TSTP Solution File: SEU221+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU221+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n022.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 18:27:36 EDT 2022
% Result : Theorem 1.49s 0.61s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of formulae : 81 ( 12 unt; 0 def)
% Number of atoms : 423 ( 130 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 555 ( 213 ~; 197 |; 109 &)
% ( 10 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 109 ( 92 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f305,plain,
$false,
inference(subsumption_resolution,[],[f304,f150]) ).
fof(f150,plain,
relation(sK5),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
( relation(sK5)
& ~ one_to_one(function_inverse(sK5))
& function(sK5)
& one_to_one(sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f82,f99]) ).
fof(f99,plain,
( ? [X0] :
( relation(X0)
& ~ one_to_one(function_inverse(X0))
& function(X0)
& one_to_one(X0) )
=> ( relation(sK5)
& ~ one_to_one(function_inverse(sK5))
& function(sK5)
& one_to_one(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
? [X0] :
( relation(X0)
& ~ one_to_one(function_inverse(X0))
& function(X0)
& one_to_one(X0) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
? [X0] :
( ~ one_to_one(function_inverse(X0))
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> one_to_one(function_inverse(X0)) ) ),
inference(negated_conjecture,[],[f36]) ).
fof(f36,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> one_to_one(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).
fof(f304,plain,
~ relation(sK5),
inference(subsumption_resolution,[],[f303,f148]) ).
fof(f148,plain,
function(sK5),
inference(cnf_transformation,[],[f100]) ).
fof(f303,plain,
( ~ function(sK5)
| ~ relation(sK5) ),
inference(resolution,[],[f302,f140]) ).
fof(f140,plain,
! [X0] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f302,plain,
~ function(function_inverse(sK5)),
inference(subsumption_resolution,[],[f301,f233]) ).
fof(f233,plain,
sK12(function_inverse(sK5)) != sK11(function_inverse(sK5)),
inference(subsumption_resolution,[],[f232,f148]) ).
fof(f232,plain,
( sK12(function_inverse(sK5)) != sK11(function_inverse(sK5))
| ~ function(sK5) ),
inference(subsumption_resolution,[],[f231,f150]) ).
fof(f231,plain,
( sK12(function_inverse(sK5)) != sK11(function_inverse(sK5))
| ~ relation(sK5)
| ~ function(sK5) ),
inference(resolution,[],[f230,f140]) ).
fof(f230,plain,
( ~ function(function_inverse(sK5))
| sK12(function_inverse(sK5)) != sK11(function_inverse(sK5)) ),
inference(subsumption_resolution,[],[f217,f224]) ).
fof(f224,plain,
relation(function_inverse(sK5)),
inference(subsumption_resolution,[],[f215,f150]) ).
fof(f215,plain,
( ~ relation(sK5)
| relation(function_inverse(sK5)) ),
inference(resolution,[],[f148,f139]) ).
fof(f139,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f217,plain,
( sK12(function_inverse(sK5)) != sK11(function_inverse(sK5))
| ~ function(function_inverse(sK5))
| ~ relation(function_inverse(sK5)) ),
inference(resolution,[],[f149,f185]) ).
fof(f185,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| sK12(X0) != sK11(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ~ relation(X0)
| ( ( one_to_one(X0)
| ( apply(X0,sK11(X0)) = apply(X0,sK12(X0))
& in(sK11(X0),relation_dom(X0))
& sK12(X0) != sK11(X0)
& in(sK12(X0),relation_dom(X0)) ) )
& ( ! [X3,X4] :
( apply(X0,X3) != apply(X0,X4)
| ~ in(X3,relation_dom(X0))
| X3 = X4
| ~ in(X4,relation_dom(X0)) )
| ~ one_to_one(X0) ) )
| ~ function(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f117,f118]) ).
fof(f118,plain,
! [X0] :
( ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X1,relation_dom(X0))
& X1 != X2
& in(X2,relation_dom(X0)) )
=> ( apply(X0,sK11(X0)) = apply(X0,sK12(X0))
& in(sK11(X0),relation_dom(X0))
& sK12(X0) != sK11(X0)
& in(sK12(X0),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
! [X0] :
( ~ relation(X0)
| ( ( one_to_one(X0)
| ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X1,relation_dom(X0))
& X1 != X2
& in(X2,relation_dom(X0)) ) )
& ( ! [X3,X4] :
( apply(X0,X3) != apply(X0,X4)
| ~ in(X3,relation_dom(X0))
| X3 = X4
| ~ in(X4,relation_dom(X0)) )
| ~ one_to_one(X0) ) )
| ~ function(X0) ),
inference(rectify,[],[f116]) ).
fof(f116,plain,
! [X0] :
( ~ relation(X0)
| ( ( one_to_one(X0)
| ? [X2,X1] :
( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& X1 != X2
& in(X1,relation_dom(X0)) ) )
& ( ! [X2,X1] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| X1 = X2
| ~ in(X1,relation_dom(X0)) )
| ~ one_to_one(X0) ) )
| ~ function(X0) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ~ relation(X0)
| ( one_to_one(X0)
<=> ! [X2,X1] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| X1 = X2
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> X1 = X2 ) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
<=> ! [X2,X1] :
( ( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f149,plain,
~ one_to_one(function_inverse(sK5)),
inference(cnf_transformation,[],[f100]) ).
fof(f301,plain,
( ~ function(function_inverse(sK5))
| sK12(function_inverse(sK5)) = sK11(function_inverse(sK5)) ),
inference(forward_demodulation,[],[f284,f287]) ).
fof(f287,plain,
apply(sK5,apply(function_inverse(sK5),sK11(function_inverse(sK5)))) = sK11(function_inverse(sK5)),
inference(subsumption_resolution,[],[f286,f150]) ).
fof(f286,plain,
( apply(sK5,apply(function_inverse(sK5),sK11(function_inverse(sK5)))) = sK11(function_inverse(sK5))
| ~ relation(sK5) ),
inference(subsumption_resolution,[],[f285,f148]) ).
fof(f285,plain,
( apply(sK5,apply(function_inverse(sK5),sK11(function_inverse(sK5)))) = sK11(function_inverse(sK5))
| ~ function(sK5)
| ~ relation(sK5) ),
inference(resolution,[],[f263,f140]) ).
fof(f263,plain,
( ~ function(function_inverse(sK5))
| apply(sK5,apply(function_inverse(sK5),sK11(function_inverse(sK5)))) = sK11(function_inverse(sK5)) ),
inference(resolution,[],[f258,f248]) ).
fof(f248,plain,
( in(sK11(function_inverse(sK5)),relation_dom(function_inverse(sK5)))
| ~ function(function_inverse(sK5)) ),
inference(subsumption_resolution,[],[f219,f224]) ).
fof(f219,plain,
( ~ relation(function_inverse(sK5))
| in(sK11(function_inverse(sK5)),relation_dom(function_inverse(sK5)))
| ~ function(function_inverse(sK5)) ),
inference(resolution,[],[f149,f186]) ).
fof(f186,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| in(sK11(X0),relation_dom(X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f258,plain,
! [X3] :
( ~ in(X3,relation_dom(function_inverse(sK5)))
| apply(sK5,apply(function_inverse(sK5),X3)) = X3 ),
inference(forward_demodulation,[],[f257,f226]) ).
fof(f226,plain,
relation_rng(sK5) = relation_dom(function_inverse(sK5)),
inference(subsumption_resolution,[],[f225,f150]) ).
fof(f225,plain,
( ~ relation(sK5)
| relation_rng(sK5) = relation_dom(function_inverse(sK5)) ),
inference(subsumption_resolution,[],[f210,f148]) ).
fof(f210,plain,
( ~ function(sK5)
| relation_rng(sK5) = relation_dom(function_inverse(sK5))
| ~ relation(sK5) ),
inference(subsumption_resolution,[],[f209,f140]) ).
fof(f209,plain,
( ~ function(sK5)
| ~ function(function_inverse(sK5))
| relation_rng(sK5) = relation_dom(function_inverse(sK5))
| ~ relation(sK5) ),
inference(subsumption_resolution,[],[f207,f139]) ).
fof(f207,plain,
( relation_rng(sK5) = relation_dom(function_inverse(sK5))
| ~ relation(function_inverse(sK5))
| ~ function(function_inverse(sK5))
| ~ relation(sK5)
| ~ function(sK5) ),
inference(resolution,[],[f147,f202]) ).
fof(f202,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ relation(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ function(X0) ),
inference(equality_resolution,[],[f171]) ).
fof(f171,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| relation_rng(X0) = relation_dom(X1)
| function_inverse(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ( ( ( ! [X2,X3] :
( ( apply(X0,X2) != X3
| ( apply(X1,X3) = X2
& in(X3,relation_rng(X0)) )
| ~ in(X2,relation_dom(X0)) )
& sP0(X0,X3,X2,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 )
& ( function_inverse(X0) = X1
| ( apply(X0,sK8(X0,X1)) = sK9(X0,X1)
& ( apply(X1,sK9(X0,X1)) != sK8(X0,X1)
| ~ in(sK9(X0,X1),relation_rng(X0)) )
& in(sK8(X0,X1),relation_dom(X0)) )
| ~ sP0(X0,sK9(X0,X1),sK8(X0,X1),X1)
| relation_rng(X0) != relation_dom(X1) ) )
| ~ relation(X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f110,f111]) ).
fof(f111,plain,
! [X0,X1] :
( ? [X4,X5] :
( ( apply(X0,X4) = X5
& ( apply(X1,X5) != X4
| ~ in(X5,relation_rng(X0)) )
& in(X4,relation_dom(X0)) )
| ~ sP0(X0,X5,X4,X1) )
=> ( ( apply(X0,sK8(X0,X1)) = sK9(X0,X1)
& ( apply(X1,sK9(X0,X1)) != sK8(X0,X1)
| ~ in(sK9(X0,X1),relation_rng(X0)) )
& in(sK8(X0,X1),relation_dom(X0)) )
| ~ sP0(X0,sK9(X0,X1),sK8(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ( ( ( ! [X2,X3] :
( ( apply(X0,X2) != X3
| ( apply(X1,X3) = X2
& in(X3,relation_rng(X0)) )
| ~ in(X2,relation_dom(X0)) )
& sP0(X0,X3,X2,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 )
& ( function_inverse(X0) = X1
| ? [X4,X5] :
( ( apply(X0,X4) = X5
& ( apply(X1,X5) != X4
| ~ in(X5,relation_rng(X0)) )
& in(X4,relation_dom(X0)) )
| ~ sP0(X0,X5,X4,X1) )
| relation_rng(X0) != relation_dom(X1) ) )
| ~ relation(X1) ) ),
inference(rectify,[],[f109]) ).
fof(f109,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ( ( ( ! [X2,X3] :
( ( apply(X0,X2) != X3
| ( apply(X1,X3) = X2
& in(X3,relation_rng(X0)) )
| ~ in(X2,relation_dom(X0)) )
& sP0(X0,X3,X2,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 )
& ( function_inverse(X0) = X1
| ? [X2,X3] :
( ( apply(X0,X2) = X3
& ( apply(X1,X3) != X2
| ~ in(X3,relation_rng(X0)) )
& in(X2,relation_dom(X0)) )
| ~ sP0(X0,X3,X2,X1) )
| relation_rng(X0) != relation_dom(X1) ) )
| ~ relation(X1) ) ),
inference(flattening,[],[f108]) ).
fof(f108,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ( ( ( ! [X2,X3] :
( ( apply(X0,X2) != X3
| ( apply(X1,X3) = X2
& in(X3,relation_rng(X0)) )
| ~ in(X2,relation_dom(X0)) )
& sP0(X0,X3,X2,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 )
& ( function_inverse(X0) = X1
| ? [X2,X3] :
( ( apply(X0,X2) = X3
& ( apply(X1,X3) != X2
| ~ in(X3,relation_rng(X0)) )
& in(X2,relation_dom(X0)) )
| ~ sP0(X0,X3,X2,X1) )
| relation_rng(X0) != relation_dom(X1) ) )
| ~ relation(X1) ) ),
inference(nnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ( ( ! [X2,X3] :
( ( apply(X0,X2) != X3
| ( apply(X1,X3) = X2
& in(X3,relation_rng(X0)) )
| ~ in(X2,relation_dom(X0)) )
& sP0(X0,X3,X2,X1) )
& relation_rng(X0) = relation_dom(X1) )
<=> function_inverse(X0) = X1 )
| ~ relation(X1) ) ),
inference(definition_folding,[],[f70,f87]) ).
fof(f87,plain,
! [X0,X3,X2,X1] :
( sP0(X0,X3,X2,X1)
<=> ( ~ in(X3,relation_rng(X0))
| apply(X1,X3) != X2
| ( apply(X0,X2) = X3
& in(X2,relation_dom(X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f70,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ( ( ! [X2,X3] :
( ( apply(X0,X2) != X3
| ( apply(X1,X3) = X2
& in(X3,relation_rng(X0)) )
| ~ in(X2,relation_dom(X0)) )
& ( ~ in(X3,relation_rng(X0))
| apply(X1,X3) != X2
| ( apply(X0,X2) = X3
& in(X2,relation_dom(X0)) ) ) )
& relation_rng(X0) = relation_dom(X1) )
<=> function_inverse(X0) = X1 )
| ~ relation(X1) ) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X3) = X2
& in(X3,relation_rng(X0)) )
| ~ in(X2,relation_dom(X0))
| apply(X0,X2) != X3 )
& ( ( apply(X0,X2) = X3
& in(X2,relation_dom(X0)) )
| ~ in(X3,relation_rng(X0))
| apply(X1,X3) != X2 ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( in(X2,relation_dom(X0))
& apply(X0,X2) = X3 )
=> ( apply(X1,X3) = X2
& in(X3,relation_rng(X0)) ) )
& ( ( in(X3,relation_rng(X0))
& apply(X1,X3) = X2 )
=> ( apply(X0,X2) = X3
& in(X2,relation_dom(X0)) ) ) )
& relation_rng(X0) = relation_dom(X1) ) ) ) ) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( function_inverse(X0) = X1
<=> ( relation_rng(X0) = relation_dom(X1)
& ! [X3,X2] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
=> ( in(X3,relation_dom(X0))
& apply(X0,X3) = X2 ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
=> ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f147,plain,
one_to_one(sK5),
inference(cnf_transformation,[],[f100]) ).
fof(f257,plain,
! [X3] :
( apply(sK5,apply(function_inverse(sK5),X3)) = X3
| ~ in(X3,relation_rng(sK5)) ),
inference(subsumption_resolution,[],[f256,f148]) ).
fof(f256,plain,
! [X3] :
( apply(sK5,apply(function_inverse(sK5),X3)) = X3
| ~ function(sK5)
| ~ in(X3,relation_rng(sK5)) ),
inference(subsumption_resolution,[],[f205,f150]) ).
fof(f205,plain,
! [X3] :
( ~ relation(sK5)
| ~ function(sK5)
| ~ in(X3,relation_rng(sK5))
| apply(sK5,apply(function_inverse(sK5),X3)) = X3 ),
inference(resolution,[],[f147,f176]) ).
fof(f176,plain,
! [X0,X1] :
( ~ one_to_one(X0)
| apply(X0,apply(function_inverse(X0),X1)) = X1
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_rng(X0)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ~ one_to_one(X0)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0)
| ~ function(X0)
| ( apply(relation_composition(function_inverse(X0),X0),X1) = X1
& apply(X0,apply(function_inverse(X0),X1)) = X1 ) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( ( apply(relation_composition(function_inverse(X0),X0),X1) = X1
& apply(X0,apply(function_inverse(X0),X1)) = X1 )
| ~ one_to_one(X0)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( ( relation(X0)
& function(X0) )
=> ( ( one_to_one(X0)
& in(X1,relation_rng(X0)) )
=> ( apply(relation_composition(function_inverse(X0),X0),X1) = X1
& apply(X0,apply(function_inverse(X0),X1)) = X1 ) ) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X1,X0] :
( ( function(X1)
& relation(X1) )
=> ( ( in(X0,relation_rng(X1))
& one_to_one(X1) )
=> ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
& apply(X1,apply(function_inverse(X1),X0)) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
fof(f284,plain,
( apply(sK5,apply(function_inverse(sK5),sK11(function_inverse(sK5)))) = sK12(function_inverse(sK5))
| ~ function(function_inverse(sK5)) ),
inference(forward_demodulation,[],[f262,f276]) ).
fof(f276,plain,
apply(function_inverse(sK5),sK11(function_inverse(sK5))) = apply(function_inverse(sK5),sK12(function_inverse(sK5))),
inference(subsumption_resolution,[],[f275,f150]) ).
fof(f275,plain,
( apply(function_inverse(sK5),sK11(function_inverse(sK5))) = apply(function_inverse(sK5),sK12(function_inverse(sK5)))
| ~ relation(sK5) ),
inference(subsumption_resolution,[],[f274,f148]) ).
fof(f274,plain,
( apply(function_inverse(sK5),sK11(function_inverse(sK5))) = apply(function_inverse(sK5),sK12(function_inverse(sK5)))
| ~ function(sK5)
| ~ relation(sK5) ),
inference(resolution,[],[f273,f140]) ).
fof(f273,plain,
( ~ function(function_inverse(sK5))
| apply(function_inverse(sK5),sK11(function_inverse(sK5))) = apply(function_inverse(sK5),sK12(function_inverse(sK5))) ),
inference(subsumption_resolution,[],[f220,f224]) ).
fof(f220,plain,
( ~ function(function_inverse(sK5))
| apply(function_inverse(sK5),sK11(function_inverse(sK5))) = apply(function_inverse(sK5),sK12(function_inverse(sK5)))
| ~ relation(function_inverse(sK5)) ),
inference(resolution,[],[f149,f187]) ).
fof(f187,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| apply(X0,sK11(X0)) = apply(X0,sK12(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f262,plain,
( ~ function(function_inverse(sK5))
| sK12(function_inverse(sK5)) = apply(sK5,apply(function_inverse(sK5),sK12(function_inverse(sK5)))) ),
inference(resolution,[],[f258,f234]) ).
fof(f234,plain,
( in(sK12(function_inverse(sK5)),relation_dom(function_inverse(sK5)))
| ~ function(function_inverse(sK5)) ),
inference(subsumption_resolution,[],[f218,f224]) ).
fof(f218,plain,
( ~ relation(function_inverse(sK5))
| ~ function(function_inverse(sK5))
| in(sK12(function_inverse(sK5)),relation_dom(function_inverse(sK5))) ),
inference(resolution,[],[f149,f184]) ).
fof(f184,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| in(sK12(X0),relation_dom(X0)) ),
inference(cnf_transformation,[],[f119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU221+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 14:53:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.30/0.53 % (21963)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)
% 1.49/0.55 % (21955)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 1.49/0.56 % (21962)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 1.49/0.56 % (21963)Instruction limit reached!
% 1.49/0.56 % (21963)------------------------------
% 1.49/0.56 % (21963)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.49/0.56 % (21955)Instruction limit reached!
% 1.49/0.56 % (21955)------------------------------
% 1.49/0.56 % (21955)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.49/0.56 % (21955)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.49/0.56 % (21955)Termination reason: Unknown
% 1.49/0.56 % (21955)Termination phase: Property scanning
% 1.49/0.56
% 1.49/0.56 % (21955)Memory used [KB]: 1535
% 1.49/0.56 % (21955)Time elapsed: 0.004 s
% 1.49/0.56 % (21955)Instructions burned: 3 (million)
% 1.49/0.56 % (21955)------------------------------
% 1.49/0.56 % (21955)------------------------------
% 1.49/0.56 % (21954)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 1.49/0.56 % (21963)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.49/0.56 % (21963)Termination reason: Unknown
% 1.49/0.56 % (21963)Termination phase: Saturation
% 1.49/0.56
% 1.49/0.56 % (21963)Memory used [KB]: 6268
% 1.49/0.56 % (21963)Time elapsed: 0.140 s
% 1.49/0.56 % (21963)Instructions burned: 12 (million)
% 1.49/0.56 % (21963)------------------------------
% 1.49/0.56 % (21963)------------------------------
% 1.49/0.57 % (21975)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)
% 1.49/0.58 % (21958)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)
% 1.49/0.58 % (21957)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)
% 1.49/0.58 % (21954)Refutation not found, incomplete strategy% (21954)------------------------------
% 1.49/0.58 % (21954)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.49/0.58 % (21957)Refutation not found, incomplete strategy% (21957)------------------------------
% 1.49/0.58 % (21957)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.49/0.58 % (21957)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.49/0.58 % (21957)Termination reason: Refutation not found, incomplete strategy
% 1.49/0.58
% 1.49/0.58 % (21957)Memory used [KB]: 5884
% 1.49/0.58 % (21957)Time elapsed: 0.166 s
% 1.49/0.58 % (21957)Instructions burned: 2 (million)
% 1.49/0.58 % (21957)------------------------------
% 1.49/0.58 % (21957)------------------------------
% 1.49/0.58 % (21954)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.49/0.58 % (21954)Termination reason: Refutation not found, incomplete strategy
% 1.49/0.58
% 1.49/0.58 % (21954)Memory used [KB]: 6012
% 1.49/0.58 % (21954)Time elapsed: 0.165 s
% 1.49/0.58 % (21954)Instructions burned: 4 (million)
% 1.49/0.58 % (21954)------------------------------
% 1.49/0.58 % (21954)------------------------------
% 1.49/0.59 % (21961)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)
% 1.49/0.59 % (21959)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)
% 1.49/0.59 % (21976)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)
% 1.49/0.59 % (21978)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 1.49/0.59 % (21959)Refutation not found, incomplete strategy% (21959)------------------------------
% 1.49/0.59 % (21959)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.49/0.59 % (21959)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.49/0.59 % (21959)Termination reason: Refutation not found, incomplete strategy
% 1.49/0.59
% 1.49/0.59 % (21959)Memory used [KB]: 5884
% 1.49/0.59 % (21959)Time elapsed: 0.176 s
% 1.49/0.59 % (21959)Instructions burned: 2 (million)
% 1.49/0.59 % (21959)------------------------------
% 1.49/0.59 % (21959)------------------------------
% 1.49/0.59 % (21964)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)
% 1.49/0.60 % (21968)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)
% 1.49/0.60 % (21960)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 1.49/0.60 % (21958)First to succeed.
% 1.49/0.60 % (21982)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 1.49/0.61 % (21958)Refutation found. Thanks to Tanya!
% 1.49/0.61 % SZS status Theorem for theBenchmark
% 1.49/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 1.49/0.61 % (21958)------------------------------
% 1.49/0.61 % (21958)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.49/0.61 % (21958)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.49/0.61 % (21958)Termination reason: Refutation
% 1.49/0.61
% 1.49/0.61 % (21958)Memory used [KB]: 1663
% 1.49/0.61 % (21958)Time elapsed: 0.173 s
% 1.49/0.61 % (21958)Instructions burned: 8 (million)
% 1.49/0.61 % (21958)------------------------------
% 1.49/0.61 % (21958)------------------------------
% 1.49/0.61 % (21952)Success in time 0.256 s
%------------------------------------------------------------------------------