TSTP Solution File: SEU277+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU277+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_sat --cores 0 -t %d %s
% Computer : n023.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 18:32:58 EDT 2022
% Result : Theorem 2.21s 0.62s
% Output : Refutation 2.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 17
% Syntax : Number of formulae : 125 ( 6 unt; 0 def)
% Number of atoms : 703 ( 157 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 878 ( 300 ~; 371 |; 175 &)
% ( 12 <=>; 18 =>; 0 <=; 2 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 4 con; 0-4 aty)
% Number of variables : 349 ( 194 !; 155 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f407,plain,
$false,
inference(avatar_sat_refutation,[],[f198,f234,f293,f306,f365,f389]) ).
fof(f389,plain,
( spl27_1
| ~ spl27_2
| ~ spl27_6
| spl27_7 ),
inference(avatar_contradiction_clause,[],[f388]) ).
fof(f388,plain,
( $false
| spl27_1
| ~ spl27_2
| ~ spl27_6
| spl27_7 ),
inference(subsumption_resolution,[],[f387,f373]) ).
fof(f373,plain,
( in(sK21(sK12(sK19,sK18,sK20)),sF26)
| spl27_1
| ~ spl27_6 ),
inference(subsumption_resolution,[],[f372,f132]) ).
fof(f132,plain,
! [X3] :
( in(sK21(X3),sF26)
| in(sK21(X3),X3) ),
inference(definition_folding,[],[f111,f130]) ).
fof(f130,plain,
sF26 = cartesian_product2(sK18,sK18),
introduced(function_definition,[]) ).
fof(f111,plain,
! [X3] :
( in(sK21(X3),X3)
| in(sK21(X3),cartesian_product2(sK18,sK18)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
( function(sK19)
& relation(sK19)
& relation(sK20)
& ! [X3] :
( ( ~ in(sK21(X3),X3)
| ! [X5,X6] :
( sK21(X3) != ordered_pair(X6,X5)
| ~ in(ordered_pair(apply(sK19,X6),apply(sK19,X5)),sK20) )
| ~ in(sK21(X3),cartesian_product2(sK18,sK18)) )
& ( in(sK21(X3),X3)
| ( sK21(X3) = ordered_pair(sK23(X3),sK22(X3))
& in(ordered_pair(apply(sK19,sK23(X3)),apply(sK19,sK22(X3))),sK20)
& in(sK21(X3),cartesian_product2(sK18,sK18)) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22,sK23])],[f67,f70,f69,f68]) ).
fof(f68,plain,
( ? [X0,X1,X2] :
( function(X1)
& relation(X1)
& relation(X2)
& ! [X3] :
? [X4] :
( ( ~ in(X4,X3)
| ! [X5,X6] :
( ordered_pair(X6,X5) != X4
| ~ in(ordered_pair(apply(X1,X6),apply(X1,X5)),X2) )
| ~ in(X4,cartesian_product2(X0,X0)) )
& ( in(X4,X3)
| ( ? [X7,X8] :
( ordered_pair(X8,X7) = X4
& in(ordered_pair(apply(X1,X8),apply(X1,X7)),X2) )
& in(X4,cartesian_product2(X0,X0)) ) ) ) )
=> ( function(sK19)
& relation(sK19)
& relation(sK20)
& ! [X3] :
? [X4] :
( ( ~ in(X4,X3)
| ! [X6,X5] :
( ordered_pair(X6,X5) != X4
| ~ in(ordered_pair(apply(sK19,X6),apply(sK19,X5)),sK20) )
| ~ in(X4,cartesian_product2(sK18,sK18)) )
& ( in(X4,X3)
| ( ? [X8,X7] :
( ordered_pair(X8,X7) = X4
& in(ordered_pair(apply(sK19,X8),apply(sK19,X7)),sK20) )
& in(X4,cartesian_product2(sK18,sK18)) ) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X3] :
( ? [X4] :
( ( ~ in(X4,X3)
| ! [X6,X5] :
( ordered_pair(X6,X5) != X4
| ~ in(ordered_pair(apply(sK19,X6),apply(sK19,X5)),sK20) )
| ~ in(X4,cartesian_product2(sK18,sK18)) )
& ( in(X4,X3)
| ( ? [X8,X7] :
( ordered_pair(X8,X7) = X4
& in(ordered_pair(apply(sK19,X8),apply(sK19,X7)),sK20) )
& in(X4,cartesian_product2(sK18,sK18)) ) ) )
=> ( ( ~ in(sK21(X3),X3)
| ! [X6,X5] :
( sK21(X3) != ordered_pair(X6,X5)
| ~ in(ordered_pair(apply(sK19,X6),apply(sK19,X5)),sK20) )
| ~ in(sK21(X3),cartesian_product2(sK18,sK18)) )
& ( in(sK21(X3),X3)
| ( ? [X8,X7] :
( ordered_pair(X8,X7) = sK21(X3)
& in(ordered_pair(apply(sK19,X8),apply(sK19,X7)),sK20) )
& in(sK21(X3),cartesian_product2(sK18,sK18)) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
! [X3] :
( ? [X8,X7] :
( ordered_pair(X8,X7) = sK21(X3)
& in(ordered_pair(apply(sK19,X8),apply(sK19,X7)),sK20) )
=> ( sK21(X3) = ordered_pair(sK23(X3),sK22(X3))
& in(ordered_pair(apply(sK19,sK23(X3)),apply(sK19,sK22(X3))),sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
? [X0,X1,X2] :
( function(X1)
& relation(X1)
& relation(X2)
& ! [X3] :
? [X4] :
( ( ~ in(X4,X3)
| ! [X5,X6] :
( ordered_pair(X6,X5) != X4
| ~ in(ordered_pair(apply(X1,X6),apply(X1,X5)),X2) )
| ~ in(X4,cartesian_product2(X0,X0)) )
& ( in(X4,X3)
| ( ? [X7,X8] :
( ordered_pair(X8,X7) = X4
& in(ordered_pair(apply(X1,X8),apply(X1,X7)),X2) )
& in(X4,cartesian_product2(X0,X0)) ) ) ) ),
inference(rectify,[],[f66]) ).
fof(f66,plain,
? [X2,X1,X0] :
( function(X1)
& relation(X1)
& relation(X0)
& ! [X3] :
? [X4] :
( ( ~ in(X4,X3)
| ! [X5,X6] :
( ordered_pair(X6,X5) != X4
| ~ in(ordered_pair(apply(X1,X6),apply(X1,X5)),X0) )
| ~ in(X4,cartesian_product2(X2,X2)) )
& ( in(X4,X3)
| ( ? [X5,X6] :
( ordered_pair(X6,X5) = X4
& in(ordered_pair(apply(X1,X6),apply(X1,X5)),X0) )
& in(X4,cartesian_product2(X2,X2)) ) ) ) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
? [X2,X1,X0] :
( function(X1)
& relation(X1)
& relation(X0)
& ! [X3] :
? [X4] :
( ( ~ in(X4,X3)
| ! [X5,X6] :
( ordered_pair(X6,X5) != X4
| ~ in(ordered_pair(apply(X1,X6),apply(X1,X5)),X0) )
| ~ in(X4,cartesian_product2(X2,X2)) )
& ( in(X4,X3)
| ( ? [X5,X6] :
( ordered_pair(X6,X5) = X4
& in(ordered_pair(apply(X1,X6),apply(X1,X5)),X0) )
& in(X4,cartesian_product2(X2,X2)) ) ) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f34,plain,
? [X2,X1,X0] :
( function(X1)
& relation(X1)
& relation(X0)
& ! [X3] :
? [X4] :
( ( ? [X5,X6] :
( ordered_pair(X6,X5) = X4
& in(ordered_pair(apply(X1,X6),apply(X1,X5)),X0) )
& in(X4,cartesian_product2(X2,X2)) )
<~> in(X4,X3) ) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ? [X5,X6] :
( ordered_pair(X6,X5) = X4
& in(ordered_pair(apply(X1,X6),apply(X1,X5)),X0) )
& in(X4,cartesian_product2(X2,X2)) )
<~> in(X4,X3) )
& relation(X1)
& relation(X0)
& function(X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
~ ! [X0,X1,X2] :
( ( relation(X1)
& relation(X0)
& function(X1) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( ordered_pair(X6,X5) = X4
& in(ordered_pair(apply(X1,X6),apply(X1,X5)),X0) )
& in(X4,cartesian_product2(X2,X2)) ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X1,X2,X0] :
( ( relation(X1)
& function(X2)
& relation(X2) )
=> ? [X3] :
! [X4] :
( ( ? [X6,X5] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X0)) )
<=> in(X4,X3) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X1,X2,X0] :
( ( relation(X1)
& function(X2)
& relation(X2) )
=> ? [X3] :
! [X4] :
( ( ? [X6,X5] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X0)) )
<=> in(X4,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_21__wellord2__1) ).
fof(f372,plain,
( in(sK21(sK12(sK19,sK18,sK20)),sF26)
| ~ in(sK21(sK12(sK19,sK18,sK20)),sK12(sK19,sK18,sK20))
| spl27_1
| ~ spl27_6 ),
inference(forward_demodulation,[],[f371,f130]) ).
fof(f371,plain,
( in(sK21(sK12(sK19,sK18,sK20)),cartesian_product2(sK18,sK18))
| ~ in(sK21(sK12(sK19,sK18,sK20)),sK12(sK19,sK18,sK20))
| spl27_1
| ~ spl27_6 ),
inference(subsumption_resolution,[],[f345,f115]) ).
fof(f115,plain,
relation(sK20),
inference(cnf_transformation,[],[f71]) ).
fof(f345,plain,
( ~ in(sK21(sK12(sK19,sK18,sK20)),sK12(sK19,sK18,sK20))
| in(sK21(sK12(sK19,sK18,sK20)),cartesian_product2(sK18,sK18))
| ~ relation(sK20)
| spl27_1
| ~ spl27_6 ),
inference(subsumption_resolution,[],[f344,f116]) ).
fof(f116,plain,
relation(sK19),
inference(cnf_transformation,[],[f71]) ).
fof(f344,plain,
( ~ relation(sK19)
| in(sK21(sK12(sK19,sK18,sK20)),cartesian_product2(sK18,sK18))
| ~ in(sK21(sK12(sK19,sK18,sK20)),sK12(sK19,sK18,sK20))
| ~ relation(sK20)
| spl27_1
| ~ spl27_6 ),
inference(subsumption_resolution,[],[f343,f193]) ).
fof(f193,plain,
( ~ sP0(sK20,sK19)
| spl27_1 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f192,plain,
( spl27_1
<=> sP0(sK20,sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_1])]) ).
fof(f343,plain,
( sP0(sK20,sK19)
| in(sK21(sK12(sK19,sK18,sK20)),cartesian_product2(sK18,sK18))
| ~ relation(sK19)
| ~ in(sK21(sK12(sK19,sK18,sK20)),sK12(sK19,sK18,sK20))
| ~ relation(sK20)
| ~ spl27_6 ),
inference(subsumption_resolution,[],[f326,f117]) ).
fof(f117,plain,
function(sK19),
inference(cnf_transformation,[],[f71]) ).
fof(f326,plain,
( in(sK21(sK12(sK19,sK18,sK20)),cartesian_product2(sK18,sK18))
| ~ function(sK19)
| ~ relation(sK19)
| ~ relation(sK20)
| sP0(sK20,sK19)
| ~ in(sK21(sK12(sK19,sK18,sK20)),sK12(sK19,sK18,sK20))
| ~ spl27_6 ),
inference(superposition,[],[f97,f288]) ).
fof(f288,plain,
( sK13(sK19,sK18,sK20,sK21(sK12(sK19,sK18,sK20))) = sK21(sK12(sK19,sK18,sK20))
| ~ spl27_6 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f286,plain,
( spl27_6
<=> sK13(sK19,sK18,sK20,sK21(sK12(sK19,sK18,sK20))) = sK21(sK12(sK19,sK18,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_6])]) ).
fof(f97,plain,
! [X2,X0,X1,X4] :
( in(sK13(X0,X1,X2,X4),cartesian_product2(X1,X1))
| sP0(X2,X0)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X4,sK12(X0,X1,X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ function(X0)
| ~ relation(X0)
| sP0(X2,X0)
| ! [X4] :
( ( ( sK13(X0,X1,X2,X4) = X4
& in(sK13(X0,X1,X2,X4),cartesian_product2(X1,X1))
& in(ordered_pair(apply(X0,sK15(X0,X2,X4)),apply(X0,sK14(X0,X2,X4))),X2)
& ordered_pair(sK15(X0,X2,X4),sK14(X0,X2,X4)) = X4 )
| ~ in(X4,sK12(X0,X1,X2)) )
& ( in(X4,sK12(X0,X1,X2))
| ! [X8] :
( X4 != X8
| ~ in(X8,cartesian_product2(X1,X1))
| ! [X9,X10] :
( ~ in(ordered_pair(apply(X0,X10),apply(X0,X9)),X2)
| ordered_pair(X10,X9) != X4 ) ) ) )
| ~ relation(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15])],[f56,f59,f58,f57]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( ? [X5] :
( X4 = X5
& in(X5,cartesian_product2(X1,X1))
& ? [X6,X7] :
( in(ordered_pair(apply(X0,X7),apply(X0,X6)),X2)
& ordered_pair(X7,X6) = X4 ) )
| ~ in(X4,X3) )
& ( in(X4,X3)
| ! [X8] :
( X4 != X8
| ~ in(X8,cartesian_product2(X1,X1))
| ! [X9,X10] :
( ~ in(ordered_pair(apply(X0,X10),apply(X0,X9)),X2)
| ordered_pair(X10,X9) != X4 ) ) ) )
=> ! [X4] :
( ( ? [X5] :
( X4 = X5
& in(X5,cartesian_product2(X1,X1))
& ? [X6,X7] :
( in(ordered_pair(apply(X0,X7),apply(X0,X6)),X2)
& ordered_pair(X7,X6) = X4 ) )
| ~ in(X4,sK12(X0,X1,X2)) )
& ( in(X4,sK12(X0,X1,X2))
| ! [X8] :
( X4 != X8
| ~ in(X8,cartesian_product2(X1,X1))
| ! [X9,X10] :
( ~ in(ordered_pair(apply(X0,X10),apply(X0,X9)),X2)
| ordered_pair(X10,X9) != X4 ) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
! [X0,X1,X2,X4] :
( ? [X5] :
( X4 = X5
& in(X5,cartesian_product2(X1,X1))
& ? [X6,X7] :
( in(ordered_pair(apply(X0,X7),apply(X0,X6)),X2)
& ordered_pair(X7,X6) = X4 ) )
=> ( sK13(X0,X1,X2,X4) = X4
& in(sK13(X0,X1,X2,X4),cartesian_product2(X1,X1))
& ? [X6,X7] :
( in(ordered_pair(apply(X0,X7),apply(X0,X6)),X2)
& ordered_pair(X7,X6) = X4 ) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0,X2,X4] :
( ? [X6,X7] :
( in(ordered_pair(apply(X0,X7),apply(X0,X6)),X2)
& ordered_pair(X7,X6) = X4 )
=> ( in(ordered_pair(apply(X0,sK15(X0,X2,X4)),apply(X0,sK14(X0,X2,X4))),X2)
& ordered_pair(sK15(X0,X2,X4),sK14(X0,X2,X4)) = X4 ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ function(X0)
| ~ relation(X0)
| sP0(X2,X0)
| ? [X3] :
! [X4] :
( ( ? [X5] :
( X4 = X5
& in(X5,cartesian_product2(X1,X1))
& ? [X6,X7] :
( in(ordered_pair(apply(X0,X7),apply(X0,X6)),X2)
& ordered_pair(X7,X6) = X4 ) )
| ~ in(X4,X3) )
& ( in(X4,X3)
| ! [X8] :
( X4 != X8
| ~ in(X8,cartesian_product2(X1,X1))
| ! [X9,X10] :
( ~ in(ordered_pair(apply(X0,X10),apply(X0,X9)),X2)
| ordered_pair(X10,X9) != X4 ) ) ) )
| ~ relation(X2) ),
inference(rectify,[],[f55]) ).
fof(f55,plain,
! [X1,X2,X0] :
( ~ function(X1)
| ~ relation(X1)
| sP0(X0,X1)
| ? [X10] :
! [X11] :
( ( ? [X12] :
( X11 = X12
& in(X12,cartesian_product2(X2,X2))
& ? [X14,X13] :
( in(ordered_pair(apply(X1,X13),apply(X1,X14)),X0)
& ordered_pair(X13,X14) = X11 ) )
| ~ in(X11,X10) )
& ( in(X11,X10)
| ! [X12] :
( X11 != X12
| ~ in(X12,cartesian_product2(X2,X2))
| ! [X14,X13] :
( ~ in(ordered_pair(apply(X1,X13),apply(X1,X14)),X0)
| ordered_pair(X13,X14) != X11 ) ) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X1,X2,X0] :
( ~ function(X1)
| ~ relation(X1)
| sP0(X0,X1)
| ? [X10] :
! [X11] :
( ? [X12] :
( X11 = X12
& in(X12,cartesian_product2(X2,X2))
& ? [X14,X13] :
( in(ordered_pair(apply(X1,X13),apply(X1,X14)),X0)
& ordered_pair(X13,X14) = X11 ) )
<=> in(X11,X10) )
| ~ relation(X0) ),
inference(definition_folding,[],[f32,f39]) ).
fof(f39,plain,
! [X0,X1] :
( ? [X3,X4,X5] :
( ? [X6,X7] :
( in(ordered_pair(apply(X1,X7),apply(X1,X6)),X0)
& ordered_pair(X7,X6) = X4 )
& X4 = X5
& X3 != X4
& ? [X9,X8] :
( in(ordered_pair(apply(X1,X9),apply(X1,X8)),X0)
& ordered_pair(X9,X8) = X3 )
& X3 = X5 )
| ~ sP0(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f32,plain,
! [X1,X2,X0] :
( ~ function(X1)
| ~ relation(X1)
| ? [X3,X4,X5] :
( ? [X6,X7] :
( in(ordered_pair(apply(X1,X7),apply(X1,X6)),X0)
& ordered_pair(X7,X6) = X4 )
& X4 = X5
& X3 != X4
& ? [X9,X8] :
( in(ordered_pair(apply(X1,X9),apply(X1,X8)),X0)
& ordered_pair(X9,X8) = X3 )
& X3 = X5 )
| ? [X10] :
! [X11] :
( ? [X12] :
( X11 = X12
& in(X12,cartesian_product2(X2,X2))
& ? [X14,X13] :
( in(ordered_pair(apply(X1,X13),apply(X1,X14)),X0)
& ordered_pair(X13,X14) = X11 ) )
<=> in(X11,X10) )
| ~ relation(X0) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X1,X0,X2] :
( ? [X10] :
! [X11] :
( ? [X12] :
( X11 = X12
& in(X12,cartesian_product2(X2,X2))
& ? [X14,X13] :
( in(ordered_pair(apply(X1,X13),apply(X1,X14)),X0)
& ordered_pair(X13,X14) = X11 ) )
<=> in(X11,X10) )
| ? [X3,X5,X4] :
( X3 != X4
& ? [X6,X7] :
( in(ordered_pair(apply(X1,X7),apply(X1,X6)),X0)
& ordered_pair(X7,X6) = X4 )
& X3 = X5
& ? [X9,X8] :
( in(ordered_pair(apply(X1,X9),apply(X1,X8)),X0)
& ordered_pair(X9,X8) = X3 )
& X4 = X5 )
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
! [X1,X0,X2] :
( ( function(X1)
& relation(X0)
& relation(X1) )
=> ( ! [X3,X5,X4] :
( ( ? [X6,X7] :
( in(ordered_pair(apply(X1,X7),apply(X1,X6)),X0)
& ordered_pair(X7,X6) = X4 )
& X3 = X5
& ? [X9,X8] :
( in(ordered_pair(apply(X1,X9),apply(X1,X8)),X0)
& ordered_pair(X9,X8) = X3 )
& X4 = X5 )
=> X3 = X4 )
=> ? [X10] :
! [X11] :
( ? [X12] :
( X11 = X12
& in(X12,cartesian_product2(X2,X2))
& ? [X14,X13] :
( in(ordered_pair(apply(X1,X13),apply(X1,X14)),X0)
& ordered_pair(X13,X14) = X11 ) )
<=> in(X11,X10) ) ) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X1,X2,X0] :
( ( relation(X2)
& function(X2)
& relation(X1) )
=> ( ! [X4,X5,X3] :
( ( X3 = X4
& ? [X9,X8] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& ordered_pair(X8,X9) = X5 )
& X3 = X5
& ? [X7,X6] :
( ordered_pair(X6,X7) = X4
& in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( ? [X5] :
( X4 = X5
& in(X5,cartesian_product2(X0,X0))
& ? [X10,X11] :
( in(ordered_pair(apply(X2,X10),apply(X2,X11)),X1)
& ordered_pair(X10,X11) = X4 ) )
<=> in(X4,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_21__wellord2__1) ).
fof(f387,plain,
( ~ in(sK21(sK12(sK19,sK18,sK20)),sF26)
| ~ spl27_2
| spl27_7 ),
inference(subsumption_resolution,[],[f386,f291]) ).
fof(f291,plain,
( ~ in(sK21(sK12(sK19,sK18,sK20)),sK12(sK19,sK18,sK20))
| spl27_7 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f290,plain,
( spl27_7
<=> in(sK21(sK12(sK19,sK18,sK20)),sK12(sK19,sK18,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_7])]) ).
fof(f386,plain,
( in(sK21(sK12(sK19,sK18,sK20)),sK12(sK19,sK18,sK20))
| ~ in(sK21(sK12(sK19,sK18,sK20)),sF26)
| ~ spl27_2
| spl27_7 ),
inference(duplicate_literal_removal,[],[f378]) ).
fof(f378,plain,
( in(sK21(sK12(sK19,sK18,sK20)),sK12(sK19,sK18,sK20))
| in(sK21(sK12(sK19,sK18,sK20)),sK12(sK19,sK18,sK20))
| ~ in(sK21(sK12(sK19,sK18,sK20)),sF26)
| ~ spl27_2
| spl27_7 ),
inference(superposition,[],[f199,f375]) ).
fof(f375,plain,
( ordered_pair(sK23(sK12(sK19,sK18,sK20)),sK22(sK12(sK19,sK18,sK20))) = sK21(sK12(sK19,sK18,sK20))
| spl27_7 ),
inference(resolution,[],[f291,f113]) ).
fof(f113,plain,
! [X3] :
( in(sK21(X3),X3)
| sK21(X3) = ordered_pair(sK23(X3),sK22(X3)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f199,plain,
( ! [X0] :
( in(ordered_pair(sK23(X0),sK22(X0)),sK12(sK19,sK18,sK20))
| in(sK21(X0),X0)
| ~ in(ordered_pair(sK23(X0),sK22(X0)),sF26) )
| ~ spl27_2 ),
inference(superposition,[],[f197,f130]) ).
fof(f197,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(sK23(X0),sK22(X0)),cartesian_product2(X1,X1))
| in(sK21(X0),X0)
| in(ordered_pair(sK23(X0),sK22(X0)),sK12(sK19,X1,sK20)) )
| ~ spl27_2 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f196,plain,
( spl27_2
<=> ! [X0,X1] :
( ~ in(ordered_pair(sK23(X0),sK22(X0)),cartesian_product2(X1,X1))
| in(ordered_pair(sK23(X0),sK22(X0)),sK12(sK19,X1,sK20))
| in(sK21(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_2])]) ).
fof(f365,plain,
( spl27_1
| ~ spl27_6
| ~ spl27_7 ),
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f364,plain,
( $false
| spl27_1
| ~ spl27_6
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f363,f292]) ).
fof(f292,plain,
( in(sK21(sK12(sK19,sK18,sK20)),sK12(sK19,sK18,sK20))
| ~ spl27_7 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f363,plain,
( ~ in(sK21(sK12(sK19,sK18,sK20)),sK12(sK19,sK18,sK20))
| spl27_1
| ~ spl27_6
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f362,f342]) ).
fof(f342,plain,
( in(sK21(sK12(sK19,sK18,sK20)),sF26)
| spl27_1
| ~ spl27_6
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f341,f117]) ).
fof(f341,plain,
( ~ function(sK19)
| in(sK21(sK12(sK19,sK18,sK20)),sF26)
| spl27_1
| ~ spl27_6
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f340,f116]) ).
fof(f340,plain,
( ~ relation(sK19)
| in(sK21(sK12(sK19,sK18,sK20)),sF26)
| ~ function(sK19)
| spl27_1
| ~ spl27_6
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f339,f115]) ).
fof(f339,plain,
( ~ relation(sK20)
| in(sK21(sK12(sK19,sK18,sK20)),sF26)
| ~ function(sK19)
| ~ relation(sK19)
| spl27_1
| ~ spl27_6
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f338,f193]) ).
fof(f338,plain,
( sP0(sK20,sK19)
| ~ function(sK19)
| ~ relation(sK20)
| ~ relation(sK19)
| in(sK21(sK12(sK19,sK18,sK20)),sF26)
| ~ spl27_6
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f324,f292]) ).
fof(f324,plain,
( ~ function(sK19)
| in(sK21(sK12(sK19,sK18,sK20)),sF26)
| ~ relation(sK19)
| ~ relation(sK20)
| ~ in(sK21(sK12(sK19,sK18,sK20)),sK12(sK19,sK18,sK20))
| sP0(sK20,sK19)
| ~ spl27_6 ),
inference(superposition,[],[f173,f288]) ).
fof(f173,plain,
! [X2,X0,X1] :
( in(sK13(X0,sK18,X1,X2),sF26)
| sP0(X1,X0)
| ~ relation(X0)
| ~ relation(X1)
| ~ function(X0)
| ~ in(X2,sK12(X0,sK18,X1)) ),
inference(superposition,[],[f97,f130]) ).
fof(f362,plain,
( ~ in(sK21(sK12(sK19,sK18,sK20)),sF26)
| ~ in(sK21(sK12(sK19,sK18,sK20)),sK12(sK19,sK18,sK20))
| spl27_1
| ~ spl27_7 ),
inference(equality_resolution,[],[f361]) ).
fof(f361,plain,
( ! [X0] :
( sK21(sK12(sK19,sK18,sK20)) != sK21(X0)
| ~ in(sK21(X0),X0)
| ~ in(sK21(X0),sF26) )
| spl27_1
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f359,f310]) ).
fof(f310,plain,
( in(ordered_pair(apply(sK19,sK15(sK19,sK20,sK21(sK12(sK19,sK18,sK20)))),apply(sK19,sK14(sK19,sK20,sK21(sK12(sK19,sK18,sK20))))),sK20)
| spl27_1
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f309,f115]) ).
fof(f309,plain,
( in(ordered_pair(apply(sK19,sK15(sK19,sK20,sK21(sK12(sK19,sK18,sK20)))),apply(sK19,sK14(sK19,sK20,sK21(sK12(sK19,sK18,sK20))))),sK20)
| ~ relation(sK20)
| spl27_1
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f308,f116]) ).
fof(f308,plain,
( ~ relation(sK19)
| ~ relation(sK20)
| in(ordered_pair(apply(sK19,sK15(sK19,sK20,sK21(sK12(sK19,sK18,sK20)))),apply(sK19,sK14(sK19,sK20,sK21(sK12(sK19,sK18,sK20))))),sK20)
| spl27_1
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f307,f117]) ).
fof(f307,plain,
( ~ function(sK19)
| ~ relation(sK20)
| ~ relation(sK19)
| in(ordered_pair(apply(sK19,sK15(sK19,sK20,sK21(sK12(sK19,sK18,sK20)))),apply(sK19,sK14(sK19,sK20,sK21(sK12(sK19,sK18,sK20))))),sK20)
| spl27_1
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f298,f193]) ).
fof(f298,plain,
( sP0(sK20,sK19)
| ~ relation(sK19)
| ~ function(sK19)
| in(ordered_pair(apply(sK19,sK15(sK19,sK20,sK21(sK12(sK19,sK18,sK20)))),apply(sK19,sK14(sK19,sK20,sK21(sK12(sK19,sK18,sK20))))),sK20)
| ~ relation(sK20)
| ~ spl27_7 ),
inference(resolution,[],[f292,f96]) ).
fof(f96,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK12(X0,X1,X2))
| ~ function(X0)
| ~ relation(X0)
| ~ relation(X2)
| in(ordered_pair(apply(X0,sK15(X0,X2,X4)),apply(X0,sK14(X0,X2,X4))),X2)
| sP0(X2,X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f359,plain,
( ! [X0] :
( ~ in(sK21(X0),sF26)
| sK21(sK12(sK19,sK18,sK20)) != sK21(X0)
| ~ in(sK21(X0),X0)
| ~ in(ordered_pair(apply(sK19,sK15(sK19,sK20,sK21(sK12(sK19,sK18,sK20)))),apply(sK19,sK14(sK19,sK20,sK21(sK12(sK19,sK18,sK20))))),sK20) )
| spl27_1
| ~ spl27_7 ),
inference(superposition,[],[f131,f314]) ).
fof(f314,plain,
( sK21(sK12(sK19,sK18,sK20)) = ordered_pair(sK15(sK19,sK20,sK21(sK12(sK19,sK18,sK20))),sK14(sK19,sK20,sK21(sK12(sK19,sK18,sK20))))
| spl27_1
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f313,f116]) ).
fof(f313,plain,
( ~ relation(sK19)
| sK21(sK12(sK19,sK18,sK20)) = ordered_pair(sK15(sK19,sK20,sK21(sK12(sK19,sK18,sK20))),sK14(sK19,sK20,sK21(sK12(sK19,sK18,sK20))))
| spl27_1
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f312,f117]) ).
fof(f312,plain,
( sK21(sK12(sK19,sK18,sK20)) = ordered_pair(sK15(sK19,sK20,sK21(sK12(sK19,sK18,sK20))),sK14(sK19,sK20,sK21(sK12(sK19,sK18,sK20))))
| ~ function(sK19)
| ~ relation(sK19)
| spl27_1
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f311,f115]) ).
fof(f311,plain,
( ~ relation(sK20)
| ~ relation(sK19)
| ~ function(sK19)
| sK21(sK12(sK19,sK18,sK20)) = ordered_pair(sK15(sK19,sK20,sK21(sK12(sK19,sK18,sK20))),sK14(sK19,sK20,sK21(sK12(sK19,sK18,sK20))))
| spl27_1
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f299,f193]) ).
fof(f299,plain,
( sP0(sK20,sK19)
| ~ relation(sK19)
| ~ function(sK19)
| ~ relation(sK20)
| sK21(sK12(sK19,sK18,sK20)) = ordered_pair(sK15(sK19,sK20,sK21(sK12(sK19,sK18,sK20))),sK14(sK19,sK20,sK21(sK12(sK19,sK18,sK20))))
| ~ spl27_7 ),
inference(resolution,[],[f292,f95]) ).
fof(f95,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK12(X0,X1,X2))
| ~ relation(X0)
| ~ relation(X2)
| ordered_pair(sK15(X0,X2,X4),sK14(X0,X2,X4)) = X4
| sP0(X2,X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f131,plain,
! [X3,X6,X5] :
( sK21(X3) != ordered_pair(X6,X5)
| ~ in(sK21(X3),sF26)
| ~ in(sK21(X3),X3)
| ~ in(ordered_pair(apply(sK19,X6),apply(sK19,X5)),sK20) ),
inference(definition_folding,[],[f114,f130]) ).
fof(f114,plain,
! [X3,X6,X5] :
( ~ in(sK21(X3),X3)
| sK21(X3) != ordered_pair(X6,X5)
| ~ in(ordered_pair(apply(sK19,X6),apply(sK19,X5)),sK20)
| ~ in(sK21(X3),cartesian_product2(sK18,sK18)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f306,plain,
( spl27_6
| spl27_1
| ~ spl27_7 ),
inference(avatar_split_clause,[],[f305,f290,f192,f286]) ).
fof(f305,plain,
( sK13(sK19,sK18,sK20,sK21(sK12(sK19,sK18,sK20))) = sK21(sK12(sK19,sK18,sK20))
| spl27_1
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f304,f115]) ).
fof(f304,plain,
( sK13(sK19,sK18,sK20,sK21(sK12(sK19,sK18,sK20))) = sK21(sK12(sK19,sK18,sK20))
| ~ relation(sK20)
| spl27_1
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f303,f116]) ).
fof(f303,plain,
( sK13(sK19,sK18,sK20,sK21(sK12(sK19,sK18,sK20))) = sK21(sK12(sK19,sK18,sK20))
| ~ relation(sK19)
| ~ relation(sK20)
| spl27_1
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f302,f117]) ).
fof(f302,plain,
( sK13(sK19,sK18,sK20,sK21(sK12(sK19,sK18,sK20))) = sK21(sK12(sK19,sK18,sK20))
| ~ function(sK19)
| ~ relation(sK19)
| ~ relation(sK20)
| spl27_1
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f300,f193]) ).
fof(f300,plain,
( sP0(sK20,sK19)
| ~ relation(sK20)
| ~ function(sK19)
| sK13(sK19,sK18,sK20,sK21(sK12(sK19,sK18,sK20))) = sK21(sK12(sK19,sK18,sK20))
| ~ relation(sK19)
| ~ spl27_7 ),
inference(resolution,[],[f292,f98]) ).
fof(f98,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK12(X0,X1,X2))
| ~ function(X0)
| ~ relation(X2)
| sP0(X2,X0)
| sK13(X0,X1,X2,X4) = X4
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f293,plain,
( spl27_6
| spl27_7
| spl27_1
| ~ spl27_2 ),
inference(avatar_split_clause,[],[f279,f196,f192,f290,f286]) ).
fof(f279,plain,
( in(sK21(sK12(sK19,sK18,sK20)),sK12(sK19,sK18,sK20))
| sK13(sK19,sK18,sK20,sK21(sK12(sK19,sK18,sK20))) = sK21(sK12(sK19,sK18,sK20))
| spl27_1
| ~ spl27_2 ),
inference(factoring,[],[f269]) ).
fof(f269,plain,
( ! [X2] :
( in(sK21(sK12(sK19,X2,sK20)),sK12(sK19,sK18,sK20))
| in(sK21(sK12(sK19,X2,sK20)),sK12(sK19,X2,sK20))
| sK21(sK12(sK19,X2,sK20)) = sK13(sK19,X2,sK20,sK21(sK12(sK19,X2,sK20))) )
| spl27_1
| ~ spl27_2 ),
inference(subsumption_resolution,[],[f257,f132]) ).
fof(f257,plain,
( ! [X2] :
( in(sK21(sK12(sK19,X2,sK20)),sK12(sK19,sK18,sK20))
| ~ in(sK21(sK12(sK19,X2,sK20)),sF26)
| sK21(sK12(sK19,X2,sK20)) = sK13(sK19,X2,sK20,sK21(sK12(sK19,X2,sK20)))
| in(sK21(sK12(sK19,X2,sK20)),sK12(sK19,X2,sK20)) )
| spl27_1
| ~ spl27_2 ),
inference(superposition,[],[f199,f255]) ).
fof(f255,plain,
( ! [X12] :
( ordered_pair(sK23(sK12(sK19,X12,sK20)),sK22(sK12(sK19,X12,sK20))) = sK21(sK12(sK19,X12,sK20))
| sK13(sK19,X12,sK20,sK21(sK12(sK19,X12,sK20))) = sK21(sK12(sK19,X12,sK20)) )
| spl27_1 ),
inference(subsumption_resolution,[],[f254,f116]) ).
fof(f254,plain,
( ! [X12] :
( ~ relation(sK19)
| ordered_pair(sK23(sK12(sK19,X12,sK20)),sK22(sK12(sK19,X12,sK20))) = sK21(sK12(sK19,X12,sK20))
| sK13(sK19,X12,sK20,sK21(sK12(sK19,X12,sK20))) = sK21(sK12(sK19,X12,sK20)) )
| spl27_1 ),
inference(subsumption_resolution,[],[f253,f117]) ).
fof(f253,plain,
( ! [X12] :
( sK13(sK19,X12,sK20,sK21(sK12(sK19,X12,sK20))) = sK21(sK12(sK19,X12,sK20))
| ~ function(sK19)
| ordered_pair(sK23(sK12(sK19,X12,sK20)),sK22(sK12(sK19,X12,sK20))) = sK21(sK12(sK19,X12,sK20))
| ~ relation(sK19) )
| spl27_1 ),
inference(subsumption_resolution,[],[f252,f115]) ).
fof(f252,plain,
( ! [X12] :
( ordered_pair(sK23(sK12(sK19,X12,sK20)),sK22(sK12(sK19,X12,sK20))) = sK21(sK12(sK19,X12,sK20))
| ~ relation(sK20)
| ~ function(sK19)
| sK13(sK19,X12,sK20,sK21(sK12(sK19,X12,sK20))) = sK21(sK12(sK19,X12,sK20))
| ~ relation(sK19) )
| spl27_1 ),
inference(resolution,[],[f168,f193]) ).
fof(f168,plain,
! [X2,X0,X1] :
( sP0(X1,X0)
| ~ relation(X1)
| ordered_pair(sK23(sK12(X0,X2,X1)),sK22(sK12(X0,X2,X1))) = sK21(sK12(X0,X2,X1))
| ~ function(X0)
| sK13(X0,X2,X1,sK21(sK12(X0,X2,X1))) = sK21(sK12(X0,X2,X1))
| ~ relation(X0) ),
inference(resolution,[],[f98,f113]) ).
fof(f234,plain,
~ spl27_1,
inference(avatar_contradiction_clause,[],[f233]) ).
fof(f233,plain,
( $false
| ~ spl27_1 ),
inference(subsumption_resolution,[],[f232,f194]) ).
fof(f194,plain,
( sP0(sK20,sK19)
| ~ spl27_1 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f232,plain,
( ~ sP0(sK20,sK19)
| ~ spl27_1 ),
inference(trivial_inequality_removal,[],[f231]) ).
fof(f231,plain,
( sK5(sK20,sK19) != sK5(sK20,sK19)
| ~ sP0(sK20,sK19)
| ~ spl27_1 ),
inference(superposition,[],[f90,f229]) ).
fof(f229,plain,
( sK5(sK20,sK19) = sK6(sK20,sK19)
| ~ spl27_1 ),
inference(superposition,[],[f228,f227]) ).
fof(f227,plain,
( sK6(sK20,sK19) = sK7(sK20,sK19)
| ~ spl27_1 ),
inference(resolution,[],[f194,f91]) ).
fof(f91,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK6(X0,X1) = sK7(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( ( in(ordered_pair(apply(X1,sK9(X0,X1)),apply(X1,sK8(X0,X1))),X0)
& ordered_pair(sK9(X0,X1),sK8(X0,X1)) = sK6(X0,X1)
& sK6(X0,X1) = sK7(X0,X1)
& sK5(X0,X1) != sK6(X0,X1)
& in(ordered_pair(apply(X1,sK10(X0,X1)),apply(X1,sK11(X0,X1))),X0)
& sK5(X0,X1) = ordered_pair(sK10(X0,X1),sK11(X0,X1))
& sK5(X0,X1) = sK7(X0,X1) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9,sK10,sK11])],[f50,f53,f52,f51]) ).
fof(f51,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ? [X5,X6] :
( in(ordered_pair(apply(X1,X6),apply(X1,X5)),X0)
& ordered_pair(X6,X5) = X3 )
& X3 = X4
& X2 != X3
& ? [X7,X8] :
( in(ordered_pair(apply(X1,X7),apply(X1,X8)),X0)
& ordered_pair(X7,X8) = X2 )
& X2 = X4 )
=> ( ? [X6,X5] :
( in(ordered_pair(apply(X1,X6),apply(X1,X5)),X0)
& ordered_pair(X6,X5) = sK6(X0,X1) )
& sK6(X0,X1) = sK7(X0,X1)
& sK5(X0,X1) != sK6(X0,X1)
& ? [X8,X7] :
( in(ordered_pair(apply(X1,X7),apply(X1,X8)),X0)
& sK5(X0,X1) = ordered_pair(X7,X8) )
& sK5(X0,X1) = sK7(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
! [X0,X1] :
( ? [X6,X5] :
( in(ordered_pair(apply(X1,X6),apply(X1,X5)),X0)
& ordered_pair(X6,X5) = sK6(X0,X1) )
=> ( in(ordered_pair(apply(X1,sK9(X0,X1)),apply(X1,sK8(X0,X1))),X0)
& ordered_pair(sK9(X0,X1),sK8(X0,X1)) = sK6(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
! [X0,X1] :
( ? [X8,X7] :
( in(ordered_pair(apply(X1,X7),apply(X1,X8)),X0)
& sK5(X0,X1) = ordered_pair(X7,X8) )
=> ( in(ordered_pair(apply(X1,sK10(X0,X1)),apply(X1,sK11(X0,X1))),X0)
& sK5(X0,X1) = ordered_pair(sK10(X0,X1),sK11(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ? [X5,X6] :
( in(ordered_pair(apply(X1,X6),apply(X1,X5)),X0)
& ordered_pair(X6,X5) = X3 )
& X3 = X4
& X2 != X3
& ? [X7,X8] :
( in(ordered_pair(apply(X1,X7),apply(X1,X8)),X0)
& ordered_pair(X7,X8) = X2 )
& X2 = X4 )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( ? [X3,X4,X5] :
( ? [X6,X7] :
( in(ordered_pair(apply(X1,X7),apply(X1,X6)),X0)
& ordered_pair(X7,X6) = X4 )
& X4 = X5
& X3 != X4
& ? [X9,X8] :
( in(ordered_pair(apply(X1,X9),apply(X1,X8)),X0)
& ordered_pair(X9,X8) = X3 )
& X3 = X5 )
| ~ sP0(X0,X1) ),
inference(nnf_transformation,[],[f39]) ).
fof(f228,plain,
( sK5(sK20,sK19) = sK7(sK20,sK19)
| ~ spl27_1 ),
inference(resolution,[],[f194,f87]) ).
fof(f87,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK5(X0,X1) = sK7(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f90,plain,
! [X0,X1] :
( sK5(X0,X1) != sK6(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f198,plain,
( spl27_1
| spl27_2 ),
inference(avatar_split_clause,[],[f190,f196,f192]) ).
fof(f190,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK23(X0),sK22(X0)),cartesian_product2(X1,X1))
| sP0(sK20,sK19)
| in(sK21(X0),X0)
| in(ordered_pair(sK23(X0),sK22(X0)),sK12(sK19,X1,sK20)) ),
inference(subsumption_resolution,[],[f189,f117]) ).
fof(f189,plain,
! [X0,X1] :
( in(ordered_pair(sK23(X0),sK22(X0)),sK12(sK19,X1,sK20))
| in(sK21(X0),X0)
| ~ in(ordered_pair(sK23(X0),sK22(X0)),cartesian_product2(X1,X1))
| ~ function(sK19)
| sP0(sK20,sK19) ),
inference(subsumption_resolution,[],[f188,f116]) ).
fof(f188,plain,
! [X0,X1] :
( in(ordered_pair(sK23(X0),sK22(X0)),sK12(sK19,X1,sK20))
| ~ in(ordered_pair(sK23(X0),sK22(X0)),cartesian_product2(X1,X1))
| ~ relation(sK19)
| sP0(sK20,sK19)
| in(sK21(X0),X0)
| ~ function(sK19) ),
inference(subsumption_resolution,[],[f185,f115]) ).
fof(f185,plain,
! [X0,X1] :
( ~ relation(sK20)
| sP0(sK20,sK19)
| ~ relation(sK19)
| ~ in(ordered_pair(sK23(X0),sK22(X0)),cartesian_product2(X1,X1))
| in(ordered_pair(sK23(X0),sK22(X0)),sK12(sK19,X1,sK20))
| ~ function(sK19)
| in(sK21(X0),X0) ),
inference(resolution,[],[f129,f112]) ).
fof(f112,plain,
! [X3] :
( in(ordered_pair(apply(sK19,sK23(X3)),apply(sK19,sK22(X3))),sK20)
| in(sK21(X3),X3) ),
inference(cnf_transformation,[],[f71]) ).
fof(f129,plain,
! [X2,X10,X0,X1,X9] :
( ~ in(ordered_pair(apply(X0,X10),apply(X0,X9)),X2)
| ~ relation(X0)
| ~ function(X0)
| in(ordered_pair(X10,X9),sK12(X0,X1,X2))
| ~ relation(X2)
| ~ in(ordered_pair(X10,X9),cartesian_product2(X1,X1))
| sP0(X2,X0) ),
inference(equality_resolution,[],[f128]) ).
fof(f128,plain,
! [X2,X10,X0,X1,X8,X9] :
( ~ function(X0)
| ~ relation(X0)
| sP0(X2,X0)
| in(X8,sK12(X0,X1,X2))
| ~ in(X8,cartesian_product2(X1,X1))
| ~ in(ordered_pair(apply(X0,X10),apply(X0,X9)),X2)
| ordered_pair(X10,X9) != X8
| ~ relation(X2) ),
inference(equality_resolution,[],[f94]) ).
fof(f94,plain,
! [X2,X10,X0,X1,X8,X9,X4] :
( ~ function(X0)
| ~ relation(X0)
| sP0(X2,X0)
| in(X4,sK12(X0,X1,X2))
| X4 != X8
| ~ in(X8,cartesian_product2(X1,X1))
| ~ in(ordered_pair(apply(X0,X10),apply(X0,X9)),X2)
| ordered_pair(X10,X9) != X4
| ~ relation(X2) ),
inference(cnf_transformation,[],[f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU277+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.11 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.11/0.32 % Computer : n023.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Aug 30 15:23:35 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.17/0.47 % (32690)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.17/0.48 % (32708)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.17/0.49 % (32698)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.17/0.49 % (32699)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.17/0.49 TRYING [1]
% 0.17/0.49 TRYING [2]
% 0.17/0.49 % (32705)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.17/0.50 TRYING [3]
% 0.17/0.50 % (32691)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.17/0.51 % (32688)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.17/0.51 % (32685)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.17/0.51 % (32685)Refutation not found, incomplete strategy% (32685)------------------------------
% 0.17/0.51 % (32685)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.51 % (32685)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.51 % (32685)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.51
% 0.17/0.51 % (32685)Memory used [KB]: 5500
% 0.17/0.51 % (32685)Time elapsed: 0.131 s
% 0.17/0.51 % (32685)Instructions burned: 5 (million)
% 0.17/0.51 % (32685)------------------------------
% 0.17/0.51 % (32685)------------------------------
% 0.17/0.51 % (32687)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.17/0.51 % (32686)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.17/0.51 % (32684)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.17/0.51 % (32691)Instruction limit reached!
% 0.17/0.51 % (32691)------------------------------
% 0.17/0.51 % (32691)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.51 % (32691)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.51 % (32691)Termination reason: Unknown
% 0.17/0.51 % (32691)Termination phase: Saturation
% 0.17/0.51
% 0.17/0.51 % (32691)Memory used [KB]: 5500
% 0.17/0.51 % (32691)Time elapsed: 0.080 s
% 0.17/0.51 % (32691)Instructions burned: 7 (million)
% 0.17/0.51 % (32691)------------------------------
% 0.17/0.51 % (32691)------------------------------
% 0.17/0.52 TRYING [1]
% 0.17/0.52 % (32689)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.17/0.52 % (32701)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.17/0.53 TRYING [2]
% 0.17/0.54 % (32693)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.17/0.54 % (32692)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.17/0.54 % (32695)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.17/0.54 % (32692)Instruction limit reached!
% 0.17/0.54 % (32692)------------------------------
% 0.17/0.54 % (32692)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.54 % (32694)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.17/0.54 % (32697)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.17/0.54 % (32702)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.17/0.54 TRYING [1]
% 0.17/0.54 % (32706)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.17/0.54 % (32696)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.17/0.54 % (32713)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.17/0.54 TRYING [3]
% 0.17/0.54 % (32710)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.17/0.54 % (32703)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.17/0.54 % (32704)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.17/0.54 % (32700)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.17/0.55 % (32690)Instruction limit reached!
% 0.17/0.55 % (32690)------------------------------
% 0.17/0.55 % (32690)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.55 % (32707)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.17/0.55 % (32690)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.55 % (32690)Termination reason: Unknown
% 0.17/0.55 % (32690)Termination phase: Finite model building SAT solving
% 0.17/0.55
% 0.17/0.55 % (32690)Memory used [KB]: 7419
% 0.17/0.55 % (32690)Time elapsed: 0.136 s
% 0.17/0.55 % (32690)Instructions burned: 52 (million)
% 0.17/0.55 % (32690)------------------------------
% 0.17/0.55 % (32690)------------------------------
% 0.17/0.55 % (32711)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.17/0.55 % (32712)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.17/0.55 % (32709)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.17/0.56 % (32692)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.56 % (32692)Termination reason: Unknown
% 0.17/0.56 % (32692)Termination phase: Preprocessing 3
% 0.17/0.56
% 0.17/0.56 % (32692)Memory used [KB]: 895
% 0.17/0.56 % (32692)Time elapsed: 0.003 s
% 0.17/0.56 % (32692)Instructions burned: 2 (million)
% 0.17/0.56 % (32692)------------------------------
% 0.17/0.56 % (32692)------------------------------
% 0.17/0.56 TRYING [2]
% 0.17/0.59 TRYING [3]
% 0.17/0.59 % (32696)First to succeed.
% 0.17/0.60 % (32686)Instruction limit reached!
% 0.17/0.60 % (32686)------------------------------
% 0.17/0.60 % (32686)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.60 % (32686)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.60 % (32686)Termination reason: Unknown
% 0.17/0.60 % (32686)Termination phase: Saturation
% 0.17/0.60
% 0.17/0.60 % (32686)Memory used [KB]: 1663
% 0.17/0.60 % (32686)Time elapsed: 0.225 s
% 0.17/0.60 % (32686)Instructions burned: 37 (million)
% 0.17/0.60 % (32686)------------------------------
% 0.17/0.60 % (32686)------------------------------
% 2.21/0.62 % (32708)Also succeeded, but the first one will report.
% 2.21/0.62 % (32696)Refutation found. Thanks to Tanya!
% 2.21/0.62 % SZS status Theorem for theBenchmark
% 2.21/0.62 % SZS output start Proof for theBenchmark
% See solution above
% 2.21/0.62 % (32696)------------------------------
% 2.21/0.62 % (32696)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.21/0.62 % (32696)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.21/0.62 % (32696)Termination reason: Refutation
% 2.21/0.62
% 2.21/0.62 % (32696)Memory used [KB]: 5884
% 2.21/0.62 % (32696)Time elapsed: 0.218 s
% 2.21/0.62 % (32696)Instructions burned: 20 (million)
% 2.21/0.62 % (32696)------------------------------
% 2.21/0.62 % (32696)------------------------------
% 2.21/0.62 % (32683)Success in time 0.289 s
%------------------------------------------------------------------------------