TSTP Solution File: SEU220+3 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU220+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_sat --cores 0 -t %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 18:32:37 EDT 2022
% Result : Theorem 0.20s 0.59s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 83 ( 25 unt; 0 def)
% Number of atoms : 399 ( 133 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 532 ( 216 ~; 202 |; 89 &)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 113 ( 97 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f959,plain,
$false,
inference(subsumption_resolution,[],[f958,f545]) ).
fof(f545,plain,
sF21 != sK12,
inference(trivial_inequality_removal,[],[f544]) ).
fof(f544,plain,
( sF21 != sK12
| sK12 != sK12 ),
inference(backward_demodulation,[],[f230,f543]) ).
fof(f543,plain,
sF19 = sK12,
inference(backward_demodulation,[],[f227,f542]) ).
fof(f542,plain,
sK12 = apply(sK13,sF18),
inference(forward_demodulation,[],[f541,f226]) ).
fof(f226,plain,
sF18 = apply(sF17,sK12),
introduced(function_definition,[]) ).
fof(f541,plain,
apply(sK13,apply(sF17,sK12)) = sK12,
inference(resolution,[],[f500,f224]) ).
fof(f224,plain,
in(sK12,sF16),
inference(definition_folding,[],[f200,f223]) ).
fof(f223,plain,
sF16 = relation_rng(sK13),
introduced(function_definition,[]) ).
fof(f200,plain,
in(sK12,relation_rng(sK13)),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
( in(sK12,relation_rng(sK13))
& one_to_one(sK13)
& ( sK12 != apply(sK13,apply(function_inverse(sK13),sK12))
| sK12 != apply(relation_composition(function_inverse(sK13),sK13),sK12) )
& relation(sK13)
& function(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f128,f129]) ).
fof(f129,plain,
( ? [X0,X1] :
( in(X0,relation_rng(X1))
& one_to_one(X1)
& ( apply(X1,apply(function_inverse(X1),X0)) != X0
| apply(relation_composition(function_inverse(X1),X1),X0) != X0 )
& relation(X1)
& function(X1) )
=> ( in(sK12,relation_rng(sK13))
& one_to_one(sK13)
& ( sK12 != apply(sK13,apply(function_inverse(sK13),sK12))
| sK12 != apply(relation_composition(function_inverse(sK13),sK13),sK12) )
& relation(sK13)
& function(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f128,plain,
? [X0,X1] :
( in(X0,relation_rng(X1))
& one_to_one(X1)
& ( apply(X1,apply(function_inverse(X1),X0)) != X0
| apply(relation_composition(function_inverse(X1),X1),X0) != X0 )
& relation(X1)
& function(X1) ),
inference(rectify,[],[f87]) ).
fof(f87,plain,
? [X1,X0] :
( in(X1,relation_rng(X0))
& one_to_one(X0)
& ( apply(X0,apply(function_inverse(X0),X1)) != X1
| apply(relation_composition(function_inverse(X0),X0),X1) != X1 )
& relation(X0)
& function(X0) ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
? [X1,X0] :
( ( apply(X0,apply(function_inverse(X0),X1)) != X1
| apply(relation_composition(function_inverse(X0),X0),X1) != X1 )
& one_to_one(X0)
& in(X1,relation_rng(X0))
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,plain,
~ ! [X1,X0] :
( ( function(X0)
& relation(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,[],[f38]) ).
fof(f38,negated_conjecture,
~ ! [X1,X0] :
( ( function(X1)
& relation(X1) )
=> ( ( one_to_one(X1)
& in(X0,relation_rng(X1)) )
=> ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
& apply(X1,apply(function_inverse(X1),X0)) = X0 ) ) ),
inference(negated_conjecture,[],[f37]) ).
fof(f37,conjecture,
! [X1,X0] :
( ( function(X1)
& relation(X1) )
=> ( ( one_to_one(X1)
& in(X0,relation_rng(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(f500,plain,
! [X0] :
( ~ in(X0,sF16)
| apply(sK13,apply(sF17,X0)) = X0 ),
inference(forward_demodulation,[],[f499,f223]) ).
fof(f499,plain,
! [X0] :
( ~ in(X0,relation_rng(sK13))
| apply(sK13,apply(sF17,X0)) = X0 ),
inference(subsumption_resolution,[],[f498,f199]) ).
fof(f199,plain,
one_to_one(sK13),
inference(cnf_transformation,[],[f130]) ).
fof(f498,plain,
! [X0] :
( ~ one_to_one(sK13)
| apply(sK13,apply(sF17,X0)) = X0
| ~ in(X0,relation_rng(sK13)) ),
inference(subsumption_resolution,[],[f497,f197]) ).
fof(f197,plain,
relation(sK13),
inference(cnf_transformation,[],[f130]) ).
fof(f497,plain,
! [X0] :
( ~ in(X0,relation_rng(sK13))
| ~ relation(sK13)
| ~ one_to_one(sK13)
| apply(sK13,apply(sF17,X0)) = X0 ),
inference(subsumption_resolution,[],[f496,f196]) ).
fof(f196,plain,
function(sK13),
inference(cnf_transformation,[],[f130]) ).
fof(f496,plain,
! [X0] :
( ~ in(X0,relation_rng(sK13))
| ~ function(sK13)
| ~ one_to_one(sK13)
| ~ relation(sK13)
| apply(sK13,apply(sF17,X0)) = X0 ),
inference(subsumption_resolution,[],[f494,f275]) ).
fof(f275,plain,
function(sF17),
inference(subsumption_resolution,[],[f274,f196]) ).
fof(f274,plain,
( function(sF17)
| ~ function(sK13) ),
inference(subsumption_resolution,[],[f273,f197]) ).
fof(f273,plain,
( ~ relation(sK13)
| function(sF17)
| ~ function(sK13) ),
inference(superposition,[],[f168,f225]) ).
fof(f225,plain,
sF17 = function_inverse(sK13),
introduced(function_definition,[]) ).
fof(f168,plain,
! [X0] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ~ function(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ relation(X0) ),
inference(flattening,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,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(f494,plain,
! [X0] :
( ~ in(X0,relation_rng(sK13))
| ~ function(sF17)
| apply(sK13,apply(sF17,X0)) = X0
| ~ relation(sK13)
| ~ function(sK13)
| ~ one_to_one(sK13) ),
inference(superposition,[],[f231,f225]) ).
fof(f231,plain,
! [X0,X4] :
( ~ function(function_inverse(X0))
| ~ relation(X0)
| ~ one_to_one(X0)
| apply(X0,apply(function_inverse(X0),X4)) = X4
| ~ in(X4,relation_rng(X0))
| ~ function(X0) ),
inference(subsumption_resolution,[],[f218,f167]) ).
fof(f167,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f218,plain,
! [X0,X4] :
( ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(function_inverse(X0))
| ~ in(X4,relation_rng(X0))
| ~ function(X0)
| apply(X0,apply(function_inverse(X0),X4)) = X4
| ~ relation(function_inverse(X0)) ),
inference(equality_resolution,[],[f217]) ).
fof(f217,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ in(X4,relation_rng(X0))
| apply(X0,apply(X1,X4)) = X4
| function_inverse(X0) != X1
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ one_to_one(X0) ),
inference(equality_resolution,[],[f188]) ).
fof(f188,plain,
! [X0,X1,X4,X5] :
( ~ function(X0)
| ~ in(X4,relation_rng(X0))
| apply(X1,X4) != X5
| apply(X0,X5) = X4
| function_inverse(X0) != X1
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ one_to_one(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ~ function(X0)
| ! [X1] :
( ( ( function_inverse(X0) = X1
| ( in(sK9(X0,X1),relation_rng(X0))
& sK10(X0,X1) = apply(X1,sK9(X0,X1))
& ( sK9(X0,X1) != apply(X0,sK10(X0,X1))
| ~ in(sK10(X0,X1),relation_dom(X0)) ) )
| ~ sP0(X0,sK9(X0,X1),sK10(X0,X1),X1)
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X4,X5] :
( ( ~ in(X4,relation_rng(X0))
| apply(X1,X4) != X5
| ( apply(X0,X5) = X4
& in(X5,relation_dom(X0)) ) )
& sP0(X0,X4,X5,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ one_to_one(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f123,f124]) ).
fof(f124,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( in(X2,relation_rng(X0))
& apply(X1,X2) = X3
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
| ~ sP0(X0,X2,X3,X1) )
=> ( ( in(sK9(X0,X1),relation_rng(X0))
& sK10(X0,X1) = apply(X1,sK9(X0,X1))
& ( sK9(X0,X1) != apply(X0,sK10(X0,X1))
| ~ in(sK10(X0,X1),relation_dom(X0)) ) )
| ~ sP0(X0,sK9(X0,X1),sK10(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f123,plain,
! [X0] :
( ~ function(X0)
| ! [X1] :
( ( ( function_inverse(X0) = X1
| ? [X2,X3] :
( ( in(X2,relation_rng(X0))
& apply(X1,X2) = X3
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
| ~ sP0(X0,X2,X3,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X4,X5] :
( ( ~ in(X4,relation_rng(X0))
| apply(X1,X4) != X5
| ( apply(X0,X5) = X4
& in(X5,relation_dom(X0)) ) )
& sP0(X0,X4,X5,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ one_to_one(X0) ),
inference(rectify,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ~ function(X0)
| ! [X1] :
( ( ( function_inverse(X0) = X1
| ? [X2,X3] :
( ( in(X2,relation_rng(X0))
& apply(X1,X2) = X3
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
| ~ sP0(X0,X2,X3,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( ( ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3
| ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) )
& sP0(X0,X2,X3,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ one_to_one(X0) ),
inference(flattening,[],[f121]) ).
fof(f121,plain,
! [X0] :
( ~ function(X0)
| ! [X1] :
( ( ( function_inverse(X0) = X1
| ? [X2,X3] :
( ( in(X2,relation_rng(X0))
& apply(X1,X2) = X3
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
| ~ sP0(X0,X2,X3,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( ( ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3
| ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) )
& sP0(X0,X2,X3,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ one_to_one(X0) ),
inference(nnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0] :
( ~ function(X0)
| ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3
| ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) )
& sP0(X0,X2,X3,X1) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ one_to_one(X0) ),
inference(definition_folding,[],[f60,f93]) ).
fof(f93,plain,
! [X0,X2,X3,X1] :
( sP0(X0,X2,X3,X1)
<=> ( ( in(X2,relation_rng(X0))
& apply(X1,X2) = X3 )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f60,plain,
! [X0] :
( ~ function(X0)
| ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3
| ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) )
& ( ( in(X2,relation_rng(X0))
& apply(X1,X2) = X3 )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ one_to_one(X0) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( relation_rng(X0) = relation_dom(X1)
& ! [X3,X2] :
( ( ( in(X2,relation_rng(X0))
& apply(X1,X2) = X3 )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 ) ) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,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(X0,X3) = X2
& in(X3,relation_dom(X0)) )
=> ( in(X2,relation_rng(X0))
& apply(X1,X2) = X3 ) )
& ( ( in(X2,relation_rng(X0))
& apply(X1,X2) = X3 )
=> ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f227,plain,
sF19 = apply(sK13,sF18),
introduced(function_definition,[]) ).
fof(f230,plain,
( sF21 != sK12
| sF19 != sK12 ),
inference(definition_folding,[],[f198,f229,f228,f225,f227,f226,f225]) ).
fof(f228,plain,
relation_composition(sF17,sK13) = sF20,
introduced(function_definition,[]) ).
fof(f229,plain,
sF21 = apply(sF20,sK12),
introduced(function_definition,[]) ).
fof(f198,plain,
( sK12 != apply(sK13,apply(function_inverse(sK13),sK12))
| sK12 != apply(relation_composition(function_inverse(sK13),sK13),sK12) ),
inference(cnf_transformation,[],[f130]) ).
fof(f958,plain,
sF21 = sK12,
inference(backward_demodulation,[],[f229,f957]) ).
fof(f957,plain,
sK12 = apply(sF20,sK12),
inference(forward_demodulation,[],[f956,f228]) ).
fof(f956,plain,
sK12 = apply(relation_composition(sF17,sK13),sK12),
inference(forward_demodulation,[],[f955,f542]) ).
fof(f955,plain,
apply(relation_composition(sF17,sK13),sK12) = apply(sK13,sF18),
inference(subsumption_resolution,[],[f945,f197]) ).
fof(f945,plain,
( apply(relation_composition(sF17,sK13),sK12) = apply(sK13,sF18)
| ~ relation(sK13) ),
inference(resolution,[],[f931,f196]) ).
fof(f931,plain,
! [X2] :
( ~ function(X2)
| apply(relation_composition(sF17,X2),sK12) = apply(X2,sF18)
| ~ relation(X2) ),
inference(forward_demodulation,[],[f929,f226]) ).
fof(f929,plain,
! [X2] :
( ~ relation(X2)
| apply(X2,apply(sF17,sK12)) = apply(relation_composition(sF17,X2),sK12)
| ~ function(X2) ),
inference(resolution,[],[f510,f224]) ).
fof(f510,plain,
! [X2,X3] :
( ~ in(X2,sF16)
| ~ relation(X3)
| apply(X3,apply(sF17,X2)) = apply(relation_composition(sF17,X3),X2)
| ~ function(X3) ),
inference(subsumption_resolution,[],[f509,f275]) ).
fof(f509,plain,
! [X2,X3] :
( ~ relation(X3)
| apply(X3,apply(sF17,X2)) = apply(relation_composition(sF17,X3),X2)
| ~ function(X3)
| ~ in(X2,sF16)
| ~ function(sF17) ),
inference(subsumption_resolution,[],[f506,f272]) ).
fof(f272,plain,
relation(sF17),
inference(subsumption_resolution,[],[f271,f196]) ).
fof(f271,plain,
( ~ function(sK13)
| relation(sF17) ),
inference(subsumption_resolution,[],[f270,f197]) ).
fof(f270,plain,
( ~ relation(sK13)
| ~ function(sK13)
| relation(sF17) ),
inference(superposition,[],[f167,f225]) ).
fof(f506,plain,
! [X2,X3] :
( ~ in(X2,sF16)
| ~ relation(sF17)
| ~ function(X3)
| ~ relation(X3)
| ~ function(sF17)
| apply(X3,apply(sF17,X2)) = apply(relation_composition(sF17,X3),X2) ),
inference(superposition,[],[f160,f463]) ).
fof(f463,plain,
sF16 = relation_dom(sF17),
inference(forward_demodulation,[],[f462,f223]) ).
fof(f462,plain,
relation_dom(sF17) = relation_rng(sK13),
inference(forward_demodulation,[],[f461,f225]) ).
fof(f461,plain,
relation_rng(sK13) = relation_dom(function_inverse(sK13)),
inference(subsumption_resolution,[],[f460,f196]) ).
fof(f460,plain,
( ~ function(sK13)
| relation_rng(sK13) = relation_dom(function_inverse(sK13)) ),
inference(subsumption_resolution,[],[f452,f197]) ).
fof(f452,plain,
( ~ relation(sK13)
| ~ function(sK13)
| relation_rng(sK13) = relation_dom(function_inverse(sK13)) ),
inference(resolution,[],[f233,f199]) ).
fof(f233,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ function(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ relation(X0) ),
inference(subsumption_resolution,[],[f232,f168]) ).
fof(f232,plain,
! [X0] :
( ~ function(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ function(function_inverse(X0))
| ~ relation(X0)
| ~ one_to_one(X0) ),
inference(subsumption_resolution,[],[f222,f167]) ).
fof(f222,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ function(function_inverse(X0))
| ~ one_to_one(X0) ),
inference(equality_resolution,[],[f185]) ).
fof(f185,plain,
! [X0,X1] :
( ~ function(X0)
| relation_rng(X0) = relation_dom(X1)
| function_inverse(X0) != X1
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ one_to_one(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f160,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ function(X1)
| ~ relation(X1)
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ function(X1)
| ! [X2] :
( ~ relation(X2)
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2) ) ),
inference(rectify,[],[f85]) ).
fof(f85,plain,
! [X1,X0] :
( ~ relation(X0)
| ~ function(X0)
| ! [X2] :
( ~ relation(X2)
| apply(relation_composition(X0,X2),X1) = apply(X2,apply(X0,X1))
| ~ in(X1,relation_dom(X0))
| ~ function(X2) ) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
! [X1,X0] :
( ! [X2] :
( apply(relation_composition(X0,X2),X1) = apply(X2,apply(X0,X1))
| ~ in(X1,relation_dom(X0))
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,plain,
! [X1,X0] :
( ( relation(X0)
& function(X0) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(X0))
=> apply(relation_composition(X0,X2),X1) = apply(X2,apply(X0,X1)) ) ) ),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X1,X0] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU220+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_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n027.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 15:07:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.50 % (21715)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.50 % (21735)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.51 % (21714)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.51 % (21726)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.52 % (21720)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.52 % (21728)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.52 % (21727)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.52 % (21717)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52 % (21732)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.52 % (21738)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.52 % (21718)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.53 % (21714)Refutation not found, incomplete strategy% (21714)------------------------------
% 0.20/0.53 % (21714)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (21714)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (21714)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.53
% 0.20/0.53 % (21714)Memory used [KB]: 5500
% 0.20/0.53 % (21714)Time elapsed: 0.127 s
% 0.20/0.53 % (21714)Instructions burned: 6 (million)
% 0.20/0.53 % (21714)------------------------------
% 0.20/0.53 % (21714)------------------------------
% 0.20/0.53 % (21713)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.53 % (21741)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.53 % (21724)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.53 % (21739)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.53 TRYING [1]
% 0.20/0.53 TRYING [2]
% 0.20/0.53 % (21733)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.53 % (21716)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53 % (21720)Instruction limit reached!
% 0.20/0.53 % (21720)------------------------------
% 0.20/0.53 % (21720)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (21719)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54 % (21737)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.54 % (21731)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.54 % (21742)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.20/0.54 % (21725)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.54 TRYING [1]
% 0.20/0.54 TRYING [2]
% 0.20/0.54 % (21720)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (21720)Termination reason: Unknown
% 0.20/0.54 % (21720)Termination phase: Saturation
% 0.20/0.54
% 0.20/0.54 % (21720)Memory used [KB]: 5500
% 0.20/0.54 % (21720)Time elapsed: 0.128 s
% 0.20/0.54 % (21720)Instructions burned: 7 (million)
% 0.20/0.54 % (21720)------------------------------
% 0.20/0.54 % (21720)------------------------------
% 0.20/0.54 % (21736)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.54 TRYING [3]
% 0.20/0.54 % (21729)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.54 % (21721)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.54 % (21734)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.54 % (21721)Instruction limit reached!
% 0.20/0.54 % (21721)------------------------------
% 0.20/0.54 % (21721)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (21721)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (21721)Termination reason: Unknown
% 0.20/0.54 % (21721)Termination phase: Blocked clause elimination
% 0.20/0.54
% 0.20/0.54 % (21721)Memory used [KB]: 1023
% 0.20/0.54 % (21721)Time elapsed: 0.003 s
% 0.20/0.54 % (21721)Instructions burned: 4 (million)
% 0.20/0.54 % (21721)------------------------------
% 0.20/0.54 % (21721)------------------------------
% 0.20/0.55 % (21740)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.20/0.55 % (21730)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.55 % (21723)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.55 TRYING [1]
% 0.20/0.55 TRYING [2]
% 0.20/0.55 TRYING [3]
% 0.20/0.55 % (21722)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.57 TRYING [3]
% 0.20/0.58 % (21715)Instruction limit reached!
% 0.20/0.58 % (21715)------------------------------
% 0.20/0.58 % (21715)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.58 % (21715)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.58 % (21715)Termination reason: Unknown
% 0.20/0.58 % (21715)Termination phase: Saturation
% 0.20/0.58
% 0.20/0.58 % (21715)Memory used [KB]: 1407
% 0.20/0.58 % (21715)Time elapsed: 0.162 s
% 0.20/0.58 % (21715)Instructions burned: 38 (million)
% 0.20/0.58 % (21715)------------------------------
% 0.20/0.58 % (21715)------------------------------
% 0.20/0.58 TRYING [4]
% 0.20/0.59 % (21728)First to succeed.
% 0.20/0.59 TRYING [4]
% 0.20/0.59 % (21728)Refutation found. Thanks to Tanya!
% 0.20/0.59 % SZS status Theorem for theBenchmark
% 0.20/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.59 % (21728)------------------------------
% 0.20/0.59 % (21728)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.59 % (21728)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.59 % (21728)Termination reason: Refutation
% 0.20/0.59
% 0.20/0.59 % (21728)Memory used [KB]: 1663
% 0.20/0.59 % (21728)Time elapsed: 0.172 s
% 0.20/0.59 % (21728)Instructions burned: 43 (million)
% 0.20/0.59 % (21728)------------------------------
% 0.20/0.59 % (21728)------------------------------
% 0.20/0.59 % (21712)Success in time 0.242 s
%------------------------------------------------------------------------------