%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU165+1 : 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 : n014.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 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 7 unt; 3 def)
% Number of atoms : 136 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 140 ( 58 ~; 61 |; 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 : 72 ( 0 sgn 60 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,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(f11,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(f12,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)],[f11]) ).
fof(f13,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(f15,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<~> ( in(X0,X2)
& in(X1,X3) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f18,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,[],[f15]) ).
fof(f19,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,[],[f18]) ).
fof(f20,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)],[f19]) ).
fof(f21,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,[],[f13]) ).
fof(f22,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,[],[f21]) ).
fof(f28,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f29,plain,
( in(sK3,sK5)
| in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
( in(sK2,sK4)
| in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f31,plain,
( ~ in(sK2,sK4)
| ~ in(sK3,sK5)
| ~ in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
( ~ in(sK2,sK4)
| ~ in(sK3,sK5)
| ~ in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
inference(definition_unfolding,[],[f31,f28]) ).
fof(f37,plain,
( in(sK2,sK4)
| in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
inference(definition_unfolding,[],[f30,f28]) ).
fof(f38,plain,
( in(sK3,sK5)
| in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
inference(definition_unfolding,[],[f29,f28]) ).
fof(f39,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,[],[f34,f28]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f33,f28]) ).
fof(f41,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f32,f28]) ).
fof(f46,plain,
( in(sK2,sK4)
| in(sK3,sK5)
| in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
inference(consistent_polarity_flipping,[],[f36]) ).
fof(f47,plain,
( ~ in(sK2,sK4)
| ~ in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
inference(consistent_polarity_flipping,[],[f37]) ).
fof(f48,plain,
( ~ in(sK3,sK5)
| ~ in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
inference(consistent_polarity_flipping,[],[f38]) ).
fof(f49,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(consistent_polarity_flipping,[],[f39]) ).
fof(f50,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2) ),
inference(consistent_polarity_flipping,[],[f40]) ).
fof(f51,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X1,X3) ),
inference(consistent_polarity_flipping,[],[f41]) ).
fof(f53,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(f54,plain,
( in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5))
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f55,plain,
( ~ in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5))
| spl6_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f57,definition,
( spl6_2
<=> in(sK3,sK5) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f60,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f48,f57,f53]) ).
fof(f62,definition,
( spl6_3
<=> in(sK2,sK4) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f65,plain,
( ~ spl6_1
| ~ spl6_3 ),
inference(avatar_split_clause,[],[f47,f62,f53]) ).
fof(f66,plain,
( spl6_1
| spl6_2
| spl6_3 ),
inference(avatar_split_clause,[],[f46,f62,f57,f53]) ).
fof(f86,plain,
( ~ in(sK2,sK4)
| spl6_1 ),
inference(resolution,[],[f50,f55]) ).
fof(f91,plain,
( ~ in(sK3,sK5)
| spl6_1 ),
inference(resolution,[],[f51,f55]) ).
fof(f96,plain,
( ~ spl6_2
| spl6_1 ),
inference(avatar_split_clause,[],[f91,f53,f57]) ).
fof(f97,plain,
( ~ spl6_3
| spl6_1 ),
inference(avatar_split_clause,[],[f86,f53,f62]) ).
fof(f122,plain,
( in(sK2,sK4)
| in(sK3,sK5)
| ~ spl6_1 ),
inference(resolution,[],[f49,f54]) ).
fof(f128,plain,
( spl6_2
| spl6_3
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f122,f53,f62,f57]) ).
cnf(s1,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f60]) ).
cnf(s2,plain,
( ~ spl6_1
| ~ spl6_3 ),
inference(sat_conversion,[],[f65]) ).
cnf(s3,plain,
( spl6_1
| spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f66]) ).
cnf(s4,plain,
( spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f96]) ).
cnf(s5,plain,
( spl6_1
| ~ spl6_3 ),
inference(sat_conversion,[],[f97]) ).
cnf(s6,plain,
( ~ spl6_1
| spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f128]) ).
cnf(s7,plain,
spl6_1,
inference(rat,[],[s3,s4,s5]) ).
cnf(s8,plain,
~ spl6_3,
inference(rat,[],[s2,s7]) ).
cnf(s9,plain,
~ spl6_2,
inference(rat,[],[s1,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s6,s8,s7,s9]) ).
fof(f129,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU165+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n014.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 03:51:02 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 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
% 0.16/0.46 % (1417424)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (1417435)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2582313062:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.46 % (1417435) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1417424-1417435"...
% 0.16/0.46 % (1417430)% WARNING: option uhcvi not known.
% 0.16/0.46 % (1417435)...printing done.
% 0.16/0.46 % (1417435)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (1417435)------------------------------
% 0.16/0.46 % (1417435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (1417435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (1417435)CaDiCaL version: 2.1.3
% 0.16/0.46 % (1417435)Termination reason: Refutation
% 0.16/0.46 % (1417435)Time elapsed: 0.003 s
% 0.16/0.46 % (1417435)Peak memory usage: 12 MB
% 0.16/0.46 % (1417435)Instructions burned: 5 (million)
% 0.16/0.46 % (1417424)Success in time 0.029 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------