%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU165+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 0.09s 0.44s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 57 ( 13 unt; 3 def)
% Number of atoms : 138 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 137 ( 56 ~; 60 |; 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 : 76 ( 0 sgn 64 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,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(f7,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(f8,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)],[f7]) ).
fof(f9,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(f11,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<~> ( in(X0,X2)
& in(X1,X3) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f14,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,[],[f11]) ).
fof(f15,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,[],[f14]) ).
fof(f16,plain,
( ( ~ in(sK2,sK4)
| ~ in(sK3,sK5)
| ~ in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)) )
& ( ( in(sK2,sK4)
& in(sK3,sK5) )
| in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f15]) ).
fof(f17,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,[],[f9]) ).
fof(f18,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,[],[f17]) ).
fof(f19,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f24,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f25,plain,
( in(sK3,sK5)
| in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
( in(sK2,sK4)
| in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
( ~ in(sK2,sK4)
| ~ in(sK3,sK5)
| ~ in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
( ~ in(sK2,sK4)
| ~ in(sK3,sK5)
| ~ in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
inference(definition_unfolding,[],[f27,f24]) ).
fof(f33,plain,
( in(sK2,sK4)
| in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
inference(definition_unfolding,[],[f26,f24]) ).
fof(f34,plain,
( in(sK3,sK5)
| in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
inference(definition_unfolding,[],[f25,f24]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f30,f24]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f29,f24]) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f28,f24]) ).
fof(f39,definition,
( spl6_1
<=> in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f41,plain,
( ~ in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5))
| spl6_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f43,definition,
( spl6_2
<=> in(sK3,sK5) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f44,plain,
( in(sK3,sK5)
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( ~ in(sK3,sK5)
| spl6_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f47,definition,
( spl6_3
<=> in(sK2,sK4) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f48,plain,
( in(sK2,sK4)
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f49,plain,
( ~ in(sK2,sK4)
| spl6_3 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,plain,
( ~ spl6_1
| ~ spl6_2
| ~ spl6_3 ),
inference(avatar_split_clause,[],[f32,f47,f43,f39]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(forward_demodulation,[],[f36,f19]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(forward_demodulation,[],[f37,f19]) ).
fof(f94,plain,
( ~ in(unordered_pair(singleton(sK2),unordered_pair(sK2,sK3)),cartesian_product2(sK4,sK5))
| spl6_1 ),
inference(forward_demodulation,[],[f41,f19]) ).
fof(f95,plain,
( in(unordered_pair(singleton(sK2),unordered_pair(sK2,sK3)),cartesian_product2(sK4,sK5))
| in(sK2,sK4) ),
inference(forward_demodulation,[],[f33,f19]) ).
fof(f97,plain,
in(sK2,sK4),
inference(forward_subsumption_resolution,[],[f95,f77]) ).
fof(f104,plain,
( in(unordered_pair(singleton(sK2),unordered_pair(sK2,sK3)),cartesian_product2(sK4,sK5))
| in(sK3,sK5) ),
inference(forward_demodulation,[],[f34,f19]) ).
fof(f128,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(forward_demodulation,[],[f35,f19]) ).
fof(f141,plain,
( ~ in(sK2,sK4)
| ~ in(sK3,sK5)
| spl6_1 ),
inference(resolution,[],[f128,f94]) ).
fof(f145,plain,
( ~ in(sK3,sK5)
| spl6_1
| ~ spl6_3 ),
inference(forward_subsumption_resolution,[],[f141,f48]) ).
fof(f146,plain,
( $false
| spl6_1
| ~ spl6_2
| ~ spl6_3 ),
inference(forward_subsumption_resolution,[],[f145,f44]) ).
fof(f147,plain,
( spl6_1
| ~ spl6_2
| ~ spl6_3 ),
inference(avatar_contradiction_clause,[],[f146]) ).
fof(f149,plain,
in(sK3,sK5),
inference(forward_subsumption_resolution,[],[f104,f78]) ).
fof(f150,plain,
( $false
| spl6_2 ),
inference(global_subsumption,[],[f45,f149]) ).
fof(f151,plain,
spl6_2,
inference(avatar_contradiction_clause,[],[f150]) ).
fof(f153,plain,
( $false
| spl6_3 ),
inference(global_subsumption,[],[f49,f97]) ).
fof(f154,plain,
spl6_3,
inference(avatar_contradiction_clause,[],[f153]) ).
cnf(s13,plain,
( ~ spl6_1
| ~ spl6_2
| ~ spl6_3 ),
inference(sat_conversion,[],[f50]) ).
cnf(s108,plain,
( spl6_1
| ~ spl6_2
| ~ spl6_3 ),
inference(sat_conversion,[],[f147]) ).
cnf(s114,plain,
spl6_2,
inference(sat_conversion,[],[f151]) ).
cnf(s117,plain,
spl6_3,
inference(sat_conversion,[],[f154]) ).
cnf(s120,plain,
spl6_1,
inference(rat,[],[s108,s117,s114]) ).
cnf(s123,plain,
$false,
inference(rat,[],[s13,s117,s114,s120]) ).
fof(f155,plain,
$false,
inference(avatar_sat_refutation,[],[s123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU165+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 03:52:58 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 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
% 0.09/0.44 % (1167189)Will run a generic schedule for satisfiability detection.
% 0.09/0.44 % (1167196)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3817750819:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.44 % (1167196) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1167189-1167196"...
% 0.09/0.44 % (1167195)% WARNING: option uhcvi not known.
% 0.09/0.44 % (1167196)...printing done.
% 0.09/0.44 % (1167196)Refutation found. Thanks to Tanya!
% 0.09/0.44 % SZS status Theorem for theBenchmark
% 0.09/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.44 % (1167196)------------------------------
% 0.09/0.44 % (1167196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.44 % (1167196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.44 % (1167196)CaDiCaL version: 2.1.3
% 0.09/0.44 % (1167196)Termination reason: Refutation
% 0.09/0.44 % (1167196)Time elapsed: 0.003 s
% 0.09/0.44 % (1167196)Peak memory usage: 12 MB
% 0.09/0.44 % (1167196)Instructions burned: 7 (million)
% 0.09/0.44 % (1167189)Success in time 0.033 s
% 0.09/0.44 % Vampire exiting
%------------------------------------------------------------------------------