%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL042-6 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 3.91s 0.88s
% Output : Refutation 3.91s
% 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 : 8 ( 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/sandbox2/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(w1,X0),X1) = apply(apply(X1,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w1_definition) ).
fof(f3,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b),
file('/export/starexec/sandbox2/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/sandbox2/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(apply(b,apply(w1,w1)),apply(b,w1))),b),apply(b,X0)) = apply(strong_fixed_point,X0),
inference(superposition,[],[f1,f3]) ).
fof(f23,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(b,apply(w1,w1)),apply(b,w1)),apply(b,apply(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(f213,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(f215,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(f1987,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,[],[f215,f213]) ).
fof(f2217,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(forward_demodulation,[],[f1987,f24]) ).
fof(f2262,plain,
sF0 = apply(fixed_pt,sF0),
inference(superposition,[],[f2217,f6]) ).
fof(f2392,plain,
sF0 = sF1,
inference(superposition,[],[f8,f2262]) ).
fof(f2406,plain,
$false,
inference(forward_subsumption_resolution,[],[f2392,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL042-6 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n005.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 : Mon Sep 28 21:30:17 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.91/0.88 % (1206439)Will run a generic schedule for satisfiability detection.
% 3.91/0.88 % (1206449)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2223196852:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 3.91/0.88 % (1206448)% WARNING: option uhcvi not known.
% 3.91/0.88 % (1206447)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3100459687_3000 on theBenchmark for (3000ds/0Mi)
% 3.91/0.88 % (1206450)dis+10_1_sil=32000:sp=arity:random_seed=432173143:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 3.91/0.88 % (1206448)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2002513436:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 3.91/0.88 % (1206451)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2239721279:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 3.91/0.88 % (1206452)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1876726116:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 3.91/0.88 % TRYING [1]
% 3.91/0.88 % TRYING [2]
% 3.91/0.88 % TRYING [3]
% 3.91/0.88 % (1206453)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2684219973:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 3.91/0.88 % TRYING [4]
% 3.91/0.88 % TRYING [5]
% 3.91/0.88 % (1206450)Instruction limit reached!
% 3.91/0.88 % (1206450)------------------------------
% 3.91/0.88 % (1206450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.88 % (1206450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.88 % (1206450)CaDiCaL version: 2.1.3
% 3.91/0.88 % (1206450)Termination reason: Instruction limit
% 3.91/0.88 % (1206450)Termination phase: Saturation
% 3.91/0.88 % (1206450)Time elapsed: 0.058 s
% 3.91/0.88 % (1206450)Peak memory usage: 12 MB
% 3.91/0.88 % (1206450)Instructions burned: 103 (million)
% 3.91/0.88 % (1206451)Instruction limit reached!
% 3.91/0.88 % (1206451)------------------------------
% 3.91/0.88 % (1206451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.88 % (1206451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.88 % (1206451)CaDiCaL version: 2.1.3
% 3.91/0.88 % (1206451)Termination reason: Instruction limit
% 3.91/0.88 % (1206451)Termination phase: Saturation
% 3.91/0.88 % (1206451)Time elapsed: 0.073 s
% 3.91/0.88 % (1206451)Peak memory usage: 12 MB
% 3.91/0.88 % (1206451)Instructions burned: 117 (million)
% 3.91/0.88 % (1206486)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3168952418:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.91/0.88 % TRYING [1]
% 3.91/0.88 % TRYING [2]
% 3.91/0.88 % TRYING [3]
% 3.91/0.88 % TRYING [4]
% 3.91/0.88 % (1206452)Instruction limit reached!
% 3.91/0.88 % (1206452)------------------------------
% 3.91/0.88 % (1206452)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.88 % (1206452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.88 % (1206452)CaDiCaL version: 2.1.3
% 3.91/0.88 % (1206452)Termination reason: Instruction limit
% 3.91/0.88 % (1206452)Termination phase: Saturation
% 3.91/0.88 % (1206452)Time elapsed: 0.084 s
% 3.91/0.88 % (1206452)Peak memory usage: 13 MB
% 3.91/0.88 % (1206452)Instructions burned: 132 (million)
% 3.91/0.88 % (1206493)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=196386869:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.91/0.88 % (1206453)Instruction limit reached!
% 3.91/0.88 % (1206453)------------------------------
% 3.91/0.88 % (1206453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.88 % (1206453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.88 % (1206453)CaDiCaL version: 2.1.3
% 3.91/0.88 % (1206453)Termination reason: Instruction limit
% 3.91/0.88 % (1206453)Termination phase: Saturation
% 3.91/0.88 % (1206453)Time elapsed: 0.099 s
% 3.91/0.88 % (1206453)Peak memory usage: 13 MB
% 3.91/0.88 % (1206453)Instructions burned: 160 (million)
% 3.91/0.88 % (1206500)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=36226159:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.91/0.88 % (1206511)ott-21_1_sil=16000:fs=off:random_seed=3428869864:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.91/0.88 % TRYING [5]
% 3.91/0.88 % (1206493)Instruction limit reached!
% 3.91/0.88 % (1206493)------------------------------
% 3.91/0.88 % (1206493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.88 % (1206493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.88 % (1206493)CaDiCaL version: 2.1.3
% 3.91/0.88 % (1206493)Termination reason: Instruction limit
% 3.91/0.88 % (1206493)Termination phase: Saturation
% 3.91/0.88 % (1206493)Time elapsed: 0.086 s
% 3.91/0.88 % (1206493)Peak memory usage: 13 MB
% 3.91/0.88 % (1206493)Instructions burned: 132 (million)
% 3.91/0.88 % (1206534)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3610357164:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 3.91/0.88 % (1206511)Instruction limit reached!
% 3.91/0.88 % (1206511)------------------------------
% 3.91/0.88 % (1206511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.88 % (1206511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.88 % (1206511)CaDiCaL version: 2.1.3
% 3.91/0.88 % (1206511)Termination reason: Instruction limit
% 3.91/0.88 % (1206511)Termination phase: Saturation
% 3.91/0.88 % (1206511)Time elapsed: 0.084 s
% 3.91/0.88 % (1206511)Peak memory usage: 11 MB
% 3.91/0.88 % (1206511)Instructions burned: 182 (million)
% 3.91/0.88 % (1206542)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1500519913:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 3.91/0.88 % TRYING [1]
% 3.91/0.88 % TRYING [2]
% 3.91/0.88 % TRYING [3]
% 3.91/0.88 % TRYING [4]
% 3.91/0.88 % TRYING [6]
% 3.91/0.88 % TRYING [5]
% 3.91/0.88 % TRYING [6]
% 3.91/0.88 % TRYING [6]
% 3.91/0.88 % (1206534)Instruction limit reached!
% 3.91/0.88 % (1206534)------------------------------
% 3.91/0.88 % (1206534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.88 % (1206534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.88 % (1206534)CaDiCaL version: 2.1.3
% 3.91/0.88 % (1206534)Termination reason: Instruction limit
% 3.91/0.88 % (1206534)Termination phase: Saturation
% 3.91/0.88 % (1206534)Time elapsed: 0.256 s
% 3.91/0.88 % (1206534)Peak memory usage: 14 MB
% 3.91/0.88 % (1206534)Instructions burned: 477 (million)
% 3.91/0.88 % (1206500)Instruction limit reached!
% 3.91/0.88 % (1206500)------------------------------
% 3.91/0.88 % (1206500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.88 % (1206500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.88 % (1206500)CaDiCaL version: 2.1.3
% 3.91/0.88 % (1206500)Termination reason: Instruction limit
% 3.91/0.88 % (1206500)Termination phase: Saturation
% 3.91/0.88 % (1206500)Time elapsed: 0.367 s
% 3.91/0.88 % (1206500)Peak memory usage: 16 MB
% 3.91/0.88 % (1206500)Instructions burned: 684 (million)
% 3.91/0.88 % (1206595)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1151105460:i=1179_2995 on theBenchmark for (2995ds/1179Mi)
% 3.91/0.88 % (1206602)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2318235281:i=889:ins=1_2995 on theBenchmark for (2995ds/889Mi)
% 3.91/0.88 % (1206486)Instruction limit reached!
% 3.91/0.88 % (1206486)------------------------------
% 3.91/0.88 % (1206486)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.88 % (1206486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.88 % (1206486)CaDiCaL version: 2.1.3
% 3.91/0.88 % (1206486)Termination reason: Instruction limit
% 3.91/0.88 % (1206486)Termination phase: Finite model building SAT solving
% 3.91/0.88 % (1206486)Time elapsed: 0.421 s
% 3.91/0.88 % (1206486)Peak memory usage: 16 MB
% 3.91/0.88 % (1206486)Instructions burned: 716 (million)
% 3.91/0.88 % (1206609)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=3706618920: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)
% 3.91/0.88 % TRYING [14]
% 3.91/0.88 % (1206595) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1206439-1206595"...
% 3.91/0.88 % (1206595)...printing done.
% 3.91/0.88 % (1206595)Refutation found. Thanks to Tanya!
% 3.91/0.88 % SZS status Unsatisfiable for theBenchmark
% 3.91/0.88 % SZS output start Proof for theBenchmark
% See solution above
% 3.91/0.88 % (1206595)------------------------------
% 3.91/0.88 % (1206595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.91/0.88 % (1206595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/0.88 % (1206595)CaDiCaL version: 2.1.3
% 3.91/0.88 % (1206595)Termination reason: Refutation
% 3.91/0.88 % (1206595)Time elapsed: 0.134 s
% 3.91/0.88 % (1206595)Peak memory usage: 14 MB
% 3.91/0.88 % (1206595)Instructions burned: 212 (million)
% 3.91/0.88 % (1206439)Success in time 0.639 s
% 3.91/0.88 % Vampire exiting
%------------------------------------------------------------------------------