%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU205+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:52:22 PM UTC 2026
% Result : Theorem 2.02s 0.85s
% Output : Refutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 110 ( 23 unt; 4 def)
% Number of atoms : 380 ( 67 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 454 ( 184 ~; 200 |; 55 &)
% ( 9 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 239 ( 220 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f6,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f7,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(f30,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_dom(X2))
& in(ordered_pair(X3,X0),X2)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
fof(f31,conjecture,
! [X0,X1] :
( relation(X1)
=> relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_relat_1) ).
fof(f32,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f36,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f43,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_dom(X2))
& in(ordered_pair(X3,X0),X2)
& in(X3,X1) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f30]) ).
fof(f50,plain,
? [X0,X1] :
( relation_image(X1,X0) != relation_image(X1,set_intersection2(relation_dom(X1),X0))
& relation(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f54,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f58,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) ) )
& ( ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f43]) ).
fof(f59,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(ordered_pair(X5,X3),X0)
& in(X5,X1) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X7,X6),X0)
| ~ in(X7,X1) ) )
& ( ? [X8] :
( in(ordered_pair(X8,X6),X0)
& in(X8,X1) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(rectify,[],[f58]) ).
fof(f60,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ( ( ! [X4] :
( ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0)
| ~ in(X4,X1) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0)
& in(sK1(X0,X1,X2),X1) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X7,X6),X0)
| ~ in(X7,X1) ) )
& ( ( in(ordered_pair(sK2(X0,X1,X6),X6),X0)
& in(sK2(X0,X1,X6),X1) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(sK3(X0,X1,X2),X0)
& in(sK3(X0,X1,X2),X1) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f63]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_dom(X2))
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,X1) ) )
& ( ? [X3] :
( in(X3,relation_dom(X2))
& in(ordered_pair(X3,X0),X2)
& in(X3,X1) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f49]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_dom(X2))
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,X1) ) )
& ( ? [X4] :
( in(X4,relation_dom(X2))
& in(ordered_pair(X4,X0),X2)
& in(X4,X1) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_dom(X2))
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,X1) ) )
& ( ( in(sK9(X0,X1,X2),relation_dom(X2))
& in(ordered_pair(sK9(X0,X1,X2),X0),X2)
& in(sK9(X0,X1,X2),X1) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X4,sK9(X0,X1,X2))],[f71]) ).
fof(f73,plain,
( relation_image(sK11,sK10) != relation_image(sK11,set_intersection2(relation_dom(sK11),sK10))
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X1,sK11)],[f50]) ).
fof(f74,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f75,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK12(X0,X1),X1)
| ~ in(sK12(X0,X1),X0) )
& ( in(sK12(X0,X1),X1)
| in(sK12(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f74]) ).
fof(f78,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f79,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f80,plain,
! [X2,X0,X1,X6] :
( in(sK2(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f81,plain,
! [X2,X0,X1,X6] :
( in(ordered_pair(sK2(X0,X1,X6),X6),X0)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f82,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(ordered_pair(X7,X6),X0)
| ~ in(X7,X1)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f86,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f64]) ).
fof(f87,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f64]) ).
fof(f88,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f64]) ).
fof(f90,plain,
! [X2,X0,X1] :
( in(sK3(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f64]) ).
fof(f91,plain,
! [X2,X0,X1] :
( ~ in(sK3(X0,X1,X2),X2)
| ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X1)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f64]) ).
fof(f92,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_image(X2,X1))
| in(sK9(X0,X1,X2),X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f112,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK9(X0,X1,X2),X0),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_image(X2,X1))
| in(sK9(X0,X1,X2),relation_dom(X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f115,plain,
relation(sK11),
inference(cnf_transformation,[],[f73]) ).
fof(f116,plain,
relation_image(sK11,sK10) != relation_image(sK11,set_intersection2(relation_dom(sK11),sK10)),
inference(cnf_transformation,[],[f73]) ).
fof(f120,plain,
! [X0,X1] :
( in(sK12(X0,X1),X1)
| in(sK12(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f75]) ).
fof(f121,plain,
! [X0,X1] :
( ~ in(sK12(X0,X1),X1)
| X0 = X1
| ~ in(sK12(X0,X1),X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f127,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| ~ in(X7,X1)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f82,f92]) ).
fof(f128,plain,
! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(sK2(X0,X1,X6),X6),singleton(sK2(X0,X1,X6))),X0)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f81,f92]) ).
fof(f131,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_image(X2,X1))
| in(unordered_pair(unordered_pair(sK9(X0,X1,X2),X0),singleton(sK9(X0,X1,X2))),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f112,f92]) ).
fof(f132,plain,
! [X0,X1,X6,X7] :
( ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| in(X6,relation_image(X0,X1))
| ~ in(X7,X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f127]) ).
fof(f133,plain,
! [X0,X1,X6] :
( ~ in(X6,relation_image(X0,X1))
| in(unordered_pair(unordered_pair(sK2(X0,X1,X6),X6),singleton(sK2(X0,X1,X6))),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f128]) ).
fof(f134,plain,
! [X0,X1,X6] :
( ~ in(X6,relation_image(X0,X1))
| in(sK2(X0,X1,X6),X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f80]) ).
fof(f135,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f88]) ).
fof(f136,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f87]) ).
fof(f137,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f86]) ).
fof(f138,definition,
sF13 = relation_image(sK11,sK10),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f139,plain,
relation_image(sK11,sK10) = sF13,
inference(reorient_equations,[],[f138]) ).
fof(f140,definition,
sF14 = relation_dom(sK11),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f141,plain,
relation_dom(sK11) = sF14,
inference(reorient_equations,[],[f140]) ).
fof(f142,definition,
sF15 = set_intersection2(sF14,sK10),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f143,plain,
set_intersection2(sF14,sK10) = sF15,
inference(reorient_equations,[],[f142]) ).
fof(f144,definition,
sF16 = relation_image(sK11,sF15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f145,plain,
relation_image(sK11,sF15) = sF16,
inference(reorient_equations,[],[f144]) ).
fof(f146,plain,
sF13 != sF16,
inference(definition_folding,[],[f116,f145,f143,f141,f139]) ).
fof(f250,plain,
! [X0] :
( ~ in(X0,sF15)
| in(X0,sK10) ),
inference(superposition,[],[f137,f143]) ).
fof(f261,plain,
! [X0] :
( ~ in(X0,sF14)
| in(X0,sF15)
| ~ in(X0,sK10) ),
inference(superposition,[],[f135,f143]) ).
fof(f267,plain,
! [X0] :
( ~ in(X0,sF13)
| in(sK9(X0,sK10,sK11),sK10)
| ~ relation(sK11) ),
inference(superposition,[],[f111,f139]) ).
fof(f270,plain,
! [X0] :
( in(sK9(X0,sK10,sK11),sK10)
| ~ in(X0,sF13) ),
inference(forward_subsumption_resolution,[],[f267,f115]) ).
fof(f292,plain,
! [X2,X0,X1] :
( in(sK12(set_intersection2(X0,X1),X2),X2)
| in(sK12(set_intersection2(X0,X1),X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(resolution,[],[f120,f136]) ).
fof(f305,plain,
! [X0] :
( ~ in(X0,sF16)
| in(sK2(sK11,sF15,X0),sF15)
| ~ relation(sK11) ),
inference(superposition,[],[f134,f145]) ).
fof(f306,plain,
! [X0] :
( in(sK2(sK11,sF15,X0),sF15)
| ~ in(X0,sF16) ),
inference(forward_subsumption_resolution,[],[f305,f115]) ).
fof(f310,plain,
! [X0] :
( ~ in(X0,sF13)
| in(sK9(X0,sK10,sK11),relation_dom(sK11))
| ~ relation(sK11) ),
inference(superposition,[],[f113,f139]) ).
fof(f313,plain,
! [X0] :
( ~ in(X0,sF13)
| in(sK9(X0,sK10,sK11),relation_dom(sK11)) ),
inference(forward_subsumption_resolution,[],[f310,f115]) ).
fof(f315,plain,
! [X0] :
( in(sK9(X0,sK10,sK11),sF14)
| ~ in(X0,sF13) ),
inference(forward_demodulation,[],[f313,f141]) ).
fof(f361,plain,
! [X0,X1] :
( in(sK3(X0,X1,X0),X0)
| set_intersection2(X0,X1) = X0 ),
inference(factoring,[],[f90]) ).
fof(f367,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X1)),X2)
| in(X0,relation_image(X2,X3))
| ~ in(X1,X3)
| ~ relation(X2) ),
inference(superposition,[],[f132,f78]) ).
fof(f370,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),X2)
| in(X0,relation_image(X2,X3))
| ~ in(X1,X3)
| ~ relation(X2) ),
inference(forward_demodulation,[],[f367,f78]) ).
fof(f396,plain,
! [X0] :
( ~ in(X0,sF13)
| in(unordered_pair(unordered_pair(sK9(X0,sK10,sK11),X0),singleton(sK9(X0,sK10,sK11))),sK11)
| ~ relation(sK11) ),
inference(superposition,[],[f131,f139]) ).
fof(f399,plain,
! [X0] :
( ~ in(X0,sF13)
| in(unordered_pair(unordered_pair(sK9(X0,sK10,sK11),X0),singleton(sK9(X0,sK10,sK11))),sK11) ),
inference(forward_subsumption_resolution,[],[f396,f115]) ).
fof(f407,plain,
! [X0] :
( in(unordered_pair(singleton(sK9(X0,sK10,sK11)),unordered_pair(sK9(X0,sK10,sK11),X0)),sK11)
| ~ in(X0,sF13) ),
inference(forward_demodulation,[],[f399,f78]) ).
fof(f415,plain,
! [X0] :
( in(unordered_pair(singleton(sK9(X0,sK10,sK11)),unordered_pair(X0,sK9(X0,sK10,sK11))),sK11)
| ~ in(X0,sF13) ),
inference(forward_demodulation,[],[f407,f78]) ).
fof(f426,plain,
! [X0] :
( ~ in(X0,sF16)
| in(unordered_pair(unordered_pair(sK2(sK11,sF15,X0),X0),singleton(sK2(sK11,sF15,X0))),sK11)
| ~ relation(sK11) ),
inference(superposition,[],[f133,f145]) ).
fof(f427,plain,
! [X0] :
( ~ in(X0,sF16)
| in(unordered_pair(unordered_pair(sK2(sK11,sF15,X0),X0),singleton(sK2(sK11,sF15,X0))),sK11) ),
inference(forward_subsumption_resolution,[],[f426,f115]) ).
fof(f435,plain,
! [X0] :
( in(unordered_pair(singleton(sK2(sK11,sF15,X0)),unordered_pair(sK2(sK11,sF15,X0),X0)),sK11)
| ~ in(X0,sF16) ),
inference(forward_demodulation,[],[f427,f78]) ).
fof(f443,plain,
! [X0] :
( in(unordered_pair(singleton(sK2(sK11,sF15,X0)),unordered_pair(X0,sK2(sK11,sF15,X0))),sK11)
| ~ in(X0,sF16) ),
inference(forward_demodulation,[],[f435,f78]) ).
fof(f559,plain,
! [X0] :
( in(sK2(sK11,sF15,X0),sK10)
| ~ in(X0,sF16) ),
inference(resolution,[],[f250,f306]) ).
fof(f591,plain,
! [X0] :
( in(sK9(X0,sK10,sK11),sF15)
| ~ in(sK9(X0,sK10,sK11),sK10)
| ~ in(X0,sF13) ),
inference(resolution,[],[f261,f315]) ).
fof(f594,plain,
! [X0] :
( in(sK9(X0,sK10,sK11),sF15)
| ~ in(X0,sF13) ),
inference(forward_subsumption_resolution,[],[f591,f270]) ).
fof(f674,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ in(sK3(X0,X1,X0),X0)
| ~ in(sK3(X0,X1,X0),X1)
| set_intersection2(X0,X1) = X0 ),
inference(resolution,[],[f361,f91]) ).
fof(f689,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ in(sK3(X0,X1,X0),X0)
| ~ in(sK3(X0,X1,X0),X1) ),
inference(duplicate_literal_removal,[],[f674]) ).
fof(f692,plain,
! [X0,X1] :
( ~ in(sK3(X0,X1,X0),X1)
| set_intersection2(X0,X1) = X0 ),
inference(forward_subsumption_resolution,[],[f689,f361]) ).
fof(f997,plain,
! [X0,X1] :
( in(X0,relation_image(sK11,X1))
| ~ in(sK9(X0,sK10,sK11),X1)
| ~ relation(sK11)
| ~ in(X0,sF13) ),
inference(resolution,[],[f370,f415]) ).
fof(f998,plain,
! [X0,X1] :
( in(X0,relation_image(sK11,X1))
| ~ in(sK2(sK11,sF15,X0),X1)
| ~ relation(sK11)
| ~ in(X0,sF16) ),
inference(resolution,[],[f370,f443]) ).
fof(f1005,plain,
! [X0,X1] :
( ~ in(sK2(sK11,sF15,X0),X1)
| in(X0,relation_image(sK11,X1))
| ~ in(X0,sF16) ),
inference(forward_subsumption_resolution,[],[f998,f115]) ).
fof(f1308,plain,
! [X0,X1] :
( in(sK12(set_intersection2(X0,X1),X0),X0)
| set_intersection2(X0,X1) = X0 ),
inference(factoring,[],[f292]) ).
fof(f3077,plain,
! [X0] :
( in(X0,relation_image(sK11,sK10))
| ~ in(X0,sF16)
| ~ in(X0,sF16) ),
inference(resolution,[],[f1005,f559]) ).
fof(f3081,plain,
! [X0] :
( in(X0,relation_image(sK11,sK10))
| ~ in(X0,sF16) ),
inference(duplicate_literal_removal,[],[f3077]) ).
fof(f3084,plain,
! [X0] :
( ~ in(X0,sF16)
| in(X0,sF13) ),
inference(forward_demodulation,[],[f3081,f139]) ).
fof(f3092,plain,
! [X0,X1] :
( ~ in(sK9(X0,sK10,sK11),X1)
| in(X0,relation_image(sK11,X1))
| ~ in(X0,sF13) ),
inference(forward_subsumption_resolution,[],[f997,f115]) ).
fof(f3209,plain,
! [X0] :
( in(sK3(sF16,X0,sF16),sF13)
| sF16 = set_intersection2(sF16,X0) ),
inference(resolution,[],[f3084,f361]) ).
fof(f3251,plain,
! [X0] :
( in(X0,relation_image(sK11,sF15))
| ~ in(X0,sF13)
| ~ in(X0,sF13) ),
inference(resolution,[],[f3092,f594]) ).
fof(f3257,plain,
! [X0] :
( in(X0,relation_image(sK11,sF15))
| ~ in(X0,sF13) ),
inference(duplicate_literal_removal,[],[f3251]) ).
fof(f3259,plain,
! [X0] :
( ~ in(X0,sF13)
| in(X0,sF16) ),
inference(forward_demodulation,[],[f3257,f145]) ).
fof(f8695,plain,
( sF16 = set_intersection2(sF16,sF13)
| sF16 = set_intersection2(sF16,sF13) ),
inference(resolution,[],[f3209,f692]) ).
fof(f8701,plain,
sF16 = set_intersection2(sF16,sF13),
inference(duplicate_literal_removal,[],[f8695]) ).
fof(f8702,plain,
sF16 = set_intersection2(sF13,sF16),
inference(forward_demodulation,[],[f8701,f79]) ).
fof(f8754,plain,
( in(sK12(sF16,sF13),sF13)
| sF13 = sF16 ),
inference(superposition,[],[f1308,f8702]) ).
fof(f8763,plain,
in(sK12(sF16,sF13),sF13),
inference(forward_subsumption_resolution,[],[f8754,f146]) ).
fof(f8790,plain,
( sF13 = sF16
| ~ in(sK12(sF16,sF13),sF16) ),
inference(resolution,[],[f8763,f121]) ).
fof(f8791,plain,
in(sK12(sF16,sF13),sF16),
inference(resolution,[],[f8763,f3259]) ).
fof(f8796,plain,
~ in(sK12(sF16,sF13),sF16),
inference(forward_subsumption_resolution,[],[f8790,f146]) ).
fof(f8797,plain,
$false,
inference(forward_subsumption_resolution,[],[f8796,f8791]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU205+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.38 % Computer : n014.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 04:02:31 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.41 Running first-order model finding
% 0.09/0.41 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
% 2.02/0.85 % (1420775)Will run a generic schedule for satisfiability detection.
% 2.02/0.85 % (1420784)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2666524112:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.02/0.85 % (1420781)% WARNING: option uhcvi not known.
% 2.02/0.85 % (1420780)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2412458685_2999 on theBenchmark for (2999ds/0Mi)
% 2.02/0.85 % (1420781)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1507940244:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.02/0.85 % (1420783)dis+10_1_sil=32000:sp=arity:random_seed=808841884:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.02/0.85 % (1420785)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1007587829:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.02/0.85 % (1420782)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2569757254:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.02/0.85 % (1420786)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4197772226:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.02/0.85 % TRYING [1]
% 2.02/0.85 % TRYING [2]
% 2.02/0.85 % TRYING [3]
% 2.02/0.85 % (1420784)Instruction limit reached!
% 2.02/0.85 % (1420784)------------------------------
% 2.02/0.85 % (1420784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.85 % (1420784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.85 % (1420784)CaDiCaL version: 2.1.3
% 2.02/0.85 % (1420784)Termination reason: Instruction limit
% 2.02/0.85 % (1420784)Termination phase: Saturation
% 2.02/0.85 % (1420784)Time elapsed: 0.037 s
% 2.02/0.85 % (1420784)Peak memory usage: 12 MB
% 2.02/0.85 % (1420784)Instructions burned: 118 (million)
% 2.02/0.85 % TRYING [4]
% 2.02/0.85 % (1420794)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1394670265:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.02/0.85 % TRYING [1]
% 2.02/0.85 % TRYING [2]
% 2.02/0.85 % TRYING [3]
% 2.02/0.85 % TRYING [4]
% 2.02/0.85 % (1420783)Instruction limit reached!
% 2.02/0.85 % (1420783)------------------------------
% 2.02/0.85 % (1420783)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.85 % (1420783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.85 % (1420783)CaDiCaL version: 2.1.3
% 2.02/0.85 % (1420783)Termination reason: Instruction limit
% 2.02/0.85 % (1420783)Termination phase: Saturation
% 2.02/0.85 % (1420783)Time elapsed: 0.062 s
% 2.02/0.85 % (1420783)Peak memory usage: 12 MB
% 2.02/0.85 % (1420783)Instructions burned: 103 (million)
% 2.02/0.85 % (1420785)Instruction limit reached!
% 2.02/0.85 % (1420785)------------------------------
% 2.02/0.85 % (1420785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.85 % (1420785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.85 % (1420785)CaDiCaL version: 2.1.3
% 2.02/0.85 % (1420785)Termination reason: Instruction limit
% 2.02/0.85 % (1420785)Termination phase: Saturation
% 2.02/0.85 % (1420785)Time elapsed: 0.081 s
% 2.02/0.85 % (1420785)Peak memory usage: 13 MB
% 2.02/0.85 % (1420785)Instructions burned: 138 (million)
% 2.02/0.85 % (1420796)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1442218396:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.02/0.85 % (1420786)Instruction limit reached!
% 2.02/0.85 % (1420786)------------------------------
% 2.02/0.85 % (1420786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.85 % (1420786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.85 % (1420786)CaDiCaL version: 2.1.3
% 2.02/0.85 % (1420786)Termination reason: Instruction limit
% 2.02/0.85 % (1420786)Termination phase: Saturation
% 2.02/0.85 % (1420786)Time elapsed: 0.096 s
% 2.02/0.85 % (1420786)Peak memory usage: 13 MB
% 2.02/0.85 % (1420786)Instructions burned: 160 (million)
% 2.02/0.85 % (1420798)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1541093669:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.02/0.85 % (1420799)ott-21_1_sil=16000:fs=off:random_seed=2450119173:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.02/0.85 % (1420796)Instruction limit reached!
% 2.02/0.85 % (1420796)------------------------------
% 2.02/0.85 % (1420796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.85 % (1420796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.85 % (1420796)CaDiCaL version: 2.1.3
% 2.02/0.85 % (1420796)Termination reason: Instruction limit
% 2.02/0.85 % (1420796)Termination phase: Saturation
% 2.02/0.85 % (1420796)Time elapsed: 0.083 s
% 2.02/0.85 % (1420796)Peak memory usage: 13 MB
% 2.02/0.85 % (1420796)Instructions burned: 131 (million)
% 2.02/0.85 % (1420802)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3741133227:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.02/0.85 % (1420799)Instruction limit reached!
% 2.02/0.85 % (1420799)------------------------------
% 2.02/0.85 % (1420799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.85 % (1420799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.85 % (1420799)CaDiCaL version: 2.1.3
% 2.02/0.85 % (1420799)Termination reason: Instruction limit
% 2.02/0.85 % (1420799)Termination phase: Saturation
% 2.02/0.85 % (1420799)Time elapsed: 0.096 s
% 2.02/0.85 % (1420799)Peak memory usage: 13 MB
% 2.02/0.85 % (1420799)Instructions burned: 181 (million)
% 2.02/0.85 % (1420804)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1403914899:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.02/0.85 % TRYING [1]
% 2.02/0.85 % TRYING [2]
% 2.02/0.85 % TRYING [3]
% 2.02/0.85 % (1420794)Instruction limit reached!
% 2.02/0.85 % (1420794)------------------------------
% 2.02/0.85 % (1420794)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.85 % (1420794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.85 % (1420794)CaDiCaL version: 2.1.3
% 2.02/0.85 % (1420794)Termination reason: Instruction limit
% 2.02/0.85 % (1420794)Termination phase: Finite model building SAT solving
% 2.02/0.85 % (1420794)Time elapsed: 0.211 s
% 2.02/0.85 % (1420794)Peak memory usage: 18 MB
% 2.02/0.85 % (1420794)Instructions burned: 714 (million)
% 2.02/0.85 % (1420806)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1042839072:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 2.02/0.85 % TRYING [4]
% 2.02/0.85 % (1420806) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1420775-1420806"...
% 2.02/0.85 % (1420806)...printing done.
% 2.02/0.85 % (1420806)Refutation found. Thanks to Tanya!
% 2.02/0.85 % SZS status Theorem for theBenchmark
% 2.02/0.85 % SZS output start Proof for theBenchmark
% See solution above
% 2.02/0.85 % (1420806)------------------------------
% 2.02/0.85 % (1420806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.02/0.85 % (1420806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.85 % (1420806)CaDiCaL version: 2.1.3
% 2.02/0.85 % (1420806)Termination reason: Refutation
% 2.02/0.85 % (1420806)Time elapsed: 0.128 s
% 2.02/0.85 % (1420806)Peak memory usage: 15 MB
% 2.02/0.85 % (1420806)Instructions burned: 411 (million)
% 2.02/0.85 % (1420775)Success in time 0.428 s
% 2.02/0.85 % Vampire exiting
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