%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU165+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:47:31 PM UTC 2026
% Result : Theorem 2.76s 1.42s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 10 unt; 3 def)
% Number of atoms : 125 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 124 ( 50 ~; 53 |; 14 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 52 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(sK18,sK20)
| ~ in(sK19,sK21)
| ~ in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21)) ),
inference(definition_unfolding,[],[f299,f357]) ).
fof(f391,plain,
( in(sK18,sK20)
| in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21)) ),
inference(definition_unfolding,[],[f298,f357]) ).
fof(f392,plain,
( in(sK19,sK21)
| in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21)) ),
inference(definition_unfolding,[],[f297,f357]) ).
fof(f523,definition,
( spl26_1
<=> in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21)) ),
introduced(definition,[new_symbols(definition,[spl26_1])],[avatar_definition]) ).
fof(f524,plain,
( in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21))
| ~ spl26_1 ),
inference(avatar_component_clause,[],[f523]) ).
fof(f526,definition,
( spl26_2
<=> in(sK19,sK21) ),
introduced(definition,[new_symbols(definition,[spl26_2])],[avatar_definition]) ).
fof(f528,plain,
( spl26_1
| spl26_2 ),
inference(avatar_split_clause,[],[f392,f526,f523]) ).
fof(f530,definition,
( spl26_3
<=> in(sK18,sK20) ),
introduced(definition,[new_symbols(definition,[spl26_3])],[avatar_definition]) ).
fof(f532,plain,
( spl26_1
| spl26_3 ),
inference(avatar_split_clause,[],[f391,f530,f523]) ).
fof(f533,plain,
( ~ in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21))
| spl26_1 ),
inference(avatar_component_clause,[],[f523]) ).
fof(f536,plain,
( ~ spl26_1
| ~ spl26_2
| ~ spl26_3 ),
inference(avatar_split_clause,[],[f390,f530,f526,f523]) ).
fof(f1135,plain,
( ~ in(sK18,sK20)
| ~ in(sK19,sK21)
| spl26_1 ),
inference(resolution,[],[f387,f533]) ).
fof(f1157,plain,
( ~ spl26_2
| ~ spl26_3
| spl26_1 ),
inference(avatar_split_clause,[],[f1135,f523,f530,f526]) ).
fof(f1158,plain,
( in(sK19,sK21)
| ~ spl26_1 ),
inference(resolution,[],[f524,f389]) ).
fof(f1159,plain,
( in(sK18,sK20)
| ~ spl26_1 ),
inference(resolution,[],[f524,f388]) ).
fof(f1162,plain,
( spl26_3
| ~ spl26_1 ),
inference(avatar_split_clause,[],[f1159,f523,f530]) ).
fof(f1163,plain,
( spl26_2
| ~ spl26_1 ),
inference(avatar_split_clause,[],[f1158,f523,f526]) ).
cnf(s1,plain,
( spl26_1
| spl26_2 ),
inference(sat_conversion,[],[f528]) ).
cnf(s2,plain,
( spl26_1
| spl26_3 ),
inference(sat_conversion,[],[f532]) ).
cnf(s3,plain,
( ~ spl26_1
| ~ spl26_2
| ~ spl26_3 ),
inference(sat_conversion,[],[f536]) ).
cnf(s8,plain,
( spl26_1
| ~ spl26_2
| ~ spl26_3 ),
inference(sat_conversion,[],[f1157]) ).
cnf(s9,plain,
( ~ spl26_1
| spl26_3 ),
inference(sat_conversion,[],[f1162]) ).
cnf(s10,plain,
( ~ spl26_1
| spl26_2 ),
inference(sat_conversion,[],[f1163]) ).
cnf(s11,plain,
spl26_1,
inference(rat,[],[s8,s1,s2]) ).
cnf(s12,plain,
spl26_2,
inference(rat,[],[s10,s11]) ).
cnf(s13,plain,
spl26_3,
inference(rat,[],[s9,s11]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s3,s12,s13,s11]) ).
fof(f1164,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU165+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.44 % Computer : n010.cluster.edu
% 0.10/0.44 % Model : x86_64 x86_64
% 0.10/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.44 % Memory : 8046.5625MB
% 0.10/0.44 % OS : Linux 6.8.0-71-generic
% 0.10/0.44 % CPULimit : 300
% 0.10/0.44 % WCLimit : 300
% 0.10/0.44 % DateTime : Mon Sep 28 03:51:17 UTC 2026
% 0.10/0.44 % CPUTime :
% 0.10/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.47 Running first-order theorem proving
% 0.12/0.47 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.76/1.42 % (1539831)Detected formulas, will run a generic FOF schedule.
% 2.76/1.42 % (1539842)dis-21_1_sil=8000:lcm=predicate:random_seed=4215957884:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.76/1.42 % (1539842)First to succeed.
% 2.76/1.42 % (1539842)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1539831"
% 2.76/1.42 % (1539836)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=224221776:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.76/1.42 % (1539841)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3689530206:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.76/1.42 % (1539838)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=135189377:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.76/1.42 % (1539837)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=468391602:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.76/1.42 % (1539840)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=450973498:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.76/1.42 % (1539839)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2950072765:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.76/1.42 % (1539841)Also succeeded, but the first one will report.
% 2.76/1.42 % (1539840)Also succeeded, but the first one will report.
% 2.76/1.42 % (1539839)Instruction limit reached!
% 2.76/1.42 % (1539839)------------------------------
% 2.76/1.42 % (1539839)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.42 % (1539839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.42 % (1539839)CaDiCaL version: 2.1.3
% 2.76/1.42 % (1539839)Termination reason: Instruction limit
% 2.76/1.42 % (1539839)Termination phase: Saturation
% 2.76/1.42 % (1539839)Time elapsed: 0.071 s
% 2.76/1.42 % (1539839)Peak memory usage: 89 MB
% 2.76/1.42 % (1539839)Instructions burned: 110 (million)
% 2.76/1.42 % (1539842)Refutation found. Thanks to Tanya!
% 2.76/1.42 % SZS status Theorem for theBenchmark
% 2.76/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 2.76/1.42 % (1539842)------------------------------
% 2.76/1.42 % (1539842)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.42 % (1539842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.42 % (1539842)CaDiCaL version: 2.1.3
% 2.76/1.42 % (1539842)Termination reason: Refutation
% 2.76/1.42 % (1539842)Time elapsed: 0.009 s
% 2.76/1.42 % (1539842)Peak memory usage: 90 MB
% 2.76/1.42 % (1539842)Instructions burned: 23 (million)
% 2.76/1.42 % (1539842)------------------------------
% 2.76/1.42 % (1539842)------------------------------
% 2.76/1.42 % (1539831)Success in time 0.306 s
% 2.76/1.42 % Vampire exiting
%------------------------------------------------------------------------------