TSTP Solution File: SEU051+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU051+1 : 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 : n017.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 18:26:27 EDT 2022
% Result : Theorem 1.65s 0.59s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 79 ( 18 unt; 0 def)
% Number of atoms : 425 ( 69 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 537 ( 191 ~; 185 |; 122 &)
% ( 19 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 238 ( 201 !; 37 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f287,plain,
$false,
inference(subsumption_resolution,[],[f286,f165]) ).
fof(f165,plain,
~ in(sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)),relation_image(sK2,sK4)),
inference(unit_resulting_resolution,[],[f102,f109]) ).
fof(f109,plain,
! [X0,X1] :
( ~ in(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ( ~ in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f70,f71]) ).
fof(f71,plain,
! [X0,X1] :
( ? [X3] :
( ~ in(X3,X1)
& in(X3,X0) )
=> ( ~ in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
! [X0,X1] :
( ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X3] :
( ~ in(X3,X1)
& in(X3,X0) ) ) ),
inference(rectify,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
<=> subset(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f102,plain,
~ subset(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
( relation(sK2)
& function(sK2)
& ~ subset(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f64,f65]) ).
fof(f65,plain,
( ? [X0,X1,X2] :
( relation(X0)
& function(X0)
& ~ subset(relation_image(relation_rng_restriction(X1,X0),X2),relation_image(X0,X2)) )
=> ( relation(sK2)
& function(sK2)
& ~ subset(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)) ) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
? [X0,X1,X2] :
( relation(X0)
& function(X0)
& ~ subset(relation_image(relation_rng_restriction(X1,X0),X2),relation_image(X0,X2)) ),
inference(rectify,[],[f48]) ).
fof(f48,plain,
? [X2,X1,X0] :
( relation(X2)
& function(X2)
& ~ subset(relation_image(relation_rng_restriction(X1,X2),X0),relation_image(X2,X0)) ),
inference(flattening,[],[f47]) ).
fof(f47,plain,
? [X0,X1,X2] :
( ~ subset(relation_image(relation_rng_restriction(X1,X2),X0),relation_image(X2,X0))
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,plain,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> subset(relation_image(relation_rng_restriction(X1,X2),X0),relation_image(X2,X0)) ),
inference(rectify,[],[f28]) ).
fof(f28,negated_conjecture,
~ ! [X1,X0,X2] :
( ( relation(X2)
& function(X2) )
=> subset(relation_image(relation_rng_restriction(X0,X2),X1),relation_image(X2,X1)) ),
inference(negated_conjecture,[],[f27]) ).
fof(f27,conjecture,
! [X1,X0,X2] :
( ( relation(X2)
& function(X2) )
=> subset(relation_image(relation_rng_restriction(X0,X2),X1),relation_image(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_funct_1) ).
fof(f286,plain,
in(sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)),relation_image(sK2,sK4)),
inference(forward_demodulation,[],[f280,f223]) ).
fof(f223,plain,
sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)) = apply(sK2,sK10(relation_rng_restriction(sK3,sK2),sK4,sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)))),
inference(forward_demodulation,[],[f222,f181]) ).
fof(f181,plain,
apply(relation_rng_restriction(sK3,sK2),sK10(relation_rng_restriction(sK3,sK2),sK4,sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)))) = sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)),
inference(unit_resulting_resolution,[],[f151,f152,f163,f148]) ).
fof(f148,plain,
! [X2,X3,X0] :
( ~ in(X3,relation_image(X0,X2))
| ~ relation(X0)
| ~ function(X0)
| apply(X0,sK10(X0,X2,X3)) = X3 ),
inference(equality_resolution,[],[f132]) ).
fof(f132,plain,
! [X2,X3,X0,X1] :
( apply(X0,sK10(X0,X2,X3)) = X3
| ~ in(X3,X1)
| relation_image(X0,X2) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ! [X1,X2] :
( ( ! [X3] :
( ( ( in(sK10(X0,X2,X3),relation_dom(X0))
& in(sK10(X0,X2,X3),X2)
& apply(X0,sK10(X0,X2,X3)) = X3 )
| ~ in(X3,X1) )
& ( in(X3,X1)
| ! [X5] :
( ~ in(X5,relation_dom(X0))
| ~ in(X5,X2)
| apply(X0,X5) != X3 ) ) )
| relation_image(X0,X2) != X1 )
& ( relation_image(X0,X2) = X1
| ( ( ~ in(sK11(X0,X1,X2),X1)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X2)
| apply(X0,X7) != sK11(X0,X1,X2) ) )
& ( in(sK11(X0,X1,X2),X1)
| ( in(sK12(X0,X1,X2),relation_dom(X0))
& in(sK12(X0,X1,X2),X2)
& sK11(X0,X1,X2) = apply(X0,sK12(X0,X1,X2)) ) ) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f84,f87,f86,f85]) ).
fof(f85,plain,
! [X0,X2,X3] :
( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X2)
& apply(X0,X4) = X3 )
=> ( in(sK10(X0,X2,X3),relation_dom(X0))
& in(sK10(X0,X2,X3),X2)
& apply(X0,sK10(X0,X2,X3)) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ? [X6] :
( ( ~ in(X6,X1)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X2)
| apply(X0,X7) != X6 ) )
& ( in(X6,X1)
| ? [X8] :
( in(X8,relation_dom(X0))
& in(X8,X2)
& apply(X0,X8) = X6 ) ) )
=> ( ( ~ in(sK11(X0,X1,X2),X1)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X2)
| apply(X0,X7) != sK11(X0,X1,X2) ) )
& ( in(sK11(X0,X1,X2),X1)
| ? [X8] :
( in(X8,relation_dom(X0))
& in(X8,X2)
& sK11(X0,X1,X2) = apply(X0,X8) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ? [X8] :
( in(X8,relation_dom(X0))
& in(X8,X2)
& sK11(X0,X1,X2) = apply(X0,X8) )
=> ( in(sK12(X0,X1,X2),relation_dom(X0))
& in(sK12(X0,X1,X2),X2)
& sK11(X0,X1,X2) = apply(X0,sK12(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
! [X0] :
( ! [X1,X2] :
( ( ! [X3] :
( ( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X2)
& apply(X0,X4) = X3 )
| ~ in(X3,X1) )
& ( in(X3,X1)
| ! [X5] :
( ~ in(X5,relation_dom(X0))
| ~ in(X5,X2)
| apply(X0,X5) != X3 ) ) )
| relation_image(X0,X2) != X1 )
& ( relation_image(X0,X2) = X1
| ? [X6] :
( ( ~ in(X6,X1)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X2)
| apply(X0,X7) != X6 ) )
& ( in(X6,X1)
| ? [X8] :
( in(X8,relation_dom(X0))
& in(X8,X2)
& apply(X0,X8) = X6 ) ) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f83]) ).
fof(f83,plain,
! [X0] :
( ! [X2,X1] :
( ( ! [X3] :
( ( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& apply(X0,X4) = X3 )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 ) ) )
| relation_image(X0,X1) != X2 )
& ( relation_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 ) )
& ( in(X3,X2)
| ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& apply(X0,X4) = X3 ) ) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ! [X2,X1] :
( ! [X3] :
( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& apply(X0,X4) = X3 )
<=> in(X3,X2) )
<=> relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ! [X2,X1] :
( ! [X3] :
( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& apply(X0,X4) = X3 )
<=> in(X3,X2) )
<=> relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X2,X1] :
( ! [X3] :
( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& apply(X0,X4) = X3 )
<=> in(X3,X2) )
<=> relation_image(X0,X1) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f163,plain,
in(sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)),relation_image(relation_rng_restriction(sK3,sK2),sK4)),
inference(unit_resulting_resolution,[],[f102,f108]) ).
fof(f108,plain,
! [X0,X1] :
( in(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f152,plain,
! [X0] : function(relation_rng_restriction(X0,sK2)),
inference(unit_resulting_resolution,[],[f103,f104,f101]) ).
fof(f101,plain,
! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( ~ relation(X1)
| ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) )
| ~ function(X1) ),
inference(rectify,[],[f52]) ).
fof(f52,plain,
! [X1,X0] :
( ~ relation(X0)
| ( function(relation_rng_restriction(X1,X0))
& relation(relation_rng_restriction(X1,X0)) )
| ~ function(X0) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( ( function(relation_rng_restriction(X1,X0))
& relation(relation_rng_restriction(X1,X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( ( function(X0)
& relation(X0) )
=> ( function(relation_rng_restriction(X1,X0))
& relation(relation_rng_restriction(X1,X0)) ) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X1,X0] :
( ( relation(X1)
& function(X1) )
=> ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(f104,plain,
relation(sK2),
inference(cnf_transformation,[],[f66]) ).
fof(f103,plain,
function(sK2),
inference(cnf_transformation,[],[f66]) ).
fof(f151,plain,
! [X0] : relation(relation_rng_restriction(X0,sK2)),
inference(unit_resulting_resolution,[],[f103,f104,f100]) ).
fof(f100,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f222,plain,
apply(relation_rng_restriction(sK3,sK2),sK10(relation_rng_restriction(sK3,sK2),sK4,sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)))) = apply(sK2,sK10(relation_rng_restriction(sK3,sK2),sK4,sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)))),
inference(unit_resulting_resolution,[],[f182,f200,f115]) ).
fof(f115,plain,
! [X2,X0,X1,X6] :
( ~ sP0(X0,X1,X2)
| ~ in(X6,relation_dom(X2))
| apply(X2,X6) = apply(X0,X6) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ~ in(sK8(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK8(X0,X1,X2)),X1)
| ~ in(sK8(X0,X1,X2),relation_dom(X2)) )
& ( ( in(sK8(X0,X1,X2),relation_dom(X0))
& in(apply(X0,sK8(X0,X1,X2)),X1) )
| in(sK8(X0,X1,X2),relation_dom(X2)) ) )
| ( apply(X2,sK9(X0,X2)) != apply(X0,sK9(X0,X2))
& in(sK9(X0,X2),relation_dom(X2)) ) )
& ( ( ! [X5] :
( ( in(X5,relation_dom(X2))
| ~ in(X5,relation_dom(X0))
| ~ in(apply(X0,X5),X1) )
& ( ( in(X5,relation_dom(X0))
& in(apply(X0,X5),X1) )
| ~ in(X5,relation_dom(X2)) ) )
& ! [X6] :
( apply(X2,X6) = apply(X0,X6)
| ~ in(X6,relation_dom(X2)) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f79,f81,f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X2)) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,relation_dom(X2)) ) )
=> ( ( ~ in(sK8(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK8(X0,X1,X2)),X1)
| ~ in(sK8(X0,X1,X2),relation_dom(X2)) )
& ( ( in(sK8(X0,X1,X2),relation_dom(X0))
& in(apply(X0,sK8(X0,X1,X2)),X1) )
| in(sK8(X0,X1,X2),relation_dom(X2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0,X2] :
( ? [X4] :
( apply(X0,X4) != apply(X2,X4)
& in(X4,relation_dom(X2)) )
=> ( apply(X2,sK9(X0,X2)) != apply(X0,sK9(X0,X2))
& in(sK9(X0,X2),relation_dom(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X2)) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,relation_dom(X2)) ) )
| ? [X4] :
( apply(X0,X4) != apply(X2,X4)
& in(X4,relation_dom(X2)) ) )
& ( ( ! [X5] :
( ( in(X5,relation_dom(X2))
| ~ in(X5,relation_dom(X0))
| ~ in(apply(X0,X5),X1) )
& ( ( in(X5,relation_dom(X0))
& in(apply(X0,X5),X1) )
| ~ in(X5,relation_dom(X2)) ) )
& ! [X6] :
( apply(X2,X6) = apply(X0,X6)
| ~ in(X6,relation_dom(X2)) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f78]) ).
fof(f78,plain,
! [X2,X1,X0] :
( ( sP0(X2,X1,X0)
| ? [X3] :
( ( ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),X1)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X1) )
| in(X3,relation_dom(X0)) ) )
| ? [X4] :
( apply(X0,X4) != apply(X2,X4)
& in(X4,relation_dom(X0)) ) )
& ( ( ! [X3] :
( ( in(X3,relation_dom(X0))
| ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),X1) )
& ( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X1) )
| ~ in(X3,relation_dom(X0)) ) )
& ! [X4] :
( apply(X0,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X0)) ) )
| ~ sP0(X2,X1,X0) ) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X2,X1,X0] :
( ( sP0(X2,X1,X0)
| ? [X3] :
( ( ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),X1)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X1) )
| in(X3,relation_dom(X0)) ) )
| ? [X4] :
( apply(X0,X4) != apply(X2,X4)
& in(X4,relation_dom(X0)) ) )
& ( ( ! [X3] :
( ( in(X3,relation_dom(X0))
| ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),X1) )
& ( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X1) )
| ~ in(X3,relation_dom(X0)) ) )
& ! [X4] :
( apply(X0,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X0)) ) )
| ~ sP0(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X2,X1,X0] :
( sP0(X2,X1,X0)
<=> ( ! [X3] :
( in(X3,relation_dom(X0))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X1) ) )
& ! [X4] :
( apply(X0,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f200,plain,
! [X0] : sP0(sK2,X0,relation_rng_restriction(X0,sK2)),
inference(unit_resulting_resolution,[],[f169,f145]) ).
fof(f145,plain,
! [X2,X1] :
( ~ sP1(relation_rng_restriction(X2,X1),X1,X2)
| sP0(X1,X2,relation_rng_restriction(X2,X1)) ),
inference(equality_resolution,[],[f114]) ).
fof(f114,plain,
! [X2,X0,X1] :
( sP0(X1,X2,X0)
| relation_rng_restriction(X2,X1) != X0
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( ( sP0(X1,X2,X0)
| relation_rng_restriction(X2,X1) != X0 )
& ( relation_rng_restriction(X2,X1) = X0
| ~ sP0(X1,X2,X0) ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f75]) ).
fof(f75,plain,
! [X0,X2,X1] :
( ( ( sP0(X2,X1,X0)
| relation_rng_restriction(X1,X2) != X0 )
& ( relation_rng_restriction(X1,X2) = X0
| ~ sP0(X2,X1,X0) ) )
| ~ sP1(X0,X2,X1) ),
inference(nnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X2,X1] :
( ( sP0(X2,X1,X0)
<=> relation_rng_restriction(X1,X2) = X0 )
| ~ sP1(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f169,plain,
! [X0,X1] : sP1(relation_rng_restriction(X0,sK2),sK2,X1),
inference(unit_resulting_resolution,[],[f103,f104,f151,f152,f125]) ).
fof(f125,plain,
! [X2,X0,X1] :
( sP1(X0,X2,X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ function(X2) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ function(X0)
| ! [X2] :
( ~ relation(X2)
| ~ function(X2)
| sP1(X0,X2,X1) )
| ~ relation(X0) ),
inference(definition_folding,[],[f56,f61,f60]) ).
fof(f56,plain,
! [X0,X1] :
( ~ function(X0)
| ! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ( ( ! [X3] :
( in(X3,relation_dom(X0))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X1) ) )
& ! [X4] :
( apply(X0,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X0)) ) )
<=> relation_rng_restriction(X1,X2) = X0 ) )
| ~ relation(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X1,X0] :
( ! [X2] :
( ( ( ! [X3] :
( in(X3,relation_dom(X0))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X1) ) )
& ! [X4] :
( apply(X0,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X0)) ) )
<=> relation_rng_restriction(X1,X2) = X0 )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,plain,
! [X1,X0] :
( ( function(X0)
& relation(X0) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_rng_restriction(X1,X2) = X0
<=> ( ! [X4] :
( in(X4,relation_dom(X0))
=> apply(X0,X4) = apply(X2,X4) )
& ! [X3] :
( in(X3,relation_dom(X0))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X1) ) ) ) ) ) ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X1,X0] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( ! [X3] :
( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) )
<=> in(X3,relation_dom(X1)) )
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X2,X3) = apply(X1,X3) ) )
<=> relation_rng_restriction(X0,X2) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_1) ).
fof(f182,plain,
in(sK10(relation_rng_restriction(sK3,sK2),sK4,sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4))),relation_dom(relation_rng_restriction(sK3,sK2))),
inference(unit_resulting_resolution,[],[f152,f151,f163,f146]) ).
fof(f146,plain,
! [X2,X3,X0] :
( in(sK10(X0,X2,X3),relation_dom(X0))
| ~ in(X3,relation_image(X0,X2))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f134]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( in(sK10(X0,X2,X3),relation_dom(X0))
| ~ in(X3,X1)
| relation_image(X0,X2) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f280,plain,
in(apply(sK2,sK10(relation_rng_restriction(sK3,sK2),sK4,sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)))),relation_image(sK2,sK4)),
inference(unit_resulting_resolution,[],[f103,f104,f180,f221,f150]) ).
fof(f150,plain,
! [X2,X0,X5] :
( in(apply(X0,X5),relation_image(X0,X2))
| ~ in(X5,X2)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f149]) ).
fof(f149,plain,
! [X2,X0,X1,X5] :
( in(apply(X0,X5),X1)
| ~ in(X5,relation_dom(X0))
| ~ in(X5,X2)
| relation_image(X0,X2) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f131]) ).
fof(f131,plain,
! [X2,X3,X0,X1,X5] :
( in(X3,X1)
| ~ in(X5,relation_dom(X0))
| ~ in(X5,X2)
| apply(X0,X5) != X3
| relation_image(X0,X2) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f221,plain,
in(sK10(relation_rng_restriction(sK3,sK2),sK4,sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4))),relation_dom(sK2)),
inference(unit_resulting_resolution,[],[f182,f200,f117]) ).
fof(f117,plain,
! [X2,X0,X1,X5] :
( ~ sP0(X0,X1,X2)
| in(X5,relation_dom(X0))
| ~ in(X5,relation_dom(X2)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f180,plain,
in(sK10(relation_rng_restriction(sK3,sK2),sK4,sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4))),sK4),
inference(unit_resulting_resolution,[],[f151,f152,f163,f147]) ).
fof(f147,plain,
! [X2,X3,X0] :
( in(sK10(X0,X2,X3),X2)
| ~ relation(X0)
| ~ function(X0)
| ~ in(X3,relation_image(X0,X2)) ),
inference(equality_resolution,[],[f133]) ).
fof(f133,plain,
! [X2,X3,X0,X1] :
( in(sK10(X0,X2,X3),X2)
| ~ in(X3,X1)
| relation_image(X0,X2) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU051+1 : 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
% 0.13/0.34 % Computer : n017.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 14:04:50 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.39/0.55 % (20718)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)
% 1.39/0.56 % (20723)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)
% 1.39/0.56 % (20715)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)
% 1.39/0.56 % (20735)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 1.65/0.57 % (20723)Instruction limit reached!
% 1.65/0.57 % (20723)------------------------------
% 1.65/0.57 % (20723)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.65/0.57 % (20726)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 1.65/0.57 % (20723)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.65/0.57 % (20723)Termination reason: Unknown
% 1.65/0.57 % (20723)Termination phase: Saturation
% 1.65/0.57
% 1.65/0.57 % (20723)Memory used [KB]: 6140
% 1.65/0.57 % (20723)Time elapsed: 0.139 s
% 1.65/0.57 % (20723)Instructions burned: 7 (million)
% 1.65/0.57 % (20723)------------------------------
% 1.65/0.57 % (20723)------------------------------
% 1.65/0.58 % (20736)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)
% 1.65/0.58 % (20732)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)
% 1.65/0.58 % (20726)Instruction limit reached!
% 1.65/0.58 % (20726)------------------------------
% 1.65/0.58 % (20726)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.65/0.58 % (20726)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.65/0.58 % (20726)Termination reason: Unknown
% 1.65/0.58 % (20726)Termination phase: Property scanning
% 1.65/0.58
% 1.65/0.58 % (20726)Memory used [KB]: 1535
% 1.65/0.58 % (20726)Time elapsed: 0.005 s
% 1.65/0.58 % (20726)Instructions burned: 3 (million)
% 1.65/0.58 % (20726)------------------------------
% 1.65/0.58 % (20726)------------------------------
% 1.65/0.58 % (20732)Refutation not found, incomplete strategy% (20732)------------------------------
% 1.65/0.58 % (20732)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.65/0.58 % (20732)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.65/0.58 % (20732)Termination reason: Refutation not found, incomplete strategy
% 1.65/0.58
% 1.65/0.58 % (20732)Memory used [KB]: 6012
% 1.65/0.58 % (20732)Time elapsed: 0.155 s
% 1.65/0.58 % (20732)Instructions burned: 4 (million)
% 1.65/0.58 % (20732)------------------------------
% 1.65/0.58 % (20732)------------------------------
% 1.65/0.58 % (20715)First to succeed.
% 1.65/0.59 % (20722)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 1.65/0.59 % (20720)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)
% 1.65/0.59 % (20716)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)
% 1.65/0.59 % (20717)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)
% 1.65/0.59 % (20715)Refutation found. Thanks to Tanya!
% 1.65/0.59 % SZS status Theorem for theBenchmark
% 1.65/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 1.65/0.59 % (20715)------------------------------
% 1.65/0.59 % (20715)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.65/0.59 % (20715)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.65/0.59 % (20715)Termination reason: Refutation
% 1.65/0.59
% 1.65/0.59 % (20715)Memory used [KB]: 6396
% 1.65/0.59 % (20715)Time elapsed: 0.160 s
% 1.65/0.59 % (20715)Instructions burned: 16 (million)
% 1.65/0.59 % (20715)------------------------------
% 1.65/0.59 % (20715)------------------------------
% 1.65/0.59 % (20711)Success in time 0.238 s
%------------------------------------------------------------------------------