%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL081-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 09:38:24 AM UTC 2026
% Result : Unsatisfiable 3.16s 0.77s
% Output : Refutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 20 unt; 3 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : apply(k(X0),X1) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',k_definition) ).
fof(f6,axiom,
! [X2,X0,X1] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',abstraction) ).
fof(f11,axiom,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',extensionality2) ).
fof(f14,negated_conjecture,
k(k(b)) != apply(abstraction,k(k(b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC2c) ).
fof(f15,definition,
sF0 = k(b),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f16,plain,
k(b) = sF0,
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
sF1 = k(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f18,plain,
k(sF0) = sF1,
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
sF2 = apply(abstraction,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f20,plain,
apply(abstraction,sF1) = sF2,
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
sF1 != sF2,
inference(definition_folding,[],[f14,f20,f18,f16,f18,f16]) ).
fof(f22,plain,
! [X0] : b = apply(sF0,X0),
inference(superposition,[],[f1,f16]) ).
fof(f23,plain,
! [X0] : sF0 = apply(sF1,X0),
inference(superposition,[],[f1,f18]) ).
fof(f34,plain,
! [X0,X1] :
( apply(X1,n(k(X0),X1)) != X0
| k(X0) = X1 ),
inference(superposition,[],[f11,f1]) ).
fof(f56,plain,
! [X0,X1] : apply(apply(apply(abstraction,sF1),X0),X1) = apply(sF0,apply(X0,X1)),
inference(superposition,[],[f6,f23]) ).
fof(f71,plain,
! [X0,X1] : b = apply(apply(apply(abstraction,sF1),X0),X1),
inference(forward_demodulation,[],[f56,f22]) ).
fof(f77,plain,
! [X0,X1] : b = apply(apply(sF2,X0),X1),
inference(forward_demodulation,[],[f71,f20]) ).
fof(f107,plain,
! [X0,X1] :
( b != X1
| k(X1) = apply(sF2,X0) ),
inference(superposition,[],[f34,f77]) ).
fof(f1060,plain,
! [X0] : k(b) = apply(sF2,X0),
inference(equality_resolution,[],[f107]) ).
fof(f1061,plain,
! [X0] : sF0 = apply(sF2,X0),
inference(forward_demodulation,[],[f1060,f16]) ).
fof(f1212,plain,
! [X0] :
( sF0 != X0
| k(X0) = sF2 ),
inference(superposition,[],[f34,f1061]) ).
fof(f2004,plain,
k(sF0) = sF2,
inference(equality_resolution,[],[f1212]) ).
fof(f2005,plain,
sF1 = sF2,
inference(forward_demodulation,[],[f2004,f18]) ).
fof(f2006,plain,
$false,
inference(forward_subsumption_resolution,[],[f2005,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL081-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n001.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:40:34 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 3.16/0.77 % (781444)Will run a generic schedule for satisfiability detection.
% 3.16/0.77 % (781450)% WARNING: option uhcvi not known.
% 3.16/0.77 % (781450)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1028428835:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.16/0.77 % (781453)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3131220128:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.16/0.77 % (781449)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4192603227_2999 on theBenchmark for (2999ds/0Mi)
% 3.16/0.77 % (781451)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3269151142:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.16/0.77 % (781452)dis+10_1_sil=32000:sp=arity:random_seed=3848497682:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.16/0.77 % TRYING [1]
% 3.16/0.77 % TRYING [2]
% 3.16/0.77 % TRYING [3]
% 3.16/0.77 % TRYING [4]
% 3.16/0.77 % (781454)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3410116462:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.16/0.77 % (781455)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3454852025:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.16/0.77 % TRYING [5]
% 3.16/0.77 % TRYING [6]
% 3.16/0.77 % (781452)Instruction limit reached!
% 3.16/0.77 % (781452)------------------------------
% 3.16/0.77 % (781452)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.16/0.77 % (781452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/0.77 % (781452)CaDiCaL version: 2.1.3
% 3.16/0.77 % (781452)Termination reason: Instruction limit
% 3.16/0.77 % (781452)Termination phase: Saturation
% 3.16/0.77 % (781452)Time elapsed: 0.061 s
% 3.16/0.77 % (781452)Peak memory usage: 12 MB
% 3.16/0.77 % (781452)Instructions burned: 104 (million)
% 3.16/0.77 % (781453)Instruction limit reached!
% 3.16/0.77 % (781453)------------------------------
% 3.16/0.77 % (781453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.16/0.77 % (781453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/0.77 % (781453)CaDiCaL version: 2.1.3
% 3.16/0.77 % (781453)Termination reason: Instruction limit
% 3.16/0.77 % (781453)Termination phase: Saturation
% 3.16/0.77 % (781453)Time elapsed: 0.074 s
% 3.16/0.77 % (781453)Peak memory usage: 12 MB
% 3.16/0.77 % (781453)Instructions burned: 117 (million)
% 3.16/0.77 % (781454)Instruction limit reached!
% 3.16/0.77 % (781454)------------------------------
% 3.16/0.77 % (781454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.16/0.77 % (781454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/0.77 % (781454)CaDiCaL version: 2.1.3
% 3.16/0.77 % (781454)Termination reason: Instruction limit
% 3.16/0.77 % (781454)Termination phase: Saturation
% 3.16/0.77 % (781454)Time elapsed: 0.083 s
% 3.16/0.77 % (781454)Peak memory usage: 13 MB
% 3.16/0.77 % (781454)Instructions burned: 132 (million)
% 3.16/0.77 % (781463)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3291665375:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.16/0.77 % TRYING [1]
% 3.16/0.77 % TRYING [2]
% 3.16/0.77 % TRYING [3]
% 3.16/0.77 % TRYING [4]
% 3.16/0.77 % TRYING [5]
% 3.16/0.77 % (781464)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=377408057:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 3.16/0.77 % (781466)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=2200504134:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.16/0.77 % TRYING [7]
% 3.16/0.77 % (781455)Instruction limit reached!
% 3.16/0.77 % (781455)------------------------------
% 3.16/0.77 % (781455)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.16/0.77 % (781455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/0.77 % (781455)CaDiCaL version: 2.1.3
% 3.16/0.77 % (781455)Termination reason: Instruction limit
% 3.16/0.77 % (781455)Termination phase: Saturation
% 3.16/0.77 % (781455)Time elapsed: 0.117 s
% 3.16/0.77 % (781455)Peak memory usage: 13 MB
% 3.16/0.77 % (781455)Instructions burned: 159 (million)
% 3.16/0.77 % (781469)ott-21_1_sil=16000:fs=off:random_seed=1659316153:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.16/0.77 % TRYING [6]
% 3.16/0.77 % (781464)Instruction limit reached!
% 3.16/0.77 % (781464)------------------------------
% 3.16/0.77 % (781464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.16/0.77 % (781464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/0.77 % (781464)CaDiCaL version: 2.1.3
% 3.16/0.77 % (781464)Termination reason: Instruction limit
% 3.16/0.77 % (781464)Termination phase: Saturation
% 3.16/0.77 % (781464)Time elapsed: 0.118 s
% 3.16/0.77 % (781464)Peak memory usage: 12 MB
% 3.16/0.77 % (781464)Instructions burned: 132 (million)
% 3.16/0.77 % TRYING [7]
% 3.16/0.77 % (781469)Instruction limit reached!
% 3.16/0.77 % (781469)------------------------------
% 3.16/0.77 % (781469)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.16/0.77 % (781469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/0.77 % (781469)CaDiCaL version: 2.1.3
% 3.16/0.77 % (781469)Termination reason: Instruction limit
% 3.16/0.77 % (781469)Termination phase: Saturation
% 3.16/0.77 % (781469)Time elapsed: 0.100 s
% 3.16/0.77 % (781469)Peak memory usage: 12 MB
% 3.16/0.77 % (781469)Instructions burned: 182 (million)
% 3.16/0.77 % (781485)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1486914975:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 3.16/0.77 % (781489)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2539311379:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 3.16/0.77 % TRYING [1]
% 3.16/0.77 % TRYING [2]
% 3.16/0.77 % TRYING [3]
% 3.16/0.77 % TRYING [4]
% 3.16/0.77 % TRYING [8]
% 3.16/0.77 % TRYING [5]
% 3.16/0.77 % TRYING [6]
% 3.16/0.77 % (781463)Instruction limit reached!
% 3.16/0.77 % (781463)------------------------------
% 3.16/0.77 % (781463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.16/0.77 % (781463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/0.77 % (781463)CaDiCaL version: 2.1.3
% 3.16/0.77 % (781463)Termination reason: Instruction limit
% 3.16/0.77 % (781463)Termination phase: Finite model building SAT solving
% 3.16/0.77 % (781463)Time elapsed: 0.290 s
% 3.16/0.77 % (781463)Peak memory usage: 34 MB
% 3.16/0.77 % (781463)Instructions burned: 716 (million)
% 3.16/0.77 % (781546)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2819326287:i=1179_2995 on theBenchmark for (2995ds/1179Mi)
% 3.16/0.77 % TRYING [7]
% 3.16/0.77 % (781546) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-781444-781546"...
% 3.16/0.77 % (781546)...printing done.
% 3.16/0.77 % (781546)Refutation found. Thanks to Tanya!
% 3.16/0.77 % SZS status Unsatisfiable for theBenchmark
% 3.16/0.77 % SZS output start Proof for theBenchmark
% See solution above
% 3.16/0.77 % (781546)------------------------------
% 3.16/0.77 % (781546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.16/0.77 % (781546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/0.77 % (781546)CaDiCaL version: 2.1.3
% 3.16/0.77 % (781546)Termination reason: Refutation
% 3.16/0.77 % (781546)Time elapsed: 0.079 s
% 3.16/0.77 % (781546)Peak memory usage: 14 MB
% 3.16/0.77 % (781546)Instructions burned: 128 (million)
% 3.16/0.77 % (781444)Success in time 0.531 s
% 3.16/0.77 % Vampire exiting
%------------------------------------------------------------------------------