TSTP Solution File: SEU265+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU265+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 18:32:54 EDT 2022
% Result : Theorem 0.18s 0.57s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 24
% Syntax : Number of formulae : 129 ( 22 unt; 0 def)
% Number of atoms : 371 ( 77 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 388 ( 146 ~; 159 |; 46 &)
% ( 10 <=>; 25 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 277 ( 231 !; 46 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f472,plain,
$false,
inference(subsumption_resolution,[],[f470,f417]) ).
fof(f417,plain,
empty_set != sF14,
inference(forward_demodulation,[],[f416,f362]) ).
fof(f362,plain,
empty_set = sK5,
inference(subsumption_resolution,[],[f361,f293]) ).
fof(f293,plain,
( sK5 = sF14
| empty_set = sK5 ),
inference(resolution,[],[f289,f141]) ).
fof(f141,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f289,plain,
( empty(sK5)
| sK5 = sF14 ),
inference(subsumption_resolution,[],[f288,f274]) ).
fof(f274,plain,
( in(sK0(sK5,sF14),sK5)
| empty(sK5)
| sK5 = sF14 ),
inference(factoring,[],[f217]) ).
fof(f217,plain,
! [X3] :
( in(sK0(X3,sF14),X3)
| in(sK0(X3,sF14),sK5)
| sF14 = X3
| empty(sK5) ),
inference(resolution,[],[f117,f200]) ).
fof(f200,plain,
! [X0] :
( ~ in(X0,sF14)
| empty(sK5)
| in(X0,sK5) ),
inference(resolution,[],[f198,f122]) ).
fof(f122,plain,
! [X0,X1] :
( ~ element(X1,X0)
| in(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ~ element(X1,X0)
| empty(X0)
| in(X1,X0) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X1,X0] :
( empty(X0)
| in(X1,X0)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,plain,
! [X1,X0] :
( element(X1,X0)
=> ( empty(X0)
| in(X1,X0) ) ),
inference(rectify,[],[f32]) ).
fof(f32,axiom,
! [X1,X0] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f198,plain,
! [X0] :
( element(X0,sK5)
| ~ in(X0,sF14) ),
inference(resolution,[],[f197,f114]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ element(X0,powerset(X2))
| element(X1,X2)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ in(X1,X0)
| ~ element(X0,powerset(X2))
| element(X1,X2) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X2,X0,X1] :
( element(X1,X2)
| ~ in(X1,X0)
| ~ element(X0,powerset(X2)) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ( in(X1,X0)
& element(X0,powerset(X2)) )
=> element(X1,X2) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X1,X0,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f197,plain,
element(sF14,powerset(sK5)),
inference(forward_demodulation,[],[f195,f152]) ).
fof(f152,plain,
sF14 = relation_dom_as_subset(sK5,sK6,sK4),
introduced(function_definition,[]) ).
fof(f195,plain,
element(relation_dom_as_subset(sK5,sK6,sK4),powerset(sK5)),
inference(resolution,[],[f138,f165]) ).
fof(f165,plain,
relation_of2(sK4,sK5,sK6),
inference(resolution,[],[f120,f132]) ).
fof(f132,plain,
relation_of2_as_subset(sK4,sK5,sK6),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
( relation_of2_as_subset(sK4,sK5,sK6)
& ( sK5 != relation_dom_as_subset(sK5,sK6,sK4)
| ( in(sK7,sK5)
& ! [X4] : ~ in(ordered_pair(sK7,X4),sK4) ) )
& ( sK5 = relation_dom_as_subset(sK5,sK6,sK4)
| ! [X5] :
( ~ in(X5,sK5)
| in(ordered_pair(X5,sK8(X5)),sK4) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f92,f95,f94,f93]) ).
fof(f93,plain,
( ? [X0,X1,X2] :
( relation_of2_as_subset(X0,X1,X2)
& ( relation_dom_as_subset(X1,X2,X0) != X1
| ? [X3] :
( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X3,X4),X0) ) )
& ( relation_dom_as_subset(X1,X2,X0) = X1
| ! [X5] :
( ~ in(X5,X1)
| ? [X6] : in(ordered_pair(X5,X6),X0) ) ) )
=> ( relation_of2_as_subset(sK4,sK5,sK6)
& ( sK5 != relation_dom_as_subset(sK5,sK6,sK4)
| ? [X3] :
( in(X3,sK5)
& ! [X4] : ~ in(ordered_pair(X3,X4),sK4) ) )
& ( sK5 = relation_dom_as_subset(sK5,sK6,sK4)
| ! [X5] :
( ~ in(X5,sK5)
| ? [X6] : in(ordered_pair(X5,X6),sK4) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
( ? [X3] :
( in(X3,sK5)
& ! [X4] : ~ in(ordered_pair(X3,X4),sK4) )
=> ( in(sK7,sK5)
& ! [X4] : ~ in(ordered_pair(sK7,X4),sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
! [X5] :
( ? [X6] : in(ordered_pair(X5,X6),sK4)
=> in(ordered_pair(X5,sK8(X5)),sK4) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
? [X0,X1,X2] :
( relation_of2_as_subset(X0,X1,X2)
& ( relation_dom_as_subset(X1,X2,X0) != X1
| ? [X3] :
( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X3,X4),X0) ) )
& ( relation_dom_as_subset(X1,X2,X0) = X1
| ! [X5] :
( ~ in(X5,X1)
| ? [X6] : in(ordered_pair(X5,X6),X0) ) ) ),
inference(rectify,[],[f91]) ).
fof(f91,plain,
? [X2,X1,X0] :
( relation_of2_as_subset(X2,X1,X0)
& ( relation_dom_as_subset(X1,X0,X2) != X1
| ? [X3] :
( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X3,X4),X2) ) )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ! [X3] :
( ~ in(X3,X1)
| ? [X4] : in(ordered_pair(X3,X4),X2) ) ) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
? [X2,X1,X0] :
( relation_of2_as_subset(X2,X1,X0)
& ( relation_dom_as_subset(X1,X0,X2) != X1
| ? [X3] :
( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X3,X4),X2) ) )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ! [X3] :
( ~ in(X3,X1)
| ? [X4] : in(ordered_pair(X3,X4),X2) ) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f66,plain,
? [X2,X1,X0] :
( relation_of2_as_subset(X2,X1,X0)
& ( ! [X3] :
( ~ in(X3,X1)
| ? [X4] : in(ordered_pair(X3,X4),X2) )
<~> relation_dom_as_subset(X1,X0,X2) = X1 ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,negated_conjecture,
~ ! [X0,X2,X1] :
( relation_of2_as_subset(X2,X1,X0)
=> ( ! [X3] :
~ ( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
& in(X3,X1) )
<=> relation_dom_as_subset(X1,X0,X2) = X1 ) ),
inference(negated_conjecture,[],[f30]) ).
fof(f30,conjecture,
! [X0,X2,X1] :
( relation_of2_as_subset(X2,X1,X0)
=> ( ! [X3] :
~ ( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
& in(X3,X1) )
<=> relation_dom_as_subset(X1,X0,X2) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_relset_1) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X2,X1)
| relation_of2(X0,X2,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ( relation_of2(X0,X2,X1)
| ~ relation_of2_as_subset(X0,X2,X1) )
& ( relation_of2_as_subset(X0,X2,X1)
| ~ relation_of2(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X2] :
( relation_of2(X0,X2,X1)
<=> relation_of2_as_subset(X0,X2,X1) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X2,X1,X0] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ relation_of2(X0,X2,X1)
| element(relation_dom_as_subset(X2,X1,X0),powerset(X2)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ~ relation_of2(X0,X2,X1)
| element(relation_dom_as_subset(X2,X1,X0),powerset(X2)) ),
inference(rectify,[],[f57]) ).
fof(f57,plain,
! [X1,X2,X0] :
( ~ relation_of2(X1,X0,X2)
| element(relation_dom_as_subset(X0,X2,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,plain,
! [X1,X0,X2] :
( relation_of2(X1,X0,X2)
=> element(relation_dom_as_subset(X0,X2,X1),powerset(X0)) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X0,X2,X1] :
( relation_of2(X2,X0,X1)
=> element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_1) ).
fof(f117,plain,
! [X0,X1] :
( in(sK0(X0,X1),X1)
| in(sK0(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK0(X0,X1),X1)
| ~ in(sK0(X0,X1),X0) )
& ( in(sK0(X0,X1),X1)
| in(sK0(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f76,f77]) ).
fof(f77,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK0(X0,X1),X1)
| ~ in(sK0(X0,X1),X0) )
& ( in(sK0(X0,X1),X1)
| in(sK0(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X1)
<=> in(X2,X0) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f288,plain,
( sK5 = sF14
| ~ in(sK0(sK5,sF14),sK5)
| empty(sK5) ),
inference(duplicate_literal_removal,[],[f284]) ).
fof(f284,plain,
( ~ in(sK0(sK5,sF14),sK5)
| sK5 = sF14
| empty(sK5)
| sK5 = sF14 ),
inference(resolution,[],[f283,f118]) ).
fof(f118,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| ~ in(sK0(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f78]) ).
fof(f283,plain,
( in(sK0(sK5,sF14),sF14)
| empty(sK5)
| sK5 = sF14 ),
inference(duplicate_literal_removal,[],[f281]) ).
fof(f281,plain,
( empty(sK5)
| in(sK0(sK5,sF14),sF14)
| sK5 = sF14
| sK5 = sF14 ),
inference(resolution,[],[f274,f214]) ).
fof(f214,plain,
! [X0] :
( ~ in(X0,sK5)
| in(X0,sF14)
| sK5 = sF14 ),
inference(forward_demodulation,[],[f213,f207]) ).
fof(f207,plain,
relation_dom(sK4) = sF14,
inference(forward_demodulation,[],[f205,f152]) ).
fof(f205,plain,
relation_dom(sK4) = relation_dom_as_subset(sK5,sK6,sK4),
inference(resolution,[],[f139,f165]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| relation_dom(X0) = relation_dom_as_subset(X1,X2,X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2] :
( relation_dom(X0) = relation_dom_as_subset(X1,X2,X0)
| ~ relation_of2(X0,X1,X2) ),
inference(rectify,[],[f56]) ).
fof(f56,plain,
! [X2,X1,X0] :
( relation_dom(X2) = relation_dom_as_subset(X1,X0,X2)
| ~ relation_of2(X2,X1,X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X2,X1] :
( relation_of2(X2,X1,X0)
=> relation_dom(X2) = relation_dom_as_subset(X1,X0,X2) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X1,X0,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f213,plain,
! [X0] :
( in(X0,relation_dom(sK4))
| sK5 = sF14
| ~ in(X0,sK5) ),
inference(subsumption_resolution,[],[f212,f191]) ).
fof(f191,plain,
relation(sK4),
inference(resolution,[],[f188,f132]) ).
fof(f188,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ),
inference(resolution,[],[f142,f123]) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X1,X0)))
| relation(X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(cartesian_product2(X1,X0)))
| relation(X2) ),
inference(rectify,[],[f67]) ).
fof(f67,plain,
! [X1,X0,X2] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f142,plain,
! [X2,X0,X1] :
( element(X0,powerset(cartesian_product2(X2,X1)))
| ~ relation_of2_as_subset(X0,X2,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1,X2] :
( element(X0,powerset(cartesian_product2(X2,X1)))
| ~ relation_of2_as_subset(X0,X2,X1) ),
inference(rectify,[],[f75]) ).
fof(f75,plain,
! [X1,X0,X2] :
( element(X1,powerset(cartesian_product2(X2,X0)))
| ~ relation_of2_as_subset(X1,X2,X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X1,X2,X0)
=> element(X1,powerset(cartesian_product2(X2,X0))) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X1,X2,X0] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f212,plain,
! [X0] :
( sK5 = sF14
| in(X0,relation_dom(sK4))
| ~ in(X0,sK5)
| ~ relation(sK4) ),
inference(resolution,[],[f150,f155]) ).
fof(f155,plain,
! [X5] :
( in(ordered_pair(X5,sK8(X5)),sK4)
| ~ in(X5,sK5)
| sK5 = sF14 ),
inference(definition_folding,[],[f129,f152]) ).
fof(f129,plain,
! [X5] :
( sK5 = relation_dom_as_subset(sK5,sK6,sK4)
| ~ in(X5,sK5)
| in(ordered_pair(X5,sK8(X5)),sK4) ),
inference(cnf_transformation,[],[f96]) ).
fof(f150,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f144]) ).
fof(f144,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK11(X0,X1),X3),X0)
| ~ in(sK11(X0,X1),X1) )
& ( in(ordered_pair(sK11(X0,X1),sK12(X0,X1)),X0)
| in(sK11(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK13(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f108,f111,f110,f109]) ).
fof(f109,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(sK11(X0,X1),X3),X0)
| ~ in(sK11(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK11(X0,X1),X4),X0)
| in(sK11(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK11(X0,X1),X4),X0)
=> in(ordered_pair(sK11(X0,X1),sK12(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK13(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f107]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f361,plain,
( empty_set = sK5
| sK5 != sF14 ),
inference(resolution,[],[f357,f153]) ).
fof(f153,plain,
( in(sK7,sK5)
| sK5 != sF14 ),
inference(definition_folding,[],[f131,f152]) ).
fof(f131,plain,
( sK5 != relation_dom_as_subset(sK5,sK6,sK4)
| in(sK7,sK5) ),
inference(cnf_transformation,[],[f96]) ).
fof(f357,plain,
( ~ in(sK7,sK5)
| empty_set = sK5 ),
inference(duplicate_literal_removal,[],[f356]) ).
fof(f356,plain,
( empty_set = sK5
| ~ in(sK7,sK5)
| empty_set = sK5 ),
inference(superposition,[],[f355,f293]) ).
fof(f355,plain,
( ~ in(sK7,sF14)
| empty_set = sK5 ),
inference(resolution,[],[f312,f230]) ).
fof(f230,plain,
! [X6] :
( in(ordered_pair(X6,sK13(sK4,X6)),sK4)
| ~ in(X6,sF14) ),
inference(forward_demodulation,[],[f228,f207]) ).
fof(f228,plain,
! [X6] :
( in(ordered_pair(X6,sK13(sK4,X6)),sK4)
| ~ in(X6,relation_dom(sK4)) ),
inference(resolution,[],[f151,f191]) ).
fof(f151,plain,
! [X0,X5] :
( ~ relation(X0)
| in(ordered_pair(X5,sK13(X0,X5)),X0)
| ~ in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f143]) ).
fof(f143,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK13(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f312,plain,
! [X0] :
( ~ in(ordered_pair(sK7,X0),sK4)
| empty_set = sK5 ),
inference(trivial_inequality_removal,[],[f295]) ).
fof(f295,plain,
! [X0] :
( ~ in(ordered_pair(sK7,X0),sK4)
| sK5 != sK5
| empty_set = sK5 ),
inference(superposition,[],[f154,f293]) ).
fof(f154,plain,
! [X4] :
( sK5 != sF14
| ~ in(ordered_pair(sK7,X4),sK4) ),
inference(definition_folding,[],[f130,f152]) ).
fof(f130,plain,
! [X4] :
( sK5 != relation_dom_as_subset(sK5,sK6,sK4)
| ~ in(ordered_pair(sK7,X4),sK4) ),
inference(cnf_transformation,[],[f96]) ).
fof(f416,plain,
sK5 != sF14,
inference(subsumption_resolution,[],[f365,f157]) ).
fof(f157,plain,
! [X1] : ~ in(X1,empty_set),
inference(resolution,[],[f128,f133]) ).
fof(f133,plain,
empty(empty_set),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f128,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ empty(X0) ),
inference(rectify,[],[f60]) ).
fof(f60,plain,
! [X1,X0] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f365,plain,
( in(sK7,empty_set)
| sK5 != sF14 ),
inference(backward_demodulation,[],[f153,f362]) ).
fof(f470,plain,
empty_set = sF14,
inference(resolution,[],[f467,f141]) ).
fof(f467,plain,
empty(sF14),
inference(resolution,[],[f462,f168]) ).
fof(f168,plain,
! [X0] :
( in(sK2(X0),X0)
| empty(X0) ),
inference(resolution,[],[f122,f125]) ).
fof(f125,plain,
! [X0] : element(sK2(X0),X0),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] : element(sK2(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f19,f85]) ).
fof(f85,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK2(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f462,plain,
! [X0] : ~ in(X0,sF14),
inference(resolution,[],[f371,f176]) ).
fof(f176,plain,
! [X0,X1] :
( ~ element(X1,powerset(empty_set))
| ~ in(X0,X1) ),
inference(resolution,[],[f137,f133]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(rectify,[],[f69]) ).
fof(f69,plain,
! [X0,X2,X1] :
( ~ empty(X2)
| ~ in(X1,X0)
| ~ element(X0,powerset(X2)) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
! [X2,X1,X0] :
~ ( element(X0,powerset(X2))
& in(X1,X0)
& empty(X2) ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X1,X0,X2] :
~ ( element(X1,powerset(X2))
& empty(X2)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f371,plain,
element(sF14,powerset(empty_set)),
inference(backward_demodulation,[],[f197,f362]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU265+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 30 15:01:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.52 % (13653)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)
% 0.18/0.52 % (13670)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)
% 0.18/0.52 % (13662)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)
% 0.18/0.53 TRYING [1]
% 0.18/0.53 % (13669)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)
% 0.18/0.53 TRYING [2]
% 0.18/0.54 % (13654)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.54 TRYING [3]
% 0.18/0.55 % (13661)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)
% 0.18/0.55 % (13654)Instruction limit reached!
% 0.18/0.55 % (13654)------------------------------
% 0.18/0.55 % (13654)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.55 % (13654)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.55 % (13654)Termination reason: Unknown
% 0.18/0.55 % (13654)Termination phase: Saturation
% 0.18/0.55
% 0.18/0.55 % (13654)Memory used [KB]: 5500
% 0.18/0.55 % (13654)Time elapsed: 0.084 s
% 0.18/0.55 % (13654)Instructions burned: 7 (million)
% 0.18/0.55 % (13654)------------------------------
% 0.18/0.55 % (13654)------------------------------
% 0.18/0.56 % (13662)First to succeed.
% 0.18/0.57 % (13662)Refutation found. Thanks to Tanya!
% 0.18/0.57 % SZS status Theorem for theBenchmark
% 0.18/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.57 % (13662)------------------------------
% 0.18/0.57 % (13662)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.57 % (13662)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.57 % (13662)Termination reason: Refutation
% 0.18/0.57
% 0.18/0.57 % (13662)Memory used [KB]: 1279
% 0.18/0.57 % (13662)Time elapsed: 0.096 s
% 0.18/0.57 % (13662)Instructions burned: 16 (million)
% 0.18/0.57 % (13662)------------------------------
% 0.18/0.57 % (13662)------------------------------
% 0.18/0.57 % (13646)Success in time 0.225 s
%------------------------------------------------------------------------------