%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL003-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 5.65s 1.10s
% Output : Refutation 5.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 13 unt; 0 def)
% Number of atoms : 17 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 8 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 14 !; 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(w,X0),X1) = apply(apply(X0,X1),X1),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f5,plain,
! [X0] :
( ~ fixed_point(X0)
| apply(X0,fixed_pt) != apply(fixed_pt,apply(X0,fixed_pt)) ),
inference(consistent_polarity_flipping,[],[f3]) ).
fof(f6,plain,
fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b)),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f10,plain,
! [X0] : apply(apply(w,w),X0) = apply(apply(X0,X0),X0),
inference(superposition,[],[f2,f2]) ).
fof(f21,plain,
apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt) != apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt)),
inference(resolution,[],[f5,f6]) ).
fof(f22,plain,
apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt)) != apply(fixed_pt,apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,fixed_pt))),
inference(forward_demodulation,[],[f21,f1]) ).
fof(f23,plain,
apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))) != apply(fixed_pt,apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt)))),
inference(forward_demodulation,[],[f22,f1]) ).
fof(f24,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt))))),
inference(forward_demodulation,[],[f23,f1]) ).
fof(f29,plain,
! [X0,X1] : apply(apply(w,apply(b,X0)),X1) = apply(X0,apply(X1,X1)),
inference(superposition,[],[f2,f1]) ).
fof(f82,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,f29]) ).
fof(f4556,plain,
! [X0] : apply(apply(w,w),apply(w,apply(b,apply(b,X0)))) = apply(X0,apply(apply(w,w),apply(w,apply(b,apply(b,X0))))),
inference(superposition,[],[f82,f10]) ).
fof(f4820,plain,
$false,
inference(backward_subsumption_resolution,[],[f24,f4556]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.21 % Computer : n003.cluster.edu
% 0.12/0.21 % Model : x86_64 x86_64
% 0.12/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.21 % Memory : 8046.5625MB
% 0.12/0.21 % OS : Linux 6.8.0-71-generic
% 0.12/0.21 % CPULimit : 300
% 0.12/0.21 % WCLimit : 300
% 0.12/0.21 % DateTime : Mon Sep 28 21:30:58 UTC 2026
% 0.12/0.21 % CPUTime :
% 0.12/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.25 Running first-order model finding
% 0.12/0.25 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
% 5.65/1.10 % (2044467)Will run a generic schedule for satisfiability detection.
% 5.65/1.10 % (2044475)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1063418678_3000 on theBenchmark for (3000ds/0Mi)
% 5.65/1.10 % TRYING [1]
% 5.65/1.10 % TRYING [2]
% 5.65/1.10 % TRYING [3]
% 5.65/1.10 % TRYING [4]
% 5.65/1.10 % (2044476)% WARNING: option uhcvi not known.
% 5.65/1.10 % (2044476)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1245016308:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 5.65/1.10 % (2044477)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3786675631:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 5.65/1.10 % (2044479)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=531385111:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 5.65/1.10 % (2044478)dis+10_1_sil=32000:sp=arity:random_seed=2626842180:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 5.65/1.10 % (2044480)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2301388583:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 5.65/1.10 % (2044481)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=891417180:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 5.65/1.10 % TRYING [5]
% 5.65/1.10 % (2044478)Instruction limit reached!
% 5.65/1.10 % (2044478)------------------------------
% 5.65/1.10 % (2044478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.65/1.10 % (2044478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.65/1.10 % (2044478)CaDiCaL version: 2.1.3
% 5.65/1.10 % (2044478)Termination reason: Instruction limit
% 5.65/1.10 % (2044478)Termination phase: Saturation
% 5.65/1.10 % (2044478)Time elapsed: 0.057 s
% 5.65/1.10 % (2044478)Peak memory usage: 12 MB
% 5.65/1.10 % (2044478)Instructions burned: 104 (million)
% 5.65/1.10 % (2044479)Instruction limit reached!
% 5.65/1.10 % (2044479)------------------------------
% 5.65/1.10 % (2044479)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.65/1.10 % (2044479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.65/1.10 % (2044479)CaDiCaL version: 2.1.3
% 5.65/1.10 % (2044479)Termination reason: Instruction limit
% 5.65/1.10 % (2044479)Termination phase: Saturation
% 5.65/1.10 % (2044479)Time elapsed: 0.070 s
% 5.65/1.10 % (2044479)Peak memory usage: 12 MB
% 5.65/1.10 % (2044479)Instructions burned: 116 (million)
% 5.65/1.10 % (2044521)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1740922164:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.65/1.10 % TRYING [1]
% 5.65/1.10 % TRYING [2]
% 5.65/1.10 % TRYING [3]
% 5.65/1.10 % (2044480)Instruction limit reached!
% 5.65/1.10 % (2044480)------------------------------
% 5.65/1.10 % (2044480)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.65/1.10 % (2044480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.65/1.10 % (2044480)CaDiCaL version: 2.1.3
% 5.65/1.10 % (2044480)Termination reason: Instruction limit
% 5.65/1.10 % (2044480)Termination phase: Saturation
% 5.65/1.10 % (2044480)Time elapsed: 0.080 s
% 5.65/1.10 % (2044480)Peak memory usage: 13 MB
% 5.65/1.10 % (2044480)Instructions burned: 132 (million)
% 5.65/1.10 % TRYING [4]
% 5.65/1.10 % (2044530)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1268444703:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 5.65/1.10 % (2044481)Instruction limit reached!
% 5.65/1.10 % (2044481)------------------------------
% 5.65/1.10 % (2044481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.65/1.10 % (2044481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.65/1.10 % (2044481)CaDiCaL version: 2.1.3
% 5.65/1.10 % (2044481)Termination reason: Instruction limit
% 5.65/1.10 % (2044481)Termination phase: Saturation
% 5.65/1.10 % (2044481)Time elapsed: 0.098 s
% 5.65/1.10 % (2044481)Peak memory usage: 13 MB
% 5.65/1.10 % (2044481)Instructions burned: 160 (million)
% 5.65/1.10 % (2044535)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=1300680818:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 5.65/1.10 % (2044542)ott-21_1_sil=16000:fs=off:random_seed=3882546008:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 5.65/1.10 % TRYING [5]
% 5.65/1.10 % (2044530)Instruction limit reached!
% 5.65/1.10 % (2044530)------------------------------
% 5.65/1.10 % (2044530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.65/1.10 % (2044530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.65/1.10 % (2044530)CaDiCaL version: 2.1.3
% 5.65/1.10 % (2044530)Termination reason: Instruction limit
% 5.65/1.10 % (2044530)Termination phase: Saturation
% 5.65/1.10 % (2044530)Time elapsed: 0.086 s
% 5.65/1.10 % (2044530)Peak memory usage: 13 MB
% 5.65/1.10 % (2044530)Instructions burned: 132 (million)
% 5.65/1.10 % TRYING [6]
% 5.65/1.10 % (2044567)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2591511175:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 5.65/1.10 % (2044542)Instruction limit reached!
% 5.65/1.10 % (2044542)------------------------------
% 5.65/1.10 % (2044542)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.65/1.10 % (2044542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.65/1.10 % (2044542)CaDiCaL version: 2.1.3
% 5.65/1.10 % (2044542)Termination reason: Instruction limit
% 5.65/1.10 % (2044542)Termination phase: Saturation
% 5.65/1.10 % (2044542)Time elapsed: 0.085 s
% 5.65/1.10 % (2044542)Peak memory usage: 11 MB
% 5.65/1.10 % (2044542)Instructions burned: 180 (million)
% 5.65/1.10 % (2044576)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=686676651:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 5.65/1.10 % TRYING [1]
% 5.65/1.10 % TRYING [2]
% 5.65/1.10 % TRYING [3]
% 5.65/1.10 % TRYING [4]
% 5.65/1.10 % TRYING [5]
% 5.65/1.10 % TRYING [6]
% 5.65/1.10 % (2044567)Instruction limit reached!
% 5.65/1.10 % (2044567)------------------------------
% 5.65/1.10 % (2044567)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.65/1.10 % (2044567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.65/1.10 % (2044567)CaDiCaL version: 2.1.3
% 5.65/1.10 % (2044567)Termination reason: Instruction limit
% 5.65/1.10 % (2044567)Termination phase: Saturation
% 5.65/1.10 % (2044567)Time elapsed: 0.256 s
% 5.65/1.10 % (2044567)Peak memory usage: 15 MB
% 5.65/1.10 % (2044567)Instructions burned: 478 (million)
% 5.65/1.10 % (2044535)Instruction limit reached!
% 5.65/1.10 % (2044535)------------------------------
% 5.65/1.10 % (2044535)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.65/1.10 % (2044535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.65/1.10 % (2044535)CaDiCaL version: 2.1.3
% 5.65/1.10 % (2044535)Termination reason: Instruction limit
% 5.65/1.10 % (2044535)Termination phase: Saturation
% 5.65/1.10 % (2044535)Time elapsed: 0.355 s
% 5.65/1.10 % (2044535)Peak memory usage: 16 MB
% 5.65/1.10 % (2044535)Instructions burned: 685 (million)
% 5.65/1.10 % (2044629)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3269946940:i=1179_2995 on theBenchmark for (2995ds/1179Mi)
% 5.65/1.10 % (2044630)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2349415052:i=889:ins=1_2995 on theBenchmark for (2995ds/889Mi)
% 5.65/1.10 % TRYING [14]
% 5.65/1.10 % TRYING [6]
% 5.65/1.10 % (2044521)Instruction limit reached!
% 5.65/1.10 % (2044521)------------------------------
% 5.65/1.10 % (2044521)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.65/1.10 % (2044521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.65/1.10 % (2044521)CaDiCaL version: 2.1.3
% 5.65/1.10 % (2044521)Termination reason: Instruction limit
% 5.65/1.10 % (2044521)Termination phase: Finite model building constraint generation
% 5.65/1.10 % (2044521)Time elapsed: 0.446 s
% 5.65/1.10 % (2044521)Peak memory usage: 15 MB
% 5.65/1.10 % (2044521)Instructions burned: 717 (million)
% 5.65/1.10 % (2044633)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=512837870: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)
% 5.65/1.10 % (2044576)Instruction limit reached!
% 5.65/1.10 % (2044576)------------------------------
% 5.65/1.10 % (2044576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.65/1.10 % (2044576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.65/1.10 % (2044576)CaDiCaL version: 2.1.3
% 5.65/1.10 % (2044576)Termination reason: Instruction limit
% 5.65/1.10 % (2044576)Termination phase: Finite model building SAT solving
% 5.65/1.10 % (2044576)Time elapsed: 0.427 s
% 5.65/1.10 % (2044576)Peak memory usage: 14 MB
% 5.65/1.10 % (2044576)Instructions burned: 865 (million)
% 5.65/1.10 % (2044635)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1076522133:i=879:kws=inv_precedence:fsr=off_2993 on theBenchmark for (2993ds/879Mi)
% 5.65/1.10 % (2044630)Instruction limit reached!
% 5.65/1.10 % (2044630)------------------------------
% 5.65/1.10 % (2044630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.65/1.10 % (2044630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.65/1.10 % (2044630)CaDiCaL version: 2.1.3
% 5.65/1.10 % (2044630)Termination reason: Instruction limit
% 5.65/1.10 % (2044630)Termination phase: Finite model building constraint generation
% 5.65/1.10 % (2044630)Time elapsed: 0.317 s
% 5.65/1.10 % (2044630)Peak memory usage: 78 MB
% 5.65/1.10 % (2044630)Instructions burned: 889 (million)
% 5.65/1.10 % (2044633) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2044467-2044633"...
% 5.65/1.10 % (2044633)...printing done.
% 5.65/1.10 % (2044637)fmb+10_1_sil=64000:random_seed=2864425618:i=22061:nm=2:gsp=on_2991 on theBenchmark for (2991ds/22061Mi)
% 5.65/1.10 % (2044633)Refutation found. Thanks to Tanya!
% 5.65/1.10 % SZS status Unsatisfiable for theBenchmark
% 5.65/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 5.65/1.10 % (2044633)------------------------------
% 5.65/1.10 % (2044633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.65/1.10 % (2044633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.65/1.10 % (2044633)CaDiCaL version: 2.1.3
% 5.65/1.10 % (2044633)Termination reason: Refutation
% 5.65/1.10 % (2044633)Time elapsed: 0.272 s
% 5.65/1.10 % (2044633)Peak memory usage: 16 MB
% 5.65/1.10 % (2044633)Instructions burned: 436 (million)
% 5.65/1.10 % (2044467)Success in time 0.843 s
% 5.65/1.10 % Vampire exiting
%------------------------------------------------------------------------------