%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET978+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 12:45:07 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 7 unt; 2 def)
% Number of atoms : 61 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 25 ~; 19 |; 5 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2,X3] :
( ( disjoint(X0,X1)
| disjoint(X2,X3) )
=> disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).
fof(f5,conjecture,
! [X0,X1,X2,X3] :
( X0 != X1
=> ( disjoint(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X3))
& disjoint(cartesian_product2(X2,singleton(X0)),cartesian_product2(X3,singleton(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( X0 != X1
=> ( disjoint(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X3))
& disjoint(cartesian_product2(X2,singleton(X0)),cartesian_product2(X3,singleton(X1))) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [X0,X1] :
( X0 != X1
=> disjoint(singleton(X0),singleton(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_zfmisc_1) ).
fof(f9,plain,
! [X0,X1,X2,X3] :
( disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ( ~ disjoint(X0,X1)
& ~ disjoint(X2,X3) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
? [X0,X1,X2,X3] :
( ( ~ disjoint(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X3))
| ~ disjoint(cartesian_product2(X2,singleton(X0)),cartesian_product2(X3,singleton(X1))) )
& X0 != X1 ),
inference(ennf_transformation,[],[f6]) ).
fof(f11,plain,
! [X0,X1] :
( disjoint(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(ennf_transformation,[],[f7]) ).
fof(f14,plain,
( ( ~ disjoint(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK5))
| ~ disjoint(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK5,singleton(sK3))) )
& sK2 != sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f10]) ).
fof(f18,plain,
! [X2,X3,X0,X1] :
( disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ disjoint(X2,X3) ),
inference(cnf_transformation,[],[f9]) ).
fof(f19,plain,
! [X2,X3,X0,X1] :
( disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f20,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
( ~ disjoint(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK5))
| ~ disjoint(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK5,singleton(sK3))) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X0,X1] :
( disjoint(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f11]) ).
fof(f24,definition,
( spl6_1
<=> disjoint(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK5,singleton(sK3))) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f26,plain,
( ~ disjoint(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK5,singleton(sK3)))
| spl6_1 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f28,definition,
( spl6_2
<=> disjoint(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK5)) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f30,plain,
( ~ disjoint(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK5))
| spl6_2 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f31,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f21,f28,f24]) ).
fof(f33,plain,
( ~ disjoint(singleton(sK2),singleton(sK3))
| spl6_1 ),
inference(resolution,[],[f18,f26]) ).
fof(f37,plain,
( sK2 = sK3
| spl6_1 ),
inference(resolution,[],[f33,f22]) ).
fof(f38,plain,
( $false
| spl6_1 ),
inference(forward_subsumption_resolution,[],[f37,f20]) ).
fof(f39,plain,
spl6_1,
inference(avatar_contradiction_clause,[],[f38]) ).
fof(f41,plain,
( ~ disjoint(singleton(sK2),singleton(sK3))
| spl6_2 ),
inference(resolution,[],[f30,f19]) ).
fof(f43,plain,
( sK2 = sK3
| spl6_2 ),
inference(resolution,[],[f41,f22]) ).
fof(f44,plain,
( $false
| spl6_2 ),
inference(forward_subsumption_resolution,[],[f43,f20]) ).
fof(f45,plain,
spl6_2,
inference(avatar_contradiction_clause,[],[f44]) ).
cnf(s1,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f31]) ).
cnf(s2,plain,
spl6_1,
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
spl6_2,
inference(sat_conversion,[],[f45]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f46,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET978+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:15:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.45 % (1994370)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (1994378)dis+10_1_sil=32000:sp=arity:random_seed=2543704365:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (1994378) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1994370-1994378"...
% 0.11/0.45 % (1994378)...printing done.
% 0.11/0.45 % (1994378)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (1994378)------------------------------
% 0.11/0.45 % (1994378)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (1994378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (1994378)CaDiCaL version: 2.1.3
% 0.11/0.45 % (1994378)Termination reason: Refutation
% 0.11/0.45 % (1994378)Time elapsed: 0.001 s
% 0.11/0.45 % (1994378)Peak memory usage: 12 MB
% 0.11/0.45 % (1994378)Instructions burned: 1 (million)
% 0.11/0.45 % (1994370)Success in time 0.027 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------