TSTP Solution File: SEU228+3 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU228+3 : TPTP v8.1.0. Released v3.2.0.
% 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 : n008.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 18:27:44 EDT 2022
% Result : Theorem 1.39s 0.51s
% Output : Refutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of formulae : 84 ( 14 unt; 0 def)
% Number of atoms : 488 ( 102 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 634 ( 230 ~; 227 |; 134 &)
% ( 22 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 2 con; 0-3 aty)
% Number of variables : 236 ( 193 !; 43 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f316,plain,
$false,
inference(subsumption_resolution,[],[f312,f309]) ).
fof(f309,plain,
in(sK2(sK10,sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9)),relation_inverse_image(sK10,sK9)),
inference(unit_resulting_resolution,[],[f183,f233]) ).
fof(f233,plain,
! [X4] :
( in(sK2(sK10,sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9)),relation_inverse_image(sK10,X4))
| ~ in(sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9),X4) ),
inference(subsumption_resolution,[],[f232,f145]) ).
fof(f145,plain,
function(sK10),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
( subset(sK9,relation_rng(sK10))
& sK9 != relation_image(sK10,relation_inverse_image(sK10,sK9))
& function(sK10)
& relation(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f95,f96]) ).
fof(f96,plain,
( ? [X0,X1] :
( subset(X0,relation_rng(X1))
& relation_image(X1,relation_inverse_image(X1,X0)) != X0
& function(X1)
& relation(X1) )
=> ( subset(sK9,relation_rng(sK10))
& sK9 != relation_image(sK10,relation_inverse_image(sK10,sK9))
& function(sK10)
& relation(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
? [X0,X1] :
( subset(X0,relation_rng(X1))
& relation_image(X1,relation_inverse_image(X1,X0)) != X0
& function(X1)
& relation(X1) ),
inference(rectify,[],[f55]) ).
fof(f55,plain,
? [X1,X0] :
( subset(X1,relation_rng(X0))
& relation_image(X0,relation_inverse_image(X0,X1)) != X1
& function(X0)
& relation(X0) ),
inference(flattening,[],[f54]) ).
fof(f54,plain,
? [X1,X0] :
( relation_image(X0,relation_inverse_image(X0,X1)) != X1
& subset(X1,relation_rng(X0))
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,plain,
~ ! [X1,X0] :
( ( function(X0)
& relation(X0) )
=> ( subset(X1,relation_rng(X0))
=> relation_image(X0,relation_inverse_image(X0,X1)) = X1 ) ),
inference(rectify,[],[f32]) ).
fof(f32,negated_conjecture,
~ ! [X1,X0] :
( ( function(X1)
& relation(X1) )
=> ( subset(X0,relation_rng(X1))
=> relation_image(X1,relation_inverse_image(X1,X0)) = X0 ) ),
inference(negated_conjecture,[],[f31]) ).
fof(f31,conjecture,
! [X1,X0] :
( ( function(X1)
& relation(X1) )
=> ( subset(X0,relation_rng(X1))
=> relation_image(X1,relation_inverse_image(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).
fof(f232,plain,
! [X4] :
( in(sK2(sK10,sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9)),relation_inverse_image(sK10,X4))
| ~ in(sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9),X4)
| ~ function(sK10) ),
inference(subsumption_resolution,[],[f231,f191]) ).
fof(f191,plain,
in(sK2(sK10,sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9)),relation_dom(sK10)),
inference(unit_resulting_resolution,[],[f144,f145,f187,f165]) ).
fof(f165,plain,
! [X0,X5] :
( in(sK2(X0,X5),relation_dom(X0))
| ~ in(X5,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f108]) ).
fof(f108,plain,
! [X0,X1,X5] :
( ~ function(X0)
| in(sK2(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0] :
( ~ function(X0)
| ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] :
( apply(X0,X3) != sK0(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK0(X0,X1),X1) )
& ( ( apply(X0,sK1(X0,X1)) = sK0(X0,X1)
& in(sK1(X0,X1),relation_dom(X0)) )
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ( apply(X0,sK2(X0,X5)) = X5
& in(sK2(X0,X5),relation_dom(X0)) )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f69,f72,f71,f70]) ).
fof(f70,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( apply(X0,X3) != sK0(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK0(X0,X1),X1) )
& ( ? [X4] :
( apply(X0,X4) = sK0(X0,X1)
& in(X4,relation_dom(X0)) )
| in(sK0(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [X0,X1] :
( ? [X4] :
( apply(X0,X4) = sK0(X0,X1)
& in(X4,relation_dom(X0)) )
=> ( apply(X0,sK1(X0,X1)) = sK0(X0,X1)
& in(sK1(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X0,X5] :
( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
=> ( apply(X0,sK2(X0,X5)) = X5
& in(sK2(X0,X5),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X0] :
( ~ function(X0)
| ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ~ function(X0)
| ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ~ function(X0)
| ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ relation(X0) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f187,plain,
in(sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9),relation_rng(sK10)),
inference(unit_resulting_resolution,[],[f147,f183,f153]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ subset(X1,X0)
| in(X2,X0)
| ~ in(X2,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ( in(sK12(X0,X1),X1)
& ~ in(sK12(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f101,f102]) ).
fof(f102,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X1)
& ~ in(X3,X0) )
=> ( in(sK12(X0,X1),X1)
& ~ in(sK12(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X3] :
( in(X3,X1)
& ~ in(X3,X0) ) ) ),
inference(rectify,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X2] :
( in(X2,X1)
& ~ in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) )
<=> subset(X1,X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,plain,
! [X1,X0] :
( subset(X1,X0)
<=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f147,plain,
subset(sK9,relation_rng(sK10)),
inference(cnf_transformation,[],[f97]) ).
fof(f144,plain,
relation(sK10),
inference(cnf_transformation,[],[f97]) ).
fof(f231,plain,
! [X4] :
( ~ in(sK2(sK10,sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9)),relation_dom(sK10))
| ~ function(sK10)
| ~ in(sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9),X4)
| in(sK2(sK10,sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9)),relation_inverse_image(sK10,X4)) ),
inference(subsumption_resolution,[],[f230,f144]) ).
fof(f230,plain,
! [X4] :
( ~ relation(sK10)
| ~ function(sK10)
| ~ in(sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9),X4)
| in(sK2(sK10,sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9)),relation_inverse_image(sK10,X4))
| ~ in(sK2(sK10,sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9)),relation_dom(sK10)) ),
inference(superposition,[],[f166,f192]) ).
fof(f192,plain,
apply(sK10,sK2(sK10,sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9))) = sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9),
inference(unit_resulting_resolution,[],[f145,f144,f187,f164]) ).
fof(f164,plain,
! [X0,X5] :
( ~ in(X5,relation_rng(X0))
| ~ relation(X0)
| apply(X0,sK2(X0,X5)) = X5
| ~ function(X0) ),
inference(equality_resolution,[],[f109]) ).
fof(f109,plain,
! [X0,X1,X5] :
( ~ function(X0)
| apply(X0,sK2(X0,X5)) = X5
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f166,plain,
! [X2,X3,X0] :
( ~ in(apply(X0,X3),X2)
| in(X3,relation_inverse_image(X0,X2))
| ~ relation(X0)
| ~ function(X0)
| ~ in(X3,relation_dom(X0)) ),
inference(equality_resolution,[],[f123]) ).
fof(f123,plain,
! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X3,X1)
| ~ in(apply(X0,X3),X2)
| ~ in(X3,relation_dom(X0))
| relation_inverse_image(X0,X2) != X1 ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| ~ in(apply(X0,X3),X2)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X2)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X1) ) )
| relation_inverse_image(X0,X2) != X1 )
& ( relation_inverse_image(X0,X2) = X1
| ( ( ~ in(apply(X0,sK4(X0,X1,X2)),X2)
| ~ in(sK4(X0,X1,X2),relation_dom(X0))
| ~ in(sK4(X0,X1,X2),X1) )
& ( ( in(apply(X0,sK4(X0,X1,X2)),X2)
& in(sK4(X0,X1,X2),relation_dom(X0)) )
| in(sK4(X0,X1,X2),X1) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f78,f79]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(apply(X0,X4),X2)
| ~ in(X4,relation_dom(X0))
| ~ in(X4,X1) )
& ( ( in(apply(X0,X4),X2)
& in(X4,relation_dom(X0)) )
| in(X4,X1) ) )
=> ( ( ~ in(apply(X0,sK4(X0,X1,X2)),X2)
| ~ in(sK4(X0,X1,X2),relation_dom(X0))
| ~ in(sK4(X0,X1,X2),X1) )
& ( ( in(apply(X0,sK4(X0,X1,X2)),X2)
& in(sK4(X0,X1,X2),relation_dom(X0)) )
| in(sK4(X0,X1,X2),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| ~ in(apply(X0,X3),X2)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X2)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X1) ) )
| relation_inverse_image(X0,X2) != X1 )
& ( relation_inverse_image(X0,X2) = X1
| ? [X4] :
( ( ~ in(apply(X0,X4),X2)
| ~ in(X4,relation_dom(X0))
| ~ in(X4,X1) )
& ( ( in(apply(X0,X4),X2)
& in(X4,relation_dom(X0)) )
| in(X4,X1) ) ) ) ) ),
inference(rectify,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X2,X1] :
( ( ! [X3] :
( ( in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 )
& ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) ) ) ) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X2,X1] :
( ( ! [X3] :
( ( in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 )
& ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) ) ) ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X2,X1] :
( ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
<=> relation_inverse_image(X0,X1) = X2 ) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ! [X2,X1] :
( ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
<=> relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X2,X1] :
( ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
<=> relation_inverse_image(X0,X1) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f183,plain,
in(sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9),sK9),
inference(unit_resulting_resolution,[],[f181,f152]) ).
fof(f152,plain,
! [X0,X1] :
( in(sK12(X0,X1),X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f181,plain,
~ subset(sK9,relation_image(sK10,relation_inverse_image(sK10,sK9))),
inference(unit_resulting_resolution,[],[f146,f176,f138]) ).
fof(f138,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f91]) ).
fof(f91,plain,
! [X1,X0] :
( ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X1,X0] :
( ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] :
( ( subset(X0,X1)
& subset(X1,X0) )
<=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f176,plain,
! [X0] : subset(relation_image(sK10,relation_inverse_image(sK10,X0)),X0),
inference(unit_resulting_resolution,[],[f144,f145,f127]) ).
fof(f127,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X1,X0] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X1,X0] :
( ( function(X1)
& relation(X1) )
=> subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_1) ).
fof(f146,plain,
sK9 != relation_image(sK10,relation_inverse_image(sK10,sK9)),
inference(cnf_transformation,[],[f97]) ).
fof(f312,plain,
~ in(sK2(sK10,sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9)),relation_inverse_image(sK10,sK9)),
inference(unit_resulting_resolution,[],[f184,f236]) ).
fof(f236,plain,
! [X0] :
( ~ in(sK2(sK10,sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9)),X0)
| in(sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9),relation_image(sK10,X0)) ),
inference(subsumption_resolution,[],[f235,f191]) ).
fof(f235,plain,
! [X0] :
( in(sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9),relation_image(sK10,X0))
| ~ in(sK2(sK10,sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9)),relation_dom(sK10))
| ~ in(sK2(sK10,sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9)),X0) ),
inference(subsumption_resolution,[],[f234,f145]) ).
fof(f234,plain,
! [X0] :
( ~ function(sK10)
| in(sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9),relation_image(sK10,X0))
| ~ in(sK2(sK10,sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9)),X0)
| ~ in(sK2(sK10,sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9)),relation_dom(sK10)) ),
inference(subsumption_resolution,[],[f226,f144]) ).
fof(f226,plain,
! [X0] :
( ~ relation(sK10)
| ~ function(sK10)
| ~ in(sK2(sK10,sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9)),X0)
| in(sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9),relation_image(sK10,X0))
| ~ in(sK2(sK10,sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9)),relation_dom(sK10)) ),
inference(superposition,[],[f173,f192]) ).
fof(f173,plain,
! [X2,X0,X8] :
( in(apply(X0,X8),relation_image(X0,X2))
| ~ in(X8,X2)
| ~ relation(X0)
| ~ in(X8,relation_dom(X0))
| ~ function(X0) ),
inference(equality_resolution,[],[f172]) ).
fof(f172,plain,
! [X2,X0,X1,X8] :
( in(apply(X0,X8),X1)
| ~ in(X8,X2)
| ~ in(X8,relation_dom(X0))
| relation_image(X0,X2) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f128]) ).
fof(f128,plain,
! [X2,X0,X1,X8,X6] :
( in(X6,X1)
| ~ in(X8,X2)
| apply(X0,X8) != X6
| ~ in(X8,relation_dom(X0))
| relation_image(X0,X2) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X2) = X1
| ( ( ~ in(sK5(X0,X1,X2),X1)
| ! [X4] :
( ~ in(X4,X2)
| apply(X0,X4) != sK5(X0,X1,X2)
| ~ in(X4,relation_dom(X0)) ) )
& ( in(sK5(X0,X1,X2),X1)
| ( in(sK6(X0,X1,X2),X2)
& sK5(X0,X1,X2) = apply(X0,sK6(X0,X1,X2))
& in(sK6(X0,X1,X2),relation_dom(X0)) ) ) ) )
& ( ! [X6] :
( ( ( in(sK7(X0,X2,X6),X2)
& apply(X0,sK7(X0,X2,X6)) = X6
& in(sK7(X0,X2,X6),relation_dom(X0)) )
| ~ in(X6,X1) )
& ( in(X6,X1)
| ! [X8] :
( ~ in(X8,X2)
| apply(X0,X8) != X6
| ~ in(X8,relation_dom(X0)) ) ) )
| relation_image(X0,X2) != X1 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f83,f86,f85,f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ! [X4] :
( ~ in(X4,X2)
| apply(X0,X4) != X3
| ~ in(X4,relation_dom(X0)) ) )
& ( in(X3,X1)
| ? [X5] :
( in(X5,X2)
& apply(X0,X5) = X3
& in(X5,relation_dom(X0)) ) ) )
=> ( ( ~ in(sK5(X0,X1,X2),X1)
| ! [X4] :
( ~ in(X4,X2)
| apply(X0,X4) != sK5(X0,X1,X2)
| ~ in(X4,relation_dom(X0)) ) )
& ( in(sK5(X0,X1,X2),X1)
| ? [X5] :
( in(X5,X2)
& apply(X0,X5) = sK5(X0,X1,X2)
& in(X5,relation_dom(X0)) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ? [X5] :
( in(X5,X2)
& apply(X0,X5) = sK5(X0,X1,X2)
& in(X5,relation_dom(X0)) )
=> ( in(sK6(X0,X1,X2),X2)
& sK5(X0,X1,X2) = apply(X0,sK6(X0,X1,X2))
& in(sK6(X0,X1,X2),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
! [X0,X2,X6] :
( ? [X7] :
( in(X7,X2)
& apply(X0,X7) = X6
& in(X7,relation_dom(X0)) )
=> ( in(sK7(X0,X2,X6),X2)
& apply(X0,sK7(X0,X2,X6)) = X6
& in(sK7(X0,X2,X6),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X2) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ! [X4] :
( ~ in(X4,X2)
| apply(X0,X4) != X3
| ~ in(X4,relation_dom(X0)) ) )
& ( in(X3,X1)
| ? [X5] :
( in(X5,X2)
& apply(X0,X5) = X3
& in(X5,relation_dom(X0)) ) ) ) )
& ( ! [X6] :
( ( ? [X7] :
( in(X7,X2)
& apply(X0,X7) = X6
& in(X7,relation_dom(X0)) )
| ~ in(X6,X1) )
& ( in(X6,X1)
| ! [X8] :
( ~ in(X8,X2)
| apply(X0,X8) != X6
| ~ in(X8,relation_dom(X0)) ) ) )
| relation_image(X0,X2) != X1 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f82]) ).
fof(f82,plain,
! [X0] :
( ! [X2,X1] :
( ( relation_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| apply(X0,X4) != X3
| ~ in(X4,relation_dom(X0)) ) )
& ( in(X3,X2)
| ? [X4] :
( in(X4,X1)
& apply(X0,X4) = X3
& in(X4,relation_dom(X0)) ) ) ) )
& ( ! [X3] :
( ( ? [X4] :
( in(X4,X1)
& apply(X0,X4) = X3
& in(X4,relation_dom(X0)) )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| apply(X0,X4) != X3
| ~ in(X4,relation_dom(X0)) ) ) )
| relation_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ! [X2,X1] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( ? [X4] :
( in(X4,X1)
& apply(X0,X4) = X3
& in(X4,relation_dom(X0)) )
<=> in(X3,X2) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ! [X2,X1] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( ? [X4] :
( in(X4,X1)
& apply(X0,X4) = X3
& in(X4,relation_dom(X0)) )
<=> in(X3,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X2,X1] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( ? [X4] :
( in(X4,X1)
& apply(X0,X4) = X3
& in(X4,relation_dom(X0)) )
<=> in(X3,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f184,plain,
~ in(sK12(relation_image(sK10,relation_inverse_image(sK10,sK9)),sK9),relation_image(sK10,relation_inverse_image(sK10,sK9))),
inference(unit_resulting_resolution,[],[f181,f151]) ).
fof(f151,plain,
! [X0,X1] :
( ~ in(sK12(X0,X1),X0)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU228+3 : TPTP v8.1.0. Released v3.2.0.
% 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
% 0.12/0.32 % Computer : n008.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Aug 30 14:56:55 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.17/0.44 % (19017)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)
% 0.17/0.47 % (19017)Instruction limit reached!
% 0.17/0.47 % (19017)------------------------------
% 0.17/0.47 % (19017)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.47 % (19026)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)
% 0.17/0.47 % (19034)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.17/0.47 % (19026)Refutation not found, incomplete strategy% (19026)------------------------------
% 0.17/0.47 % (19026)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.48 % (19017)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.48 % (19017)Termination reason: Unknown
% 0.17/0.48 % (19017)Termination phase: Saturation
% 0.17/0.48
% 0.17/0.48 % (19017)Memory used [KB]: 6140
% 0.17/0.48 % (19017)Time elapsed: 0.093 s
% 0.17/0.48 % (19017)Instructions burned: 14 (million)
% 0.17/0.48 % (19017)------------------------------
% 0.17/0.48 % (19017)------------------------------
% 0.17/0.48 % (19026)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.48 % (19026)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.48
% 0.17/0.48 % (19026)Memory used [KB]: 1535
% 0.17/0.48 % (19026)Time elapsed: 0.111 s
% 0.17/0.48 % (19026)Instructions burned: 5 (million)
% 0.17/0.48 % (19026)------------------------------
% 0.17/0.48 % (19026)------------------------------
% 0.17/0.48 % (19013)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.17/0.48 % (19016)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)
% 0.17/0.49 % (19019)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)
% 0.17/0.49 % (19016)First to succeed.
% 0.17/0.49 % (19021)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)
% 0.17/0.50 % (19025)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)
% 0.17/0.50 % (19018)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)
% 0.17/0.50 % (19014)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)
% 0.17/0.50 % (19035)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.17/0.50 % (19037)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)
% 0.17/0.50 % (19027)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)
% 0.17/0.50 % (19029)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.17/0.50 % (19042)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)
% 0.17/0.51 % (19029)Instruction limit reached!
% 0.17/0.51 % (19029)------------------------------
% 0.17/0.51 % (19029)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.51 % (19018)Instruction limit reached!
% 0.17/0.51 % (19018)------------------------------
% 0.17/0.51 % (19018)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.51 % (19040)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.17/0.51 % (19034)Instruction limit reached!
% 0.17/0.51 % (19034)------------------------------
% 0.17/0.51 % (19034)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.51 % (19034)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.51 % (19034)Termination reason: Unknown
% 0.17/0.51 % (19034)Termination phase: Saturation
% 0.17/0.51
% 0.17/0.51 % (19034)Memory used [KB]: 6396
% 0.17/0.51 % (19034)Time elapsed: 0.132 s
% 0.17/0.51 % (19034)Instructions burned: 31 (million)
% 0.17/0.51 % (19034)------------------------------
% 0.17/0.51 % (19034)------------------------------
% 0.17/0.51 % (19038)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.17/0.51 % (19030)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.17/0.51 % (19042)Instruction limit reached!
% 0.17/0.51 % (19042)------------------------------
% 0.17/0.51 % (19042)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.39/0.51 % (19025)Instruction limit reached!
% 1.39/0.51 % (19025)------------------------------
% 1.39/0.51 % (19025)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.39/0.51 % (19041)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 1.39/0.51 % (19016)Refutation found. Thanks to Tanya!
% 1.39/0.51 % SZS status Theorem for theBenchmark
% 1.39/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 1.39/0.52 % (19016)------------------------------
% 1.39/0.52 % (19016)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.39/0.52 % (19016)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.39/0.52 % (19016)Termination reason: Refutation
% 1.39/0.52
% 1.39/0.52 % (19016)Memory used [KB]: 6268
% 1.39/0.52 % (19016)Time elapsed: 0.109 s
% 1.39/0.52 % (19016)Instructions burned: 10 (million)
% 1.39/0.52 % (19016)------------------------------
% 1.39/0.52 % (19016)------------------------------
% 1.39/0.52 % (19009)Success in time 0.181 s
%------------------------------------------------------------------------------