%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET956+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 : 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 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 13 unt; 2 def)
% Number of atoms : 117 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 114 ( 44 ~; 39 |; 22 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 91 ( 0 sgn 79 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f4,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(f9,axiom,
! [X0,X1,X2,X3] :
~ ( subset(X0,cartesian_product2(X1,X2))
& in(X3,X0)
& ! [X4,X5] :
~ ( in(X4,X1)
& in(X5,X2)
& X3 = ordered_pair(X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
fof(f10,conjecture,
! [X0,X1,X2,X3] :
( ( subset(X0,cartesian_product2(X1,X2))
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X0)
=> in(ordered_pair(X4,X5),X3) ) )
=> subset(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( subset(X0,cartesian_product2(X1,X2))
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X0)
=> in(ordered_pair(X4,X5),X3) ) )
=> subset(X0,X3) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( ~ subset(X0,cartesian_product2(X1,X2))
| ~ in(X3,X0)
| ? [X4,X5] :
( in(X4,X1)
& in(X5,X2)
& X3 = ordered_pair(X4,X5) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f16,plain,
? [X0,X1,X2,X3] :
( ~ subset(X0,X3)
& subset(X0,cartesian_product2(X1,X2))
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
| ~ in(ordered_pair(X4,X5),X0) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f17,plain,
? [X0,X1,X2,X3] :
( ~ subset(X0,X3)
& subset(X0,cartesian_product2(X1,X2))
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
| ~ in(ordered_pair(X4,X5),X0) ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f19,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f19]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( ~ subset(X0,cartesian_product2(X1,X2))
| ~ in(X3,X0)
| ( in(sK3(X1,X2,X3),X1)
& in(sK4(X1,X2,X3),X2)
& ordered_pair(sK3(X1,X2,X3),sK4(X1,X2,X3)) = X3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X4,sK3(X1,X2,X3)),skolemize(X5,sK4(X1,X2,X3))],[f15]) ).
fof(f24,plain,
( ~ subset(sK5,sK8)
& subset(sK5,cartesian_product2(sK6,sK7))
& ! [X4,X5] :
( in(ordered_pair(X4,X5),sK8)
| ~ in(ordered_pair(X4,X5),sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7),skolemize(X3,sK8)],[f17]) ).
fof(f26,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f28,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f29,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( ~ subset(X0,cartesian_product2(X1,X2))
| ~ in(X3,X0)
| ordered_pair(sK3(X1,X2,X3),sK4(X1,X2,X3)) = X3 ),
inference(cnf_transformation,[],[f23]) ).
fof(f38,plain,
! [X4,X5] :
( in(ordered_pair(X4,X5),sK8)
| ~ in(ordered_pair(X4,X5),sK5) ),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
subset(sK5,cartesian_product2(sK6,sK7)),
inference(cnf_transformation,[],[f24]) ).
fof(f40,plain,
~ subset(sK5,sK8),
inference(cnf_transformation,[],[f24]) ).
fof(f42,plain,
! [X2,X3,X0,X1] :
( ~ subset(X0,cartesian_product2(X1,X2))
| ~ in(X3,X0)
| unordered_pair(unordered_pair(sK3(X1,X2,X3),sK4(X1,X2,X3)),singleton(sK3(X1,X2,X3))) = X3 ),
inference(definition_unfolding,[],[f35,f30]) ).
fof(f43,plain,
! [X4,X5] :
( ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),sK5)
| in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),sK8) ),
inference(definition_unfolding,[],[f38,f30,f30]) ).
fof(f45,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK8) ),
inference(superposition,[],[f43,f26]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( ~ subset(X0,cartesian_product2(X1,X2))
| unordered_pair(singleton(sK3(X1,X2,X3)),unordered_pair(sK3(X1,X2,X3),sK4(X1,X2,X3))) = X3
| ~ in(X3,X0) ),
inference(forward_demodulation,[],[f42,f26]) ).
fof(f74,plain,
! [X0] :
( ~ in(X0,sK5)
| unordered_pair(singleton(sK3(sK6,sK7,X0)),unordered_pair(sK3(sK6,sK7,X0),sK4(sK6,sK7,X0))) = X0 ),
inference(resolution,[],[f72,f39]) ).
fof(f77,plain,
! [X0] :
( subset(sK5,X0)
| sK0(sK5,X0) = unordered_pair(singleton(sK3(sK6,sK7,sK0(sK5,X0))),unordered_pair(sK3(sK6,sK7,sK0(sK5,X0)),sK4(sK6,sK7,sK0(sK5,X0)))) ),
inference(resolution,[],[f74,f28]) ).
fof(f84,plain,
sK0(sK5,sK8) = unordered_pair(singleton(sK3(sK6,sK7,sK0(sK5,sK8))),unordered_pair(sK3(sK6,sK7,sK0(sK5,sK8)),sK4(sK6,sK7,sK0(sK5,sK8)))),
inference(resolution,[],[f77,f40]) ).
fof(f92,plain,
( ~ in(sK0(sK5,sK8),sK5)
| in(sK0(sK5,sK8),sK8) ),
inference(superposition,[],[f45,f84]) ).
fof(f112,definition,
( spl9_3
<=> in(sK0(sK5,sK8),sK8) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f114,plain,
( in(sK0(sK5,sK8),sK8)
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f116,definition,
( spl9_4
<=> in(sK0(sK5,sK8),sK5) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
fof(f118,plain,
( ~ in(sK0(sK5,sK8),sK5)
| spl9_4 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,plain,
( spl9_3
| ~ spl9_4 ),
inference(avatar_split_clause,[],[f92,f116,f112]) ).
fof(f139,plain,
( subset(sK5,sK8)
| spl9_4 ),
inference(resolution,[],[f118,f28]) ).
fof(f140,plain,
( $false
| spl9_4 ),
inference(forward_subsumption_resolution,[],[f139,f40]) ).
fof(f141,plain,
spl9_4,
inference(avatar_contradiction_clause,[],[f140]) ).
fof(f145,plain,
( subset(sK5,sK8)
| ~ spl9_3 ),
inference(resolution,[],[f114,f29]) ).
fof(f147,plain,
( $false
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f145,f40]) ).
fof(f148,plain,
~ spl9_3,
inference(avatar_contradiction_clause,[],[f147]) ).
cnf(s2,plain,
( spl9_3
| ~ spl9_4 ),
inference(sat_conversion,[],[f119]) ).
cnf(s5,plain,
spl9_4,
inference(sat_conversion,[],[f141]) ).
cnf(s6,plain,
~ spl9_3,
inference(sat_conversion,[],[f148]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s5,s6]) ).
fof(f149,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET956+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n019.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 03:16:18 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 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
% 0.19/0.48 % (3628657)Will run a generic schedule for satisfiability detection.
% 0.19/0.48 % (3628665)dis+10_1_sil=32000:sp=arity:random_seed=1436807506:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.48 % (3628663)% WARNING: option uhcvi not known.
% 0.19/0.48 % (3628665) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3628657-3628665"...
% 0.19/0.48 % (3628665)...printing done.
% 0.19/0.48 % (3628665)Refutation found. Thanks to Tanya!
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.48 % (3628665)------------------------------
% 0.19/0.48 % (3628665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.48 % (3628665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.48 % (3628665)CaDiCaL version: 2.1.3
% 0.19/0.48 % (3628665)Termination reason: Refutation
% 0.19/0.48 % (3628665)Time elapsed: 0.004 s
% 0.19/0.48 % (3628665)Peak memory usage: 12 MB
% 0.19/0.48 % (3628665)Instructions burned: 7 (million)
% 0.19/0.48 % (3628657)Success in time 0.038 s
% 0.19/0.48 % Vampire exiting
%------------------------------------------------------------------------------