TSTP Solution File: SEU027+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU027+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n019.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 May 1 03:49:50 EDT 2024
% Result : Theorem 0.61s 0.78s
% Output : Refutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 69 ( 20 unt; 0 def)
% Number of atoms : 509 ( 197 equ)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 685 ( 245 ~; 234 |; 165 &)
% ( 15 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-2 aty)
% Number of variables : 173 ( 138 !; 35 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f422,plain,
$false,
inference(subsumption_resolution,[],[f419,f325]) ).
fof(f325,plain,
apply(function_inverse(sK1),sK3(sK2,function_inverse(sK1))) != apply(sK2,sK3(sK2,function_inverse(sK1))),
inference(unit_resulting_resolution,[],[f96,f97,f285,f290,f103,f314,f114]) ).
fof(f114,plain,
! [X0,X1] :
( X0 = X1
| apply(X1,sK3(X0,X1)) != apply(X0,sK3(X0,X1))
| relation_dom(X0) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ( apply(X1,sK3(X0,X1)) != apply(X0,sK3(X0,X1))
& in(sK3(X0,X1),relation_dom(X0)) )
| relation_dom(X0) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f51,f68]) ).
fof(f68,plain,
! [X0,X1] :
( ? [X2] :
( apply(X1,X2) != apply(X0,X2)
& in(X2,relation_dom(X0)) )
=> ( apply(X1,sK3(X0,X1)) != apply(X0,sK3(X0,X1))
& in(sK3(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( apply(X1,X2) != apply(X0,X2)
& in(X2,relation_dom(X0)) )
| relation_dom(X0) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( apply(X1,X2) != apply(X0,X2)
& in(X2,relation_dom(X0)) )
| relation_dom(X0) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( ! [X2] :
( in(X2,relation_dom(X0))
=> apply(X1,X2) = apply(X0,X2) )
& relation_dom(X0) = relation_dom(X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FCnV5lXYYv/Vampire---4.8_12925',t9_funct_1) ).
fof(f314,plain,
relation_dom(sK2) = relation_dom(function_inverse(sK1)),
inference(forward_demodulation,[],[f310,f100]) ).
fof(f100,plain,
relation_rng(sK1) = relation_dom(sK2),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
( function_inverse(sK1) != sK2
& ! [X2,X3] :
( ( ( apply(sK1,X2) = X3
| apply(sK2,X3) != X2 )
& ( apply(sK2,X3) = X2
| apply(sK1,X2) != X3 ) )
| ~ in(X3,relation_dom(sK2))
| ~ in(X2,relation_dom(sK1)) )
& relation_rng(sK1) = relation_dom(sK2)
& relation_dom(sK1) = relation_rng(sK2)
& one_to_one(sK1)
& function(sK2)
& relation(sK2)
& function(sK1)
& relation(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f64,f66,f65]) ).
fof(f65,plain,
( ? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& ! [X2,X3] :
( ( ( apply(X0,X2) = X3
| apply(X1,X3) != X2 )
& ( apply(X1,X3) = X2
| apply(X0,X2) != X3 ) )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X0)) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0)
& function(X1)
& relation(X1) )
& function(X0)
& relation(X0) )
=> ( ? [X1] :
( function_inverse(sK1) != X1
& ! [X3,X2] :
( ( ( apply(sK1,X2) = X3
| apply(X1,X3) != X2 )
& ( apply(X1,X3) = X2
| apply(sK1,X2) != X3 ) )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(sK1)) )
& relation_dom(X1) = relation_rng(sK1)
& relation_rng(X1) = relation_dom(sK1)
& one_to_one(sK1)
& function(X1)
& relation(X1) )
& function(sK1)
& relation(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
( ? [X1] :
( function_inverse(sK1) != X1
& ! [X3,X2] :
( ( ( apply(sK1,X2) = X3
| apply(X1,X3) != X2 )
& ( apply(X1,X3) = X2
| apply(sK1,X2) != X3 ) )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(sK1)) )
& relation_dom(X1) = relation_rng(sK1)
& relation_rng(X1) = relation_dom(sK1)
& one_to_one(sK1)
& function(X1)
& relation(X1) )
=> ( function_inverse(sK1) != sK2
& ! [X3,X2] :
( ( ( apply(sK1,X2) = X3
| apply(sK2,X3) != X2 )
& ( apply(sK2,X3) = X2
| apply(sK1,X2) != X3 ) )
| ~ in(X3,relation_dom(sK2))
| ~ in(X2,relation_dom(sK1)) )
& relation_rng(sK1) = relation_dom(sK2)
& relation_dom(sK1) = relation_rng(sK2)
& one_to_one(sK1)
& function(sK2)
& relation(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& ! [X2,X3] :
( ( ( apply(X0,X2) = X3
| apply(X1,X3) != X2 )
& ( apply(X1,X3) = X2
| apply(X0,X2) != X3 ) )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X0)) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0)
& function(X1)
& relation(X1) )
& function(X0)
& relation(X0) ),
inference(nnf_transformation,[],[f40]) ).
fof(f40,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& ! [X2,X3] :
( ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X0)) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0)
& function(X1)
& relation(X1) )
& function(X0)
& relation(X0) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
? [X0] :
( ? [X1] :
( function_inverse(X0) != X1
& ! [X2,X3] :
( ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 )
| ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X0)) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0)
& function(X1)
& relation(X1) )
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( ! [X2,X3] :
( ( in(X3,relation_dom(X1))
& in(X2,relation_dom(X0)) )
=> ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 ) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0) )
=> function_inverse(X0) = X1 ) ) ),
inference(negated_conjecture,[],[f33]) ).
fof(f33,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( ! [X2,X3] :
( ( in(X3,relation_dom(X1))
& in(X2,relation_dom(X0)) )
=> ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 ) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0) )
=> function_inverse(X0) = X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FCnV5lXYYv/Vampire---4.8_12925',t60_funct_1) ).
fof(f310,plain,
relation_rng(sK1) = relation_dom(function_inverse(sK1)),
inference(unit_resulting_resolution,[],[f94,f95,f98,f285,f290,f166]) ).
fof(f166,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f132]) ).
fof(f132,plain,
! [X0,X1] :
( relation_rng(X0) = relation_dom(X1)
| function_inverse(X0) != X1
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( ( ( function_inverse(X0) = X1
| ( ( sK10(X0,X1) != apply(X1,sK9(X0,X1))
| ~ in(sK9(X0,X1),relation_rng(X0)) )
& sK9(X0,X1) = apply(X0,sK10(X0,X1))
& in(sK10(X0,X1),relation_dom(X0)) )
| ~ sP0(sK9(X0,X1),sK10(X0,X1),X0,X1)
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X4,X5] :
( ( ( apply(X1,X4) = X5
& in(X4,relation_rng(X0)) )
| apply(X0,X5) != X4
| ~ in(X5,relation_dom(X0)) )
& sP0(X4,X5,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f85,f86]) ).
fof(f86,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP0(X2,X3,X0,X1) )
=> ( ( ( sK10(X0,X1) != apply(X1,sK9(X0,X1))
| ~ in(sK9(X0,X1),relation_rng(X0)) )
& sK9(X0,X1) = apply(X0,sK10(X0,X1))
& in(sK10(X0,X1),relation_dom(X0)) )
| ~ sP0(sK9(X0,X1),sK10(X0,X1),X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( ( ( function_inverse(X0) = X1
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP0(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X4,X5] :
( ( ( apply(X1,X4) = X5
& in(X4,relation_rng(X0)) )
| apply(X0,X5) != X4
| ~ in(X5,relation_dom(X0)) )
& sP0(X4,X5,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f84]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( ( ( function_inverse(X0) = X1
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP0(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ( ( function_inverse(X0) = X1
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP0(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f56,f62]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( sP0(X2,X3,X0,X1)
<=> ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
=> ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
=> ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
& relation_rng(X0) = relation_dom(X1) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FCnV5lXYYv/Vampire---4.8_12925',t54_funct_1) ).
fof(f98,plain,
one_to_one(sK1),
inference(cnf_transformation,[],[f67]) ).
fof(f95,plain,
function(sK1),
inference(cnf_transformation,[],[f67]) ).
fof(f94,plain,
relation(sK1),
inference(cnf_transformation,[],[f67]) ).
fof(f103,plain,
function_inverse(sK1) != sK2,
inference(cnf_transformation,[],[f67]) ).
fof(f290,plain,
function(function_inverse(sK1)),
inference(unit_resulting_resolution,[],[f94,f95,f140]) ).
fof(f140,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/tmp/tmp.FCnV5lXYYv/Vampire---4.8_12925',dt_k2_funct_1) ).
fof(f285,plain,
relation(function_inverse(sK1)),
inference(unit_resulting_resolution,[],[f94,f95,f139]) ).
fof(f139,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f97,plain,
function(sK2),
inference(cnf_transformation,[],[f67]) ).
fof(f96,plain,
relation(sK2),
inference(cnf_transformation,[],[f67]) ).
fof(f419,plain,
apply(function_inverse(sK1),sK3(sK2,function_inverse(sK1))) = apply(sK2,sK3(sK2,function_inverse(sK1))),
inference(backward_demodulation,[],[f406,f405]) ).
fof(f405,plain,
sK3(sK2,function_inverse(sK1)) = apply(sK1,apply(sK2,sK3(sK2,function_inverse(sK1)))),
inference(unit_resulting_resolution,[],[f326,f348,f152]) ).
fof(f152,plain,
! [X3] :
( ~ in(apply(sK2,X3),relation_dom(sK1))
| ~ in(X3,relation_dom(sK2))
| apply(sK1,apply(sK2,X3)) = X3 ),
inference(equality_resolution,[],[f102]) ).
fof(f102,plain,
! [X2,X3] :
( apply(sK1,X2) = X3
| apply(sK2,X3) != X2
| ~ in(X3,relation_dom(sK2))
| ~ in(X2,relation_dom(sK1)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f348,plain,
in(apply(sK2,sK3(sK2,function_inverse(sK1))),relation_dom(sK1)),
inference(forward_demodulation,[],[f338,f99]) ).
fof(f99,plain,
relation_dom(sK1) = relation_rng(sK2),
inference(cnf_transformation,[],[f67]) ).
fof(f338,plain,
in(apply(sK2,sK3(sK2,function_inverse(sK1))),relation_rng(sK2)),
inference(unit_resulting_resolution,[],[f96,f97,f326,f155]) ).
fof(f155,plain,
! [X0,X6] :
( ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f154]) ).
fof(f154,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f117]) ).
fof(f117,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] :
( apply(X0,X3) != sK4(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK4(X0,X1),X1) )
& ( ( sK4(X0,X1) = apply(X0,sK5(X0,X1))
& in(sK5(X0,X1),relation_dom(X0)) )
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ( apply(X0,sK6(X0,X5)) = X5
& in(sK6(X0,X5),relation_dom(X0)) )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f71,f74,f73,f72]) ).
fof(f72,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) != sK4(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK4(X0,X1),X1) )
& ( ? [X4] :
( apply(X0,X4) = sK4(X0,X1)
& in(X4,relation_dom(X0)) )
| in(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0,X1] :
( ? [X4] :
( apply(X0,X4) = sK4(X0,X1)
& in(X4,relation_dom(X0)) )
=> ( sK4(X0,X1) = apply(X0,sK5(X0,X1))
& in(sK5(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
! [X0,X5] :
( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
=> ( apply(X0,sK6(X0,X5)) = X5
& in(sK6(X0,X5),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [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 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f70]) ).
fof(f70,plain,
! [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 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FCnV5lXYYv/Vampire---4.8_12925',d5_funct_1) ).
fof(f326,plain,
in(sK3(sK2,function_inverse(sK1)),relation_dom(sK2)),
inference(unit_resulting_resolution,[],[f96,f97,f285,f290,f103,f314,f113]) ).
fof(f113,plain,
! [X0,X1] :
( X0 = X1
| in(sK3(X0,X1),relation_dom(X0))
| relation_dom(X0) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f406,plain,
apply(sK2,sK3(sK2,function_inverse(sK1))) = apply(function_inverse(sK1),apply(sK1,apply(sK2,sK3(sK2,function_inverse(sK1))))),
inference(unit_resulting_resolution,[],[f94,f95,f98,f285,f290,f348,f162]) ).
fof(f162,plain,
! [X0,X5] :
( ~ in(X5,relation_dom(X0))
| apply(function_inverse(X0),apply(X0,X5)) = X5
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f161]) ).
fof(f161,plain,
! [X0,X1,X5] :
( apply(X1,apply(X0,X5)) = X5
| ~ in(X5,relation_dom(X0))
| function_inverse(X0) != X1
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f135]) ).
fof(f135,plain,
! [X0,X1,X4,X5] :
( apply(X1,X4) = X5
| apply(X0,X5) != X4
| ~ in(X5,relation_dom(X0))
| function_inverse(X0) != X1
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU027+1 : TPTP v8.1.2. Released v3.2.0.
% 0.04/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 16:18:14 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.37 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.FCnV5lXYYv/Vampire---4.8_12925
% 0.60/0.76 % (13303)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.61/0.76 % (13298)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.61/0.76 % (13296)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.61/0.76 % (13295)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.61/0.76 % (13294)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.61/0.76 % (13299)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.61/0.76 % (13300)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.61/0.76 % (13302)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.61/0.76 % (13303)Refutation not found, incomplete strategy% (13303)------------------------------
% 0.61/0.76 % (13303)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.76 % (13303)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.76
% 0.61/0.76 % (13303)Memory used [KB]: 1132
% 0.61/0.76 % (13303)Time elapsed: 0.003 s
% 0.61/0.76 % (13303)Instructions burned: 5 (million)
% 0.61/0.76 % (13303)------------------------------
% 0.61/0.76 % (13303)------------------------------
% 0.61/0.77 % (13305)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.61/0.77 % (13299)Refutation not found, incomplete strategy% (13299)------------------------------
% 0.61/0.77 % (13299)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.77 % (13299)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.77
% 0.61/0.77 % (13299)Memory used [KB]: 1172
% 0.61/0.77 % (13299)Time elapsed: 0.007 s
% 0.61/0.77 % (13299)Instructions burned: 10 (million)
% 0.61/0.77 % (13299)------------------------------
% 0.61/0.77 % (13299)------------------------------
% 0.61/0.77 % (13313)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2996ds/50Mi)
% 0.61/0.78 % (13298)First to succeed.
% 0.61/0.78 % (13294)Instruction limit reached!
% 0.61/0.78 % (13294)------------------------------
% 0.61/0.78 % (13294)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.78 % (13298)Refutation found. Thanks to Tanya!
% 0.61/0.78 % SZS status Theorem for Vampire---4
% 0.61/0.78 % SZS output start Proof for Vampire---4
% See solution above
% 0.61/0.78 % (13298)------------------------------
% 0.61/0.78 % (13298)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.78 % (13298)Termination reason: Refutation
% 0.61/0.78
% 0.61/0.78 % (13298)Memory used [KB]: 1325
% 0.61/0.78 % (13298)Time elapsed: 0.021 s
% 0.61/0.78 % (13298)Instructions burned: 36 (million)
% 0.61/0.78 % (13298)------------------------------
% 0.61/0.78 % (13298)------------------------------
% 0.61/0.78 % (13176)Success in time 0.403 s
% 0.61/0.78 % Vampire---4.8 exiting
%------------------------------------------------------------------------------