%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET949+1 : 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 : 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 12:45:04 PM UTC 2026
% Result : Theorem 0.15s 0.44s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 10 unt; 0 def)
% Number of atoms : 87 ( 38 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 108 ( 43 ~; 36 |; 27 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 85 ( 70 !; 15 ?)
% 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,X2] :
( X2 = cartesian_product2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f4,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(f8,conjecture,
! [X0,X1,X2] :
~ ( in(X0,cartesian_product2(X1,X2))
& ! [X3,X4] : ordered_pair(X3,X4) != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( in(X0,cartesian_product2(X1,X2))
& ! [X3,X4] : ordered_pair(X3,X4) != X0 ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f11,plain,
? [X0,X1,X2] :
( in(X0,cartesian_product2(X1,X2))
& ! [X3,X4] : ordered_pair(X3,X4) != X0 ),
inference(ennf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ? [X3] :
( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 ) )
& ( ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) )
| ~ in(X3,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ? [X3] :
( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( in(X6,X0)
& in(X7,X1)
& ordered_pair(X6,X7) = X3 )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8 ) )
& ( ? [X11,X12] :
( in(X11,X0)
& in(X12,X1)
& ordered_pair(X11,X12) = X8 )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(rectify,[],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != sK0(X0,X1,X2) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),X0)
& in(sK2(X0,X1,X2),X1)
& sK0(X0,X1,X2) = ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2)) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8 ) )
& ( ( in(sK3(X0,X1,X8),X0)
& in(sK4(X0,X1,X8),X1)
& ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8 )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X6,sK1(X0,X1,X2)),skolemize(X7,sK2(X0,X1,X2)),skolemize(X11,sK3(X0,X1,X8)),skolemize(X12,sK4(X0,X1,X8))],[f13]) ).
fof(f17,plain,
( in(sK7,cartesian_product2(sK8,sK9))
& ! [X3,X4] : ordered_pair(X3,X4) != sK7 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9)],[f11]) ).
fof(f19,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f20,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f32,plain,
! [X3,X4] : ordered_pair(X3,X4) != sK7,
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
in(sK7,cartesian_product2(sK8,sK9)),
inference(cnf_transformation,[],[f17]) ).
fof(f37,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f20,f28]) ).
fof(f39,plain,
! [X3,X4] : sK7 != unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(definition_unfolding,[],[f32,f28]) ).
fof(f44,plain,
! [X0,X1,X8] :
( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f37]) ).
fof(f47,plain,
! [X0,X1] : sK7 != unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f39,f19]) ).
fof(f71,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| unordered_pair(singleton(sK3(X0,X1,X8)),unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8))) = X8 ),
inference(forward_demodulation,[],[f44,f19]) ).
fof(f79,plain,
sK7 = unordered_pair(singleton(sK3(sK8,sK9,sK7)),unordered_pair(sK3(sK8,sK9,sK7),sK4(sK8,sK9,sK7))),
inference(resolution,[],[f71,f33]) ).
fof(f80,plain,
$false,
inference(forward_subsumption_resolution,[],[f79,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET949+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n019.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 03:16:04 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.41 Running first-order model finding
% 0.15/0.41 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
% 0.15/0.44 % (3627956)Will run a generic schedule for satisfiability detection.
% 0.15/0.44 % (3627964)dis+10_1_sil=32000:sp=arity:random_seed=841651363:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.15/0.44 % (3627964) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3627956-3627964"...
% 0.15/0.44 % (3627964)...printing done.
% 0.15/0.44 % (3627964)Refutation found. Thanks to Tanya!
% 0.15/0.44 % SZS status Theorem for theBenchmark
% 0.15/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.44 % (3627964)------------------------------
% 0.15/0.44 % (3627964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.44 % (3627964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.44 % (3627964)CaDiCaL version: 2.1.3
% 0.15/0.44 % (3627964)Termination reason: Refutation
% 0.15/0.44 % (3627964)Time elapsed: 0.003 s
% 0.15/0.44 % (3627964)Peak memory usage: 11 MB
% 0.15/0.44 % (3627964)Instructions burned: 4 (million)
% 0.15/0.44 % (3627956)Success in time 0.022 s
% 0.15/0.44 % Vampire exiting
%------------------------------------------------------------------------------