%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL002-2 : 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 : n020.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 09:38:05 AM UTC 2026
% Result : Unsatisfiable 1.56s 0.58s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 24 ( 21 unt; 4 def)
% Number of atoms : 27 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).
fof(f2,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(f4,axiom,
! [X0] : apply(i,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_definition) ).
fof(f5,axiom,
! [X0] :
( X0 != apply(fixed_pt,X0)
| fixed_point(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',weak_fixed_point) ).
fof(f6,plain,
! [X0] :
( apply(fixed_pt,X0) != X0
| fixed_point(X0) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
! [X0] : ~ fixed_point(apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
fof(f8,definition,
! [X0] : sF0(X0) = apply(b,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f9,plain,
! [X0] : apply(b,X0) = sF0(X0),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
! [X0] : sF1(X0) = apply(s,sF0(X0)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f11,plain,
! [X0] : apply(s,sF0(X0)) = sF1(X0),
inference(reorient_equations,[],[f10]) ).
fof(f12,definition,
! [X0] : sF2(X0) = apply(sF1(X0),i),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f13,plain,
! [X0] : apply(sF1(X0),i) = sF2(X0),
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
! [X0] : sF3(X0) = apply(sF2(X0),sF2(X0)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f15,plain,
! [X0] : apply(sF2(X0),sF2(X0)) = sF3(X0),
inference(reorient_equations,[],[f14]) ).
fof(f16,plain,
! [X0] : ~ fixed_point(sF3(X0)),
inference(definition_folding,[],[f7,f15,f13,f11,f9,f13,f11,f9]) ).
fof(f17,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(apply(sF0(X0),X1),X2),
inference(superposition,[],[f2,f9]) ).
fof(f69,plain,
! [X2,X0,X1] : apply(apply(sF0(X0),X2),apply(X1,X2)) = apply(apply(sF1(X0),X1),X2),
inference(superposition,[],[f1,f11]) ).
fof(f158,plain,
! [X2,X0,X1] : apply(apply(sF1(X0),X1),X2) = apply(X0,apply(X2,apply(X1,X2))),
inference(forward_demodulation,[],[f69,f17]) ).
fof(f263,plain,
! [X0,X1] : apply(apply(sF1(X1),i),X0) = apply(X1,apply(X0,X0)),
inference(superposition,[],[f158,f4]) ).
fof(f361,plain,
! [X0,X1] : apply(X1,apply(X0,X0)) = apply(sF2(X1),X0),
inference(forward_demodulation,[],[f263,f13]) ).
fof(f396,plain,
! [X0] : sF3(X0) = apply(X0,sF3(X0)),
inference(superposition,[],[f361,f15]) ).
fof(f674,plain,
( sF3(fixed_pt) != sF3(fixed_pt)
| fixed_point(sF3(fixed_pt)) ),
inference(superposition,[],[f6,f396]) ).
fof(f683,plain,
fixed_point(sF3(fixed_pt)),
inference(trivial_inequality_removal,[],[f674]) ).
fof(f687,plain,
$false,
inference(forward_subsumption_resolution,[],[f683,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL002-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n020.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 21:29:19 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
% 1.56/0.58 % (583827)Will run a generic schedule for satisfiability detection.
% 1.56/0.58 % (583837)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3187518942:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.56/0.58 % (583834)% WARNING: option uhcvi not known.
% 1.56/0.58 % (583832)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=385142265_2999 on theBenchmark for (2999ds/0Mi)
% 1.56/0.58 % (583836)dis+10_1_sil=32000:sp=arity:random_seed=3405018541:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.56/0.58 % (583835)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1776345897:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.56/0.58 % (583834)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2725582861:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.56/0.58 % (583839)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=851727442:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.56/0.58 % (583838)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=335910720:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.56/0.58 % TRYING [1]
% 1.56/0.58 % TRYING [2]
% 1.56/0.58 % TRYING [3]
% 1.56/0.58 % TRYING [4]
% 1.56/0.58 % TRYING [5]
% 1.56/0.58 % (583837)Instruction limit reached!
% 1.56/0.58 % (583837)------------------------------
% 1.56/0.58 % (583837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.58 % (583837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.58 % (583837)CaDiCaL version: 2.1.3
% 1.56/0.58 % (583837)Termination reason: Instruction limit
% 1.56/0.58 % (583837)Termination phase: Saturation
% 1.56/0.58 % (583837)Time elapsed: 0.039 s
% 1.56/0.58 % (583837)Peak memory usage: 13 MB
% 1.56/0.58 % (583837)Instructions burned: 116 (million)
% 1.56/0.58 % (583861)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=212885631:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.56/0.58 % TRYING [1]
% 1.56/0.58 % TRYING [2]
% 1.56/0.58 % TRYING [3]
% 1.56/0.58 % TRYING [4]
% 1.56/0.58 % (583836)Instruction limit reached!
% 1.56/0.58 % (583836)------------------------------
% 1.56/0.58 % (583836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.58 % (583836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.58 % (583836)CaDiCaL version: 2.1.3
% 1.56/0.58 % (583836)Termination reason: Instruction limit
% 1.56/0.58 % (583836)Termination phase: Saturation
% 1.56/0.58 % (583836)Time elapsed: 0.057 s
% 1.56/0.58 % (583836)Peak memory usage: 12 MB
% 1.56/0.58 % (583836)Instructions burned: 105 (million)
% 1.56/0.58 % TRYING [5]
% 1.56/0.58 % (583838)Instruction limit reached!
% 1.56/0.58 % (583838)------------------------------
% 1.56/0.58 % (583838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.58 % (583838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.58 % (583838)CaDiCaL version: 2.1.3
% 1.56/0.58 % (583838)Termination reason: Instruction limit
% 1.56/0.58 % (583838)Termination phase: Saturation
% 1.56/0.58 % (583838)Time elapsed: 0.069 s
% 1.56/0.58 % (583838)Peak memory usage: 12 MB
% 1.56/0.58 % (583838)Instructions burned: 131 (million)
% 1.56/0.58 % (583869)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1798557437:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.56/0.58 % (583876)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=655666046:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.56/0.58 % (583839)Instruction limit reached!
% 1.56/0.58 % (583839)------------------------------
% 1.56/0.58 % (583839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.58 % (583839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.58 % (583839)CaDiCaL version: 2.1.3
% 1.56/0.58 % (583839)Termination reason: Instruction limit
% 1.56/0.58 % (583839)Termination phase: Saturation
% 1.56/0.58 % (583839)Time elapsed: 0.091 s
% 1.56/0.58 % (583839)Peak memory usage: 12 MB
% 1.56/0.58 % (583839)Instructions burned: 160 (million)
% 1.56/0.58 % TRYING [6]
% 1.56/0.58 % (583888)ott-21_1_sil=16000:fs=off:random_seed=2981649063:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.56/0.58 % TRYING [6]
% 1.56/0.58 % (583869)Instruction limit reached!
% 1.56/0.58 % (583869)------------------------------
% 1.56/0.58 % (583869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.58 % (583869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.58 % (583869)CaDiCaL version: 2.1.3
% 1.56/0.58 % (583869)Termination reason: Instruction limit
% 1.56/0.58 % (583869)Termination phase: Saturation
% 1.56/0.58 % (583869)Time elapsed: 0.084 s
% 1.56/0.58 % (583869)Peak memory usage: 14 MB
% 1.56/0.58 % (583869)Instructions burned: 131 (million)
% 1.56/0.58 % (583920)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1044654167:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.56/0.58 % (583888)Instruction limit reached!
% 1.56/0.58 % (583888)------------------------------
% 1.56/0.58 % (583888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.58 % (583888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.58 % (583888)CaDiCaL version: 2.1.3
% 1.56/0.58 % (583888)Termination reason: Instruction limit
% 1.56/0.58 % (583888)Termination phase: Saturation
% 1.56/0.58 % (583888)Time elapsed: 0.108 s
% 1.56/0.58 % (583888)Peak memory usage: 13 MB
% 1.56/0.58 % (583888)Instructions burned: 182 (million)
% 1.56/0.58 % (583936)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3916022623:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.56/0.58 % TRYING [1]
% 1.56/0.58 % TRYING [2]
% 1.56/0.58 % TRYING [7]
% 1.56/0.58 % TRYING [3]
% 1.56/0.58 % TRYING [4]
% 1.56/0.58 % (583861)Instruction limit reached!
% 1.56/0.58 % (583861)------------------------------
% 1.56/0.58 % (583861)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.58 % (583861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.58 % (583861)CaDiCaL version: 2.1.3
% 1.56/0.58 % (583861)Termination reason: Instruction limit
% 1.56/0.58 % (583861)Termination phase: Finite model building constraint generation
% 1.56/0.58 % (583861)Time elapsed: 0.214 s
% 1.56/0.58 % (583861)Peak memory usage: 27 MB
% 1.56/0.58 % (583861)Instructions burned: 729 (million)
% 1.56/0.58 % (583947)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1616948343:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 1.56/0.58 % (583947) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-583827-583947"...
% 1.56/0.58 % (583947)...printing done.
% 1.56/0.58 % (583947)Refutation found. Thanks to Tanya!
% 1.56/0.58 % SZS status Unsatisfiable for theBenchmark
% 1.56/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 1.56/0.58 % (583947)------------------------------
% 1.56/0.58 % (583947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.58 % (583947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.58 % (583947)CaDiCaL version: 2.1.3
% 1.56/0.58 % (583947)Termination reason: Refutation
% 1.56/0.58 % (583947)Time elapsed: 0.021 s
% 1.56/0.58 % (583947)Peak memory usage: 12 MB
% 1.56/0.58 % (583947)Instructions burned: 63 (million)
% 1.56/0.58 % (583827)Success in time 0.331 s
% 1.56/0.58 % Vampire exiting
%------------------------------------------------------------------------------