%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL042-7 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 09:38:14 AM UTC 2026
% Result : Unsatisfiable 2.36s 0.63s
% Output : Refutation 2.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 20 unt; 2 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 18 ( 18 !; 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(w1,X0),X1) = apply(apply(X1,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w1_definition) ).
fof(f3,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),apply(apply(b,b),b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f5,definition,
sF0 = apply(strong_fixed_point,fixed_pt),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
apply(strong_fixed_point,fixed_pt) = sF0,
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
sF1 = apply(fixed_pt,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f8,plain,
apply(fixed_pt,sF0) = sF1,
inference(reorient_equations,[],[f7]) ).
fof(f9,plain,
sF0 != sF1,
inference(definition_folding,[],[f4,f8,f6,f6]) ).
fof(f19,plain,
! [X2,X0,X1] : apply(apply(w1,X2),apply(apply(b,X0),X1)) = apply(apply(X0,apply(X1,X2)),X2),
inference(superposition,[],[f2,f1]) ).
fof(f21,plain,
! [X0] : apply(apply(apply(b,apply(w1,w1)),apply(b,w1)),apply(apply(apply(b,b),b),X0)) = apply(strong_fixed_point,X0),
inference(superposition,[],[f1,f3]) ).
fof(f23,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w1,w1),apply(apply(b,w1),apply(apply(apply(b,b),b),X0))),
inference(forward_demodulation,[],[f21,f1]) ).
fof(f24,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X0)))),
inference(forward_demodulation,[],[f23,f1]) ).
fof(f212,plain,
! [X0,X1] : apply(apply(X0,apply(X1,X0)),apply(X1,X0)) = apply(apply(w1,X0),apply(apply(b,w1),X1)),
inference(superposition,[],[f2,f19]) ).
fof(f214,plain,
! [X2,X0,X1] : apply(apply(w1,X0),apply(apply(b,apply(b,X1)),X2)) = apply(X1,apply(apply(X2,X0),X0)),
inference(superposition,[],[f1,f19]) ).
fof(f1988,plain,
! [X0] : apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X0)))) = apply(X0,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X0))))),
inference(superposition,[],[f214,f212]) ).
fof(f2218,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(forward_demodulation,[],[f1988,f24]) ).
fof(f2263,plain,
sF0 = apply(fixed_pt,sF0),
inference(superposition,[],[f2218,f6]) ).
fof(f2393,plain,
sF0 = sF1,
inference(superposition,[],[f8,f2263]) ).
fof(f2407,plain,
$false,
inference(forward_subsumption_resolution,[],[f2393,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL042-7 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n013.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
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 21:29:51 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 2.36/0.63 % (1601014)Will run a generic schedule for satisfiability detection.
% 2.36/0.63 % (1601022)dis+10_1_sil=32000:sp=arity:random_seed=2092444601:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.36/0.63 % (1601020)% WARNING: option uhcvi not known.
% 2.36/0.63 % (1601019)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3564219668_2999 on theBenchmark for (2999ds/0Mi)
% 2.36/0.63 % (1601020)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=45771650:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.36/0.63 % (1601021)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3497858108:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.36/0.63 % (1601024)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4267122924:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.36/0.63 % (1601023)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4272240391:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.36/0.63 % (1601025)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3988472772:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.36/0.63 % TRYING [1]
% 2.36/0.63 % TRYING [2]
% 2.36/0.63 % TRYING [3]
% 2.36/0.63 % TRYING [4]
% 2.36/0.63 % (1601022)Instruction limit reached!
% 2.36/0.63 % (1601022)------------------------------
% 2.36/0.63 % (1601022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/0.63 % (1601022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/0.63 % (1601022)CaDiCaL version: 2.1.3
% 2.36/0.63 % (1601022)Termination reason: Instruction limit
% 2.36/0.63 % (1601022)Termination phase: Saturation
% 2.36/0.63 % (1601022)Time elapsed: 0.032 s
% 2.36/0.63 % (1601022)Peak memory usage: 12 MB
% 2.36/0.63 % (1601022)Instructions burned: 105 (million)
% 2.36/0.63 % (1601033)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2220104238:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.36/0.63 % TRYING [1]
% 2.36/0.63 % TRYING [2]
% 2.36/0.63 % TRYING [3]
% 2.36/0.63 % TRYING [4]
% 2.36/0.63 % TRYING [5]
% 2.36/0.63 % TRYING [5]
% 2.36/0.63 % (1601023)Instruction limit reached!
% 2.36/0.63 % (1601023)------------------------------
% 2.36/0.63 % (1601023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/0.63 % (1601023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/0.63 % (1601023)CaDiCaL version: 2.1.3
% 2.36/0.63 % (1601023)Termination reason: Instruction limit
% 2.36/0.63 % (1601023)Termination phase: Saturation
% 2.36/0.63 % (1601023)Time elapsed: 0.074 s
% 2.36/0.63 % (1601023)Peak memory usage: 12 MB
% 2.36/0.63 % (1601023)Instructions burned: 117 (million)
% 2.36/0.63 % (1601024)Instruction limit reached!
% 2.36/0.63 % (1601024)------------------------------
% 2.36/0.63 % (1601024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/0.63 % (1601024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/0.63 % (1601024)CaDiCaL version: 2.1.3
% 2.36/0.63 % (1601024)Termination reason: Instruction limit
% 2.36/0.63 % (1601024)Termination phase: Saturation
% 2.36/0.63 % (1601024)Time elapsed: 0.084 s
% 2.36/0.63 % (1601024)Peak memory usage: 13 MB
% 2.36/0.63 % (1601024)Instructions burned: 132 (million)
% 2.36/0.63 % (1601025)Instruction limit reached!
% 2.36/0.63 % (1601025)------------------------------
% 2.36/0.63 % (1601025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/0.63 % (1601025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/0.63 % (1601025)CaDiCaL version: 2.1.3
% 2.36/0.63 % (1601025)Termination reason: Instruction limit
% 2.36/0.63 % (1601025)Termination phase: Saturation
% 2.36/0.63 % (1601025)Time elapsed: 0.098 s
% 2.36/0.63 % (1601025)Peak memory usage: 13 MB
% 2.36/0.63 % (1601025)Instructions burned: 160 (million)
% 2.36/0.63 % (1601036)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=3516481692:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.36/0.63 % (1601035)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1792053504:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.36/0.63 % (1601037)ott-21_1_sil=16000:fs=off:random_seed=4186746430:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.36/0.63 % (1601035)Instruction limit reached!
% 2.36/0.63 % (1601035)------------------------------
% 2.36/0.63 % (1601035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/0.63 % (1601035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/0.63 % (1601035)CaDiCaL version: 2.1.3
% 2.36/0.63 % (1601035)Termination reason: Instruction limit
% 2.36/0.63 % (1601035)Termination phase: Saturation
% 2.36/0.63 % (1601035)Time elapsed: 0.086 s
% 2.36/0.63 % (1601035)Peak memory usage: 13 MB
% 2.36/0.63 % (1601035)Instructions burned: 132 (million)
% 2.36/0.63 % (1601037)Instruction limit reached!
% 2.36/0.63 % (1601037)------------------------------
% 2.36/0.63 % (1601037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/0.63 % (1601037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/0.63 % (1601037)CaDiCaL version: 2.1.3
% 2.36/0.63 % (1601037)Termination reason: Instruction limit
% 2.36/0.63 % (1601037)Termination phase: Saturation
% 2.36/0.63 % (1601037)Time elapsed: 0.082 s
% 2.36/0.63 % (1601037)Peak memory usage: 11 MB
% 2.36/0.63 % (1601037)Instructions burned: 180 (million)
% 2.36/0.63 % (1601041)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1065762622:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 2.36/0.63 % (1601042)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4106749644:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.36/0.63 % TRYING [1]
% 2.36/0.63 % TRYING [2]
% 2.36/0.63 % TRYING [3]
% 2.36/0.63 % TRYING [4]
% 2.36/0.63 % TRYING [5]
% 2.36/0.63 % TRYING [6]
% 2.36/0.63 % (1601033)Instruction limit reached!
% 2.36/0.63 % (1601033)------------------------------
% 2.36/0.63 % (1601033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/0.63 % (1601033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/0.63 % (1601033)CaDiCaL version: 2.1.3
% 2.36/0.63 % (1601033)Termination reason: Instruction limit
% 2.36/0.63 % (1601033)Termination phase: Finite model building constraint generation
% 2.36/0.63 % (1601033)Time elapsed: 0.244 s
% 2.36/0.63 % (1601033)Peak memory usage: 14 MB
% 2.36/0.63 % (1601033)Instructions burned: 718 (million)
% 2.36/0.63 % (1601045)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1641872373:i=1179_2996 on theBenchmark for (2996ds/1179Mi)
% 2.36/0.63 % TRYING [6]
% 2.36/0.63 % (1601045) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1601014-1601045"...
% 2.36/0.63 % (1601045)...printing done.
% 2.36/0.63 % (1601045)Refutation found. Thanks to Tanya!
% 2.36/0.63 % SZS status Unsatisfiable for theBenchmark
% 2.36/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 2.36/0.63 % (1601045)------------------------------
% 2.36/0.63 % (1601045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/0.63 % (1601045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/0.63 % (1601045)CaDiCaL version: 2.1.3
% 2.36/0.63 % (1601045)Termination reason: Refutation
% 2.36/0.63 % (1601045)Time elapsed: 0.071 s
% 2.36/0.63 % (1601045)Peak memory usage: 15 MB
% 2.36/0.63 % (1601045)Instructions burned: 212 (million)
% 2.36/0.63 % (1601014)Success in time 0.403 s
% 2.36/0.63 % Vampire exiting
%------------------------------------------------------------------------------