TSTP Solution File: SET684+3 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET684+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : n024.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 18:25:20 EDT 2022
% Result : Theorem 0.15s 0.56s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 28
% Syntax : Number of formulae : 167 ( 13 unt; 0 def)
% Number of atoms : 963 ( 32 equ)
% Maximal formula atoms : 36 ( 5 avg)
% Number of connectives : 1310 ( 514 ~; 474 |; 240 &)
% ( 20 <=>; 60 =>; 0 <=; 2 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 10 con; 0-5 aty)
% Number of variables : 469 ( 355 !; 114 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f654,plain,
$false,
inference(avatar_sat_refutation,[],[f200,f209,f213,f217,f243,f561,f573,f653]) ).
fof(f653,plain,
( ~ spl19_2
| spl19_3
| ~ spl19_4
| ~ spl19_7 ),
inference(avatar_contradiction_clause,[],[f652]) ).
fof(f652,plain,
( $false
| ~ spl19_2
| spl19_3
| ~ spl19_4
| ~ spl19_7 ),
inference(subsumption_resolution,[],[f651,f315]) ).
fof(f315,plain,
ilf_type(sK10,binary_relation_type),
inference(resolution,[],[f314,f262]) ).
fof(f262,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(subsumption_resolution,[],[f190,f173]) ).
fof(f173,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p29) ).
fof(f190,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f174]) ).
fof(f174,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ( relation_like(X0)
& ilf_type(X0,set_type) )
| ~ ilf_type(X0,binary_relation_type) )
& ( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ) ) ),
inference(flattening,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ( relation_like(X0)
& ilf_type(X0,set_type) )
| ~ ilf_type(X0,binary_relation_type) )
& ( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( relation_like(X0)
& ilf_type(X0,set_type) )
<=> ilf_type(X0,binary_relation_type) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ( relation_like(X0)
& ilf_type(X0,set_type) )
<=> ilf_type(X0,binary_relation_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
fof(f314,plain,
relation_like(sK10),
inference(resolution,[],[f311,f219]) ).
fof(f219,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(subsumption_resolution,[],[f218,f173]) ).
fof(f218,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| relation_like(X2) ),
inference(subsumption_resolution,[],[f171,f173]) ).
fof(f171,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type)
| relation_like(X2)
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ! [X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
| ~ ilf_type(X1,set_type) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).
fof(f311,plain,
ilf_type(sK10,subset_type(cross_product(sK7,sK8))),
inference(resolution,[],[f258,f147]) ).
fof(f147,plain,
ilf_type(sK10,relation_type(sK7,sK8)),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
( ~ empty(sK7)
& ~ empty(sK9)
& ilf_type(sK11,relation_type(sK8,sK9))
& ilf_type(sK12,member_type(sK7))
& ( ~ member(ordered_pair(sK12,sK13),compose5(sK7,sK8,sK9,sK10,sK11))
| ! [X7] :
( ~ member(ordered_pair(sK12,X7),sK10)
| ~ member(ordered_pair(X7,sK13),sK11)
| ~ ilf_type(X7,member_type(sK8)) ) )
& ( member(ordered_pair(sK12,sK13),compose5(sK7,sK8,sK9,sK10,sK11))
| ( member(ordered_pair(sK12,sK14),sK10)
& member(ordered_pair(sK14,sK13),sK11)
& ilf_type(sK14,member_type(sK8)) ) )
& ilf_type(sK13,member_type(sK9))
& ilf_type(sK10,relation_type(sK7,sK8))
& ilf_type(sK9,set_type)
& ~ empty(sK8)
& ilf_type(sK8,set_type)
& ilf_type(sK7,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14])],[f93,f101,f100,f99,f98,f97,f96,f95,f94]) ).
fof(f94,plain,
( ? [X0] :
( ~ empty(X0)
& ? [X1] :
( ? [X2] :
( ~ empty(X2)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,relation_type(X1,X2))
& ? [X5] :
( ilf_type(X5,member_type(X0))
& ? [X6] :
( ( ~ member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
| ! [X7] :
( ~ member(ordered_pair(X5,X7),X3)
| ~ member(ordered_pair(X7,X6),X4)
| ~ ilf_type(X7,member_type(X1)) ) )
& ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
| ? [X8] :
( member(ordered_pair(X5,X8),X3)
& member(ordered_pair(X8,X6),X4)
& ilf_type(X8,member_type(X1)) ) )
& ilf_type(X6,member_type(X2)) ) ) )
& ilf_type(X3,relation_type(X0,X1)) )
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ~ empty(sK7)
& ? [X1] :
( ? [X2] :
( ~ empty(X2)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,relation_type(X1,X2))
& ? [X5] :
( ilf_type(X5,member_type(sK7))
& ? [X6] :
( ( ~ member(ordered_pair(X5,X6),compose5(sK7,X1,X2,X3,X4))
| ! [X7] :
( ~ member(ordered_pair(X5,X7),X3)
| ~ member(ordered_pair(X7,X6),X4)
| ~ ilf_type(X7,member_type(X1)) ) )
& ( member(ordered_pair(X5,X6),compose5(sK7,X1,X2,X3,X4))
| ? [X8] :
( member(ordered_pair(X5,X8),X3)
& member(ordered_pair(X8,X6),X4)
& ilf_type(X8,member_type(X1)) ) )
& ilf_type(X6,member_type(X2)) ) ) )
& ilf_type(X3,relation_type(sK7,X1)) )
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ilf_type(sK7,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
( ? [X1] :
( ? [X2] :
( ~ empty(X2)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,relation_type(X1,X2))
& ? [X5] :
( ilf_type(X5,member_type(sK7))
& ? [X6] :
( ( ~ member(ordered_pair(X5,X6),compose5(sK7,X1,X2,X3,X4))
| ! [X7] :
( ~ member(ordered_pair(X5,X7),X3)
| ~ member(ordered_pair(X7,X6),X4)
| ~ ilf_type(X7,member_type(X1)) ) )
& ( member(ordered_pair(X5,X6),compose5(sK7,X1,X2,X3,X4))
| ? [X8] :
( member(ordered_pair(X5,X8),X3)
& member(ordered_pair(X8,X6),X4)
& ilf_type(X8,member_type(X1)) ) )
& ilf_type(X6,member_type(X2)) ) ) )
& ilf_type(X3,relation_type(sK7,X1)) )
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ~ empty(X2)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,relation_type(sK8,X2))
& ? [X5] :
( ilf_type(X5,member_type(sK7))
& ? [X6] :
( ( ~ member(ordered_pair(X5,X6),compose5(sK7,sK8,X2,X3,X4))
| ! [X7] :
( ~ member(ordered_pair(X5,X7),X3)
| ~ member(ordered_pair(X7,X6),X4)
| ~ ilf_type(X7,member_type(sK8)) ) )
& ( member(ordered_pair(X5,X6),compose5(sK7,sK8,X2,X3,X4))
| ? [X8] :
( member(ordered_pair(X5,X8),X3)
& member(ordered_pair(X8,X6),X4)
& ilf_type(X8,member_type(sK8)) ) )
& ilf_type(X6,member_type(X2)) ) ) )
& ilf_type(X3,relation_type(sK7,sK8)) )
& ilf_type(X2,set_type) )
& ~ empty(sK8)
& ilf_type(sK8,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
( ? [X2] :
( ~ empty(X2)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,relation_type(sK8,X2))
& ? [X5] :
( ilf_type(X5,member_type(sK7))
& ? [X6] :
( ( ~ member(ordered_pair(X5,X6),compose5(sK7,sK8,X2,X3,X4))
| ! [X7] :
( ~ member(ordered_pair(X5,X7),X3)
| ~ member(ordered_pair(X7,X6),X4)
| ~ ilf_type(X7,member_type(sK8)) ) )
& ( member(ordered_pair(X5,X6),compose5(sK7,sK8,X2,X3,X4))
| ? [X8] :
( member(ordered_pair(X5,X8),X3)
& member(ordered_pair(X8,X6),X4)
& ilf_type(X8,member_type(sK8)) ) )
& ilf_type(X6,member_type(X2)) ) ) )
& ilf_type(X3,relation_type(sK7,sK8)) )
& ilf_type(X2,set_type) )
=> ( ~ empty(sK9)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,relation_type(sK8,sK9))
& ? [X5] :
( ilf_type(X5,member_type(sK7))
& ? [X6] :
( ( ~ member(ordered_pair(X5,X6),compose5(sK7,sK8,sK9,X3,X4))
| ! [X7] :
( ~ member(ordered_pair(X5,X7),X3)
| ~ member(ordered_pair(X7,X6),X4)
| ~ ilf_type(X7,member_type(sK8)) ) )
& ( member(ordered_pair(X5,X6),compose5(sK7,sK8,sK9,X3,X4))
| ? [X8] :
( member(ordered_pair(X5,X8),X3)
& member(ordered_pair(X8,X6),X4)
& ilf_type(X8,member_type(sK8)) ) )
& ilf_type(X6,member_type(sK9)) ) ) )
& ilf_type(X3,relation_type(sK7,sK8)) )
& ilf_type(sK9,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
( ? [X3] :
( ? [X4] :
( ilf_type(X4,relation_type(sK8,sK9))
& ? [X5] :
( ilf_type(X5,member_type(sK7))
& ? [X6] :
( ( ~ member(ordered_pair(X5,X6),compose5(sK7,sK8,sK9,X3,X4))
| ! [X7] :
( ~ member(ordered_pair(X5,X7),X3)
| ~ member(ordered_pair(X7,X6),X4)
| ~ ilf_type(X7,member_type(sK8)) ) )
& ( member(ordered_pair(X5,X6),compose5(sK7,sK8,sK9,X3,X4))
| ? [X8] :
( member(ordered_pair(X5,X8),X3)
& member(ordered_pair(X8,X6),X4)
& ilf_type(X8,member_type(sK8)) ) )
& ilf_type(X6,member_type(sK9)) ) ) )
& ilf_type(X3,relation_type(sK7,sK8)) )
=> ( ? [X4] :
( ilf_type(X4,relation_type(sK8,sK9))
& ? [X5] :
( ilf_type(X5,member_type(sK7))
& ? [X6] :
( ( ~ member(ordered_pair(X5,X6),compose5(sK7,sK8,sK9,sK10,X4))
| ! [X7] :
( ~ member(ordered_pair(X5,X7),sK10)
| ~ member(ordered_pair(X7,X6),X4)
| ~ ilf_type(X7,member_type(sK8)) ) )
& ( member(ordered_pair(X5,X6),compose5(sK7,sK8,sK9,sK10,X4))
| ? [X8] :
( member(ordered_pair(X5,X8),sK10)
& member(ordered_pair(X8,X6),X4)
& ilf_type(X8,member_type(sK8)) ) )
& ilf_type(X6,member_type(sK9)) ) ) )
& ilf_type(sK10,relation_type(sK7,sK8)) ) ),
introduced(choice_axiom,[]) ).
fof(f98,plain,
( ? [X4] :
( ilf_type(X4,relation_type(sK8,sK9))
& ? [X5] :
( ilf_type(X5,member_type(sK7))
& ? [X6] :
( ( ~ member(ordered_pair(X5,X6),compose5(sK7,sK8,sK9,sK10,X4))
| ! [X7] :
( ~ member(ordered_pair(X5,X7),sK10)
| ~ member(ordered_pair(X7,X6),X4)
| ~ ilf_type(X7,member_type(sK8)) ) )
& ( member(ordered_pair(X5,X6),compose5(sK7,sK8,sK9,sK10,X4))
| ? [X8] :
( member(ordered_pair(X5,X8),sK10)
& member(ordered_pair(X8,X6),X4)
& ilf_type(X8,member_type(sK8)) ) )
& ilf_type(X6,member_type(sK9)) ) ) )
=> ( ilf_type(sK11,relation_type(sK8,sK9))
& ? [X5] :
( ilf_type(X5,member_type(sK7))
& ? [X6] :
( ( ~ member(ordered_pair(X5,X6),compose5(sK7,sK8,sK9,sK10,sK11))
| ! [X7] :
( ~ member(ordered_pair(X5,X7),sK10)
| ~ member(ordered_pair(X7,X6),sK11)
| ~ ilf_type(X7,member_type(sK8)) ) )
& ( member(ordered_pair(X5,X6),compose5(sK7,sK8,sK9,sK10,sK11))
| ? [X8] :
( member(ordered_pair(X5,X8),sK10)
& member(ordered_pair(X8,X6),sK11)
& ilf_type(X8,member_type(sK8)) ) )
& ilf_type(X6,member_type(sK9)) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
( ? [X5] :
( ilf_type(X5,member_type(sK7))
& ? [X6] :
( ( ~ member(ordered_pair(X5,X6),compose5(sK7,sK8,sK9,sK10,sK11))
| ! [X7] :
( ~ member(ordered_pair(X5,X7),sK10)
| ~ member(ordered_pair(X7,X6),sK11)
| ~ ilf_type(X7,member_type(sK8)) ) )
& ( member(ordered_pair(X5,X6),compose5(sK7,sK8,sK9,sK10,sK11))
| ? [X8] :
( member(ordered_pair(X5,X8),sK10)
& member(ordered_pair(X8,X6),sK11)
& ilf_type(X8,member_type(sK8)) ) )
& ilf_type(X6,member_type(sK9)) ) )
=> ( ilf_type(sK12,member_type(sK7))
& ? [X6] :
( ( ~ member(ordered_pair(sK12,X6),compose5(sK7,sK8,sK9,sK10,sK11))
| ! [X7] :
( ~ member(ordered_pair(sK12,X7),sK10)
| ~ member(ordered_pair(X7,X6),sK11)
| ~ ilf_type(X7,member_type(sK8)) ) )
& ( member(ordered_pair(sK12,X6),compose5(sK7,sK8,sK9,sK10,sK11))
| ? [X8] :
( member(ordered_pair(sK12,X8),sK10)
& member(ordered_pair(X8,X6),sK11)
& ilf_type(X8,member_type(sK8)) ) )
& ilf_type(X6,member_type(sK9)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
( ? [X6] :
( ( ~ member(ordered_pair(sK12,X6),compose5(sK7,sK8,sK9,sK10,sK11))
| ! [X7] :
( ~ member(ordered_pair(sK12,X7),sK10)
| ~ member(ordered_pair(X7,X6),sK11)
| ~ ilf_type(X7,member_type(sK8)) ) )
& ( member(ordered_pair(sK12,X6),compose5(sK7,sK8,sK9,sK10,sK11))
| ? [X8] :
( member(ordered_pair(sK12,X8),sK10)
& member(ordered_pair(X8,X6),sK11)
& ilf_type(X8,member_type(sK8)) ) )
& ilf_type(X6,member_type(sK9)) )
=> ( ( ~ member(ordered_pair(sK12,sK13),compose5(sK7,sK8,sK9,sK10,sK11))
| ! [X7] :
( ~ member(ordered_pair(sK12,X7),sK10)
| ~ member(ordered_pair(X7,sK13),sK11)
| ~ ilf_type(X7,member_type(sK8)) ) )
& ( member(ordered_pair(sK12,sK13),compose5(sK7,sK8,sK9,sK10,sK11))
| ? [X8] :
( member(ordered_pair(sK12,X8),sK10)
& member(ordered_pair(X8,sK13),sK11)
& ilf_type(X8,member_type(sK8)) ) )
& ilf_type(sK13,member_type(sK9)) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
( ? [X8] :
( member(ordered_pair(sK12,X8),sK10)
& member(ordered_pair(X8,sK13),sK11)
& ilf_type(X8,member_type(sK8)) )
=> ( member(ordered_pair(sK12,sK14),sK10)
& member(ordered_pair(sK14,sK13),sK11)
& ilf_type(sK14,member_type(sK8)) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
? [X0] :
( ~ empty(X0)
& ? [X1] :
( ? [X2] :
( ~ empty(X2)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,relation_type(X1,X2))
& ? [X5] :
( ilf_type(X5,member_type(X0))
& ? [X6] :
( ( ~ member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
| ! [X7] :
( ~ member(ordered_pair(X5,X7),X3)
| ~ member(ordered_pair(X7,X6),X4)
| ~ ilf_type(X7,member_type(X1)) ) )
& ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
| ? [X8] :
( member(ordered_pair(X5,X8),X3)
& member(ordered_pair(X8,X6),X4)
& ilf_type(X8,member_type(X1)) ) )
& ilf_type(X6,member_type(X2)) ) ) )
& ilf_type(X3,relation_type(X0,X1)) )
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(rectify,[],[f92]) ).
fof(f92,plain,
? [X0] :
( ~ empty(X0)
& ? [X1] :
( ? [X2] :
( ~ empty(X2)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,relation_type(X1,X2))
& ? [X5] :
( ilf_type(X5,member_type(X0))
& ? [X6] :
( ( ~ member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
| ! [X7] :
( ~ member(ordered_pair(X5,X7),X3)
| ~ member(ordered_pair(X7,X6),X4)
| ~ ilf_type(X7,member_type(X1)) ) )
& ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
| ? [X7] :
( member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4)
& ilf_type(X7,member_type(X1)) ) )
& ilf_type(X6,member_type(X2)) ) ) )
& ilf_type(X3,relation_type(X0,X1)) )
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
? [X0] :
( ~ empty(X0)
& ? [X1] :
( ? [X2] :
( ~ empty(X2)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,relation_type(X1,X2))
& ? [X5] :
( ilf_type(X5,member_type(X0))
& ? [X6] :
( ( ~ member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
| ! [X7] :
( ~ member(ordered_pair(X5,X7),X3)
| ~ member(ordered_pair(X7,X6),X4)
| ~ ilf_type(X7,member_type(X1)) ) )
& ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
| ? [X7] :
( member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4)
& ilf_type(X7,member_type(X1)) ) )
& ilf_type(X6,member_type(X2)) ) ) )
& ilf_type(X3,relation_type(X0,X1)) )
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f63]) ).
fof(f63,plain,
? [X0] :
( ~ empty(X0)
& ? [X1] :
( ? [X2] :
( ~ empty(X2)
& ? [X3] :
( ? [X4] :
( ilf_type(X4,relation_type(X1,X2))
& ? [X5] :
( ilf_type(X5,member_type(X0))
& ? [X6] :
( ( ? [X7] :
( member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4)
& ilf_type(X7,member_type(X1)) )
<~> member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ilf_type(X6,member_type(X2)) ) ) )
& ilf_type(X3,relation_type(X0,X1)) )
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ilf_type(X4,relation_type(X1,X2))
& ? [X5] :
( ilf_type(X5,member_type(X0))
& ? [X6] :
( ( ? [X7] :
( member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4)
& ilf_type(X7,member_type(X1)) )
<~> member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ilf_type(X6,member_type(X2)) ) ) )
& ilf_type(X3,relation_type(X0,X1)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,member_type(X0))
=> ! [X6] :
( ilf_type(X6,member_type(X2))
=> ( ? [X7] :
( member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4)
& ilf_type(X7,member_type(X1)) )
<=> member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f30]) ).
fof(f30,conjecture,
! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,member_type(X0))
=> ! [X6] :
( ilf_type(X6,member_type(X2))
=> ( ? [X7] :
( member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4)
& ilf_type(X7,member_type(X1)) )
<=> member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_51) ).
fof(f258,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(subsumption_resolution,[],[f257,f173]) ).
fof(f257,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f170,f173]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ) ) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
=> ilf_type(X3,relation_type(X0,X1)) ) ) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(f651,plain,
( ~ ilf_type(sK10,binary_relation_type)
| ~ spl19_2
| spl19_3
| ~ spl19_4
| ~ spl19_7 ),
inference(subsumption_resolution,[],[f649,f592]) ).
fof(f592,plain,
( ~ member(unordered_pair(unordered_pair(sK12,sK13),singleton(sK12)),compose(sK10,sK11))
| ~ spl19_2
| spl19_3 ),
inference(forward_demodulation,[],[f591,f564]) ).
fof(f564,plain,
( ! [X2,X3] : ordered_pair(X2,X3) = unordered_pair(unordered_pair(X2,X3),singleton(X2))
| ~ spl19_2 ),
inference(subsumption_resolution,[],[f563,f173]) ).
fof(f563,plain,
( ! [X2,X3] :
( ordered_pair(X2,X3) = unordered_pair(unordered_pair(X2,X3),singleton(X2))
| ~ ilf_type(ordered_pair(X2,X3),set_type) )
| ~ spl19_2 ),
inference(subsumption_resolution,[],[f562,f173]) ).
fof(f562,plain,
( ! [X2,X3] :
( ~ ilf_type(X3,set_type)
| ~ ilf_type(ordered_pair(X2,X3),set_type)
| ordered_pair(X2,X3) = unordered_pair(unordered_pair(X2,X3),singleton(X2)) )
| ~ spl19_2 ),
inference(subsumption_resolution,[],[f199,f173]) ).
fof(f199,plain,
( ! [X2,X3] :
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(ordered_pair(X2,X3),set_type)
| ordered_pair(X2,X3) = unordered_pair(unordered_pair(X2,X3),singleton(X2)) )
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f198,plain,
( spl19_2
<=> ! [X2,X3] :
( ~ ilf_type(X2,set_type)
| ~ ilf_type(ordered_pair(X2,X3),set_type)
| ordered_pair(X2,X3) = unordered_pair(unordered_pair(X2,X3),singleton(X2))
| ~ ilf_type(X3,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_2])]) ).
fof(f591,plain,
( ~ member(ordered_pair(sK12,sK13),compose(sK10,sK11))
| spl19_3 ),
inference(forward_demodulation,[],[f203,f374]) ).
fof(f374,plain,
compose5(sK7,sK8,sK9,sK10,sK11) = compose(sK10,sK11),
inference(resolution,[],[f352,f147]) ).
fof(f352,plain,
! [X14,X15] :
( ~ ilf_type(X14,relation_type(X15,sK8))
| compose(X14,sK11) = compose5(X15,sK8,sK9,X14,sK11) ),
inference(resolution,[],[f261,f154]) ).
fof(f154,plain,
ilf_type(sK11,relation_type(sK8,sK9)),
inference(cnf_transformation,[],[f102]) ).
fof(f261,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X4,relation_type(X1,X2))
| ~ ilf_type(X3,relation_type(X0,X1))
| compose5(X0,X1,X2,X3,X4) = compose(X3,X4) ),
inference(subsumption_resolution,[],[f260,f173]) ).
fof(f260,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X4,relation_type(X1,X2))
| compose5(X0,X1,X2,X3,X4) = compose(X3,X4)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f259,f173]) ).
fof(f259,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X4,relation_type(X1,X2))
| compose5(X0,X1,X2,X3,X4) = compose(X3,X4)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f181,f173]) ).
fof(f181,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X4,relation_type(X1,X2))
| compose5(X0,X1,X2,X3,X4) = compose(X3,X4)
| ~ ilf_type(X2,set_type) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ ilf_type(X3,relation_type(X0,X1))
| ! [X4] :
( compose5(X0,X1,X2,X3,X4) = compose(X3,X4)
| ~ ilf_type(X4,relation_type(X1,X2)) ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> compose5(X0,X1,X2,X3,X4) = compose(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(f203,plain,
( ~ member(ordered_pair(sK12,sK13),compose5(sK7,sK8,sK9,sK10,sK11))
| spl19_3 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f202,plain,
( spl19_3
<=> member(ordered_pair(sK12,sK13),compose5(sK7,sK8,sK9,sK10,sK11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_3])]) ).
fof(f649,plain,
( member(unordered_pair(unordered_pair(sK12,sK13),singleton(sK12)),compose(sK10,sK11))
| ~ ilf_type(sK10,binary_relation_type)
| ~ spl19_2
| ~ spl19_4
| ~ spl19_7 ),
inference(resolution,[],[f643,f579]) ).
fof(f579,plain,
( member(unordered_pair(unordered_pair(sK12,sK14),singleton(sK12)),sK10)
| ~ spl19_2
| ~ spl19_7 ),
inference(forward_demodulation,[],[f242,f564]) ).
fof(f242,plain,
( member(ordered_pair(sK12,sK14),sK10)
| ~ spl19_7 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f240,plain,
( spl19_7
<=> member(ordered_pair(sK12,sK14),sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_7])]) ).
fof(f643,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,sK14),singleton(X0)),X1)
| ~ ilf_type(X1,binary_relation_type)
| member(unordered_pair(unordered_pair(X0,sK13),singleton(X0)),compose(X1,sK11)) )
| ~ spl19_2
| ~ spl19_4 ),
inference(subsumption_resolution,[],[f640,f318]) ).
fof(f318,plain,
ilf_type(sK11,binary_relation_type),
inference(resolution,[],[f317,f262]) ).
fof(f317,plain,
relation_like(sK11),
inference(resolution,[],[f312,f219]) ).
fof(f312,plain,
ilf_type(sK11,subset_type(cross_product(sK8,sK9))),
inference(resolution,[],[f258,f154]) ).
fof(f640,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,sK14),singleton(X0)),X1)
| member(unordered_pair(unordered_pair(X0,sK13),singleton(X0)),compose(X1,sK11))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(sK11,binary_relation_type) )
| ~ spl19_2
| ~ spl19_4 ),
inference(resolution,[],[f585,f566]) ).
fof(f566,plain,
( member(unordered_pair(unordered_pair(sK14,sK13),singleton(sK14)),sK11)
| ~ spl19_2
| ~ spl19_4 ),
inference(forward_demodulation,[],[f208,f564]) ).
fof(f208,plain,
( member(ordered_pair(sK14,sK13),sK11)
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f206,plain,
( spl19_4
<=> member(ordered_pair(sK14,sK13),sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_4])]) ).
fof(f585,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X4,X1),singleton(X4)),X3)
| ~ member(unordered_pair(unordered_pair(X0,X4),singleton(X0)),X2)
| member(unordered_pair(unordered_pair(X0,X1),singleton(X0)),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type) )
| ~ spl19_2 ),
inference(forward_demodulation,[],[f584,f564]) ).
fof(f584,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X4,X1),X3)
| ~ ilf_type(X3,binary_relation_type)
| member(unordered_pair(unordered_pair(X0,X1),singleton(X0)),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X4),singleton(X0)),X2)
| ~ ilf_type(X2,binary_relation_type) )
| ~ spl19_2 ),
inference(forward_demodulation,[],[f583,f564]) ).
fof(f583,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X2,binary_relation_type)
| member(ordered_pair(X0,X1),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X4),singleton(X0)),X2)
| ~ member(ordered_pair(X4,X1),X3)
| ~ ilf_type(X3,binary_relation_type) )
| ~ spl19_2 ),
inference(forward_demodulation,[],[f226,f564]) ).
fof(f226,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X0,X4),X2)
| member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X4,X1),X3) ),
inference(subsumption_resolution,[],[f225,f173]) ).
fof(f225,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X4,X1),X3)
| ~ member(ordered_pair(X0,X4),X2)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X4,set_type) ),
inference(subsumption_resolution,[],[f224,f173]) ).
fof(f224,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X0,X4),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| member(ordered_pair(X0,X1),compose(X2,X3))
| ~ member(ordered_pair(X4,X1),X3)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,binary_relation_type) ),
inference(subsumption_resolution,[],[f168,f173]) ).
fof(f168,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X2,binary_relation_type)
| member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X0,X4),X2)
| ~ member(ordered_pair(X4,X1),X3) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ! [X3] :
( ( ( member(ordered_pair(X0,X1),compose(X2,X3))
| ! [X4] :
( ~ member(ordered_pair(X4,X1),X3)
| ~ member(ordered_pair(X0,X4),X2)
| ~ ilf_type(X4,set_type) ) )
& ( ( member(ordered_pair(sK16(X0,X1,X2,X3),X1),X3)
& member(ordered_pair(X0,sK16(X0,X1,X2,X3)),X2)
& ilf_type(sK16(X0,X1,X2,X3),set_type) )
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ) )
| ~ ilf_type(X3,binary_relation_type) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f107,f108]) ).
fof(f108,plain,
! [X0,X1,X2,X3] :
( ? [X5] :
( member(ordered_pair(X5,X1),X3)
& member(ordered_pair(X0,X5),X2)
& ilf_type(X5,set_type) )
=> ( member(ordered_pair(sK16(X0,X1,X2,X3),X1),X3)
& member(ordered_pair(X0,sK16(X0,X1,X2,X3)),X2)
& ilf_type(sK16(X0,X1,X2,X3),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ! [X3] :
( ( ( member(ordered_pair(X0,X1),compose(X2,X3))
| ! [X4] :
( ~ member(ordered_pair(X4,X1),X3)
| ~ member(ordered_pair(X0,X4),X2)
| ~ ilf_type(X4,set_type) ) )
& ( ? [X5] :
( member(ordered_pair(X5,X1),X3)
& member(ordered_pair(X0,X5),X2)
& ilf_type(X5,set_type) )
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ) )
| ~ ilf_type(X3,binary_relation_type) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f106]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ! [X3] :
( ( ( member(ordered_pair(X0,X1),compose(X2,X3))
| ! [X4] :
( ~ member(ordered_pair(X4,X1),X3)
| ~ member(ordered_pair(X0,X4),X2)
| ~ ilf_type(X4,set_type) ) )
& ( ? [X4] :
( member(ordered_pair(X4,X1),X3)
& member(ordered_pair(X0,X4),X2)
& ilf_type(X4,set_type) )
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ) )
| ~ ilf_type(X3,binary_relation_type) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,binary_relation_type)
| ! [X3] :
( ( member(ordered_pair(X0,X1),compose(X2,X3))
<=> ? [X4] :
( member(ordered_pair(X4,X1),X3)
& member(ordered_pair(X0,X4),X2)
& ilf_type(X4,set_type) ) )
| ~ ilf_type(X3,binary_relation_type) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(ordered_pair(X0,X1),compose(X2,X3))
<=> ? [X4] :
( member(ordered_pair(X4,X1),X3)
& member(ordered_pair(X0,X4),X2)
& ilf_type(X4,set_type) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f573,plain,
~ spl19_1,
inference(avatar_contradiction_clause,[],[f572]) ).
fof(f572,plain,
( $false
| ~ spl19_1 ),
inference(subsumption_resolution,[],[f196,f173]) ).
fof(f196,plain,
( ! [X1] : ~ ilf_type(X1,set_type)
| ~ spl19_1 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f195,plain,
( spl19_1
<=> ! [X1] : ~ ilf_type(X1,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_1])]) ).
fof(f561,plain,
( ~ spl19_3
| ~ spl19_5
| ~ spl19_6 ),
inference(avatar_contradiction_clause,[],[f560]) ).
fof(f560,plain,
( $false
| ~ spl19_3
| ~ spl19_5
| ~ spl19_6 ),
inference(subsumption_resolution,[],[f558,f545]) ).
fof(f545,plain,
( ~ member(sK16(sK12,sK13,sK10,sK11),sK8)
| ~ spl19_3
| ~ spl19_5
| ~ spl19_6 ),
inference(resolution,[],[f538,f265]) ).
fof(f265,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(subsumption_resolution,[],[f264,f250]) ).
fof(f250,plain,
! [X2,X0] :
( ~ empty(X0)
| ~ member(X2,X0) ),
inference(subsumption_resolution,[],[f249,f173]) ).
fof(f249,plain,
! [X2,X0] :
( ~ empty(X0)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ),
inference(subsumption_resolution,[],[f133,f173]) ).
fof(f133,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X0,set_type)
| ~ empty(X0)
| ~ ilf_type(X2,set_type) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( empty(X0)
| ( member(sK5(X0),X0)
& ilf_type(sK5(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f83,f84]) ).
fof(f84,plain,
! [X0] :
( ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) )
=> ( member(sK5(X0),X0)
& ilf_type(sK5(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) ) ),
inference(rectify,[],[f82]) ).
fof(f82,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ empty(X0) ) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) )
<=> empty(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).
fof(f264,plain,
! [X0,X1] :
( ~ member(X0,X1)
| empty(X1)
| ilf_type(X0,member_type(X1)) ),
inference(subsumption_resolution,[],[f263,f173]) ).
fof(f263,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ member(X0,X1)
| empty(X1)
| ilf_type(X0,member_type(X1)) ),
inference(subsumption_resolution,[],[f132,f173]) ).
fof(f132,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| ilf_type(X0,member_type(X1))
| empty(X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(f538,plain,
( ~ ilf_type(sK16(sK12,sK13,sK10,sK11),member_type(sK8))
| ~ spl19_3
| ~ spl19_5
| ~ spl19_6 ),
inference(subsumption_resolution,[],[f531,f513]) ).
fof(f513,plain,
( member(unordered_pair(unordered_pair(sK16(sK12,sK13,sK10,sK11),sK13),singleton(sK16(sK12,sK13,sK10,sK11))),sK11)
| ~ spl19_3
| ~ spl19_6 ),
inference(subsumption_resolution,[],[f512,f318]) ).
fof(f512,plain,
( member(unordered_pair(unordered_pair(sK16(sK12,sK13,sK10,sK11),sK13),singleton(sK16(sK12,sK13,sK10,sK11))),sK11)
| ~ ilf_type(sK11,binary_relation_type)
| ~ spl19_3
| ~ spl19_6 ),
inference(subsumption_resolution,[],[f504,f315]) ).
fof(f504,plain,
( member(unordered_pair(unordered_pair(sK16(sK12,sK13,sK10,sK11),sK13),singleton(sK16(sK12,sK13,sK10,sK11))),sK11)
| ~ ilf_type(sK10,binary_relation_type)
| ~ ilf_type(sK11,binary_relation_type)
| ~ spl19_3
| ~ spl19_6 ),
inference(resolution,[],[f500,f296]) ).
fof(f296,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X1),singleton(X0)),compose(X2,X3))
| ~ ilf_type(X2,binary_relation_type)
| member(unordered_pair(unordered_pair(sK16(X0,X1,X2,X3),X1),singleton(sK16(X0,X1,X2,X3))),X3)
| ~ ilf_type(X3,binary_relation_type) )
| ~ spl19_6 ),
inference(forward_demodulation,[],[f278,f274]) ).
fof(f274,plain,
( ! [X2,X3] : ordered_pair(X2,X3) = unordered_pair(unordered_pair(X2,X3),singleton(X2))
| ~ spl19_6 ),
inference(subsumption_resolution,[],[f273,f173]) ).
fof(f273,plain,
( ! [X2,X3] :
( ~ ilf_type(X2,set_type)
| ordered_pair(X2,X3) = unordered_pair(unordered_pair(X2,X3),singleton(X2)) )
| ~ spl19_6 ),
inference(subsumption_resolution,[],[f272,f173]) ).
fof(f272,plain,
( ! [X2,X3] :
( ~ ilf_type(unordered_pair(unordered_pair(X2,X3),singleton(X2)),set_type)
| ordered_pair(X2,X3) = unordered_pair(unordered_pair(X2,X3),singleton(X2))
| ~ ilf_type(X2,set_type) )
| ~ spl19_6 ),
inference(subsumption_resolution,[],[f216,f173]) ).
fof(f216,plain,
( ! [X2,X3] :
( ordered_pair(X2,X3) = unordered_pair(unordered_pair(X2,X3),singleton(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(unordered_pair(unordered_pair(X2,X3),singleton(X2)),set_type)
| ~ ilf_type(X3,set_type) )
| ~ spl19_6 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f215,plain,
( spl19_6
<=> ! [X2,X3] :
( ~ ilf_type(unordered_pair(unordered_pair(X2,X3),singleton(X2)),set_type)
| ~ ilf_type(X2,set_type)
| ordered_pair(X2,X3) = unordered_pair(unordered_pair(X2,X3),singleton(X2))
| ~ ilf_type(X3,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_6])]) ).
fof(f278,plain,
( ! [X2,X3,X0,X1] :
( member(ordered_pair(sK16(X0,X1,X2,X3),X1),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(unordered_pair(unordered_pair(X0,X1),singleton(X0)),compose(X2,X3))
| ~ ilf_type(X2,binary_relation_type) )
| ~ spl19_6 ),
inference(backward_demodulation,[],[f223,f274]) ).
fof(f223,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X2,binary_relation_type)
| member(ordered_pair(sK16(X0,X1,X2,X3),X1),X3) ),
inference(subsumption_resolution,[],[f222,f173]) ).
fof(f222,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| member(ordered_pair(sK16(X0,X1,X2,X3),X1),X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type) ),
inference(subsumption_resolution,[],[f167,f173]) ).
fof(f167,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ member(ordered_pair(X0,X1),compose(X2,X3))
| member(ordered_pair(sK16(X0,X1,X2,X3),X1),X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type) ),
inference(cnf_transformation,[],[f109]) ).
fof(f500,plain,
( member(unordered_pair(unordered_pair(sK12,sK13),singleton(sK12)),compose(sK10,sK11))
| ~ spl19_3
| ~ spl19_6 ),
inference(forward_demodulation,[],[f499,f274]) ).
fof(f499,plain,
( member(ordered_pair(sK12,sK13),compose(sK10,sK11))
| ~ spl19_3 ),
inference(forward_demodulation,[],[f204,f374]) ).
fof(f204,plain,
( member(ordered_pair(sK12,sK13),compose5(sK7,sK8,sK9,sK10,sK11))
| ~ spl19_3 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f531,plain,
( ~ ilf_type(sK16(sK12,sK13,sK10,sK11),member_type(sK8))
| ~ member(unordered_pair(unordered_pair(sK16(sK12,sK13,sK10,sK11),sK13),singleton(sK16(sK12,sK13,sK10,sK11))),sK11)
| ~ spl19_3
| ~ spl19_5
| ~ spl19_6 ),
inference(resolution,[],[f511,f295]) ).
fof(f295,plain,
( ! [X7] :
( ~ member(unordered_pair(unordered_pair(sK12,X7),singleton(sK12)),sK10)
| ~ member(unordered_pair(unordered_pair(X7,sK13),singleton(X7)),sK11)
| ~ ilf_type(X7,member_type(sK8)) )
| ~ spl19_5
| ~ spl19_6 ),
inference(forward_demodulation,[],[f282,f274]) ).
fof(f282,plain,
( ! [X7] :
( ~ member(unordered_pair(unordered_pair(X7,sK13),singleton(X7)),sK11)
| ~ ilf_type(X7,member_type(sK8))
| ~ member(ordered_pair(sK12,X7),sK10) )
| ~ spl19_5
| ~ spl19_6 ),
inference(backward_demodulation,[],[f212,f274]) ).
fof(f212,plain,
( ! [X7] :
( ~ member(ordered_pair(sK12,X7),sK10)
| ~ member(ordered_pair(X7,sK13),sK11)
| ~ ilf_type(X7,member_type(sK8)) )
| ~ spl19_5 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f211,plain,
( spl19_5
<=> ! [X7] :
( ~ member(ordered_pair(sK12,X7),sK10)
| ~ member(ordered_pair(X7,sK13),sK11)
| ~ ilf_type(X7,member_type(sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_5])]) ).
fof(f511,plain,
( member(unordered_pair(unordered_pair(sK12,sK16(sK12,sK13,sK10,sK11)),singleton(sK12)),sK10)
| ~ spl19_3
| ~ spl19_6 ),
inference(subsumption_resolution,[],[f510,f315]) ).
fof(f510,plain,
( ~ ilf_type(sK10,binary_relation_type)
| member(unordered_pair(unordered_pair(sK12,sK16(sK12,sK13,sK10,sK11)),singleton(sK12)),sK10)
| ~ spl19_3
| ~ spl19_6 ),
inference(subsumption_resolution,[],[f505,f318]) ).
fof(f505,plain,
( ~ ilf_type(sK11,binary_relation_type)
| member(unordered_pair(unordered_pair(sK12,sK16(sK12,sK13,sK10,sK11)),singleton(sK12)),sK10)
| ~ ilf_type(sK10,binary_relation_type)
| ~ spl19_3
| ~ spl19_6 ),
inference(resolution,[],[f500,f292]) ).
fof(f292,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X1),singleton(X0)),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| member(unordered_pair(unordered_pair(X0,sK16(X0,X1,X2,X3)),singleton(X0)),X2)
| ~ ilf_type(X2,binary_relation_type) )
| ~ spl19_6 ),
inference(forward_demodulation,[],[f291,f274]) ).
fof(f291,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X1),singleton(X0)),compose(X2,X3))
| member(ordered_pair(X0,sK16(X0,X1,X2,X3)),X2)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type) )
| ~ spl19_6 ),
inference(subsumption_resolution,[],[f290,f173]) ).
fof(f290,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ member(unordered_pair(unordered_pair(X0,X1),singleton(X0)),compose(X2,X3))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type)
| member(ordered_pair(X0,sK16(X0,X1,X2,X3)),X2) )
| ~ spl19_6 ),
inference(subsumption_resolution,[],[f276,f173]) ).
fof(f276,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(X2,binary_relation_type)
| member(ordered_pair(X0,sK16(X0,X1,X2,X3)),X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(unordered_pair(unordered_pair(X0,X1),singleton(X0)),compose(X2,X3)) )
| ~ spl19_6 ),
inference(backward_demodulation,[],[f166,f274]) ).
fof(f166,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type)
| member(ordered_pair(X0,sK16(X0,X1,X2,X3)),X2)
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f109]) ).
fof(f558,plain,
( member(sK16(sK12,sK13,sK10,sK11),sK8)
| ~ spl19_3
| ~ spl19_6 ),
inference(resolution,[],[f534,f147]) ).
fof(f534,plain,
( ! [X4,X5] :
( ~ ilf_type(sK10,relation_type(X5,X4))
| member(sK16(sK12,sK13,sK10,sK11),X4) )
| ~ spl19_3
| ~ spl19_6 ),
inference(resolution,[],[f511,f281]) ).
fof(f281,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X4)
| member(X3,X1)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ spl19_6 ),
inference(backward_demodulation,[],[f269,f274]) ).
fof(f269,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X4,relation_type(X0,X1))
| member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4) ),
inference(subsumption_resolution,[],[f268,f173]) ).
fof(f268,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| member(X3,X1) ),
inference(subsumption_resolution,[],[f267,f173]) ).
fof(f267,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4) ),
inference(subsumption_resolution,[],[f266,f173]) ).
fof(f266,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X4,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f184,f173]) ).
fof(f184,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| member(X3,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ! [X4] :
( ~ member(ordered_pair(X2,X3),X4)
| ( member(X3,X1)
& member(X2,X0) )
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X3,X1)
& member(X2,X0) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f243,plain,
( spl19_3
| spl19_7 ),
inference(avatar_split_clause,[],[f151,f240,f202]) ).
fof(f151,plain,
( member(ordered_pair(sK12,sK14),sK10)
| member(ordered_pair(sK12,sK13),compose5(sK7,sK8,sK9,sK10,sK11)) ),
inference(cnf_transformation,[],[f102]) ).
fof(f217,plain,
( spl19_1
| spl19_1
| spl19_6 ),
inference(avatar_split_clause,[],[f188,f215,f195,f195]) ).
fof(f188,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(unordered_pair(unordered_pair(X2,X3),singleton(X2)),set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ordered_pair(X2,X3) = unordered_pair(unordered_pair(X2,X3),singleton(X2))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type) ),
inference(equality_resolution,[],[f180]) ).
fof(f180,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X4,set_type)
| ordered_pair(X2,X3) = X4
| unordered_pair(unordered_pair(X2,X3),singleton(X2)) != X4
| ~ ilf_type(X3,set_type) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ! [X4] :
( ~ ilf_type(X4,set_type)
| ( ( ordered_pair(X2,X3) = X4
| unordered_pair(unordered_pair(X2,X3),singleton(X2)) != X4 )
& ( unordered_pair(unordered_pair(X2,X3),singleton(X2)) = X4
| ordered_pair(X2,X3) != X4 ) ) )
| ~ ilf_type(X3,set_type) ) ) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ! [X4] :
( ~ ilf_type(X4,set_type)
| ( ordered_pair(X2,X3) = X4
<=> unordered_pair(unordered_pair(X2,X3),singleton(X2)) = X4 ) )
| ~ ilf_type(X3,set_type) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ( ordered_pair(X2,X3) = X4
<=> unordered_pair(unordered_pair(X2,X3),singleton(X2)) = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f213,plain,
( ~ spl19_3
| spl19_5 ),
inference(avatar_split_clause,[],[f152,f211,f202]) ).
fof(f152,plain,
! [X7] :
( ~ member(ordered_pair(sK12,X7),sK10)
| ~ ilf_type(X7,member_type(sK8))
| ~ member(ordered_pair(X7,sK13),sK11)
| ~ member(ordered_pair(sK12,sK13),compose5(sK7,sK8,sK9,sK10,sK11)) ),
inference(cnf_transformation,[],[f102]) ).
fof(f209,plain,
( spl19_3
| spl19_4 ),
inference(avatar_split_clause,[],[f150,f206,f202]) ).
fof(f150,plain,
( member(ordered_pair(sK14,sK13),sK11)
| member(ordered_pair(sK12,sK13),compose5(sK7,sK8,sK9,sK10,sK11)) ),
inference(cnf_transformation,[],[f102]) ).
fof(f200,plain,
( spl19_1
| spl19_2
| spl19_1 ),
inference(avatar_split_clause,[],[f189,f195,f198,f195]) ).
fof(f189,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ordered_pair(X2,X3) = unordered_pair(unordered_pair(X2,X3),singleton(X2))
| ~ ilf_type(ordered_pair(X2,X3),set_type)
| ~ ilf_type(X1,set_type) ),
inference(equality_resolution,[],[f179]) ).
fof(f179,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X4,set_type)
| unordered_pair(unordered_pair(X2,X3),singleton(X2)) = X4
| ordered_pair(X2,X3) != X4
| ~ ilf_type(X3,set_type) ),
inference(cnf_transformation,[],[f114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET684+3 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.10/0.31 % Computer : n024.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Aug 30 14:16:19 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.15/0.47 % (13296)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)
% 0.15/0.48 % (13305)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)
% 0.15/0.48 % (13297)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)
% 0.15/0.48 % (13288)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)
% 0.15/0.49 % (13284)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)
% 0.15/0.49 % (13290)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.50 % (13290)Instruction limit reached!
% 0.15/0.50 % (13290)------------------------------
% 0.15/0.50 % (13290)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.50 % (13290)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.50 % (13290)Termination reason: Unknown
% 0.15/0.50 % (13290)Termination phase: shuffling
% 0.15/0.50
% 0.15/0.50 % (13290)Memory used [KB]: 895
% 0.15/0.50 % (13290)Time elapsed: 0.006 s
% 0.15/0.50 % (13290)Instructions burned: 2 (million)
% 0.15/0.50 % (13290)------------------------------
% 0.15/0.50 % (13290)------------------------------
% 0.15/0.50 % (13292)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.15/0.50 % (13283)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)
% 0.15/0.50 % (13295)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.15/0.50 % (13293)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)
% 0.15/0.50 TRYING [1]
% 0.15/0.50 % (13304)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)
% 0.15/0.51 % (13282)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)
% 0.15/0.51 TRYING [2]
% 0.15/0.52 % (13286)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.15/0.52 % (13285)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)
% 0.15/0.52 % (13287)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)
% 0.15/0.52 % (13307)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.15/0.52 % (13298)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)
% 0.15/0.53 % (13299)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.15/0.53 % (13294)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.15/0.53 % (13308)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)
% 0.15/0.53 % (13302)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)
% 0.15/0.53 % (13291)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)
% 0.15/0.53 % (13306)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.15/0.54 % (13309)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)
% 0.15/0.54 % (13311)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)
% 0.15/0.54 % (13305)First to succeed.
% 0.15/0.54 % (13300)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.15/0.54 % (13301)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)
% 0.15/0.54 % (13303)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.15/0.54 TRYING [1]
% 0.15/0.55 % (13310)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.15/0.56 TRYING [3]
% 0.15/0.56 % (13288)Instruction limit reached!
% 0.15/0.56 % (13288)------------------------------
% 0.15/0.56 % (13288)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.56 % (13288)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.56 % (13288)Termination reason: Unknown
% 0.15/0.56 % (13288)Termination phase: Finite model building constraint generation
% 0.15/0.56
% 0.15/0.56 % (13288)Memory used [KB]: 7419
% 0.15/0.56 % (13288)Time elapsed: 0.191 s
% 0.15/0.56 % (13288)Instructions burned: 52 (million)
% 0.15/0.56 % (13288)------------------------------
% 0.15/0.56 % (13288)------------------------------
% 0.15/0.56 % (13305)Refutation found. Thanks to Tanya!
% 0.15/0.56 % SZS status Theorem for theBenchmark
% 0.15/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.56 % (13305)------------------------------
% 0.15/0.56 % (13305)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.56 % (13305)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.56 % (13305)Termination reason: Refutation
% 0.15/0.56
% 0.15/0.56 % (13305)Memory used [KB]: 6012
% 0.15/0.56 % (13305)Time elapsed: 0.113 s
% 0.15/0.56 % (13305)Instructions burned: 30 (million)
% 0.15/0.56 % (13305)------------------------------
% 0.15/0.56 % (13305)------------------------------
% 0.15/0.56 % (13281)Success in time 0.245 s
%------------------------------------------------------------------------------