%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL002-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 1.07s 0.57s
% Output : Refutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 29 ( 29 unt; 5 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 40 ( 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
fof(f3,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(f5,axiom,
! [X0] : apply(i,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_definition) ).
fof(f6,axiom,
! [X0] : ifeq(X0,apply(fixed_pt,X0),fixed_point(X0),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',weak_fixed_point) ).
fof(f7,plain,
! [X0] : true = ifeq(X0,apply(fixed_pt,X0),fixed_point(X0),true),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
! [X0] : fixed_point(apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
fof(f9,plain,
! [X0] : true != fixed_point(apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i))),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
! [X0] : sF0(X0) = apply(b,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f11,plain,
! [X0] : apply(b,X0) = sF0(X0),
inference(reorient_equations,[],[f10]) ).
fof(f12,definition,
! [X0] : sF1(X0) = apply(s,sF0(X0)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f13,plain,
! [X0] : apply(s,sF0(X0)) = sF1(X0),
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
! [X0] : sF2(X0) = apply(sF1(X0),i),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f15,plain,
! [X0] : apply(sF1(X0),i) = sF2(X0),
inference(reorient_equations,[],[f14]) ).
fof(f16,definition,
! [X0] : sF3(X0) = apply(sF2(X0),sF2(X0)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f17,plain,
! [X0] : apply(sF2(X0),sF2(X0)) = sF3(X0),
inference(reorient_equations,[],[f16]) ).
fof(f18,definition,
! [X0] : sF4(X0) = fixed_point(sF3(X0)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f19,plain,
! [X0] : fixed_point(sF3(X0)) = sF4(X0),
inference(reorient_equations,[],[f18]) ).
fof(f20,plain,
! [X0] : true != sF4(X0),
inference(definition_folding,[],[f9,f19,f17,f15,f13,f11,f15,f13,f11]) ).
fof(f21,plain,
! [X0] : true != fixed_point(sF3(X0)),
inference(superposition,[],[f20,f19]) ).
fof(f22,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(apply(sF0(X0),X1),X2),
inference(superposition,[],[f3,f11]) ).
fof(f67,plain,
! [X2,X0,X1] : apply(apply(sF0(X0),X2),apply(X1,X2)) = apply(apply(sF1(X0),X1),X2),
inference(superposition,[],[f2,f13]) ).
fof(f148,plain,
! [X2,X0,X1] : apply(apply(sF1(X0),X1),X2) = apply(X0,apply(X2,apply(X1,X2))),
inference(forward_demodulation,[],[f67,f22]) ).
fof(f503,plain,
! [X0,X1] : apply(apply(sF1(X1),i),X0) = apply(X1,apply(X0,X0)),
inference(superposition,[],[f148,f5]) ).
fof(f624,plain,
! [X0,X1] : apply(X1,apply(X0,X0)) = apply(sF2(X1),X0),
inference(forward_demodulation,[],[f503,f15]) ).
fof(f666,plain,
! [X0] : sF3(X0) = apply(X0,sF3(X0)),
inference(superposition,[],[f624,f17]) ).
fof(f1007,plain,
true = ifeq(sF3(fixed_pt),sF3(fixed_pt),fixed_point(sF3(fixed_pt)),true),
inference(superposition,[],[f7,f666]) ).
fof(f1020,plain,
true = fixed_point(sF3(fixed_pt)),
inference(forward_demodulation,[],[f1007,f1]) ).
fof(f1023,plain,
$false,
inference(forward_subsumption_resolution,[],[f1020,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL002-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 % Computer : n011.cluster.edu
% 0.07/0.21 % Model : x86_64 x86_64
% 0.07/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.21 % Memory : 8046.5625MB
% 0.07/0.21 % OS : Linux 6.8.0-71-generic
% 0.07/0.21 % CPULimit : 300
% 0.07/0.21 % WCLimit : 300
% 0.07/0.21 % DateTime : Mon Sep 28 21:28:03 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.24 Running first-order model finding
% 0.07/0.24 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
% 1.07/0.57 % (3799976)Will run a generic schedule for satisfiability detection.
% 1.07/0.57 % (3799985)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3080725281:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.07/0.57 % (3799982)% WARNING: option uhcvi not known.
% 1.07/0.57 % (3799982)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1556254249:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.07/0.57 % (3799981)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3944649161_2999 on theBenchmark for (2999ds/0Mi)
% 1.07/0.57 % (3799983)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2619507590:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.07/0.57 % (3799984)dis+10_1_sil=32000:sp=arity:random_seed=2041517788:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.07/0.57 % (3799986)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3244630584:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.07/0.57 % (3799987)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=14367280:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.07/0.57 % TRYING [1]
% 1.07/0.57 % TRYING [2]
% 1.07/0.57 % TRYING [3]
% 1.07/0.57 % TRYING [4]
% 1.07/0.57 % (3799985)Instruction limit reached!
% 1.07/0.57 % (3799985)------------------------------
% 1.07/0.57 % (3799985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.57 % (3799985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.57 % (3799985)CaDiCaL version: 2.1.3
% 1.07/0.57 % (3799985)Termination reason: Instruction limit
% 1.07/0.57 % (3799985)Termination phase: Saturation
% 1.07/0.57 % (3799985)Time elapsed: 0.040 s
% 1.07/0.57 % (3799985)Peak memory usage: 13 MB
% 1.07/0.57 % (3799985)Instructions burned: 117 (million)
% 1.07/0.57 % TRYING [5]
% 1.07/0.57 % (3799995)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4103970349:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.07/0.57 % TRYING [1]
% 1.07/0.57 % TRYING [2]
% 1.07/0.57 % TRYING [3]
% 1.07/0.57 % TRYING [4]
% 1.07/0.57 % (3799984)Instruction limit reached!
% 1.07/0.57 % (3799984)------------------------------
% 1.07/0.57 % (3799984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.57 % (3799984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.57 % (3799984)CaDiCaL version: 2.1.3
% 1.07/0.57 % (3799984)Termination reason: Instruction limit
% 1.07/0.57 % (3799984)Termination phase: Saturation
% 1.07/0.57 % (3799984)Time elapsed: 0.057 s
% 1.07/0.57 % (3799984)Peak memory usage: 12 MB
% 1.07/0.57 % (3799984)Instructions burned: 104 (million)
% 1.07/0.57 % (3799986)Instruction limit reached!
% 1.07/0.57 % (3799986)------------------------------
% 1.07/0.57 % (3799986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.57 % (3799986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.57 % (3799986)CaDiCaL version: 2.1.3
% 1.07/0.57 % (3799986)Termination reason: Instruction limit
% 1.07/0.57 % (3799986)Termination phase: Saturation
% 1.07/0.57 % (3799986)Time elapsed: 0.069 s
% 1.07/0.57 % (3799986)Peak memory usage: 12 MB
% 1.07/0.57 % (3799986)Instructions burned: 131 (million)
% 1.07/0.57 % (3799997)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1627767297:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.07/0.57 % TRYING [5]
% 1.07/0.57 % (3799987)Instruction limit reached!
% 1.07/0.57 % (3799987)------------------------------
% 1.07/0.57 % (3799987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.57 % (3799987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.57 % (3799987)CaDiCaL version: 2.1.3
% 1.07/0.57 % (3799987)Termination reason: Instruction limit
% 1.07/0.57 % (3799987)Termination phase: Saturation
% 1.07/0.57 % (3799987)Time elapsed: 0.089 s
% 1.07/0.57 % (3799987)Peak memory usage: 12 MB
% 1.07/0.57 % (3799987)Instructions burned: 160 (million)
% 1.07/0.57 % (3799998)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=2934101220:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.07/0.57 % (3800000)ott-21_1_sil=16000:fs=off:random_seed=4100747779:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.07/0.57 % TRYING [6]
% 1.07/0.57 % TRYING [6]
% 1.07/0.57 % (3799997)Instruction limit reached!
% 1.07/0.57 % (3799997)------------------------------
% 1.07/0.57 % (3799997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.57 % (3799997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.57 % (3799997)CaDiCaL version: 2.1.3
% 1.07/0.57 % (3799997)Termination reason: Instruction limit
% 1.07/0.57 % (3799997)Termination phase: Saturation
% 1.07/0.57 % (3799997)Time elapsed: 0.086 s
% 1.07/0.57 % (3799997)Peak memory usage: 13 MB
% 1.07/0.57 % (3799997)Instructions burned: 132 (million)
% 1.07/0.57 % (3800003)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2775848123:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.07/0.57 % (3800000)Instruction limit reached!
% 1.07/0.57 % (3800000)------------------------------
% 1.07/0.57 % (3800000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.57 % (3800000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.57 % (3800000)CaDiCaL version: 2.1.3
% 1.07/0.57 % (3800000)Termination reason: Instruction limit
% 1.07/0.57 % (3800000)Termination phase: Saturation
% 1.07/0.57 % (3800000)Time elapsed: 0.103 s
% 1.07/0.57 % (3800000)Peak memory usage: 13 MB
% 1.07/0.57 % (3800000)Instructions burned: 180 (million)
% 1.07/0.57 % (3799995)Instruction limit reached!
% 1.07/0.57 % (3799995)------------------------------
% 1.07/0.57 % (3799995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.57 % (3799995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.57 % (3799995)CaDiCaL version: 2.1.3
% 1.07/0.57 % (3799995)Termination reason: Instruction limit
% 1.07/0.57 % (3799995)Termination phase: Finite model building SAT solving
% 1.07/0.57 % (3799995)Time elapsed: 0.188 s
% 1.07/0.57 % (3799995)Peak memory usage: 30 MB
% 1.07/0.57 % (3799995)Instructions burned: 717 (million)
% 1.07/0.57 % (3800005)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2557708893:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.07/0.57 % TRYING [1]
% 1.07/0.57 % TRYING [2]
% 1.07/0.57 % TRYING [3]
% 1.07/0.57 % (3800007)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1712139528:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 1.07/0.57 % TRYING [4]
% 1.07/0.57 % (3800007) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3799976-3800007"...
% 1.07/0.57 % (3800007)...printing done.
% 1.07/0.57 % (3800007)Refutation found. Thanks to Tanya!
% 1.07/0.57 % SZS status Unsatisfiable for theBenchmark
% 1.07/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 1.07/0.57 % (3800007)------------------------------
% 1.07/0.57 % (3800007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.57 % (3800007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.57 % (3800007)CaDiCaL version: 2.1.3
% 1.07/0.57 % (3800007)Termination reason: Refutation
% 1.07/0.57 % (3800007)Time elapsed: 0.033 s
% 1.07/0.57 % (3800007)Peak memory usage: 13 MB
% 1.07/0.57 % (3800007)Instructions burned: 106 (million)
% 1.07/0.57 % (3799976)Success in time 0.314 s
% 1.07/0.57 % Vampire exiting
%------------------------------------------------------------------------------