%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 : Tue Sep 29 09:38:07 AM UTC 2026
% Result : Unsatisfiable 3.34s 0.79s
% Output : Refutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 34 unt; 7 def)
% Number of atoms : 38 ( 33 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(w,X0),X1) = apply(apply(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_definition) ).
fof(f3,axiom,
! [X0] :
( apply(X0,fixed_pt) != apply(fixed_pt,apply(X0,fixed_pt))
| fixed_point(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
~ fixed_point(apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f5,definition,
sF0 = apply(w,w),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
apply(w,w) = sF0,
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
sF1 = apply(b,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f8,plain,
apply(b,sF0) = sF1,
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
sF2 = apply(b,w),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f10,plain,
apply(b,w) = sF2,
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
sF3 = apply(b,b),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f12,plain,
apply(b,b) = sF3,
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
sF4 = apply(sF3,b),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f14,plain,
apply(sF3,b) = sF4,
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
sF5 = apply(sF2,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f16,plain,
apply(sF2,sF4) = sF5,
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
sF6 = apply(sF1,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f18,plain,
apply(sF1,sF5) = sF6,
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
~ fixed_point(sF6),
inference(definition_folding,[],[f4,f18,f16,f14,f12,f10,f8,f6]) ).
fof(f24,plain,
! [X0] : apply(apply(w,w),X0) = apply(apply(X0,X0),X0),
inference(superposition,[],[f2,f2]) ).
fof(f25,plain,
! [X0] : apply(sF0,X0) = apply(apply(X0,X0),X0),
inference(forward_demodulation,[],[f24,f6]) ).
fof(f46,plain,
! [X0,X1] : apply(sF0,apply(X0,X1)) = apply(apply(sF1,X0),X1),
inference(superposition,[],[f1,f8]) ).
fof(f47,plain,
! [X0,X1] : apply(w,apply(X0,X1)) = apply(apply(sF2,X0),X1),
inference(superposition,[],[f1,f10]) ).
fof(f48,plain,
! [X0,X1] : apply(b,apply(X0,X1)) = apply(apply(sF3,X0),X1),
inference(superposition,[],[f1,f12]) ).
fof(f51,plain,
! [X0,X1] : apply(apply(w,apply(b,X0)),X1) = apply(X0,apply(X1,X1)),
inference(superposition,[],[f2,f1]) ).
fof(f64,plain,
! [X0] : apply(sF0,apply(sF5,X0)) = apply(sF6,X0),
inference(superposition,[],[f46,f18]) ).
fof(f72,plain,
! [X0] : apply(sF5,X0) = apply(w,apply(sF4,X0)),
inference(superposition,[],[f47,f16]) ).
fof(f80,plain,
! [X0] : apply(b,apply(b,X0)) = apply(sF4,X0),
inference(superposition,[],[f48,f14]) ).
fof(f89,plain,
( apply(sF0,apply(sF5,fixed_pt)) != apply(fixed_pt,apply(sF0,apply(sF5,fixed_pt)))
| fixed_point(sF6) ),
inference(superposition,[],[f3,f64]) ).
fof(f91,plain,
apply(sF0,apply(sF5,fixed_pt)) != apply(fixed_pt,apply(sF0,apply(sF5,fixed_pt))),
inference(forward_subsumption_resolution,[],[f89,f19]) ).
fof(f127,plain,
! [X2,X0,X1] : apply(X0,apply(apply(X1,X1),X2)) = apply(apply(apply(w,apply(b,apply(b,X0))),X1),X2),
inference(superposition,[],[f1,f51]) ).
fof(f141,plain,
! [X2,X0,X1] : apply(X0,apply(apply(X1,X1),X2)) = apply(apply(apply(w,apply(sF4,X0)),X1),X2),
inference(forward_demodulation,[],[f127,f80]) ).
fof(f146,plain,
! [X2,X0,X1] : apply(X0,apply(apply(X1,X1),X2)) = apply(apply(apply(sF5,X0),X1),X2),
inference(forward_demodulation,[],[f141,f72]) ).
fof(f2617,plain,
! [X0] : apply(sF0,apply(sF5,X0)) = apply(X0,apply(sF0,apply(sF5,X0))),
inference(superposition,[],[f146,f25]) ).
fof(f6489,plain,
apply(sF0,apply(sF5,fixed_pt)) != apply(sF0,apply(sF5,fixed_pt)),
inference(superposition,[],[f91,f2617]) ).
fof(f6512,plain,
$false,
inference(trivial_inequality_removal,[],[f6489]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.17 % Computer : n003.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 21:30:57 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.34/0.79 % (2044281)Will run a generic schedule for satisfiability detection.
% 3.34/0.79 % (2044289)dis+10_1_sil=32000:sp=arity:random_seed=2584088694:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.34/0.79 % (2044287)% WARNING: option uhcvi not known.
% 3.34/0.79 % (2044287)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1298734439:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.34/0.79 % (2044286)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1469437146_2999 on theBenchmark for (2999ds/0Mi)
% 3.34/0.79 % (2044288)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2187240117:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.34/0.79 % (2044291)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1036836453:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.34/0.79 % (2044292)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=773708554:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.34/0.79 % TRYING [1]
% 3.34/0.79 % TRYING [2]
% 3.34/0.79 % TRYING [3]
% 3.34/0.79 % TRYING [4]
% 3.34/0.79 % (2044290)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2746469965:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.34/0.79 % (2044289)Instruction limit reached!
% 3.34/0.79 % (2044289)------------------------------
% 3.34/0.79 % (2044289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.34/0.79 % (2044289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/0.79 % (2044289)CaDiCaL version: 2.1.3
% 3.34/0.79 % (2044289)Termination reason: Instruction limit
% 3.34/0.79 % (2044289)Termination phase: Saturation
% 3.34/0.79 % (2044289)Time elapsed: 0.032 s
% 3.34/0.79 % (2044289)Peak memory usage: 12 MB
% 3.34/0.79 % (2044289)Instructions burned: 105 (million)
% 3.34/0.79 % (2044300)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=915843180:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.34/0.79 % TRYING [1]
% 3.34/0.79 % TRYING [2]
% 3.34/0.79 % TRYING [3]
% 3.34/0.79 % TRYING [4]
% 3.34/0.79 % TRYING [5]
% 3.34/0.79 % TRYING [5]
% 3.34/0.79 % (2044291)Instruction limit reached!
% 3.34/0.79 % (2044291)------------------------------
% 3.34/0.79 % (2044291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.34/0.79 % (2044291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/0.79 % (2044291)CaDiCaL version: 2.1.3
% 3.34/0.79 % (2044291)Termination reason: Instruction limit
% 3.34/0.79 % (2044291)Termination phase: Saturation
% 3.34/0.79 % (2044291)Time elapsed: 0.080 s
% 3.34/0.79 % (2044291)Peak memory usage: 13 MB
% 3.34/0.79 % (2044291)Instructions burned: 131 (million)
% 3.34/0.79 % (2044292)Instruction limit reached!
% 3.34/0.79 % (2044292)------------------------------
% 3.34/0.79 % (2044292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.34/0.79 % (2044292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/0.79 % (2044292)CaDiCaL version: 2.1.3
% 3.34/0.79 % (2044292)Termination reason: Instruction limit
% 3.34/0.79 % (2044292)Termination phase: Saturation
% 3.34/0.79 % (2044292)Time elapsed: 0.098 s
% 3.34/0.79 % (2044292)Peak memory usage: 13 MB
% 3.34/0.79 % (2044292)Instructions burned: 160 (million)
% 3.34/0.79 % (2044302)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2314743530:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 3.34/0.79 % (2044290)Instruction limit reached!
% 3.34/0.79 % (2044290)------------------------------
% 3.34/0.79 % (2044290)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.34/0.79 % (2044290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/0.79 % (2044290)CaDiCaL version: 2.1.3
% 3.34/0.79 % (2044290)Termination reason: Instruction limit
% 3.34/0.79 % (2044290)Termination phase: Saturation
% 3.34/0.79 % (2044290)Time elapsed: 0.084 s
% 3.34/0.79 % (2044290)Peak memory usage: 12 MB
% 3.34/0.79 % (2044290)Instructions burned: 117 (million)
% 3.34/0.79 % (2044303)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=2003494307:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.34/0.79 % (2044305)ott-21_1_sil=16000:fs=off:random_seed=97936997:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.34/0.79 % (2044302)Instruction limit reached!
% 3.34/0.79 % (2044302)------------------------------
% 3.34/0.79 % (2044302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.34/0.79 % (2044302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/0.79 % (2044302)CaDiCaL version: 2.1.3
% 3.34/0.79 % (2044302)Termination reason: Instruction limit
% 3.34/0.79 % (2044302)Termination phase: Saturation
% 3.34/0.79 % (2044302)Time elapsed: 0.084 s
% 3.34/0.79 % (2044302)Peak memory usage: 13 MB
% 3.34/0.79 % (2044302)Instructions burned: 131 (million)
% 3.34/0.79 % (2044308)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=271618027:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 3.34/0.79 % TRYING [6]
% 3.34/0.79 % (2044300)Instruction limit reached!
% 3.34/0.79 % (2044300)------------------------------
% 3.34/0.79 % (2044300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.34/0.79 % (2044300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/0.79 % (2044300)CaDiCaL version: 2.1.3
% 3.34/0.79 % (2044300)Termination reason: Instruction limit
% 3.34/0.79 % (2044300)Termination phase: Finite model building SAT solving
% 3.34/0.79 % (2044300)Time elapsed: 0.228 s
% 3.34/0.79 % (2044300)Peak memory usage: 15 MB
% 3.34/0.79 % (2044300)Instructions burned: 715 (million)
% 3.34/0.79 % (2044310)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3894447144:fmbsr=1.3:i=865:ins=25_2996 on theBenchmark for (2996ds/865Mi)
% 3.34/0.79 % TRYING [1]
% 3.34/0.79 % (2044305)Instruction limit reached!
% 3.34/0.79 % (2044305)------------------------------
% 3.34/0.79 % (2044305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.34/0.79 % (2044305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/0.79 % (2044305)CaDiCaL version: 2.1.3
% 3.34/0.79 % (2044305)Termination reason: Instruction limit
% 3.34/0.79 % (2044305)Termination phase: Saturation
% 3.34/0.79 % (2044305)Time elapsed: 0.131 s
% 3.34/0.79 % (2044305)Peak memory usage: 11 MB
% 3.34/0.79 % (2044305)Instructions burned: 181 (million)
% 3.34/0.79 % TRYING [2]
% 3.34/0.79 % TRYING [3]
% 3.34/0.79 % TRYING [4]
% 3.34/0.79 % (2044317)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2845127381:i=1179_2996 on theBenchmark for (2996ds/1179Mi)
% 3.34/0.79 % TRYING [5]
% 3.34/0.79 % TRYING [6]
% 3.34/0.79 % TRYING [6]
% 3.34/0.79 % (2044308)Instruction limit reached!
% 3.34/0.79 % (2044308)------------------------------
% 3.34/0.79 % (2044308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.34/0.79 % (2044308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/0.79 % (2044308)CaDiCaL version: 2.1.3
% 3.34/0.79 % (2044308)Termination reason: Instruction limit
% 3.34/0.79 % (2044308)Termination phase: Saturation
% 3.34/0.79 % (2044308)Time elapsed: 0.257 s
% 3.34/0.79 % (2044308)Peak memory usage: 15 MB
% 3.34/0.79 % (2044308)Instructions burned: 479 (million)
% 3.34/0.79 % (2044303)Instruction limit reached!
% 3.34/0.79 % (2044303)------------------------------
% 3.34/0.79 % (2044303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.34/0.79 % (2044303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/0.79 % (2044303)CaDiCaL version: 2.1.3
% 3.34/0.79 % (2044303)Termination reason: Instruction limit
% 3.34/0.79 % (2044303)Termination phase: Saturation
% 3.34/0.79 % (2044303)Time elapsed: 0.359 s
% 3.34/0.79 % (2044303)Peak memory usage: 16 MB
% 3.34/0.79 % (2044303)Instructions burned: 686 (million)
% 3.34/0.79 % (2044385)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2639025589:i=889:ins=1_2995 on theBenchmark for (2995ds/889Mi)
% 3.34/0.79 % (2044391)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=1396450056:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2994 on theBenchmark for (2994ds/692Mi)
% 3.34/0.79 % TRYING [14]
% 3.34/0.79 % (2044310)Instruction limit reached!
% 3.34/0.79 % (2044310)------------------------------
% 3.34/0.79 % (2044310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.34/0.79 % (2044310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/0.79 % (2044310)CaDiCaL version: 2.1.3
% 3.34/0.79 % (2044310)Termination reason: Instruction limit
% 3.34/0.79 % (2044310)Termination phase: Finite model building SAT solving
% 3.34/0.79 % (2044310)Time elapsed: 0.234 s
% 3.34/0.79 % (2044310)Peak memory usage: 14 MB
% 3.34/0.79 % (2044310)Instructions burned: 867 (million)
% 3.34/0.79 % (2044401)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4219661802:i=879:kws=inv_precedence:fsr=off_2994 on theBenchmark for (2994ds/879Mi)
% 3.34/0.79 % (2044317) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2044281-2044317"...
% 3.34/0.79 % (2044317)...printing done.
% 3.34/0.79 % (2044317)Refutation found. Thanks to Tanya!
% 3.34/0.79 % SZS status Unsatisfiable for theBenchmark
% 3.34/0.79 % SZS output start Proof for theBenchmark
% See solution above
% 3.34/0.79 % (2044317)------------------------------
% 3.34/0.79 % (2044317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.34/0.79 % (2044317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/0.79 % (2044317)CaDiCaL version: 2.1.3
% 3.34/0.79 % (2044317)Termination reason: Refutation
% 3.34/0.79 % (2044317)Time elapsed: 0.233 s
% 3.34/0.79 % (2044317)Peak memory usage: 16 MB
% 3.34/0.79 % (2044317)Instructions burned: 382 (million)
% 3.34/0.79 % (2044281)Success in time 0.571 s
% 3.34/0.79 % Vampire exiting
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