%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP103^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 08:10:42 AM UTC 2026
% Result : Theorem 13.67s 2.28s
% Output : Refutation 13.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP103^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n002.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:56:38 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 5.64/1.15 % (1768299)Will run a generic schedule for satisfiability detection.
% 5.64/1.15 % (1768305)% WARNING: option uhcvi not known.
% 5.64/1.15 % (1768305)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3608964610:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.64/1.15 % (1768304)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2013083310_2999 on theBenchmark for (2999ds/0Mi)
% 5.64/1.15 % (1768305)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.64/1.15 % (1768307)dis+10_1_sil=32000:sp=arity:random_seed=18037591:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.64/1.15 % (1768310)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1562867511:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.64/1.15 % (1768306)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4234918661:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.64/1.15 % (1768305)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.64/1.15 % (1768308)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2526563376:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.64/1.15 % (1768309)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=532535672:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.64/1.15 % Exception at run slice level
% 5.64/1.15 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.64/1.15 % (1768308)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.64/1.15 % (1768318)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3060619574:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.64/1.15 % (1768307)Instruction limit reached!
% 5.64/1.15 % (1768307)------------------------------
% 5.64/1.15 % (1768307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.64/1.15 % (1768307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.15 % (1768307)CaDiCaL version: 2.1.3
% 5.64/1.15 % (1768307)Termination reason: Instruction limit
% 5.64/1.15 % (1768307)Termination phase: Saturation
% 5.64/1.15 % (1768307)Time elapsed: 0.047 s
% 5.64/1.15 % (1768307)Peak memory usage: 13 MB
% 5.64/1.15 % (1768307)Instructions burned: 103 (million)
% 5.64/1.15 % (1768320)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4288530236:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 5.64/1.15 % Exception at run slice level
% 5.64/1.15 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.64/1.15 % (1768310)Instruction limit reached!
% 5.64/1.15 % (1768310)------------------------------
% 5.64/1.15 % (1768310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.64/1.15 % (1768310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.15 % (1768310)CaDiCaL version: 2.1.3
% 5.64/1.15 % (1768310)Termination reason: Instruction limit
% 5.64/1.15 % (1768310)Termination phase: Saturation
% 5.64/1.15 % (1768310)Time elapsed: 0.076 s
% 5.64/1.15 % (1768310)Peak memory usage: 14 MB
% 5.64/1.15 % (1768310)Instructions burned: 160 (million)
% 5.64/1.15 % (1768322)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=1086124668:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 5.64/1.15 % (1768323)ott-21_1_sil=16000:fs=off:random_seed=2270968459:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 5.64/1.15 % (1768308)Instruction limit reached!
% 5.64/1.15 % (1768308)------------------------------
% 5.64/1.15 % (1768308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.64/1.15 % (1768308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.15 % (1768308)CaDiCaL version: 2.1.3
% 5.64/1.15 % (1768308)Termination reason: Instruction limit
% 5.64/1.15 % (1768308)Termination phase: Saturation
% 5.64/1.15 % (1768308)Time elapsed: 0.094 s
% 5.64/1.15 % (1768308)Peak memory usage: 13 MB
% 5.64/1.15 % (1768308)Instructions burned: 117 (million)
% 5.64/1.15 % (1768322)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.64/1.15 % (1768322)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.64/1.15 % (1768326)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2408972641:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 13.67/2.28 % (1768309)Instruction limit reached!
% 13.67/2.28 % (1768309)------------------------------
% 13.67/2.28 % (1768309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.28 % (1768309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.28 % (1768309)CaDiCaL version: 2.1.3
% 13.67/2.28 % (1768309)Termination reason: Instruction limit
% 13.67/2.28 % (1768309)Termination phase: Saturation
% 13.67/2.28 % (1768309)Time elapsed: 0.110 s
% 13.67/2.28 % (1768309)Peak memory usage: 13 MB
% 13.67/2.28 % (1768309)Instructions burned: 131 (million)
% 13.67/2.28 % (1768320)Instruction limit reached!
% 13.67/2.28 % (1768320)------------------------------
% 13.67/2.28 % (1768320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.28 % (1768320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.28 % (1768320)CaDiCaL version: 2.1.3
% 13.67/2.28 % (1768320)Termination reason: Instruction limit
% 13.67/2.28 % (1768320)Termination phase: Saturation
% 13.67/2.28 % (1768320)Time elapsed: 0.063 s
% 13.67/2.28 % (1768320)Peak memory usage: 13 MB
% 13.67/2.28 % (1768320)Instructions burned: 131 (million)
% 13.67/2.28 % (1768328)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2505718784:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 13.67/2.28 % (1768329)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=215778944:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 13.67/2.28 % Exception at run slice level
% 13.67/2.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 13.67/2.28 % (1768323)Instruction limit reached!
% 13.67/2.28 % (1768323)------------------------------
% 13.67/2.28 % (1768323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.28 % (1768323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.28 % (1768323)CaDiCaL version: 2.1.3
% 13.67/2.28 % (1768323)Termination reason: Instruction limit
% 13.67/2.28 % (1768323)Termination phase: Saturation
% 13.67/2.28 % (1768323)Time elapsed: 0.082 s
% 13.67/2.28 % (1768323)Peak memory usage: 13 MB
% 13.67/2.28 % (1768323)Instructions burned: 181 (million)
% 13.67/2.28 % (1768332)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3597125373:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 13.67/2.28 % (1768333)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=642053416: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)
% 13.67/2.28 % (1768333)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 13.67/2.28 % Exception at run slice level
% 13.67/2.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 13.67/2.28 % (1768336)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2887325071:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 13.67/2.28 % (1768336)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 13.67/2.28 % (1768326)Instruction limit reached!
% 13.67/2.28 % (1768326)------------------------------
% 13.67/2.28 % (1768326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.28 % (1768326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.28 % (1768326)CaDiCaL version: 2.1.3
% 13.67/2.28 % (1768326)Termination reason: Instruction limit
% 13.67/2.28 % (1768326)Termination phase: Saturation
% 13.67/2.28 % (1768326)Time elapsed: 0.263 s
% 13.67/2.28 % (1768326)Peak memory usage: 14 MB
% 13.67/2.28 % (1768326)Instructions burned: 477 (million)
% 13.67/2.28 % (1768338)fmb+10_1_sil=64000:random_seed=1673252082:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 13.67/2.28 % (1768322)Instruction limit reached!
% 13.67/2.28 % (1768322)------------------------------
% 13.67/2.28 % (1768322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.28 % (1768322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.28 % (1768322)CaDiCaL version: 2.1.3
% 13.67/2.28 % (1768322)Termination reason: Instruction limit
% 13.67/2.28 % (1768322)Termination phase: Saturation
% 13.67/2.28 % (1768322)Time elapsed: 0.335 s
% 13.67/2.28 % (1768322)Peak memory usage: 16 MB
% 13.67/2.28 % (1768322)Instructions burned: 686 (million)
% 13.67/2.28 % (1768338)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 13.67/2.28 % (1768340)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1786181475:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 13.67/2.28 % Exception at run slice level
% 13.67/2.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 13.67/2.28 % (1768342)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1563639160:fmbsr=1.7:i=920_2994 on theBenchmark for (2994ds/920Mi)
% 13.67/2.28 % Exception at run slice level
% 13.67/2.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 13.67/2.28 % (1768344)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=182874200:i=5131_2994 on theBenchmark for (2994ds/5131Mi)
% 13.67/2.28 % Exception at run slice level
% 13.67/2.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 13.67/2.28 % (1768344)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 13.67/2.28 % (1768346)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1705242750:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 13.67/2.28 % (1768333)Instruction limit reached!
% 13.67/2.28 % (1768333)------------------------------
% 13.67/2.28 % (1768333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.28 % (1768333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.28 % (1768333)CaDiCaL version: 2.1.3
% 13.67/2.28 % (1768333)Termination reason: Instruction limit
% 13.67/2.28 % (1768333)Termination phase: Saturation
% 13.67/2.28 % (1768333)Time elapsed: 0.326 s
% 13.67/2.28 % (1768333)Peak memory usage: 16 MB
% 13.67/2.28 % (1768333)Instructions burned: 699 (million)
% 13.67/2.28 % (1768348)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2345509729:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 13.67/2.28 % (1768346)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 13.67/2.28 % (1768346)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 13.67/2.28 % Exception at run slice level
% 13.67/2.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 13.67/2.28 % (1768350)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1389750160:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 13.67/2.28 % Exception at run slice level
% 13.67/2.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 13.67/2.28 % (1768354)ott-2_1_sil=16000:newcnf=on:random_seed=70894763:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 13.67/2.28 % (1768354)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 13.67/2.28 % (1768336)Instruction limit reached!
% 13.67/2.28 % (1768336)------------------------------
% 13.67/2.28 % (1768336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.28 % (1768336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.28 % (1768336)CaDiCaL version: 2.1.3
% 13.67/2.28 % (1768336)Termination reason: Instruction limit
% 13.67/2.28 % (1768336)Termination phase: Saturation
% 13.67/2.28 % (1768336)Time elapsed: 0.432 s
% 13.67/2.28 % (1768336)Peak memory usage: 18 MB
% 13.67/2.28 % (1768336)Instructions burned: 880 (million)
% 13.67/2.28 % (1768356)ott+10_1_sil=32000:tgt=ground:random_seed=736951015:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 13.67/2.28 % (1768329)Instruction limit reached!
% 13.67/2.28 % (1768329)------------------------------
% 13.67/2.28 % (1768329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.28 % (1768329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.28 % (1768329)CaDiCaL version: 2.1.3
% 13.67/2.28 % (1768329)Termination reason: Instruction limit
% 13.67/2.28 % (1768329)Termination phase: Saturation
% 13.67/2.28 % (1768329)Time elapsed: 0.616 s
% 13.67/2.28 % (1768329)Peak memory usage: 16 MB
% 13.67/2.28 % (1768329)Instructions burned: 1187 (million)
% 13.67/2.28 % (1768358)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2435449806:i=54282_2991 on theBenchmark for (2991ds/54282Mi)
% 13.67/2.28 % Exception at run slice level
% 13.67/2.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 13.67/2.28 % (1768360)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=1867131596:i=3512:aac=none_2990 on theBenchmark for (2990ds/3512Mi)
% 13.67/2.28 % (1768360)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 13.67/2.28 % (1768354)Instruction limit reached!
% 13.67/2.28 % (1768354)------------------------------
% 13.67/2.28 % (1768354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.28 % (1768354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.28 % (1768354)CaDiCaL version: 2.1.3
% 13.67/2.28 % (1768354)Termination reason: Instruction limit
% 13.67/2.28 % (1768354)Termination phase: Saturation
% 13.67/2.28 % (1768354)Time elapsed: 0.341 s
% 13.67/2.28 % (1768354)Peak memory usage: 14 MB
% 13.67/2.28 % (1768354)Instructions burned: 871 (million)
% 13.67/2.28 % (1768362)dis+21_1_sil=32000:sas=cadical:random_seed=2732953698:i=3773:amm=off_2989 on theBenchmark for (2989ds/3773Mi)
% 13.67/2.28 % (1768346)Instruction limit reached!
% 13.67/2.28 % (1768346)------------------------------
% 13.67/2.28 % (1768346)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.28 % (1768346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.28 % (1768346)CaDiCaL version: 2.1.3
% 13.67/2.28 % (1768346)Termination reason: Instruction limit
% 13.67/2.28 % (1768346)Termination phase: Saturation
% 13.67/2.28 % (1768346)Time elapsed: 0.896 s
% 13.67/2.28 % (1768346)Peak memory usage: 16 MB
% 13.67/2.28 % (1768346)Instructions burned: 1473 (million)
% 13.67/2.28 % (1768364)ott+11_1_sil=16000:gs=on:random_seed=2106998160:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2985 on theBenchmark for (2985ds/2251Mi)
% 13.67/2.28 % (1768364)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 13.67/2.28 % (1768344) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1768299-1768344"...
% 13.67/2.28 % (1768344)...printing done.
% 13.67/2.28 % (1768344)Refutation found. Thanks to Tanya!
% 13.67/2.28 % SZS status Theorem for theBenchmark
% 13.67/2.28 % SZS output start Proof for theBenchmark
% 13.67/2.28 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 13.67/2.28 thf(type_def_6, type, list: $tType > $tType).
% 13.67/2.28 thf(type_def_7, type, nat: $tType).
% 13.67/2.28 thf(type_def_8, type, a: $tType).
% 13.67/2.28 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 13.67/2.28 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_1, type, size: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_2, type, zero: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_3, type, field: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_4, type, order: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_5, type, mult_zero: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_6, type, linorder: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_7, type, ordered_ring: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_8, type, wellorder: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_9, type, division_ring: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_10, type, semiring_bits: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_11, type, semidom_divide: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_12, type, semigroup_mult: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_13, type, linordered_idom: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_14, type, linordered_ring: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_15, type, ordered_semiring: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_16, type, linordered_field: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_17, type, ab_semigroup_mult: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_18, type, ordered_semiring_0: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_19, type, ordere1490568538miring: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_20, type, linord581940658strict: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_21, type, semiri1193490041visors: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_22, type, linord20386208strict: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_23, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_24, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_25, type, linord893533164strict: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_26, type, semiri1923998003cancel: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_27, type, euclid191655569cancel: !>[X0: $tType]:($o)).
% 13.67/2.28 thf(func_def_28, type, times_times: !>[X0: $tType]:((X0 > X0 > X0))).
% 13.67/2.28 thf(func_def_29, type, zero_zero: !>[X0: $tType]:(X0)).
% 13.67/2.28 thf(func_def_30, type, product: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > list @ product_prod @ X0 @ X1))).
% 13.67/2.28 thf(func_def_31, type, suc: (nat > nat)).
% 13.67/2.28 thf(func_def_32, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 13.67/2.28 thf(func_def_33, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 13.67/2.28 thf(func_def_34, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 13.67/2.28 thf(func_def_35, type, divide_divide: !>[X0: $tType]:((X0 > X0 > X0))).
% 13.67/2.28 thf(func_def_36, type, k: nat).
% 13.67/2.28 thf(func_def_37, type, n: nat).
% 13.67/2.28 thf(func_def_38, type, xs: list @ a).
% 13.67/2.28 thf(func_def_42, type, vAND: ($o > $o > $o)).
% 13.67/2.28 thf(func_def_43, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 13.67/2.28 thf(func_def_44, type, vNOT: ($o > $o)).
% 13.67/2.28 thf(func_def_45, type, vOR: ($o > $o > $o)).
% 13.67/2.28 thf(func_def_46, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 13.67/2.28 thf(func_def_47, type, db0: !>[X0: $tType]:(X0)).
% 13.67/2.28 thf(func_def_48, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 13.67/2.28 thf(func_def_49, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 13.67/2.28 thf(func_def_50, type, vIMP: ($o > $o > $o)).
% 13.67/2.28 thf(func_def_51, type, db1: !>[X0: $tType]:(X0)).
% 13.67/2.28 thf(func_def_52, type, db2: !>[X0: $tType]:(X0)).
% 13.67/2.28 thf(func_def_53, type, sK0: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > X1))).
% 13.67/2.28 thf(func_def_54, type, sK1: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > X1))).
% 13.67/2.28 thf(func_def_55, type, sK2: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 13.67/2.28 thf(func_def_56, type, sK3: ((nat > $o) > nat)).
% 13.67/2.28 thf(func_def_57, type, sK4: ((nat > $o) > nat)).
% 13.67/2.28 thf(func_def_58, type, sK5: (nat > nat)).
% 13.67/2.28 thf(func_def_59, type, sK6: ((nat > $o) > nat)).
% 13.67/2.28 thf(func_def_60, type, sK7: (nat > nat)).
% 13.67/2.28 thf(func_def_61, type, sK8: ((nat > $o) > nat)).
% 13.67/2.28 thf(func_def_62, type, sK9: ((nat > nat > $o) > nat)).
% 13.67/2.28 thf(func_def_63, type, sK10: ((nat > nat > $o) > nat)).
% 13.67/2.28 thf(func_def_64, type, sK11: ((nat > nat > $o) > nat)).
% 13.67/2.28 thf(func_def_65, type, sK12: ((nat > nat > $o) > nat)).
% 13.67/2.28 thf(func_def_66, type, sK13: ((nat > $o) > nat)).
% 13.67/2.28 thf(func_def_67, type, sK14: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 13.67/2.28 thf(func_def_68, type, sK15: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 13.67/2.28 thf(func_def_69, type, sK16: ((nat > $o) > nat)).
% 13.67/2.28 thf(func_def_70, type, sK17: ((nat > $o) > nat > nat)).
% 13.67/2.28 thf(func_def_71, type, sK18: ((nat > $o) > nat > nat)).
% 13.67/2.28 thf(func_def_72, type, sK19: ((nat > nat > $o) > nat)).
% 13.67/2.28 thf(func_def_73, type, sK20: ((nat > nat > $o) > nat)).
% 13.67/2.28 thf(func_def_74, type, sK21: ((nat > nat > $o) > nat)).
% 13.67/2.28 thf(func_def_75, type, sK22: ((nat > nat > $o) > nat)).
% 13.67/2.28 thf(func_def_76, type, sK23: (nat > nat > nat)).
% 13.67/2.28 thf(func_def_77, type, sK24: (nat > nat > nat)).
% 13.67/2.28 thf(func_def_78, type, sK25: !>[X0: $tType]:(((nat > X0) > nat))).
% 13.67/2.28 thf(func_def_79, type, sK26: !>[X0: $tType]:(((nat > X0) > nat))).
% 13.67/2.28 thf(func_def_80, type, sK27: (nat > nat)).
% 13.67/2.28 thf(func_def_81, type, sK28: !>[X0: $tType]:((X0 > X0))).
% 13.67/2.28 thf(func_def_82, type, sK29: !>[X0: $tType]:((X0 > X0))).
% 13.67/2.28 thf(func_def_83, type, sK30: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 13.67/2.28 thf(func_def_84, type, sK31: !>[X0: $tType]:((nat > list @ X0))).
% 13.67/2.28 thf(func_def_85, type, sK32: (nat > nat)).
% 13.67/2.28 thf(func_def_86, type, sK33: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat > X0))).
% 13.67/2.28 thf(func_def_87, type, sK34: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > X0))).
% 13.67/2.28 thf(func_def_88, type, sK35: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat))).
% 13.67/2.28 thf(func_def_89, type, sK36: ((nat > $o) > nat)).
% 13.67/2.28 thf(func_def_90, type, sK37: !>[X0: $tType]:((X0 > X0 > X0))).
% 13.67/2.28 thf(func_def_91, type, sK38: (nat > (nat > $o) > nat > nat)).
% 13.67/2.28 thf(func_def_92, type, sK39: ((nat > $o) > nat > nat)).
% 13.67/2.28 thf(func_def_93, type, sK40: ((nat > $o) > nat > nat)).
% 13.67/2.28 thf(func_def_94, type, sK41: (nat > nat)).
% 13.67/2.28 thf(func_def_95, type, sK42: ((nat > $o) > nat > nat)).
% 13.67/2.28 thf(func_def_96, type, sK43: ((nat > $o) > nat > nat)).
% 13.67/2.28 thf(func_def_97, type, sK44: (nat > nat > nat)).
% 13.67/2.28 thf(func_def_98, type, sK45: ((nat > $o) > nat > nat)).
% 13.67/2.28 thf(func_def_99, type, sK46: ((nat > $o) > nat > nat)).
% 13.67/2.28 thf(func_def_100, type, sK47: ((nat > $o) > nat > nat)).
% 13.67/2.28 thf(func_def_101, type, sK48: ((nat > $o) > nat > nat)).
% 13.67/2.28 thf(func_def_102, type, sK49: (nat > nat > nat)).
% 13.67/2.28 thf(f30,axiom,(
% 13.67/2.28 ! [X0 : nat] : (X0 != ((suc @ X0)))),
% 13.67/2.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_n__not__Suc__n)).
% 13.67/2.28 thf(f33,axiom,(
% 13.67/2.28 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(ord_less @ nat @ X0 @ X1) => (ord_less @ nat @ X1 @ X0)))),
% 13.67/2.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_linorder__neqE__nat)).
% 13.67/2.28 thf(f36,axiom,(
% 13.67/2.28 ! [X0 : nat] : ~(ord_less @ nat @ X0 @ X0)),
% 13.67/2.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_less__irrefl__nat)).
% 13.67/2.28 thf(f74,axiom,(
% 13.67/2.28 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ X0 @ X1) => (ord_less @ nat @ X0 @ (suc @ X1)))),
% 13.67/2.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_less__SucI)).
% 13.67/2.28 thf(f97,axiom,(
% 13.67/2.28 ! [X0 : nat,X1 : nat,X2 : nat] : ((ord_less @ nat @ X0 @ (times_times @ nat @ X1 @ X2)) => (ord_less @ nat @ (divide_divide @ nat @ X0 @ X2) @ X1))),
% 13.67/2.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Euclidean__Division_Oless__mult__imp__div__less)).
% 13.67/2.28 thf(f103,axiom,(
% 13.67/2.28 ! [X0 : $tType] : (semidom_divide @ X0 => ! [X1 : X0,X2 : X0] : ((X1 != zero_zero @ X0) => (((divide_divide @ X0 @ (times_times @ X0 @ X2 @ X1) @ X1)) = X2)))),
% 13.67/2.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_nonzero__mult__div__cancel__right)).
% 13.67/2.28 thf(f267,axiom,(
% 13.67/2.28 semidom_divide @ nat),
% 13.67/2.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemidom__divide)).
% 13.67/2.28 thf(f279,axiom,(
% 13.67/2.28 (((divide_divide @ nat @ (size_size @ list @ a @ xs) @ k)) = ((suc @ n)))),
% 13.67/2.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 13.67/2.28 thf(f280,axiom,(
% 13.67/2.28 (k != zero_zero @ nat)),
% 13.67/2.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 13.67/2.28 thf(f281,conjecture,(
% 13.67/2.28 (ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs))),
% 13.67/2.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)).
% 13.67/2.28 thf(f282,negated_conjecture,(
% 13.67/2.28 ~(ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs))),
% 13.67/2.28 inference(negated_conjecture,[status(cth)],[f281])).
% 13.67/2.28 thf(f325,plain,(
% 13.67/2.28 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(ord_less @ nat @ X0 @ X1) => (ord_less @ nat @ X1 @ X0)))),
% 13.67/2.28 inference(rectify,[],[f33])).
% 13.67/2.28 thf(f326,plain,(
% 13.67/2.28 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~ (((ord_less @ nat @ X0 @ X1)) = $true) => (((ord_less @ nat @ X1 @ X0)) = $true)))),
% 13.67/2.28 inference(fool_elimination,[],[f325])).
% 13.67/2.28 thf(f331,plain,(
% 13.67/2.28 ! [X0 : nat] : ~(ord_less @ nat @ X0 @ X0)),
% 13.67/2.28 inference(rectify,[],[f36])).
% 13.67/2.28 thf(f332,plain,(
% 13.67/2.28 ! [X0 : nat] : ~ (((ord_less @ nat @ X0 @ X0)) = $true)),
% 13.67/2.28 inference(fool_elimination,[],[f331])).
% 13.67/2.28 thf(f389,plain,(
% 13.67/2.28 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ X0 @ X1) => (ord_less @ nat @ X0 @ (suc @ X1)))),
% 13.67/2.28 inference(rectify,[],[f74])).
% 13.67/2.28 thf(f390,plain,(
% 13.67/2.28 ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ X0 @ X1)) = $true) => (((ord_less @ nat @ X0 @ (suc @ X1))) = $true))),
% 13.67/2.28 inference(fool_elimination,[],[f389])).
% 13.67/2.28 thf(f426,plain,(
% 13.67/2.28 ! [X0 : nat,X1 : nat,X2 : nat] : ((ord_less @ nat @ X0 @ (times_times @ nat @ X1 @ X2)) => (ord_less @ nat @ (divide_divide @ nat @ X0 @ X2) @ X1))),
% 13.67/2.28 inference(rectify,[],[f97])).
% 13.67/2.28 thf(f427,plain,(
% 13.67/2.28 ! [X0 : nat,X1 : nat,X2 : nat] : ((((ord_less @ nat @ X0 @ (times_times @ nat @ X1 @ X2))) = $true) => (((ord_less @ nat @ (divide_divide @ nat @ X0 @ X2) @ X1)) = $true))),
% 13.67/2.28 inference(fool_elimination,[],[f426])).
% 13.67/2.28 thf(f438,plain,(
% 13.67/2.28 ! [X0 : $tType] : (semidom_divide @ X0 => ! [X1 : X0,X2 : X0] : ((X1 != zero_zero @ X0) => (((divide_divide @ X0 @ (times_times @ X0 @ X2 @ X1) @ X1)) = X2)))),
% 13.67/2.28 inference(rectify,[],[f103])).
% 13.67/2.28 thf(f439,plain,(
% 13.67/2.28 ! [X0 : $tType] : ((semidom_divide @ X0 = $true) => ! [X1 : X0,X2 : X0] : ((zero_zero @ X0 != X1) => (((divide_divide @ X0 @ (times_times @ X0 @ X2 @ X1) @ X1)) = X2)))),
% 13.67/2.28 inference(fool_elimination,[],[f438])).
% 13.67/2.28 thf(f752,plain,(
% 13.67/2.28 semidom_divide @ nat),
% 13.67/2.28 inference(rectify,[],[f267])).
% 13.67/2.28 thf(f753,plain,(
% 13.67/2.28 (semidom_divide @ nat = $true)),
% 13.67/2.28 inference(fool_elimination,[],[f752])).
% 13.67/2.28 thf(f776,plain,(
% 13.67/2.28 ~(ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs))),
% 13.67/2.28 inference(rectify,[],[f282])).
% 13.67/2.28 thf(f777,plain,(
% 13.67/2.28 ~ (((ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs))) = $true)),
% 13.67/2.28 inference(fool_elimination,[],[f776])).
% 13.67/2.28 thf(f780,plain,(
% 13.67/2.28 ! [X0 : nat,X1 : nat] : ((X0 != X1) => ((((ord_less @ nat @ X0 @ X1)) != $true) => (((ord_less @ nat @ X1 @ X0)) = $true)))),
% 13.67/2.28 inference(flattening,[],[f326])).
% 13.67/2.28 thf(f782,plain,(
% 13.67/2.28 ! [X0 : nat] : (((ord_less @ nat @ X0 @ X0)) != $true)),
% 13.67/2.28 inference(flattening,[],[f332])).
% 13.67/2.28 thf(f797,plain,(
% 13.67/2.28 (((ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs))) != $true)),
% 13.67/2.28 inference(flattening,[],[f777])).
% 13.67/2.28 thf(f810,plain,(
% 13.67/2.28 ! [X0 : nat,X1 : nat] : (((((ord_less @ nat @ X1 @ X0)) = $true) | (((ord_less @ nat @ X0 @ X1)) = $true)) | (X0 = X1))),
% 13.67/2.28 inference(ennf_transformation,[],[f780])).
% 13.67/2.28 thf(f811,plain,(
% 13.67/2.28 ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ X1 @ X0)) = $true) | (((ord_less @ nat @ X0 @ X1)) = $true) | (X0 = X1))),
% 13.67/2.28 inference(flattening,[],[f810])).
% 13.67/2.28 thf(f844,plain,(
% 13.67/2.28 ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ X0 @ (suc @ X1))) = $true) | (((ord_less @ nat @ X0 @ X1)) != $true))),
% 13.67/2.28 inference(ennf_transformation,[],[f390])).
% 13.67/2.28 thf(f863,plain,(
% 13.67/2.28 ! [X0 : nat,X1 : nat,X2 : nat] : ((((ord_less @ nat @ (divide_divide @ nat @ X0 @ X2) @ X1)) = $true) | (((ord_less @ nat @ X0 @ (times_times @ nat @ X1 @ X2))) != $true))),
% 13.67/2.28 inference(ennf_transformation,[],[f427])).
% 13.67/2.28 thf(f872,plain,(
% 13.67/2.28 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((((divide_divide @ X0 @ (times_times @ X0 @ X2 @ X1) @ X1)) = X2) | (zero_zero @ X0 = X1)) | (semidom_divide @ X0 != $true))),
% 13.67/2.28 inference(ennf_transformation,[],[f439])).
% 13.67/2.28 thf(f1127,plain,(
% 13.67/2.28 ( ! [X0 : nat] : ((((suc @ X0)) != X0)) )),
% 13.67/2.28 inference(cnf_transformation,[],[f30])).
% 13.67/2.28 thf(f1131,plain,(
% 13.67/2.28 ( ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ X1 @ X0)) = $true) | (((ord_less @ nat @ X0 @ X1)) = $true) | (X0 = X1)) )),
% 13.67/2.28 inference(cnf_transformation,[],[f811])).
% 13.67/2.28 thf(f1136,plain,(
% 13.67/2.28 ( ! [X0 : nat] : ((((ord_less @ nat @ X0 @ X0)) != $true)) )),
% 13.67/2.28 inference(cnf_transformation,[],[f782])).
% 13.67/2.28 thf(f1194,plain,(
% 13.67/2.28 ( ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ X0 @ X1)) != $true) | (((ord_less @ nat @ X0 @ (suc @ X1))) = $true)) )),
% 13.67/2.28 inference(cnf_transformation,[],[f844])).
% 13.67/2.28 thf(f1219,plain,(
% 13.67/2.28 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((((ord_less @ nat @ X0 @ (times_times @ nat @ X1 @ X2))) != $true) | (((ord_less @ nat @ (divide_divide @ nat @ X0 @ X2) @ X1)) = $true)) )),
% 13.67/2.28 inference(cnf_transformation,[],[f863])).
% 13.67/2.28 thf(f1225,plain,(
% 13.67/2.28 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((semidom_divide @ X0 != $true) | (zero_zero @ X0 = X1) | (((divide_divide @ X0 @ (times_times @ X0 @ X2 @ X1) @ X1)) = X2)) )),
% 13.67/2.28 inference(cnf_transformation,[],[f872])).
% 13.67/2.28 thf(f1400,plain,(
% 13.67/2.28 (semidom_divide @ nat = $true)),
% 13.67/2.28 inference(cnf_transformation,[],[f753])).
% 13.67/2.28 thf(f1412,plain,(
% 13.67/2.28 (((divide_divide @ nat @ (size_size @ list @ a @ xs) @ k)) = ((suc @ n)))),
% 13.67/2.28 inference(cnf_transformation,[],[f279])).
% 13.67/2.28 thf(f1413,plain,(
% 13.67/2.28 (zero_zero @ nat != k)),
% 13.67/2.28 inference(cnf_transformation,[],[f280])).
% 13.67/2.28 thf(f1414,plain,(
% 13.67/2.28 (((ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs))) != $true)),
% 13.67/2.28 inference(cnf_transformation,[],[f797])).
% 13.67/2.28 thf(f4237,plain,(
% 13.67/2.28 ($true != $true) | ($true = ((ord_less @ nat @ (size_size @ list @ a @ xs) @ (times_times @ nat @ n @ k)))) | (((size_size @ list @ a @ xs)) = ((times_times @ nat @ n @ k)))),
% 13.67/2.28 inference(constrained_superposition,[],[f1414,f1131])).
% 13.67/2.28 thf(f4269,plain,(
% 13.67/2.28 ($true = ((ord_less @ nat @ (size_size @ list @ a @ xs) @ (times_times @ nat @ n @ k)))) | (((size_size @ list @ a @ xs)) = ((times_times @ nat @ n @ k)))),
% 13.67/2.28 inference(trivial_inequality_removal,[],[f4237])).
% 13.67/2.28 thf(f5190,plain,(
% 13.67/2.28 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (zero_zero @ nat = X0) | (((divide_divide @ nat @ (times_times @ nat @ X1 @ X0) @ X0)) = X1)) )),
% 13.67/2.28 inference(constrained_superposition,[],[f1225,f1400])).
% 13.67/2.28 thf(f5191,plain,(
% 13.67/2.28 ( ! [X0 : nat,X1 : nat] : ((((divide_divide @ nat @ (times_times @ nat @ X1 @ X0) @ X0)) = X1) | (zero_zero @ nat = X0)) )),
% 13.67/2.28 inference(trivial_inequality_removal,[],[f5190])).
% 13.67/2.28 thf(f9902,definition,(
% 13.67/2.28 spl50_3 <=> (((size_size @ list @ a @ xs)) = ((times_times @ nat @ n @ k)))),
% 13.67/2.28 introduced(definition,[new_symbols(definition,[spl50_3])],[avatar_definition])).
% 13.67/2.28 thf(f9904,plain,(
% 13.67/2.28 (((size_size @ list @ a @ xs)) = ((times_times @ nat @ n @ k))) | ~spl50_3),
% 13.67/2.28 inference(avatar_component_clause,[],[f9902])).
% 13.67/2.28 thf(f9906,definition,(
% 13.67/2.28 spl50_4 <=> ($true = ((ord_less @ nat @ (size_size @ list @ a @ xs) @ (times_times @ nat @ n @ k))))),
% 13.67/2.28 introduced(definition,[new_symbols(definition,[spl50_4])],[avatar_definition])).
% 13.67/2.28 thf(f9908,plain,(
% 13.67/2.28 ($true = ((ord_less @ nat @ (size_size @ list @ a @ xs) @ (times_times @ nat @ n @ k)))) | ~spl50_4),
% 13.67/2.28 inference(avatar_component_clause,[],[f9906])).
% 13.67/2.28 thf(f9909,plain,(
% 13.67/2.28 spl50_3 | spl50_4),
% 13.67/2.28 inference(avatar_split_clause,[],[f4269,f9906,f9902])).
% 13.67/2.28 thf(f27758,plain,(
% 13.67/2.28 (((divide_divide @ nat @ (size_size @ list @ a @ xs) @ k)) = n) | (zero_zero @ nat = k) | ~spl50_3),
% 13.67/2.28 inference(constrained_superposition,[],[f5191,f9904])).
% 13.67/2.28 thf(f27784,plain,(
% 13.67/2.28 (((divide_divide @ nat @ (size_size @ list @ a @ xs) @ k)) = n) | ~spl50_3),
% 13.67/2.28 inference(forward_subsumption_resolution,[],[f27758,f1413])).
% 13.67/2.28 thf(f27786,plain,(
% 13.67/2.28 (n = ((suc @ n))) | ~spl50_3),
% 13.67/2.28 inference(constrained_superposition,[],[f27784,f1412])).
% 13.67/2.28 thf(f27805,plain,(
% 13.67/2.28 $false | ~spl50_3),
% 13.67/2.28 inference(forward_subsumption_resolution,[],[f27786,f1127])).
% 13.67/2.28 thf(f27806,plain,(
% 13.67/2.28 ~spl50_3),
% 13.67/2.28 inference(avatar_contradiction_clause,[],[f27805])).
% 13.67/2.28 thf(f27836,plain,(
% 13.67/2.28 ($true != $true) | ($true = ((ord_less @ nat @ (divide_divide @ nat @ (size_size @ list @ a @ xs) @ k) @ n))) | ~spl50_4),
% 13.67/2.28 inference(constrained_superposition,[],[f1219,f9908])).
% 13.67/2.28 thf(f27942,plain,(
% 13.67/2.28 ($true = ((ord_less @ nat @ (divide_divide @ nat @ (size_size @ list @ a @ xs) @ k) @ n))) | ~spl50_4),
% 13.67/2.28 inference(trivial_inequality_removal,[],[f27836])).
% 13.67/2.28 thf(f27976,plain,(
% 13.67/2.28 ($true = ((ord_less @ nat @ (suc @ n) @ n))) | ~spl50_4),
% 13.67/2.28 inference(forward_demodulation,[],[f27942,f1412])).
% 13.67/2.28 thf(f28001,plain,(
% 13.67/2.28 ($true != $true) | ($true = ((ord_less @ nat @ (suc @ n) @ (suc @ n)))) | ~spl50_4),
% 13.67/2.28 inference(constrained_superposition,[],[f1194,f27976])).
% 13.67/2.28 thf(f28125,plain,(
% 13.67/2.28 ($true = ((ord_less @ nat @ (suc @ n) @ (suc @ n)))) | ~spl50_4),
% 13.67/2.28 inference(trivial_inequality_removal,[],[f28001])).
% 13.67/2.28 thf(f28154,plain,(
% 13.67/2.28 $false | ~spl50_4),
% 13.67/2.28 inference(forward_subsumption_resolution,[],[f28125,f1136])).
% 13.67/2.28 thf(f28155,plain,(
% 13.67/2.28 ~spl50_4),
% 13.67/2.28 inference(avatar_contradiction_clause,[],[f28154])).
% 13.67/2.28 cnf(s2, plain, spl50_3 | spl50_4, inference(sat_conversion,[],[f9909])).
% 13.67/2.28 cnf(s59, plain, ~spl50_3, inference(sat_conversion,[],[f27806])).
% 13.67/2.28 cnf(s61, plain, ~spl50_4, inference(sat_conversion,[],[f28155])).
% 13.67/2.28 cnf(s65, plain, $false, inference(rat,[],[s2,s61,s59])).
% 13.67/2.28 thf(f28156,plain,(
% 13.67/2.28 $false),
% 13.67/2.28 inference(avatar_sat_refutation,[],[s65])).
% 13.67/2.28 % SZS output end Proof for theBenchmark
% 13.67/2.28 % (1768344)------------------------------
% 13.67/2.28 % (1768344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.28 % (1768344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.28 % (1768344)CaDiCaL version: 2.1.3
% 13.67/2.28 % (1768344)Termination reason: Refutation
% 13.67/2.28 % (1768344)Time elapsed: 1.492 s
% 13.67/2.28 % (1768344)Peak memory usage: 23 MB
% 13.67/2.28 % (1768344)Instructions burned: 2645 (million)
% 13.67/2.28 % (1768299)Success in time 2.057 s
% 13.67/2.28 % Vampire exiting
%------------------------------------------------------------------------------