.47/1.14 inference(constrained_superposition,[],[f723,f55])).
% 6.47/1.14 thf(f6141,plain,(
% 6.47/1.14 ($true = ((cQ_3 @ a @ b @ c))) | ($false = ((cQ_2 @ a @ b @ c)))),
% 6.47/1.14 inference(trivial_inequality_removal,[],[f6128])).
% 6.47/1.14 thf(f6175,definition,(
% 6.47/1.14 spl0_386 <=> ($true = ((cQ_3 @ a @ b @ c)))),
% 6.47/1.14 introduced(definition,[new_symbols(definition,[spl0_386])],[avatar_definition])).
% 6.47/1.14 thf(f6177,plain,(
% 6.47/1.14 ($true = ((cQ_3 @ a @ b @ c))) | ~spl0_386),
% 6.47/1.14 inference(avatar_component_clause,[],[f6175])).
% 6.47/1.14 thf(f6185,definition,(
% 6.47/1.14 spl0_388 <=> ($false = ((cQ_2 @ a @ b @ c)))),
% 6.47/1.14 introduced(definition,[new_symbols(definition,[spl0_388])],[avatar_definition])).
% 6.47/1.14 thf(f6187,plain,(
% 6.47/1.14 ($false = ((cQ_2 @ a @ b @ c))) | ~spl0_388),
% 6.47/1.14 inference(avatar_component_clause,[],[f6185])).
% 6.47/1.14 thf(f6188,plain,(
% 6.47/1.14 spl0_388 | spl0_386),
% 6.47/1.14 inference(avatar_split_clause,[],[f6141,f6175,f6185])).
% 6.47/1.14 thf(f7849,plain,(
% 6.47/1.14 ($true != $true) | ($true = ((cQ_4 @ a @ b @ c))) | ($false = ((cQ_3 @ a @ b @ c)))),
% 6.47/1.14 inference(constrained_superposition,[],[f855,f65])).
% 6.47/1.14 thf(f7862,plain,(
% 6.47/1.14 ($true = ((cQ_4 @ a @ b @ c))) | ($false = ((cQ_3 @ a @ b @ c)))),
% 6.47/1.14 inference(trivial_inequality_removal,[],[f7849])).
% 6.47/1.14 thf(f7896,definition,(
% 6.47/1.14 spl0_642 <=> ($true = ((cQ_4 @ a @ b @ c)))),
% 6.47/1.14 introduced(definition,[new_symbols(definition,[spl0_642])],[avatar_definition])).
% 6.47/1.14 thf(f7898,plain,(
% 6.47/1.14 ($true = ((cQ_4 @ a @ b @ c))) | ~spl0_642),
% 6.47/1.14 inference(avatar_component_clause,[],[f7896])).
% 6.47/1.14 thf(f7906,definition,(
% 6.47/1.14 spl0_644 <=> ($false = ((cQ_3 @ a @ b @ c)))),
% 6.47/1.14 introduced(definition,[new_symbols(definition,[spl0_644])],[avatar_definition])).
% 6.47/1.14 thf(f7908,plain,(
% 6.47/1.14 ($false = ((cQ_3 @ a @ b @ c))) | ~spl0_644),
% 6.47/1.14 inference(avatar_component_clause,[],[f7906])).
% 6.47/1.14 thf(f7909,plain,(
% 6.47/1.14 spl0_644 | spl0_642),
% 6.47/1.14 inference(avatar_split_clause,[],[f7862,f7896,f7906])).
% 6.47/1.14 thf(f9333,plain,(
% 6.47/1.14 ($true != $true) | ($true = ((cQ_5 @ a @ b @ c))) | ($false = ((cQ_4 @ a @ b @ c)))),
% 6.47/1.14 inference(constrained_superposition,[],[f965,f73])).
% 6.47/1.14 thf(f9346,plain,(
% 6.47/1.14 ($true = ((cQ_5 @ a @ b @ c))) | ($false = ((cQ_4 @ a @ b @ c)))),
% 6.47/1.14 inference(trivial_inequality_removal,[],[f9333])).
% 6.47/1.14 thf(f9366,plain,(
% 6.47/1.14 ($true = $false) | ($false = ((cQ_4 @ a @ b @ c)))),
% 6.47/1.14 inference(forward_demodulation,[],[f9346,f1628])).
% 6.47/1.14 thf(f9367,plain,(
% 6.47/1.14 ($false = ((cQ_4 @ a @ b @ c)))),
% 6.47/1.14 inference(trivial_inequality_removal,[],[f9366])).
% 6.47/1.14 thf(f29094,plain,(
% 6.47/1.14 ($true = $false) | ~spl0_642),
% 6.47/1.14 inference(constrained_superposition,[],[f9367,f7898])).
% 6.47/1.14 thf(f29104,plain,(
% 6.47/1.14 $false | ~spl0_642),
% 6.47/1.14 inference(trivial_inequality_removal,[],[f29094])).
% 6.47/1.14 thf(f29105,plain,(
% 6.47/1.14 ~spl0_642),
% 6.47/1.14 inference(avatar_contradiction_clause,[],[f29104])).
% 6.47/1.14 thf(f29110,plain,(
% 6.47/1.14 ($true = $false) | (~spl0_386 | ~spl0_644)),
% 6.47/1.14 inference(constrained_superposition,[],[f7908,f6177])).
% 6.47/1.14 thf(f29120,plain,(
% 6.47/1.14 $false | (~spl0_386 | ~spl0_644)),
% 6.47/1.14 inference(trivial_inequality_removal,[],[f29110])).
% 6.47/1.14 thf(f29121,plain,(
% 6.47/1.14 ~spl0_386 | ~spl0_644),
% 6.47/1.14 inference(avatar_contradiction_clause,[],[f29120])).
% 6.47/1.14 thf(f29126,plain,(
% 6.47/1.14 ($true = $false) | ~spl0_388),
% 6.47/1.14 inference(constrained_superposition,[],[f6187,f1413])).
% 6.47/1.14 thf(f29136,plain,(
% 6.47/1.14 $false | ~spl0_388),
% 6.47/1.14 inference(trivial_inequality_removal,[],[f29126])).
% 6.47/1.14 thf(f29137,plain,(
% 6.47/1.14 ~spl0_388),
% 6.47/1.14 inference(avatar_contradiction_clause,[],[f29136])).
% 6.47/1.14 cnf(s291, plain, spl0_386 | spl0_388, inference(sat_conversion,[],[f6188])).
% 6.47/1.14 cnf(s483, plain, spl0_642 | spl0_644, inference(sat_conversion,[],[f7909])).
% 6.47/1.14 cnf(s2338, plain, ~spl0_642, inference(sat_conversion,[],[f29105])).
% 6.47/1.14 cnf(s2342, plain, ~spl0_386 | ~spl0_644, inference(sat_conversion,[],[f29121])).
% 6.47/1.14 cnf(s2346, plain, ~spl0_388, inference(sat_conversion,[],[f29137])).
% 6.47/1.14 cnf(s2662, plain, spl0_644, inference(rat,[],[s483,s2338])).
% 6.47/1.14 cnf(s2664, plain, ~spl0_386, inference(rat,[],[s2342,s2662])).
% 6.47/1.14 cnf(s3036, plain, $false, inference(rat,[],[s291,s2346,s2664])).
% 6.47/1.14 thf(f29140,plain,(
% 6.47/1.14 $false),
% 6.47/1.14 inference(avatar_sat_refutation,[],[s3036])).
% 6.47/1.14 % SZS output end Proof for theBenchmark
% 6.47/1.14 % (1300593)------------------------------
% 6.47/1.14 % (1300593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.47/1.14 % (1300593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.47/1.14 % (1300593)CaDiCaL version: 2.1.3
% 6.47/1.14 % (1300593)Termination reason: Refutation
% 6.47/1.14 % (1300593)Time elapsed: 0.886 s
% 6.47/1.14 % (1300593)Peak memory usage: 22 MB
% 6.47/1.14 % (1300593)Instructions burned: 3636 (million)
% 6.47/1.14 % (1300587)Success in time 0.903 s
% 6.47/1.14 % Vampire exiting
%------------------------------------------------------------------------------