%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU165+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 12:52:12 PM UTC 2026
% Result : Theorem 1.05s 0.65s
% Output : Refutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 89 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 92 ( 37 ~; 37 |; 14 &)
% ( 3 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 64 ( 52 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f46,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f51,conjecture,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f52,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f85,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f118,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<~> ( in(X0,X2)
& in(X1,X3) ) ),
inference(ennf_transformation,[],[f52]) ).
fof(f188,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f189,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f188]) ).
fof(f192,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X0,X2)
| ~ in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
& ( ( in(X0,X2)
& in(X1,X3) )
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f193,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X0,X2)
| ~ in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
& ( ( in(X0,X2)
& in(X1,X3) )
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f192]) ).
fof(f194,plain,
( ( ~ in(sK18,sK20)
| ~ in(sK19,sK21)
| ~ in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) )
& ( ( in(sK18,sK20)
& in(sK19,sK21) )
| in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21]),skolemize(X0,sK18),skolemize(X1,sK19),skolemize(X2,sK20),skolemize(X3,sK21)],[f193]) ).
fof(f266,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f290,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f189]) ).
fof(f291,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f189]) ).
fof(f292,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f189]) ).
fof(f297,plain,
( in(sK19,sK21)
| in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) ),
inference(cnf_transformation,[],[f194]) ).
fof(f298,plain,
( in(sK18,sK20)
| in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) ),
inference(cnf_transformation,[],[f194]) ).
fof(f299,plain,
( ~ in(sK18,sK20)
| ~ in(sK19,sK21)
| ~ in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) ),
inference(cnf_transformation,[],[f194]) ).
fof(f344,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f85]) ).
fof(f357,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f266,f344]) ).
fof(f387,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f292,f357]) ).
fof(f388,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f291,f357]) ).
fof(f389,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f290,f357]) ).
fof(f390,plain,
( ~ in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21))
| ~ in(sK19,sK21)
| ~ in(sK18,sK20) ),
inference(definition_unfolding,[],[f299,f357]) ).
fof(f391,plain,
( in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21))
| in(sK18,sK20) ),
inference(definition_unfolding,[],[f298,f357]) ).
fof(f392,plain,
( in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21))
| in(sK19,sK21) ),
inference(definition_unfolding,[],[f297,f357]) ).
fof(f1967,plain,
( in(sK18,sK20)
| in(sK18,sK20) ),
inference(resolution,[],[f388,f391]) ).
fof(f1976,plain,
in(sK18,sK20),
inference(duplicate_literal_removal,[],[f1967]) ).
fof(f1984,plain,
( in(sK19,sK21)
| in(sK19,sK21) ),
inference(resolution,[],[f389,f392]) ).
fof(f1994,plain,
in(sK19,sK21),
inference(duplicate_literal_removal,[],[f1984]) ).
fof(f2173,plain,
( ~ in(sK18,sK20)
| ~ in(sK19,sK21)
| ~ in(sK19,sK21)
| ~ in(sK18,sK20) ),
inference(resolution,[],[f387,f390]) ).
fof(f2190,plain,
( ~ in(sK19,sK21)
| ~ in(sK18,sK20) ),
inference(duplicate_literal_removal,[],[f2173]) ).
fof(f2213,plain,
~ in(sK18,sK20),
inference(resolution,[],[f2190,f1994]) ).
fof(f2240,plain,
$false,
inference(resolution,[],[f2213,f1976]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU165+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 % Computer : n013.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Mon Sep 28 03:50:08 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.44 Running first-order model finding
% 0.12/0.44 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
% 1.05/0.65 % (783459)Will run a generic schedule for satisfiability detection.
% 1.05/0.65 % (783465)% WARNING: option uhcvi not known.
% 1.05/0.65 % (783465)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2827804539:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.05/0.65 % (783464)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=549270691_2999 on theBenchmark for (2999ds/0Mi)
% 1.05/0.65 % (783469)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3468907478:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.05/0.65 % (783466)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3223647126:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.05/0.65 % (783467)dis+10_1_sil=32000:sp=arity:random_seed=261647377:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.05/0.65 % (783468)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3761059368:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.05/0.65 % (783470)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=295673526:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.05/0.65 % TRYING [1]
% 1.05/0.65 % TRYING [2]
% 1.05/0.65 % TRYING [3]
% 1.05/0.65 % TRYING [4]
% 1.05/0.65 % (783467)Instruction limit reached!
% 1.05/0.65 % (783467)------------------------------
% 1.05/0.65 % (783467)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.65 % (783467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.65 % (783467)CaDiCaL version: 2.1.3
% 1.05/0.65 % (783467)Termination reason: Instruction limit
% 1.05/0.65 % (783467)Termination phase: Saturation
% 1.05/0.65 % (783467)Time elapsed: 0.066 s
% 1.05/0.65 % (783467)Peak memory usage: 12 MB
% 1.05/0.65 % (783467)Instructions burned: 103 (million)
% 1.05/0.65 % (783468)Instruction limit reached!
% 1.05/0.65 % (783468)------------------------------
% 1.05/0.65 % (783468)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.65 % (783468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.65 % (783468)CaDiCaL version: 2.1.3
% 1.05/0.65 % (783468)Termination reason: Instruction limit
% 1.05/0.65 % (783468)Termination phase: Saturation
% 1.05/0.65 % (783468)Time elapsed: 0.075 s
% 1.05/0.65 % (783468)Peak memory usage: 13 MB
% 1.05/0.65 % (783468)Instructions burned: 116 (million)
% 1.05/0.65 % (783469)Instruction limit reached!
% 1.05/0.65 % (783469)------------------------------
% 1.05/0.65 % (783469)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.65 % (783469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.65 % (783469)CaDiCaL version: 2.1.3
% 1.05/0.65 % (783469)Termination reason: Instruction limit
% 1.05/0.65 % (783469)Termination phase: Saturation
% 1.05/0.65 % (783469)Time elapsed: 0.082 s
% 1.05/0.65 % (783469)Peak memory usage: 13 MB
% 1.05/0.65 % (783469)Instructions burned: 132 (million)
% 1.05/0.65 % (783478)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2909718338:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.05/0.65 % (783479)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=451407279:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.05/0.65 % TRYING [1]
% 1.05/0.65 % TRYING [2]
% 1.05/0.65 % (783480)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=3590237633:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.05/0.65 % TRYING [3]
% 1.05/0.65 % (783470)Instruction limit reached!
% 1.05/0.65 % (783470)------------------------------
% 1.05/0.65 % (783470)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.65 % (783470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.65 % (783470)CaDiCaL version: 2.1.3
% 1.05/0.65 % (783470)Termination reason: Instruction limit
% 1.05/0.65 % (783470)Termination phase: Saturation
% 1.05/0.65 % (783470)Time elapsed: 0.102 s
% 1.05/0.65 % (783470)Peak memory usage: 13 MB
% 1.05/0.65 % (783470)Instructions burned: 160 (million)
% 1.05/0.65 % TRYING [4]
% 1.05/0.65 % (783484)ott-21_1_sil=16000:fs=off:random_seed=928931487:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.05/0.65 % TRYING [5]
% 1.05/0.65 % (783484) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-783459-783484"...
% 1.05/0.65 % (783484)...printing done.
% 1.05/0.65 % (783484)Refutation found. Thanks to Tanya!
% 1.05/0.65 % SZS status Theorem for theBenchmark
% 1.05/0.65 % SZS output start Proof for theBenchmark
% See solution above
% 1.05/0.65 % (783484)------------------------------
% 1.05/0.65 % (783484)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.05/0.65 % (783484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.05/0.65 % (783484)CaDiCaL version: 2.1.3
% 1.05/0.65 % (783484)Termination reason: Refutation
% 1.05/0.65 % (783484)Time elapsed: 0.029 s
% 1.05/0.65 % (783484)Peak memory usage: 12 MB
% 1.05/0.65 % (783484)Instructions burned: 48 (million)
% 1.05/0.65 % (783459)Success in time 0.203 s
% 1.05/0.65 % Vampire exiting
%------------------------------------------------------------------------------