TSTP Solution File: SEU281+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU281+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:21:50 EDT 2024
% Result : Theorem 0.62s 0.80s
% Output : Refutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 82 ( 7 unt; 0 def)
% Number of atoms : 470 ( 186 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 572 ( 184 ~; 193 |; 174 &)
% ( 8 <=>; 12 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 3 con; 0-3 aty)
% Number of variables : 325 ( 194 !; 131 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f191,plain,
$false,
inference(avatar_sat_refutation,[],[f184,f190]) ).
fof(f190,plain,
~ spl19_1,
inference(avatar_contradiction_clause,[],[f188]) ).
fof(f188,plain,
( $false
| ~ spl19_1 ),
inference(resolution,[],[f183,f153]) ).
fof(f153,plain,
in(sK4(sK14(sK2,sK3)),sK14(sK2,sK3)),
inference(factoring,[],[f144]) ).
fof(f144,plain,
! [X0] :
( in(sK4(X0),sK14(sK2,sK3))
| in(sK4(X0),X0) ),
inference(subsumption_resolution,[],[f143,f50]) ).
fof(f50,plain,
! [X2] :
( in(sK5(X2),sK2)
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X2] :
( ( ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,sK2)
| ordered_pair(X4,X5) != sK4(X2) )
| ~ in(sK4(X2),cartesian_product2(sK2,sK3))
| ~ in(sK4(X2),X2) )
& ( ( sK6(X2) = singleton(sK5(X2))
& in(sK5(X2),sK2)
& sK4(X2) = ordered_pair(sK5(X2),sK6(X2))
& in(sK4(X2),cartesian_product2(sK2,sK3)) )
| in(sK4(X2),X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6])],[f28,f31,f30,f29]) ).
fof(f29,plain,
( ? [X0,X1] :
! [X2] :
? [X3] :
( ( ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(X0,X1))
| ~ in(X3,X2) )
& ( ( ? [X6,X7] :
( singleton(X6) = X7
& in(X6,X0)
& ordered_pair(X6,X7) = X3 )
& in(X3,cartesian_product2(X0,X1)) )
| in(X3,X2) ) )
=> ! [X2] :
? [X3] :
( ( ! [X5,X4] :
( singleton(X4) != X5
| ~ in(X4,sK2)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(sK2,sK3))
| ~ in(X3,X2) )
& ( ( ? [X7,X6] :
( singleton(X6) = X7
& in(X6,sK2)
& ordered_pair(X6,X7) = X3 )
& in(X3,cartesian_product2(sK2,sK3)) )
| in(X3,X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
! [X2] :
( ? [X3] :
( ( ! [X5,X4] :
( singleton(X4) != X5
| ~ in(X4,sK2)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(sK2,sK3))
| ~ in(X3,X2) )
& ( ( ? [X7,X6] :
( singleton(X6) = X7
& in(X6,sK2)
& ordered_pair(X6,X7) = X3 )
& in(X3,cartesian_product2(sK2,sK3)) )
| in(X3,X2) ) )
=> ( ( ! [X5,X4] :
( singleton(X4) != X5
| ~ in(X4,sK2)
| ordered_pair(X4,X5) != sK4(X2) )
| ~ in(sK4(X2),cartesian_product2(sK2,sK3))
| ~ in(sK4(X2),X2) )
& ( ( ? [X7,X6] :
( singleton(X6) = X7
& in(X6,sK2)
& ordered_pair(X6,X7) = sK4(X2) )
& in(sK4(X2),cartesian_product2(sK2,sK3)) )
| in(sK4(X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X2] :
( ? [X7,X6] :
( singleton(X6) = X7
& in(X6,sK2)
& ordered_pair(X6,X7) = sK4(X2) )
=> ( sK6(X2) = singleton(sK5(X2))
& in(sK5(X2),sK2)
& sK4(X2) = ordered_pair(sK5(X2),sK6(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(X0,X1))
| ~ in(X3,X2) )
& ( ( ? [X6,X7] :
( singleton(X6) = X7
& in(X6,X0)
& ordered_pair(X6,X7) = X3 )
& in(X3,cartesian_product2(X0,X1)) )
| in(X3,X2) ) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(X0,X1))
| ~ in(X3,X2) )
& ( ( ? [X4,X5] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& in(X3,cartesian_product2(X0,X1)) )
| in(X3,X2) ) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(X0,X1))
| ~ in(X3,X2) )
& ( ( ? [X4,X5] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& in(X3,cartesian_product2(X0,X1)) )
| in(X3,X2) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( in(X3,X2)
<~> ( ? [X4,X5] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& in(X3,cartesian_product2(X0,X1)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4,X5] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& in(X3,cartesian_product2(X0,X1)) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0,X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4,X5] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& in(X3,cartesian_product2(X0,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.VfJKtoPSCU/Vampire---4.8_14521',s1_xboole_0__e16_22__wellord2__1) ).
fof(f143,plain,
! [X0] :
( ~ in(sK5(X0),sK2)
| in(sK4(X0),sK14(sK2,sK3))
| in(sK4(X0),X0) ),
inference(subsumption_resolution,[],[f142,f76]) ).
fof(f76,plain,
! [X2] :
( in(sK4(X2),sF18)
| in(sK4(X2),X2) ),
inference(definition_folding,[],[f48,f74]) ).
fof(f74,plain,
cartesian_product2(sK2,sK3) = sF18,
introduced(function_definition,[new_symbols(definition,[sF18])]) ).
fof(f48,plain,
! [X2] :
( in(sK4(X2),cartesian_product2(sK2,sK3))
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f142,plain,
! [X0] :
( ~ in(sK4(X0),sF18)
| ~ in(sK5(X0),sK2)
| in(sK4(X0),sK14(sK2,sK3))
| in(sK4(X0),X0) ),
inference(superposition,[],[f140,f74]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ in(sK4(X0),cartesian_product2(X1,X2))
| ~ in(sK5(X0),X1)
| in(sK4(X0),sK14(X1,X2))
| in(sK4(X0),X0) ),
inference(duplicate_literal_removal,[],[f138]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ in(sK4(X0),cartesian_product2(X1,X2))
| ~ in(sK5(X0),X1)
| in(sK4(X0),sK14(X1,X2))
| in(sK4(X0),X0)
| in(sK4(X0),X0) ),
inference(superposition,[],[f133,f49]) ).
fof(f49,plain,
! [X2] :
( sK4(X2) = ordered_pair(sK5(X2),sK6(X2))
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(sK5(X0),sK6(X0)),cartesian_product2(X1,X2))
| ~ in(sK5(X0),X1)
| in(ordered_pair(sK5(X0),sK6(X0)),sK14(X1,X2))
| in(sK4(X0),X0) ),
inference(subsumption_resolution,[],[f128,f91]) ).
fof(f91,plain,
! [X0] : ~ sP1(X0),
inference(subsumption_resolution,[],[f90,f53]) ).
fof(f53,plain,
! [X0] :
( sK7(X0) = sK8(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( ( sK8(X0) != sK9(X0)
& sK11(X0) = singleton(sK10(X0))
& in(sK10(X0),X0)
& sK9(X0) = ordered_pair(sK10(X0),sK11(X0))
& sK7(X0) = sK9(X0)
& sP0(X0,sK8(X0))
& sK7(X0) = sK8(X0) )
| ~ sP1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11])],[f34,f36,f35]) ).
fof(f35,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& ? [X4,X5] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& X1 = X3
& sP0(X0,X2)
& X1 = X2 )
=> ( sK8(X0) != sK9(X0)
& ? [X5,X4] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = sK9(X0) )
& sK7(X0) = sK9(X0)
& sP0(X0,sK8(X0))
& sK7(X0) = sK8(X0) ) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
! [X0] :
( ? [X5,X4] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = sK9(X0) )
=> ( sK11(X0) = singleton(sK10(X0))
& in(sK10(X0),X0)
& sK9(X0) = ordered_pair(sK10(X0),sK11(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& ? [X4,X5] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& X1 = X3
& sP0(X0,X2)
& X1 = X2 )
| ~ sP1(X0) ),
inference(rectify,[],[f33]) ).
fof(f33,plain,
! [X0] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5,X6] :
( singleton(X5) = X6
& in(X5,X0)
& ordered_pair(X5,X6) = X4 )
& X2 = X4
& sP0(X0,X3)
& X2 = X3 )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5,X6] :
( singleton(X5) = X6
& in(X5,X0)
& ordered_pair(X5,X6) = X4 )
& X2 = X4
& sP0(X0,X3)
& X2 = X3 )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f90,plain,
! [X0] :
( sK7(X0) != sK8(X0)
| ~ sP1(X0) ),
inference(duplicate_literal_removal,[],[f89]) ).
fof(f89,plain,
! [X0] :
( sK7(X0) != sK8(X0)
| ~ sP1(X0)
| ~ sP1(X0) ),
inference(superposition,[],[f59,f55]) ).
fof(f55,plain,
! [X0] :
( sK7(X0) = sK9(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f59,plain,
! [X0] :
( sK8(X0) != sK9(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f128,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(sK5(X0),sK6(X0)),cartesian_product2(X1,X2))
| ~ in(sK5(X0),X1)
| in(ordered_pair(sK5(X0),sK6(X0)),sK14(X1,X2))
| sP1(X1)
| in(sK4(X0),X0) ),
inference(superposition,[],[f73,f51]) ).
fof(f51,plain,
! [X2] :
( sK6(X2) = singleton(sK5(X2))
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f73,plain,
! [X0,X1,X5] :
( ~ in(ordered_pair(X5,singleton(X5)),cartesian_product2(X0,X1))
| ~ in(X5,X0)
| in(ordered_pair(X5,singleton(X5)),sK14(X0,X1))
| sP1(X0) ),
inference(equality_resolution,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X5,singleton(X5)),sK14(X0,X1))
| ~ in(X5,X0)
| ordered_pair(X5,singleton(X5)) != X4
| ~ in(X4,cartesian_product2(X0,X1))
| sP1(X0) ),
inference(equality_resolution,[],[f71]) ).
fof(f71,plain,
! [X3,X0,X1,X4,X5] :
( in(X3,sK14(X0,X1))
| ~ in(X5,X0)
| ordered_pair(X5,singleton(X5)) != X3
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1))
| sP1(X0) ),
inference(equality_resolution,[],[f68]) ).
fof(f68,plain,
! [X3,X0,X1,X6,X4,X5] :
( in(X3,sK14(X0,X1))
| singleton(X5) != X6
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X3
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1))
| sP1(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK14(X0,X1))
| ! [X4] :
( ! [X5,X6] :
( singleton(X5) != X6
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X3 )
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1)) ) )
& ( ( sK17(X0,X3) = singleton(sK16(X0,X3))
& in(sK16(X0,X3),X0)
& ordered_pair(sK16(X0,X3),sK17(X0,X3)) = X3
& sK15(X0,X1,X3) = X3
& in(sK15(X0,X1,X3),cartesian_product2(X0,X1)) )
| ~ in(X3,sK14(X0,X1)) ) )
| sP1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17])],[f43,f46,f45,f44]) ).
fof(f44,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ! [X5,X6] :
( singleton(X5) != X6
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X3 )
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1)) ) )
& ( ? [X7] :
( ? [X8,X9] :
( singleton(X8) = X9
& in(X8,X0)
& ordered_pair(X8,X9) = X3 )
& X3 = X7
& in(X7,cartesian_product2(X0,X1)) )
| ~ in(X3,X2) ) )
=> ! [X3] :
( ( in(X3,sK14(X0,X1))
| ! [X4] :
( ! [X5,X6] :
( singleton(X5) != X6
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X3 )
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1)) ) )
& ( ? [X7] :
( ? [X8,X9] :
( singleton(X8) = X9
& in(X8,X0)
& ordered_pair(X8,X9) = X3 )
& X3 = X7
& in(X7,cartesian_product2(X0,X1)) )
| ~ in(X3,sK14(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
! [X0,X1,X3] :
( ? [X7] :
( ? [X8,X9] :
( singleton(X8) = X9
& in(X8,X0)
& ordered_pair(X8,X9) = X3 )
& X3 = X7
& in(X7,cartesian_product2(X0,X1)) )
=> ( ? [X8,X9] :
( singleton(X8) = X9
& in(X8,X0)
& ordered_pair(X8,X9) = X3 )
& sK15(X0,X1,X3) = X3
& in(sK15(X0,X1,X3),cartesian_product2(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X0,X3] :
( ? [X8,X9] :
( singleton(X8) = X9
& in(X8,X0)
& ordered_pair(X8,X9) = X3 )
=> ( sK17(X0,X3) = singleton(sK16(X0,X3))
& in(sK16(X0,X3),X0)
& ordered_pair(sK16(X0,X3),sK17(X0,X3)) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ! [X5,X6] :
( singleton(X5) != X6
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X3 )
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1)) ) )
& ( ? [X7] :
( ? [X8,X9] :
( singleton(X8) = X9
& in(X8,X0)
& ordered_pair(X8,X9) = X3 )
& X3 = X7
& in(X7,cartesian_product2(X0,X1)) )
| ~ in(X3,X2) ) )
| sP1(X0) ),
inference(rectify,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( ( in(X10,X9)
| ! [X11] :
( ! [X12,X13] :
( singleton(X12) != X13
| ~ in(X12,X0)
| ordered_pair(X12,X13) != X10 )
| X10 != X11
| ~ in(X11,cartesian_product2(X0,X1)) ) )
& ( ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) )
| ~ in(X10,X9) ) )
| sP1(X0) ),
inference(nnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) )
| sP1(X0) ),
inference(definition_folding,[],[f21,f24,f23]) ).
fof(f23,plain,
! [X0,X3] :
( ? [X7,X8] :
( singleton(X7) = X8
& in(X7,X0)
& ordered_pair(X7,X8) = X3 )
| ~ sP0(X0,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f21,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) )
| ? [X2,X3,X4] :
( X3 != X4
& ? [X5,X6] :
( singleton(X5) = X6
& in(X5,X0)
& ordered_pair(X5,X6) = X4 )
& X2 = X4
& ? [X7,X8] :
( singleton(X7) = X8
& in(X7,X0)
& ordered_pair(X7,X8) = X3 )
& X2 = X3 ) ),
inference(flattening,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) )
| ? [X2,X3,X4] :
( X3 != X4
& ? [X5,X6] :
( singleton(X5) = X6
& in(X5,X0)
& ordered_pair(X5,X6) = X4 )
& X2 = X4
& ? [X7,X8] :
( singleton(X7) = X8
& in(X7,X0)
& ordered_pair(X7,X8) = X3 )
& X2 = X3 ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ! [X2,X3,X4] :
( ( ? [X5,X6] :
( singleton(X5) = X6
& in(X5,X0)
& ordered_pair(X5,X6) = X4 )
& X2 = X4
& ? [X7,X8] :
( singleton(X7) = X8
& in(X7,X0)
& ordered_pair(X7,X8) = X3 )
& X2 = X3 )
=> X3 = X4 )
=> ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) ) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ! [X2,X3,X4] :
( ( ? [X7,X8] :
( singleton(X7) = X8
& in(X7,X0)
& ordered_pair(X7,X8) = X4 )
& X2 = X4
& ? [X5,X6] :
( singleton(X5) = X6
& in(X5,X0)
& ordered_pair(X5,X6) = X3 )
& X2 = X3 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( ? [X9,X10] :
( singleton(X9) = X10
& in(X9,X0)
& ordered_pair(X9,X10) = X3 )
& X3 = X4
& in(X4,cartesian_product2(X0,X1)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.VfJKtoPSCU/Vampire---4.8_14521',s1_tarski__e16_22__wellord2__2) ).
fof(f183,plain,
( ! [X1] : ~ in(sK4(sK14(sK2,sK3)),sK14(sK2,X1))
| ~ spl19_1 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f182,plain,
( spl19_1
<=> ! [X1] : ~ in(sK4(sK14(sK2,sK3)),sK14(sK2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_1])]) ).
fof(f184,plain,
( spl19_1
| spl19_1 ),
inference(avatar_split_clause,[],[f180,f182,f182]) ).
fof(f180,plain,
! [X0,X1] :
( ~ in(sK4(sK14(sK2,sK3)),sK14(sK2,X0))
| ~ in(sK4(sK14(sK2,sK3)),sK14(sK2,X1)) ),
inference(subsumption_resolution,[],[f179,f153]) ).
fof(f179,plain,
! [X0,X1] :
( ~ in(sK4(sK14(sK2,sK3)),sK14(sK2,sK3))
| ~ in(sK4(sK14(sK2,sK3)),sK14(sK2,X0))
| ~ in(sK4(sK14(sK2,sK3)),sK14(sK2,X1)) ),
inference(subsumption_resolution,[],[f177,f156]) ).
fof(f156,plain,
in(sK4(sK14(sK2,sK3)),sF18),
inference(resolution,[],[f153,f119]) ).
fof(f119,plain,
! [X0] :
( ~ in(X0,sK14(sK2,sK3))
| in(X0,sF18) ),
inference(subsumption_resolution,[],[f118,f91]) ).
fof(f118,plain,
! [X0] :
( in(X0,sF18)
| ~ in(X0,sK14(sK2,sK3))
| sP1(sK2) ),
inference(duplicate_literal_removal,[],[f117]) ).
fof(f117,plain,
! [X0] :
( in(X0,sF18)
| ~ in(X0,sK14(sK2,sK3))
| ~ in(X0,sK14(sK2,sK3))
| sP1(sK2) ),
inference(superposition,[],[f112,f64]) ).
fof(f64,plain,
! [X3,X0,X1] :
( sK15(X0,X1,X3) = X3
| ~ in(X3,sK14(X0,X1))
| sP1(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f112,plain,
! [X0] :
( in(sK15(sK2,sK3,X0),sF18)
| ~ in(X0,sK14(sK2,sK3)) ),
inference(subsumption_resolution,[],[f108,f91]) ).
fof(f108,plain,
! [X0] :
( in(sK15(sK2,sK3,X0),sF18)
| ~ in(X0,sK14(sK2,sK3))
| sP1(sK2) ),
inference(superposition,[],[f63,f74]) ).
fof(f63,plain,
! [X3,X0,X1] :
( in(sK15(X0,X1,X3),cartesian_product2(X0,X1))
| ~ in(X3,sK14(X0,X1))
| sP1(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f177,plain,
! [X0,X1] :
( ~ in(sK4(sK14(sK2,sK3)),sF18)
| ~ in(sK4(sK14(sK2,sK3)),sK14(sK2,sK3))
| ~ in(sK4(sK14(sK2,sK3)),sK14(sK2,X0))
| ~ in(sK4(sK14(sK2,sK3)),sK14(sK2,X1)) ),
inference(resolution,[],[f161,f127]) ).
fof(f127,plain,
! [X2,X3,X0,X1] :
( ~ in(sK16(X0,sK4(X1)),sK2)
| ~ in(sK4(X1),sF18)
| ~ in(sK4(X1),X1)
| ~ in(sK4(X1),sK14(X0,X2))
| ~ in(sK4(X1),sK14(X0,X3)) ),
inference(equality_resolution,[],[f126]) ).
fof(f126,plain,
! [X2,X3,X0,X1,X4] :
( sK4(X2) != X1
| ~ in(sK16(X0,X1),sK2)
| ~ in(sK4(X2),sF18)
| ~ in(sK4(X2),X2)
| ~ in(X1,sK14(X0,X3))
| ~ in(X1,sK14(X0,X4)) ),
inference(subsumption_resolution,[],[f125,f91]) ).
fof(f125,plain,
! [X2,X3,X0,X1,X4] :
( sK4(X2) != X1
| ~ in(sK16(X0,X1),sK2)
| ~ in(sK4(X2),sF18)
| ~ in(sK4(X2),X2)
| ~ in(X1,sK14(X0,X3))
| ~ in(X1,sK14(X0,X4))
| sP1(X0) ),
inference(superposition,[],[f121,f65]) ).
fof(f65,plain,
! [X3,X0,X1] :
( ordered_pair(sK16(X0,X3),sK17(X0,X3)) = X3
| ~ in(X3,sK14(X0,X1))
| sP1(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f121,plain,
! [X2,X3,X0,X1] :
( sK4(X2) != ordered_pair(sK16(X0,X1),sK17(X0,X1))
| ~ in(sK16(X0,X1),sK2)
| ~ in(sK4(X2),sF18)
| ~ in(sK4(X2),X2)
| ~ in(X1,sK14(X0,X3)) ),
inference(subsumption_resolution,[],[f120,f91]) ).
fof(f120,plain,
! [X2,X3,X0,X1] :
( sK4(X2) != ordered_pair(sK16(X0,X1),sK17(X0,X1))
| ~ in(sK16(X0,X1),sK2)
| ~ in(sK4(X2),sF18)
| ~ in(sK4(X2),X2)
| ~ in(X1,sK14(X0,X3))
| sP1(X0) ),
inference(superposition,[],[f75,f67]) ).
fof(f67,plain,
! [X3,X0,X1] :
( sK17(X0,X3) = singleton(sK16(X0,X3))
| ~ in(X3,sK14(X0,X1))
| sP1(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f75,plain,
! [X2,X4] :
( sK4(X2) != ordered_pair(X4,singleton(X4))
| ~ in(X4,sK2)
| ~ in(sK4(X2),sF18)
| ~ in(sK4(X2),X2) ),
inference(definition_folding,[],[f70,f74]) ).
fof(f70,plain,
! [X2,X4] :
( ~ in(X4,sK2)
| sK4(X2) != ordered_pair(X4,singleton(X4))
| ~ in(sK4(X2),cartesian_product2(sK2,sK3))
| ~ in(sK4(X2),X2) ),
inference(equality_resolution,[],[f52]) ).
fof(f52,plain,
! [X2,X4,X5] :
( singleton(X4) != X5
| ~ in(X4,sK2)
| ordered_pair(X4,X5) != sK4(X2)
| ~ in(sK4(X2),cartesian_product2(sK2,sK3))
| ~ in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f161,plain,
in(sK16(sK2,sK4(sK14(sK2,sK3))),sK2),
inference(subsumption_resolution,[],[f158,f91]) ).
fof(f158,plain,
( in(sK16(sK2,sK4(sK14(sK2,sK3))),sK2)
| sP1(sK2) ),
inference(resolution,[],[f153,f66]) ).
fof(f66,plain,
! [X3,X0,X1] :
( ~ in(X3,sK14(X0,X1))
| in(sK16(X0,X3),X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU281+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 10:51:03 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.VfJKtoPSCU/Vampire---4.8_14521
% 0.62/0.78 % (14895)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2995ds/34Mi)
% 0.62/0.78 % (14899)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.62/0.78 % (14898)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.62/0.79 % (14900)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2995ds/34Mi)
% 0.62/0.79 % (14896)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2995ds/51Mi)
% 0.62/0.79 % (14901)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.62/0.79 % (14902)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2995ds/83Mi)
% 0.62/0.79 % (14903)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2995ds/56Mi)
% 0.62/0.79 % (14895)Refutation not found, incomplete strategy% (14895)------------------------------
% 0.62/0.79 % (14895)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.79 % (14895)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.79
% 0.62/0.79 % (14895)Memory used [KB]: 1050
% 0.62/0.79 % (14895)Time elapsed: 0.003 s
% 0.62/0.79 % (14895)Instructions burned: 5 (million)
% 0.62/0.79 % (14895)------------------------------
% 0.62/0.79 % (14895)------------------------------
% 0.62/0.79 % (14899)Refutation not found, incomplete strategy% (14899)------------------------------
% 0.62/0.79 % (14899)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.79 % (14899)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.79
% 0.62/0.79 % (14899)Memory used [KB]: 1046
% 0.62/0.79 % (14899)Time elapsed: 0.004 s
% 0.62/0.79 % (14899)Instructions burned: 4 (million)
% 0.62/0.79 % (14899)------------------------------
% 0.62/0.79 % (14899)------------------------------
% 0.62/0.79 % (14903)Refutation not found, incomplete strategy% (14903)------------------------------
% 0.62/0.79 % (14903)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.79 % (14903)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.79
% 0.62/0.79 % (14903)Memory used [KB]: 1047
% 0.62/0.79 % (14903)Time elapsed: 0.004 s
% 0.62/0.79 % (14903)Instructions burned: 4 (million)
% 0.62/0.79 % (14903)------------------------------
% 0.62/0.79 % (14903)------------------------------
% 0.62/0.79 % (14908)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2995ds/55Mi)
% 0.62/0.79 % (14901)Refutation not found, incomplete strategy% (14901)------------------------------
% 0.62/0.79 % (14901)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.79 % (14901)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.79
% 0.62/0.79 % (14901)Memory used [KB]: 1065
% 0.62/0.79 % (14901)Time elapsed: 0.006 s
% 0.62/0.79 % (14901)Instructions burned: 6 (million)
% 0.62/0.79 % (14901)------------------------------
% 0.62/0.79 % (14901)------------------------------
% 0.62/0.79 % (14910)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2995ds/50Mi)
% 0.62/0.79 % (14908)Refutation not found, incomplete strategy% (14908)------------------------------
% 0.62/0.79 % (14908)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.79 % (14908)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.79
% 0.62/0.79 % (14908)Memory used [KB]: 1109
% 0.62/0.79 % (14908)Time elapsed: 0.004 s
% 0.62/0.79 % (14908)Instructions burned: 10 (million)
% 0.62/0.79 % (14911)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/208Mi)
% 0.62/0.79 % (14908)------------------------------
% 0.62/0.79 % (14908)------------------------------
% 0.62/0.79 % (14913)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2995ds/52Mi)
% 0.62/0.79 % (14896)Refutation not found, incomplete strategy% (14896)------------------------------
% 0.62/0.79 % (14896)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.79 % (14915)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2995ds/518Mi)
% 0.62/0.79 % (14896)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.79
% 0.62/0.79 % (14896)Memory used [KB]: 1169
% 0.62/0.79 % (14896)Time elapsed: 0.011 s
% 0.62/0.79 % (14896)Instructions burned: 14 (million)
% 0.62/0.80 % (14896)------------------------------
% 0.62/0.80 % (14896)------------------------------
% 0.62/0.80 % (14915)Refutation not found, incomplete strategy% (14915)------------------------------
% 0.62/0.80 % (14915)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.80 % (14915)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.80
% 0.62/0.80 % (14915)Memory used [KB]: 1059
% 0.62/0.80 % (14915)Time elapsed: 0.003 s
% 0.62/0.80 % (14915)Instructions burned: 6 (million)
% 0.62/0.80 % (14915)------------------------------
% 0.62/0.80 % (14915)------------------------------
% 0.62/0.80 % (14911)First to succeed.
% 0.62/0.80 % (14918)lrs+1011_87677:1048576_sil=8000:sos=on:spb=non_intro:nwc=10.0:kmz=on:i=42:ep=RS:nm=0:ins=1:uhcvi=on:rawr=on:fde=unused:afp=2000:afq=1.444:plsq=on:nicw=on_0 on Vampire---4 for (2995ds/42Mi)
% 0.62/0.80 % (14920)dis+1011_1258907:1048576_bsr=unit_only:to=lpo:drc=off:sil=2000:tgt=full:fde=none:sp=frequency:spb=goal:rnwc=on:nwc=6.70083:sac=on:newcnf=on:st=2:i=243:bs=unit_only:sd=3:afp=300:awrs=decay:awrsf=218:nm=16:ins=3:afq=3.76821:afr=on:ss=axioms:sgt=5:rawr=on:add=off:bsd=on_0 on Vampire---4 for (2995ds/243Mi)
% 0.62/0.80 % (14898)Also succeeded, but the first one will report.
% 0.62/0.80 % (14911)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14772"
% 0.62/0.80 % (14913)Refutation not found, incomplete strategy% (14913)------------------------------
% 0.62/0.80 % (14913)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.80 % (14913)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.80
% 0.62/0.80 % (14913)Memory used [KB]: 1146
% 0.62/0.80 % (14913)Time elapsed: 0.008 s
% 0.62/0.80 % (14913)Instructions burned: 10 (million)
% 0.62/0.80 % (14900)Instruction limit reached!
% 0.62/0.80 % (14900)------------------------------
% 0.62/0.80 % (14900)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.80 % (14913)------------------------------
% 0.62/0.80 % (14913)------------------------------
% 0.62/0.80 % (14900)Termination reason: Unknown
% 0.62/0.80 % (14900)Termination phase: Saturation
% 0.62/0.80
% 0.62/0.80 % (14900)Memory used [KB]: 1219
% 0.62/0.80 % (14900)Time elapsed: 0.019 s
% 0.62/0.80 % (14900)Instructions burned: 34 (million)
% 0.62/0.80 % (14900)------------------------------
% 0.62/0.80 % (14900)------------------------------
% 0.62/0.80 % (14911)Refutation found. Thanks to Tanya!
% 0.62/0.80 % SZS status Theorem for Vampire---4
% 0.62/0.80 % SZS output start Proof for Vampire---4
% See solution above
% 0.62/0.80 % (14911)------------------------------
% 0.62/0.80 % (14911)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.80 % (14911)Termination reason: Refutation
% 0.62/0.80
% 0.62/0.80 % (14911)Memory used [KB]: 1091
% 0.62/0.80 % (14911)Time elapsed: 0.011 s
% 0.62/0.80 % (14911)Instructions burned: 14 (million)
% 0.62/0.80 % (14772)Success in time 0.435 s
% 0.62/0.80 % Vampire---4.8 exiting
%------------------------------------------------------------------------------