%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET962+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:45:05 PM UTC 2026
% Result : Theorem 0.12s 0.46s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 11 unt; 2 def)
% Number of atoms : 130 ( 28 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 122 ( 47 ~; 58 |; 9 &)
% ( 4 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 80 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,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(f5,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(f8,conjecture,
! [X0,X1] :
( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] :
( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f12,plain,
? [X0,X1] :
( X0 != X1
& cartesian_product2(X0,X0) = cartesian_product2(X1,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f13,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f14,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,[],[f5]) ).
fof(f15,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,[],[f14]) ).
fof(f18,plain,
( sK2 != sK3
& cartesian_product2(sK2,sK2) = cartesian_product2(sK3,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f20,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK4(X0,X1),X1)
| ~ in(sK4(X0,X1),X0) )
& ( in(sK4(X0,X1),X1)
| in(sK4(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f19]) ).
fof(f22,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f23,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f3]) ).
fof(f26,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
cartesian_product2(sK2,sK2) = cartesian_product2(sK3,sK3),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X0,X1] :
( X0 = X1
| in(sK4(X0,X1),X1)
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0,X1] :
( X0 = X1
| ~ in(sK4(X0,X1),X1)
| ~ in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
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,[],[f27,f23]) ).
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,[],[f26,f23]) ).
fof(f40,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,[],[f35]) ).
fof(f41,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,[],[f36]) ).
fof(f45,plain,
! [X0,X1] :
( in(sK4(X0,X1),X1)
| X0 = X1
| in(sK4(X0,X1),X0) ),
inference(consistent_polarity_flipping,[],[f33]) ).
fof(f46,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X1)
| ~ in(sK4(X0,X1),X0)
| X0 = X1 ),
inference(consistent_polarity_flipping,[],[f32]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X1)),cartesian_product2(X2,X3))
| ~ in(X1,X2) ),
inference(superposition,[],[f41,f22]) ).
fof(f63,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK2,sK2))
| ~ in(X0,sK3) ),
inference(superposition,[],[f41,f30]) ).
fof(f65,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X1)),cartesian_product2(sK2,sK2))
| ~ in(X1,sK3) ),
inference(superposition,[],[f63,f22]) ).
fof(f125,plain,
! [X0] :
( in(X0,sK2)
| in(X0,sK2)
| ~ in(X0,sK3) ),
inference(resolution,[],[f40,f65]) ).
fof(f133,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK2,sK2))
| in(X0,sK3)
| in(X1,sK3) ),
inference(superposition,[],[f40,f30]) ).
fof(f134,plain,
! [X0] :
( in(X0,sK2)
| ~ in(X0,sK3) ),
inference(duplicate_literal_removal,[],[f125]) ).
fof(f136,plain,
! [X0] :
( ~ in(sK4(X0,sK2),sK3)
| ~ in(sK4(X0,sK2),X0)
| sK2 = X0 ),
inference(resolution,[],[f134,f46]) ).
fof(f140,plain,
( ~ in(sK4(sK3,sK2),sK3)
| sK2 = sK3 ),
inference(factoring,[],[f136]) ).
fof(f142,definition,
( spl5_1
<=> sK2 = sK3 ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f144,plain,
( sK2 = sK3
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f146,definition,
( spl5_2
<=> in(sK4(sK3,sK2),sK3) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f148,plain,
( ~ in(sK4(sK3,sK2),sK3)
| spl5_2 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f140,f146,f142]) ).
fof(f158,plain,
! [X0] :
( in(X0,sK3)
| in(X0,sK3)
| ~ in(X0,sK2) ),
inference(resolution,[],[f133,f60]) ).
fof(f164,plain,
! [X0] :
( in(X0,sK3)
| ~ in(X0,sK2) ),
inference(duplicate_literal_removal,[],[f158]) ).
fof(f171,plain,
( ~ in(sK4(sK3,sK2),sK2)
| spl5_2 ),
inference(resolution,[],[f164,f148]) ).
fof(f172,plain,
( sK2 = sK3
| in(sK4(sK3,sK2),sK3)
| spl5_2 ),
inference(resolution,[],[f171,f45]) ).
fof(f175,plain,
( spl5_2
| spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f172,f146,f142,f146]) ).
fof(f176,plain,
( sK2 != sK2
| ~ spl5_1 ),
inference(superposition,[],[f31,f144]) ).
fof(f182,plain,
( $false
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f176]) ).
fof(f183,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f182]) ).
cnf(s1,plain,
( spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f149]) ).
cnf(s2,plain,
( spl5_2
| spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f175]) ).
cnf(s3,plain,
( spl5_1
| spl5_2 ),
inference(rat,[],[s2]) ).
cnf(s4,plain,
~ spl5_1,
inference(sat_conversion,[],[f183]) ).
cnf(s5,plain,
spl5_2,
inference(rat,[],[s3,s4]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5,s4]) ).
fof(f184,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET962+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:16:33 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.12/0.46 % (3629585)Will run a generic schedule for satisfiability detection.
% 0.12/0.46 % (3629596)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3189346575:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.46 % (3629596) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3629585-3629596"...
% 0.12/0.46 % (3629591)% WARNING: option uhcvi not known.
% 0.12/0.46 % (3629596)...printing done.
% 0.12/0.46 % (3629596)Refutation found. Thanks to Tanya!
% 0.12/0.46 % SZS status Theorem for theBenchmark
% 0.12/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.46 % (3629596)------------------------------
% 0.12/0.46 % (3629596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.46 % (3629596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.46 % (3629596)CaDiCaL version: 2.1.3
% 0.12/0.46 % (3629596)Termination reason: Refutation
% 0.12/0.46 % (3629596)Time elapsed: 0.003 s
% 0.12/0.46 % (3629596)Peak memory usage: 12 MB
% 0.12/0.46 % (3629596)Instructions burned: 7 (million)
% 0.12/0.46 % (3629585)Success in time 0.031 s
% 0.12/0.46 % Vampire exiting
%------------------------------------------------------------------------------