TSTP Solution File: SEU298+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU298+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n012.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 : Wed Aug 31 18:28:30 EDT 2022
% Result : Theorem 1.36s 0.54s
% Output : Refutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 5 unt; 0 def)
% Number of atoms : 457 ( 130 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 577 ( 195 ~; 197 |; 159 &)
% ( 7 <=>; 17 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 2 con; 0-3 aty)
% Number of variables : 274 ( 172 !; 102 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f417,plain,
$false,
inference(subsumption_resolution,[],[f416,f369]) ).
fof(f369,plain,
! [X0] :
( ~ in(sK14(X0),sK8(sK13,sK12))
| ~ in(sK14(X0),X0) ),
inference(subsumption_resolution,[],[f368,f299]) ).
fof(f299,plain,
! [X0] :
( ~ in(X0,sK8(sK13,sK12))
| in(X0,powerset(sK12)) ),
inference(subsumption_resolution,[],[f298,f139]) ).
fof(f139,plain,
element(sK13,powerset(powerset(succ(sK12)))),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
( element(sK13,powerset(powerset(succ(sK12))))
& ordinal(sK12)
& ! [X2] :
( ( ~ in(sK14(X2),X2)
| ! [X4] :
( ~ in(X4,sK13)
| sK14(X2) != set_difference(X4,singleton(sK12)) )
| ~ in(sK14(X2),powerset(sK12)) )
& ( in(sK14(X2),X2)
| ( in(sK15(X2),sK13)
& set_difference(sK15(X2),singleton(sK12)) = sK14(X2)
& in(sK14(X2),powerset(sK12)) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15])],[f88,f91,f90,f89]) ).
fof(f89,plain,
( ? [X0,X1] :
( element(X1,powerset(powerset(succ(X0))))
& ordinal(X0)
& ! [X2] :
? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| set_difference(X4,singleton(X0)) != X3 )
| ~ in(X3,powerset(X0)) )
& ( in(X3,X2)
| ( ? [X5] :
( in(X5,X1)
& set_difference(X5,singleton(X0)) = X3 )
& in(X3,powerset(X0)) ) ) ) )
=> ( element(sK13,powerset(powerset(succ(sK12))))
& ordinal(sK12)
& ! [X2] :
? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,sK13)
| set_difference(X4,singleton(sK12)) != X3 )
| ~ in(X3,powerset(sK12)) )
& ( in(X3,X2)
| ( ? [X5] :
( in(X5,sK13)
& set_difference(X5,singleton(sK12)) = X3 )
& in(X3,powerset(sK12)) ) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
! [X2] :
( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,sK13)
| set_difference(X4,singleton(sK12)) != X3 )
| ~ in(X3,powerset(sK12)) )
& ( in(X3,X2)
| ( ? [X5] :
( in(X5,sK13)
& set_difference(X5,singleton(sK12)) = X3 )
& in(X3,powerset(sK12)) ) ) )
=> ( ( ~ in(sK14(X2),X2)
| ! [X4] :
( ~ in(X4,sK13)
| sK14(X2) != set_difference(X4,singleton(sK12)) )
| ~ in(sK14(X2),powerset(sK12)) )
& ( in(sK14(X2),X2)
| ( ? [X5] :
( in(X5,sK13)
& set_difference(X5,singleton(sK12)) = sK14(X2) )
& in(sK14(X2),powerset(sK12)) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f91,plain,
! [X2] :
( ? [X5] :
( in(X5,sK13)
& set_difference(X5,singleton(sK12)) = sK14(X2) )
=> ( in(sK15(X2),sK13)
& set_difference(sK15(X2),singleton(sK12)) = sK14(X2) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
? [X0,X1] :
( element(X1,powerset(powerset(succ(X0))))
& ordinal(X0)
& ! [X2] :
? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| set_difference(X4,singleton(X0)) != X3 )
| ~ in(X3,powerset(X0)) )
& ( in(X3,X2)
| ( ? [X5] :
( in(X5,X1)
& set_difference(X5,singleton(X0)) = X3 )
& in(X3,powerset(X0)) ) ) ) ),
inference(rectify,[],[f87]) ).
fof(f87,plain,
? [X0,X1] :
( element(X1,powerset(powerset(succ(X0))))
& ordinal(X0)
& ! [X2] :
? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| set_difference(X4,singleton(X0)) != X3 )
| ~ in(X3,powerset(X0)) )
& ( in(X3,X2)
| ( ? [X4] :
( in(X4,X1)
& set_difference(X4,singleton(X0)) = X3 )
& in(X3,powerset(X0)) ) ) ) ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
? [X0,X1] :
( element(X1,powerset(powerset(succ(X0))))
& ordinal(X0)
& ! [X2] :
? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| set_difference(X4,singleton(X0)) != X3 )
| ~ in(X3,powerset(X0)) )
& ( in(X3,X2)
| ( ? [X4] :
( in(X4,X1)
& set_difference(X4,singleton(X0)) = X3 )
& in(X3,powerset(X0)) ) ) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f51,plain,
? [X0,X1] :
( element(X1,powerset(powerset(succ(X0))))
& ordinal(X0)
& ! [X2] :
? [X3] :
( ( ? [X4] :
( in(X4,X1)
& set_difference(X4,singleton(X0)) = X3 )
& in(X3,powerset(X0)) )
<~> in(X3,X2) ) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
? [X1,X0] :
( ! [X2] :
? [X3] :
( ( ? [X4] :
( in(X4,X1)
& set_difference(X4,singleton(X0)) = X3 )
& in(X3,powerset(X0)) )
<~> in(X3,X2) )
& ordinal(X0)
& element(X1,powerset(powerset(succ(X0)))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X1,X0] :
( ( ordinal(X0)
& element(X1,powerset(powerset(succ(X0)))) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( in(X4,X1)
& set_difference(X4,singleton(X0)) = X3 )
& in(X3,powerset(X0)) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X1,X0] :
( ( ordinal(X0)
& element(X1,powerset(powerset(succ(X0)))) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( in(X4,X1)
& set_difference(X4,singleton(X0)) = X3 )
& in(X3,powerset(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e4_27_3_1__finset_1) ).
fof(f298,plain,
! [X0] :
( ~ element(sK13,powerset(powerset(succ(sK12))))
| in(X0,powerset(sK12))
| ~ in(X0,sK8(sK13,sK12)) ),
inference(subsumption_resolution,[],[f295,f138]) ).
fof(f138,plain,
ordinal(sK12),
inference(cnf_transformation,[],[f92]) ).
fof(f295,plain,
! [X0] :
( ~ ordinal(sK12)
| ~ in(X0,sK8(sK13,sK12))
| ~ element(sK13,powerset(powerset(succ(sK12))))
| in(X0,powerset(sK12)) ),
inference(duplicate_literal_removal,[],[f290]) ).
fof(f290,plain,
! [X0] :
( ~ element(sK13,powerset(powerset(succ(sK12))))
| ~ in(X0,sK8(sK13,sK12))
| ~ ordinal(sK12)
| in(X0,powerset(sK12))
| ~ in(X0,sK8(sK13,sK12)) ),
inference(superposition,[],[f288,f284]) ).
fof(f284,plain,
! [X0] :
( sK9(sK13,sK12,X0) = X0
| ~ in(X0,sK8(sK13,sK12)) ),
inference(subsumption_resolution,[],[f278,f138]) ).
fof(f278,plain,
! [X0] :
( ~ in(X0,sK8(sK13,sK12))
| ~ ordinal(sK12)
| sK9(sK13,sK12,X0) = X0 ),
inference(resolution,[],[f277,f139]) ).
fof(f277,plain,
! [X3,X0,X1] :
( ~ element(X0,powerset(powerset(succ(X1))))
| sK9(X0,X1,X3) = X3
| ~ ordinal(X1)
| ~ in(X3,sK8(X0,X1)) ),
inference(subsumption_resolution,[],[f130,f267]) ).
fof(f267,plain,
! [X0,X1] : ~ sP0(X0,X1),
inference(subsumption_resolution,[],[f265,f127]) ).
fof(f127,plain,
! [X0,X1] :
( sK4(X0,X1) != sK3(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ( sK4(X0,X1) != sK3(X0,X1)
& sK3(X0,X1) = sK5(X0,X1)
& sK4(X0,X1) = set_difference(sK6(X0,X1),singleton(X0))
& in(sK6(X0,X1),X1)
& set_difference(sK7(X0,X1),singleton(X0)) = sK3(X0,X1)
& in(sK7(X0,X1),X1)
& sK4(X0,X1) = sK5(X0,X1) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f73,f76,f75,f74]) ).
fof(f74,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X2 != X3
& X2 = X4
& ? [X5] :
( set_difference(X5,singleton(X0)) = X3
& in(X5,X1) )
& ? [X6] :
( set_difference(X6,singleton(X0)) = X2
& in(X6,X1) )
& X3 = X4 )
=> ( sK4(X0,X1) != sK3(X0,X1)
& sK3(X0,X1) = sK5(X0,X1)
& ? [X5] :
( set_difference(X5,singleton(X0)) = sK4(X0,X1)
& in(X5,X1) )
& ? [X6] :
( set_difference(X6,singleton(X0)) = sK3(X0,X1)
& in(X6,X1) )
& sK4(X0,X1) = sK5(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
! [X0,X1] :
( ? [X5] :
( set_difference(X5,singleton(X0)) = sK4(X0,X1)
& in(X5,X1) )
=> ( sK4(X0,X1) = set_difference(sK6(X0,X1),singleton(X0))
& in(sK6(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
! [X0,X1] :
( ? [X6] :
( set_difference(X6,singleton(X0)) = sK3(X0,X1)
& in(X6,X1) )
=> ( set_difference(sK7(X0,X1),singleton(X0)) = sK3(X0,X1)
& in(sK7(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X2 != X3
& X2 = X4
& ? [X5] :
( set_difference(X5,singleton(X0)) = X3
& in(X5,X1) )
& ? [X6] :
( set_difference(X6,singleton(X0)) = X2
& in(X6,X1) )
& X3 = X4 )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f72]) ).
fof(f72,plain,
! [X1,X0] :
( ? [X4,X3,X2] :
( X3 != X4
& X2 = X4
& ? [X6] :
( set_difference(X6,singleton(X1)) = X3
& in(X6,X0) )
& ? [X5] :
( set_difference(X5,singleton(X1)) = X4
& in(X5,X0) )
& X2 = X3 )
| ~ sP0(X1,X0) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X1,X0] :
( ? [X4,X3,X2] :
( X3 != X4
& X2 = X4
& ? [X6] :
( set_difference(X6,singleton(X1)) = X3
& in(X6,X0) )
& ? [X5] :
( set_difference(X5,singleton(X1)) = X4
& in(X5,X0) )
& X2 = X3 )
| ~ sP0(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f265,plain,
! [X0,X1] :
( sK4(X0,X1) = sK3(X0,X1)
| ~ sP0(X0,X1) ),
inference(duplicate_literal_removal,[],[f264]) ).
fof(f264,plain,
! [X0,X1] :
( sK4(X0,X1) = sK3(X0,X1)
| ~ sP0(X0,X1)
| ~ sP0(X0,X1) ),
inference(superposition,[],[f121,f126]) ).
fof(f126,plain,
! [X0,X1] :
( sK3(X0,X1) = sK5(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f121,plain,
! [X0,X1] :
( sK4(X0,X1) = sK5(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f130,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| sP0(X1,X0)
| ~ element(X0,powerset(powerset(succ(X1))))
| ~ in(X3,sK8(X0,X1))
| sK9(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(succ(X1))))
| ~ ordinal(X1)
| sP0(X1,X0)
| ! [X3] :
( ( in(X3,sK8(X0,X1))
| ! [X4] :
( ~ in(X4,powerset(X1))
| X3 != X4
| ! [X5] :
( ~ in(X5,X0)
| set_difference(X5,singleton(X1)) != X3 ) ) )
& ( ( in(sK9(X0,X1,X3),powerset(X1))
& sK9(X0,X1,X3) = X3
& in(sK10(X0,X1,X3),X0)
& set_difference(sK10(X0,X1,X3),singleton(X1)) = X3 )
| ~ in(X3,sK8(X0,X1)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f79,f82,f81,f80]) ).
fof(f80,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,powerset(X1))
| X3 != X4
| ! [X5] :
( ~ in(X5,X0)
| set_difference(X5,singleton(X1)) != X3 ) ) )
& ( ? [X6] :
( in(X6,powerset(X1))
& X3 = X6
& ? [X7] :
( in(X7,X0)
& set_difference(X7,singleton(X1)) = X3 ) )
| ~ in(X3,X2) ) )
=> ! [X3] :
( ( in(X3,sK8(X0,X1))
| ! [X4] :
( ~ in(X4,powerset(X1))
| X3 != X4
| ! [X5] :
( ~ in(X5,X0)
| set_difference(X5,singleton(X1)) != X3 ) ) )
& ( ? [X6] :
( in(X6,powerset(X1))
& X3 = X6
& ? [X7] :
( in(X7,X0)
& set_difference(X7,singleton(X1)) = X3 ) )
| ~ in(X3,sK8(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0,X1,X3] :
( ? [X6] :
( in(X6,powerset(X1))
& X3 = X6
& ? [X7] :
( in(X7,X0)
& set_difference(X7,singleton(X1)) = X3 ) )
=> ( in(sK9(X0,X1,X3),powerset(X1))
& sK9(X0,X1,X3) = X3
& ? [X7] :
( in(X7,X0)
& set_difference(X7,singleton(X1)) = X3 ) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X0,X1,X3] :
( ? [X7] :
( in(X7,X0)
& set_difference(X7,singleton(X1)) = X3 )
=> ( in(sK10(X0,X1,X3),X0)
& set_difference(sK10(X0,X1,X3),singleton(X1)) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(succ(X1))))
| ~ ordinal(X1)
| sP0(X1,X0)
| ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,powerset(X1))
| X3 != X4
| ! [X5] :
( ~ in(X5,X0)
| set_difference(X5,singleton(X1)) != X3 ) ) )
& ( ? [X6] :
( in(X6,powerset(X1))
& X3 = X6
& ? [X7] :
( in(X7,X0)
& set_difference(X7,singleton(X1)) = X3 ) )
| ~ in(X3,X2) ) ) ),
inference(rectify,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(succ(X1))))
| ~ ordinal(X1)
| sP0(X1,X0)
| ? [X7] :
! [X8] :
( ( in(X8,X7)
| ! [X9] :
( ~ in(X9,powerset(X1))
| X8 != X9
| ! [X10] :
( ~ in(X10,X0)
| set_difference(X10,singleton(X1)) != X8 ) ) )
& ( ? [X9] :
( in(X9,powerset(X1))
& X8 = X9
& ? [X10] :
( in(X10,X0)
& set_difference(X10,singleton(X1)) = X8 ) )
| ~ in(X8,X7) ) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(succ(X1))))
| ~ ordinal(X1)
| sP0(X1,X0)
| ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,powerset(X1))
& X8 = X9
& ? [X10] :
( in(X10,X0)
& set_difference(X10,singleton(X1)) = X8 ) ) ) ),
inference(definition_folding,[],[f58,f65]) ).
fof(f58,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(succ(X1))))
| ~ ordinal(X1)
| ? [X4,X3,X2] :
( X3 != X4
& X2 = X4
& ? [X6] :
( set_difference(X6,singleton(X1)) = X3
& in(X6,X0) )
& ? [X5] :
( set_difference(X5,singleton(X1)) = X4
& in(X5,X0) )
& X2 = X3 )
| ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,powerset(X1))
& X8 = X9
& ? [X10] :
( in(X10,X0)
& set_difference(X10,singleton(X1)) = X8 ) ) ) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X1,X0] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,powerset(X1))
& X8 = X9
& ? [X10] :
( in(X10,X0)
& set_difference(X10,singleton(X1)) = X8 ) ) )
| ? [X4,X2,X3] :
( X3 != X4
& ? [X5] :
( set_difference(X5,singleton(X1)) = X4
& in(X5,X0) )
& X2 = X4
& ? [X6] :
( set_difference(X6,singleton(X1)) = X3
& in(X6,X0) )
& X2 = X3 )
| ~ element(X0,powerset(powerset(succ(X1))))
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,plain,
! [X1,X0] :
( ( element(X0,powerset(powerset(succ(X1))))
& ordinal(X1) )
=> ( ! [X4,X2,X3] :
( ( ? [X5] :
( set_difference(X5,singleton(X1)) = X4
& in(X5,X0) )
& X2 = X4
& ? [X6] :
( set_difference(X6,singleton(X1)) = X3
& in(X6,X0) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,powerset(X1))
& X8 = X9
& ? [X10] :
( in(X10,X0)
& set_difference(X10,singleton(X1)) = X8 ) ) ) ) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X1,X0] :
( ( element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) )
=> ( ! [X2,X3,X4] :
( ( ? [X6] :
( set_difference(X6,singleton(X0)) = X4
& in(X6,X1) )
& X2 = X4
& X2 = X3
& ? [X5] :
( in(X5,X1)
& set_difference(X5,singleton(X0)) = X3 ) )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( ? [X4] :
( ? [X7] :
( set_difference(X7,singleton(X0)) = X3
& in(X7,X1) )
& in(X4,powerset(X0))
& X3 = X4 )
<=> in(X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e4_27_3_1__finset_1__1) ).
fof(f288,plain,
! [X3,X0,X1] :
( in(sK9(X0,X1,X3),powerset(X1))
| ~ ordinal(X1)
| ~ element(X0,powerset(powerset(succ(X1))))
| ~ in(X3,sK8(X0,X1)) ),
inference(subsumption_resolution,[],[f131,f267]) ).
fof(f131,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| ~ in(X3,sK8(X0,X1))
| sP0(X1,X0)
| in(sK9(X0,X1,X3),powerset(X1))
| ~ element(X0,powerset(powerset(succ(X1)))) ),
inference(cnf_transformation,[],[f83]) ).
fof(f368,plain,
! [X0] :
( ~ in(sK14(X0),X0)
| ~ in(sK14(X0),sK8(sK13,sK12))
| ~ in(sK14(X0),powerset(sK12)) ),
inference(subsumption_resolution,[],[f367,f139]) ).
fof(f367,plain,
! [X0] :
( ~ in(sK14(X0),powerset(sK12))
| ~ in(sK14(X0),X0)
| ~ in(sK14(X0),sK8(sK13,sK12))
| ~ element(sK13,powerset(powerset(succ(sK12)))) ),
inference(duplicate_literal_removal,[],[f366]) ).
fof(f366,plain,
! [X0] :
( ~ in(sK14(X0),X0)
| ~ in(sK14(X0),sK8(sK13,sK12))
| ~ in(sK14(X0),powerset(sK12))
| ~ element(sK13,powerset(powerset(succ(sK12))))
| ~ in(sK14(X0),sK8(sK13,sK12)) ),
inference(resolution,[],[f365,f274]) ).
fof(f274,plain,
! [X0] :
( in(sK10(sK13,sK12,X0),sK13)
| ~ in(X0,sK8(sK13,sK12)) ),
inference(subsumption_resolution,[],[f269,f138]) ).
fof(f269,plain,
! [X0] :
( in(sK10(sK13,sK12,X0),sK13)
| ~ ordinal(sK12)
| ~ in(X0,sK8(sK13,sK12)) ),
inference(resolution,[],[f268,f139]) ).
fof(f268,plain,
! [X3,X0,X1] :
( ~ element(X0,powerset(powerset(succ(X1))))
| ~ in(X3,sK8(X0,X1))
| ~ ordinal(X1)
| in(sK10(X0,X1,X3),X0) ),
inference(subsumption_resolution,[],[f129,f267]) ).
fof(f129,plain,
! [X3,X0,X1] :
( ~ element(X0,powerset(powerset(succ(X1))))
| sP0(X1,X0)
| ~ in(X3,sK8(X0,X1))
| in(sK10(X0,X1,X3),X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f365,plain,
! [X0,X1] :
( ~ in(sK10(X1,sK12,sK14(X0)),sK13)
| ~ in(sK14(X0),sK8(X1,sK12))
| ~ in(sK14(X0),powerset(sK12))
| ~ in(sK14(X0),X0)
| ~ element(X1,powerset(powerset(succ(sK12)))) ),
inference(equality_resolution,[],[f364]) ).
fof(f364,plain,
! [X2,X0,X1] :
( sK14(X2) != X1
| ~ in(X1,sK8(X0,sK12))
| ~ in(sK14(X2),powerset(sK12))
| ~ in(sK10(X0,sK12,X1),sK13)
| ~ in(sK14(X2),X2)
| ~ element(X0,powerset(powerset(succ(sK12)))) ),
inference(subsumption_resolution,[],[f361,f138]) ).
fof(f361,plain,
! [X2,X0,X1] :
( ~ in(sK14(X2),powerset(sK12))
| ~ ordinal(sK12)
| ~ element(X0,powerset(powerset(succ(sK12))))
| ~ in(sK14(X2),X2)
| sK14(X2) != X1
| ~ in(sK10(X0,sK12,X1),sK13)
| ~ in(X1,sK8(X0,sK12)) ),
inference(superposition,[],[f137,f360]) ).
fof(f360,plain,
! [X3,X0,X1] :
( set_difference(sK10(X0,X1,X3),singleton(X1)) = X3
| ~ ordinal(X1)
| ~ element(X0,powerset(powerset(succ(X1))))
| ~ in(X3,sK8(X0,X1)) ),
inference(subsumption_resolution,[],[f128,f267]) ).
fof(f128,plain,
! [X3,X0,X1] :
( ~ in(X3,sK8(X0,X1))
| sP0(X1,X0)
| ~ ordinal(X1)
| ~ element(X0,powerset(powerset(succ(X1))))
| set_difference(sK10(X0,X1,X3),singleton(X1)) = X3 ),
inference(cnf_transformation,[],[f83]) ).
fof(f137,plain,
! [X2,X4] :
( sK14(X2) != set_difference(X4,singleton(sK12))
| ~ in(X4,sK13)
| ~ in(sK14(X2),powerset(sK12))
| ~ in(sK14(X2),X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f416,plain,
in(sK14(sK8(sK13,sK12)),sK8(sK13,sK12)),
inference(factoring,[],[f409]) ).
fof(f409,plain,
! [X0] :
( in(sK14(X0),sK8(sK13,sK12))
| in(sK14(X0),X0) ),
inference(subsumption_resolution,[],[f405,f136]) ).
fof(f136,plain,
! [X2] :
( in(sK15(X2),sK13)
| in(sK14(X2),X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f405,plain,
! [X0] :
( in(sK14(X0),sK8(sK13,sK12))
| in(sK14(X0),X0)
| ~ in(sK15(X0),sK13) ),
inference(resolution,[],[f404,f139]) ).
fof(f404,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(sK12))))
| ~ in(sK15(X0),X1)
| in(sK14(X0),X0)
| in(sK14(X0),sK8(X1,sK12)) ),
inference(subsumption_resolution,[],[f403,f134]) ).
fof(f134,plain,
! [X2] :
( in(sK14(X2),powerset(sK12))
| in(sK14(X2),X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f403,plain,
! [X0,X1] :
( ~ in(sK14(X0),powerset(sK12))
| ~ in(sK15(X0),X1)
| ~ element(X1,powerset(powerset(succ(sK12))))
| in(sK14(X0),X0)
| in(sK14(X0),sK8(X1,sK12)) ),
inference(subsumption_resolution,[],[f394,f138]) ).
fof(f394,plain,
! [X0,X1] :
( ~ in(sK14(X0),powerset(sK12))
| in(sK14(X0),X0)
| ~ ordinal(sK12)
| in(sK14(X0),sK8(X1,sK12))
| ~ in(sK15(X0),X1)
| ~ element(X1,powerset(powerset(succ(sK12)))) ),
inference(superposition,[],[f384,f135]) ).
fof(f135,plain,
! [X2] :
( set_difference(sK15(X2),singleton(sK12)) = sK14(X2)
| in(sK14(X2),X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f384,plain,
! [X0,X1,X5] :
( in(set_difference(X5,singleton(X1)),sK8(X0,X1))
| ~ in(set_difference(X5,singleton(X1)),powerset(X1))
| ~ ordinal(X1)
| ~ in(X5,X0)
| ~ element(X0,powerset(powerset(succ(X1)))) ),
inference(subsumption_resolution,[],[f172,f267]) ).
fof(f172,plain,
! [X0,X1,X5] :
( ~ ordinal(X1)
| ~ in(X5,X0)
| sP0(X1,X0)
| ~ element(X0,powerset(powerset(succ(X1))))
| in(set_difference(X5,singleton(X1)),sK8(X0,X1))
| ~ in(set_difference(X5,singleton(X1)),powerset(X1)) ),
inference(equality_resolution,[],[f171]) ).
fof(f171,plain,
! [X0,X1,X4,X5] :
( ~ element(X0,powerset(powerset(succ(X1))))
| ~ ordinal(X1)
| sP0(X1,X0)
| in(X4,sK8(X0,X1))
| ~ in(X4,powerset(X1))
| ~ in(X5,X0)
| set_difference(X5,singleton(X1)) != X4 ),
inference(equality_resolution,[],[f132]) ).
fof(f132,plain,
! [X3,X0,X1,X4,X5] :
( ~ element(X0,powerset(powerset(succ(X1))))
| ~ ordinal(X1)
| sP0(X1,X0)
| in(X3,sK8(X0,X1))
| ~ in(X4,powerset(X1))
| X3 != X4
| ~ in(X5,X0)
| set_difference(X5,singleton(X1)) != X3 ),
inference(cnf_transformation,[],[f83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU298+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 15:05:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.23/0.51 % (10655)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.23/0.51 % (10646)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 1.23/0.51 % (10647)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 1.23/0.51 % (10644)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.23/0.51 % (10646)Refutation not found, incomplete strategy% (10646)------------------------------
% 1.23/0.51 % (10646)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.23/0.52 % (10671)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 1.23/0.52 % (10646)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.23/0.52 % (10646)Termination reason: Refutation not found, incomplete strategy
% 1.23/0.52
% 1.23/0.52 % (10646)Memory used [KB]: 1535
% 1.23/0.52 % (10646)Time elapsed: 0.095 s
% 1.23/0.52 % (10646)Instructions burned: 5 (million)
% 1.23/0.52 % (10646)------------------------------
% 1.23/0.52 % (10646)------------------------------
% 1.23/0.52 % (10648)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 1.23/0.52 % (10642)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 1.23/0.52 % (10645)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 1.36/0.53 % (10649)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 1.36/0.53 % (10661)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 1.36/0.53 % (10652)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.36/0.53 % (10661)Refutation not found, incomplete strategy% (10661)------------------------------
% 1.36/0.53 % (10661)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.53 % (10661)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.53 % (10661)Termination reason: Refutation not found, incomplete strategy
% 1.36/0.53
% 1.36/0.53 % (10661)Memory used [KB]: 6140
% 1.36/0.53 % (10661)Time elapsed: 0.141 s
% 1.36/0.53 % (10661)Instructions burned: 6 (million)
% 1.36/0.53 % (10661)------------------------------
% 1.36/0.53 % (10661)------------------------------
% 1.36/0.53 % (10670)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 1.36/0.53 % (10665)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 1.36/0.53 % (10647)First to succeed.
% 1.36/0.54 % (10652)Instruction limit reached!
% 1.36/0.54 % (10652)------------------------------
% 1.36/0.54 % (10652)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.54 % (10670)Refutation not found, incomplete strategy% (10670)------------------------------
% 1.36/0.54 % (10670)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.54 % (10670)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.54 % (10670)Termination reason: Refutation not found, incomplete strategy
% 1.36/0.54
% 1.36/0.54 % (10670)Memory used [KB]: 6140
% 1.36/0.54 % (10670)Time elapsed: 0.138 s
% 1.36/0.54 % (10670)Instructions burned: 6 (million)
% 1.36/0.54 % (10670)------------------------------
% 1.36/0.54 % (10670)------------------------------
% 1.36/0.54 % (10653)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 1.36/0.54 % (10647)Refutation found. Thanks to Tanya!
% 1.36/0.54 % SZS status Theorem for theBenchmark
% 1.36/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 1.36/0.54 % (10647)------------------------------
% 1.36/0.54 % (10647)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.54 % (10647)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.54 % (10647)Termination reason: Refutation
% 1.36/0.54
% 1.36/0.54 % (10647)Memory used [KB]: 6268
% 1.36/0.54 % (10647)Time elapsed: 0.064 s
% 1.36/0.54 % (10647)Instructions burned: 17 (million)
% 1.36/0.54 % (10647)------------------------------
% 1.36/0.54 % (10647)------------------------------
% 1.36/0.54 % (10639)Success in time 0.181 s
%------------------------------------------------------------------------------