%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL003-3 : 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 : n008.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 6.56s 1.37s
% Output : Refutation 6.56s
% 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(w,w)),apply(apply(b,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(w,w)),apply(apply(b,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(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),fixed_pt) != apply(fixed_pt,apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),fixed_pt)),
inference(resolution,[],[f5,f6]) ).
fof(f22,plain,
apply(apply(w,w),apply(apply(apply(b,apply(apply(b,w),b)),b),fixed_pt)) != apply(fixed_pt,apply(apply(w,w),apply(apply(apply(b,apply(apply(b,w),b)),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 : COL003-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.22 % Computer : n008.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Mon Sep 28 21:29:55 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.26/0.27 Running first-order model finding
% 0.26/0.28 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
% 6.56/1.37 % (2672075)Will run a generic schedule for satisfiability detection.
% 6.56/1.37 % (2672080)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2385844060_3000 on theBenchmark for (3000ds/0Mi)
% 6.56/1.37 % TRYING [1]
% 6.56/1.37 % TRYING [2]
% 6.56/1.37 % TRYING [3]
% 6.56/1.37 % TRYING [4]
% 6.56/1.37 % (2672081)% WARNING: option uhcvi not known.
% 6.56/1.37 % (2672085)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3023450191:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 6.56/1.37 % (2672083)dis+10_1_sil=32000:sp=arity:random_seed=1250759860:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 6.56/1.37 % (2672081)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2222341777:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 6.56/1.37 % (2672082)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1614008432:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 6.56/1.37 % (2672084)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2049746409:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 6.56/1.37 % (2672086)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3802720270:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 6.56/1.37 % TRYING [5]
% 6.56/1.37 % (2672083)Instruction limit reached!
% 6.56/1.37 % (2672083)------------------------------
% 6.56/1.37 % (2672083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.37 % (2672083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.37 % (2672083)CaDiCaL version: 2.1.3
% 6.56/1.37 % (2672083)Termination reason: Instruction limit
% 6.56/1.37 % (2672083)Termination phase: Saturation
% 6.56/1.37 % (2672083)Time elapsed: 0.081 s
% 6.56/1.37 % (2672083)Peak memory usage: 12 MB
% 6.56/1.37 % (2672083)Instructions burned: 104 (million)
% 6.56/1.37 % (2672094)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=470698772:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 6.56/1.37 % TRYING [1]
% 6.56/1.37 % TRYING [2]
% 6.56/1.37 % TRYING [3]
% 6.56/1.37 % (2672085)Instruction limit reached!
% 6.56/1.37 % (2672085)------------------------------
% 6.56/1.37 % (2672085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.37 % (2672085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.37 % (2672085)CaDiCaL version: 2.1.3
% 6.56/1.37 % (2672085)Termination reason: Instruction limit
% 6.56/1.37 % (2672085)Termination phase: Saturation
% 6.56/1.37 % (2672085)Time elapsed: 0.111 s
% 6.56/1.37 % (2672085)Peak memory usage: 13 MB
% 6.56/1.37 % (2672085)Instructions burned: 131 (million)
% 6.56/1.37 % TRYING [4]
% 6.56/1.37 % (2672084)Instruction limit reached!
% 6.56/1.37 % (2672084)------------------------------
% 6.56/1.37 % (2672084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.37 % (2672084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.37 % (2672084)CaDiCaL version: 2.1.3
% 6.56/1.37 % (2672084)Termination reason: Instruction limit
% 6.56/1.37 % (2672084)Termination phase: Saturation
% 6.56/1.37 % (2672084)Time elapsed: 0.117 s
% 6.56/1.37 % (2672084)Peak memory usage: 12 MB
% 6.56/1.37 % (2672084)Instructions burned: 116 (million)
% 6.56/1.37 % (2672096)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3375679766:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 6.56/1.37 % (2672098)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=1518418336:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 6.56/1.37 % (2672086)Instruction limit reached!
% 6.56/1.37 % (2672086)------------------------------
% 6.56/1.37 % (2672086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.37 % (2672086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.37 % (2672086)CaDiCaL version: 2.1.3
% 6.56/1.37 % (2672086)Termination reason: Instruction limit
% 6.56/1.37 % (2672086)Termination phase: Saturation
% 6.56/1.37 % (2672086)Time elapsed: 0.159 s
% 6.56/1.37 % (2672086)Peak memory usage: 12 MB
% 6.56/1.37 % (2672086)Instructions burned: 160 (million)
% 6.56/1.37 % (2672101)ott-21_1_sil=16000:fs=off:random_seed=937791928:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 6.56/1.37 % TRYING [5]
% 6.56/1.37 % TRYING [6]
% 6.56/1.37 % (2672096)Instruction limit reached!
% 6.56/1.37 % (2672096)------------------------------
% 6.56/1.37 % (2672096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.37 % (2672096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.37 % (2672096)CaDiCaL version: 2.1.3
% 6.56/1.37 % (2672096)Termination reason: Instruction limit
% 6.56/1.37 % (2672096)Termination phase: Saturation
% 6.56/1.37 % (2672096)Time elapsed: 0.138 s
% 6.56/1.37 % (2672096)Peak memory usage: 13 MB
% 6.56/1.37 % (2672096)Instructions burned: 131 (million)
% 6.56/1.37 % (2672106)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2264482993:i=477:bd=all_2996 on theBenchmark for (2996ds/477Mi)
% 6.56/1.37 % (2672101)Instruction limit reached!
% 6.56/1.37 % (2672101)------------------------------
% 6.56/1.37 % (2672101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.37 % (2672101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.37 % (2672101)CaDiCaL version: 2.1.3
% 6.56/1.37 % (2672101)Termination reason: Instruction limit
% 6.56/1.37 % (2672101)Termination phase: Saturation
% 6.56/1.37 % (2672101)Time elapsed: 0.148 s
% 6.56/1.37 % (2672101)Peak memory usage: 12 MB
% 6.56/1.37 % (2672101)Instructions burned: 181 (million)
% 6.56/1.37 % (2672108)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4021556324:fmbsr=1.3:i=865:ins=25_2996 on theBenchmark for (2996ds/865Mi)
% 6.56/1.37 % TRYING [1]
% 6.56/1.37 % TRYING [2]
% 6.56/1.37 % TRYING [3]
% 6.56/1.37 % TRYING [4]
% 6.56/1.37 % TRYING [5]
% 6.56/1.37 % TRYING [6]
% 6.56/1.37 % TRYING [6]
% 6.56/1.37 % (2672106)Instruction limit reached!
% 6.56/1.37 % (2672106)------------------------------
% 6.56/1.37 % (2672106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.37 % (2672106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.37 % (2672106)CaDiCaL version: 2.1.3
% 6.56/1.37 % (2672106)Termination reason: Instruction limit
% 6.56/1.37 % (2672106)Termination phase: Saturation
% 6.56/1.37 % (2672106)Time elapsed: 0.388 s
% 6.56/1.37 % (2672106)Peak memory usage: 15 MB
% 6.56/1.37 % (2672106)Instructions burned: 478 (million)
% 6.56/1.37 % (2672094)Instruction limit reached!
% 6.56/1.37 % (2672094)------------------------------
% 6.56/1.37 % (2672094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.37 % (2672094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.37 % (2672094)CaDiCaL version: 2.1.3
% 6.56/1.37 % (2672094)Termination reason: Instruction limit
% 6.56/1.37 % (2672094)Termination phase: Finite model building SAT solving
% 6.56/1.37 % (2672094)Time elapsed: 0.626 s
% 6.56/1.37 % (2672094)Peak memory usage: 15 MB
% 6.56/1.37 % (2672094)Instructions burned: 714 (million)
% 6.56/1.37 % (2672115)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3515516802:i=1179_2992 on theBenchmark for (2992ds/1179Mi)
% 6.56/1.37 % (2672098)Instruction limit reached!
% 6.56/1.37 % (2672098)------------------------------
% 6.56/1.37 % (2672098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.37 % (2672098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.37 % (2672098)CaDiCaL version: 2.1.3
% 6.56/1.37 % (2672098)Termination reason: Instruction limit
% 6.56/1.37 % (2672098)Termination phase: Saturation
% 6.56/1.37 % (2672098)Time elapsed: 0.593 s
% 6.56/1.37 % (2672098)Peak memory usage: 16 MB
% 6.56/1.37 % (2672098)Instructions burned: 685 (million)
% 6.56/1.37 % (2672116)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=64684320:i=889:ins=1_2992 on theBenchmark for (2992ds/889Mi)
% 6.56/1.37 % (2672118)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=3878117687:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2992 on theBenchmark for (2992ds/692Mi)
% 6.56/1.37 % TRYING [14]
% 6.56/1.37 % (2672108)Instruction limit reached!
% 6.56/1.37 % (2672108)------------------------------
% 6.56/1.37 % (2672108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.37 % (2672108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.37 % (2672108)CaDiCaL version: 2.1.3
% 6.56/1.37 % (2672108)Termination reason: Instruction limit
% 6.56/1.37 % (2672108)Termination phase: Finite model building SAT solving
% 6.56/1.37 % (2672108)Time elapsed: 0.556 s
% 6.56/1.37 % (2672108)Peak memory usage: 14 MB
% 6.56/1.37 % (2672108)Instructions burned: 866 (million)
% 6.56/1.37 % (2672121)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=327171198:i=879:kws=inv_precedence:fsr=off_2990 on theBenchmark for (2990ds/879Mi)
% 6.56/1.37 % (2672118) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2672075-2672118"...
% 6.56/1.37 % (2672118)...printing done.
% 6.56/1.37 % (2672118)Refutation found. Thanks to Tanya!
% 6.56/1.37 % SZS status Unsatisfiable for theBenchmark
% 6.56/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 6.56/1.37 % (2672118)------------------------------
% 6.56/1.37 % (2672118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.56/1.37 % (2672118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.37 % (2672118)CaDiCaL version: 2.1.3
% 6.56/1.37 % (2672118)Termination reason: Refutation
% 6.56/1.37 % (2672118)Time elapsed: 0.272 s
% 6.56/1.37 % (2672118)Peak memory usage: 16 MB
% 6.56/1.37 % (2672118)Instructions burned: 435 (million)
% 6.56/1.37 % (2672075)Success in time 1.085 s
% 6.56/1.37 % Vampire exiting
%------------------------------------------------------------------------------