TSTP Solution File: SEU265+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU265+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n023.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 : Thu Aug 31 17:57:27 EDT 2023
% Result : Theorem 0.22s 0.46s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 25
% Syntax : Number of formulae : 124 ( 20 unt; 0 def)
% Number of atoms : 362 ( 65 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 392 ( 154 ~; 163 |; 44 &)
% ( 10 <=>; 19 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 256 (; 210 !; 46 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f625,plain,
$false,
inference(subsumption_resolution,[],[f624,f550]) ).
fof(f550,plain,
in(sK3,sK1),
inference(subsumption_resolution,[],[f132,f549]) ).
fof(f549,plain,
sK1 = sF15,
inference(subsumption_resolution,[],[f547,f506]) ).
fof(f506,plain,
( in(sK9(sK1,sF15),sK1)
| sK1 = sF15 ),
inference(factoring,[],[f491]) ).
fof(f491,plain,
! [X0] :
( in(sK9(X0,sF15),sK1)
| sF15 = X0
| in(sK9(X0,sF15),X0) ),
inference(subsumption_resolution,[],[f488,f395]) ).
fof(f395,plain,
~ empty(sK1),
inference(subsumption_resolution,[],[f394,f289]) ).
fof(f289,plain,
( ~ empty(sK1)
| empty(sF15) ),
inference(forward_literal_rewriting,[],[f285,f145]) ).
fof(f145,plain,
! [X2] :
( ~ sP14(X2)
| empty(X2) ),
inference(resolution,[],[f140,f129]) ).
fof(f129,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ sP14(X1) ),
inference(general_splitting,[],[f123,f128_D]) ).
fof(f128,plain,
! [X2,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| sP14(X1) ),
inference(cnf_transformation,[],[f128_D]) ).
fof(f128_D,plain,
! [X1] :
( ! [X2] :
( ~ element(X1,powerset(X2))
| ~ empty(X2) )
<=> ~ sP14(X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP14])]) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',t5_subset) ).
fof(f140,plain,
! [X0] :
( in(sK8(X0),X0)
| empty(X0) ),
inference(resolution,[],[f106,f99]) ).
fof(f99,plain,
! [X0] : element(sK8(X0),X0),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] : element(sK8(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f19,f75]) ).
fof(f75,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK8(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',existence_m1_subset_1) ).
fof(f106,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',t2_subset) ).
fof(f285,plain,
( ~ empty(sK1)
| sP14(sF15) ),
inference(resolution,[],[f283,f128]) ).
fof(f283,plain,
element(sF15,powerset(sK1)),
inference(subsumption_resolution,[],[f279,f178]) ).
fof(f178,plain,
relation_of2(sK2,sK1,sK0),
inference(resolution,[],[f121,f89]) ).
fof(f89,plain,
relation_of2_as_subset(sK2,sK1,sK0),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
( ( sK1 != relation_dom_as_subset(sK1,sK0,sK2)
| ( ! [X4] : ~ in(ordered_pair(sK3,X4),sK2)
& in(sK3,sK1) ) )
& ( sK1 = relation_dom_as_subset(sK1,sK0,sK2)
| ! [X5] :
( in(ordered_pair(X5,sK4(X5)),sK2)
| ~ in(X5,sK1) ) )
& relation_of2_as_subset(sK2,sK1,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f64,f67,f66,f65]) ).
fof(f65,plain,
( ? [X0,X1,X2] :
( ( relation_dom_as_subset(X1,X0,X2) != X1
| ? [X3] :
( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
& in(X3,X1) ) )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ! [X5] :
( ? [X6] : in(ordered_pair(X5,X6),X2)
| ~ in(X5,X1) ) )
& relation_of2_as_subset(X2,X1,X0) )
=> ( ( sK1 != relation_dom_as_subset(sK1,sK0,sK2)
| ? [X3] :
( ! [X4] : ~ in(ordered_pair(X3,X4),sK2)
& in(X3,sK1) ) )
& ( sK1 = relation_dom_as_subset(sK1,sK0,sK2)
| ! [X5] :
( ? [X6] : in(ordered_pair(X5,X6),sK2)
| ~ in(X5,sK1) ) )
& relation_of2_as_subset(sK2,sK1,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
( ? [X3] :
( ! [X4] : ~ in(ordered_pair(X3,X4),sK2)
& in(X3,sK1) )
=> ( ! [X4] : ~ in(ordered_pair(sK3,X4),sK2)
& in(sK3,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
! [X5] :
( ? [X6] : in(ordered_pair(X5,X6),sK2)
=> in(ordered_pair(X5,sK4(X5)),sK2) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
? [X0,X1,X2] :
( ( relation_dom_as_subset(X1,X0,X2) != X1
| ? [X3] :
( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
& in(X3,X1) ) )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ! [X5] :
( ? [X6] : in(ordered_pair(X5,X6),X2)
| ~ in(X5,X1) ) )
& relation_of2_as_subset(X2,X1,X0) ),
inference(rectify,[],[f63]) ).
fof(f63,plain,
? [X0,X1,X2] :
( ( relation_dom_as_subset(X1,X0,X2) != X1
| ? [X3] :
( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
& in(X3,X1) ) )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ! [X3] :
( ? [X4] : in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1) ) )
& relation_of2_as_subset(X2,X1,X0) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
? [X0,X1,X2] :
( ( relation_dom_as_subset(X1,X0,X2) != X1
| ? [X3] :
( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
& in(X3,X1) ) )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ! [X3] :
( ? [X4] : in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1) ) )
& relation_of2_as_subset(X2,X1,X0) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,plain,
? [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] : in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1) )
<~> relation_dom_as_subset(X1,X0,X2) = X1 )
& relation_of2_as_subset(X2,X1,X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,negated_conjecture,
~ ! [X0,X1,X2] :
( 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,X1,X2] :
( 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/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',t22_relset_1) ).
fof(f121,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',redefinition_m2_relset_1) ).
fof(f279,plain,
( element(sF15,powerset(sK1))
| ~ relation_of2(sK2,sK1,sK0) ),
inference(superposition,[],[f117,f130]) ).
fof(f130,plain,
relation_dom_as_subset(sK1,sK0,sK2) = sF15,
introduced(function_definition,[]) ).
fof(f117,plain,
! [X2,X0,X1] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1,X2] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',dt_k4_relset_1) ).
fof(f394,plain,
( ~ empty(sK1)
| ~ empty(sF15) ),
inference(forward_literal_rewriting,[],[f392,f187]) ).
fof(f187,plain,
! [X0] :
( ~ empty(X0)
| sP14(X0) ),
inference(resolution,[],[f184,f100]) ).
fof(f100,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',reflexivity_r1_tarski) ).
fof(f184,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| sP14(X1)
| ~ empty(X0) ),
inference(resolution,[],[f128,f109]) ).
fof(f109,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',t3_subset) ).
fof(f392,plain,
( ~ empty(sF15)
| ~ sP14(sK1) ),
inference(resolution,[],[f385,f129]) ).
fof(f385,plain,
( in(sK3,sK1)
| ~ empty(sF15) ),
inference(trivial_inequality_removal,[],[f376]) ).
fof(f376,plain,
( sK1 != sK1
| in(sK3,sK1)
| ~ empty(sF15) ),
inference(superposition,[],[f132,f374]) ).
fof(f374,plain,
( sK1 = sF15
| ~ empty(sF15) ),
inference(subsumption_resolution,[],[f373,f110]) ).
fof(f110,plain,
! [X0,X1] :
( X0 = X1
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',t8_boole) ).
fof(f373,plain,
( ~ empty(sF15)
| sK1 = sF15
| empty(sK1) ),
inference(forward_literal_rewriting,[],[f368,f187]) ).
fof(f368,plain,
( sK1 = sF15
| empty(sK1)
| ~ sP14(sF15) ),
inference(resolution,[],[f363,f129]) ).
fof(f363,plain,
( in(sK8(sK1),sF15)
| sK1 = sF15
| empty(sK1) ),
inference(resolution,[],[f332,f140]) ).
fof(f332,plain,
! [X0] :
( ~ in(X0,sK1)
| sK1 = sF15
| in(X0,sF15) ),
inference(forward_demodulation,[],[f331,f274]) ).
fof(f274,plain,
sF15 = relation_dom(sK2),
inference(subsumption_resolution,[],[f272,f178]) ).
fof(f272,plain,
( sF15 = relation_dom(sK2)
| ~ relation_of2(sK2,sK1,sK0) ),
inference(superposition,[],[f116,f130]) ).
fof(f116,plain,
! [X2,X0,X1] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',redefinition_k4_relset_1) ).
fof(f331,plain,
! [X0] :
( in(X0,relation_dom(sK2))
| sK1 = sF15
| ~ in(X0,sK1) ),
inference(subsumption_resolution,[],[f329,f208]) ).
fof(f208,plain,
relation(sK2),
inference(resolution,[],[f203,f178]) ).
fof(f203,plain,
! [X2,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| relation(X0) ),
inference(forward_literal_rewriting,[],[f200,f122]) ).
fof(f122,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f200,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ),
inference(resolution,[],[f118,f119]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',cc1_relset_1) ).
fof(f118,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',dt_m2_relset_1) ).
fof(f329,plain,
! [X0] :
( in(X0,relation_dom(sK2))
| ~ relation(sK2)
| sK1 = sF15
| ~ in(X0,sK1) ),
inference(resolution,[],[f126,f133]) ).
fof(f133,plain,
! [X5] :
( in(ordered_pair(X5,sK4(X5)),sK2)
| sK1 = sF15
| ~ in(X5,sK1) ),
inference(definition_folding,[],[f90,f130]) ).
fof(f90,plain,
! [X5] :
( sK1 = relation_dom_as_subset(sK1,sK0,sK2)
| in(ordered_pair(X5,sK4(X5)),sK2)
| ~ in(X5,sK1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f126,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK5(X0,X1),X3),X0)
| ~ in(sK5(X0,X1),X1) )
& ( in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0)
| in(sK5(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK7(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f70,f73,f72,f71]) ).
fof(f71,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(sK5(X0,X1),X3),X0)
| ~ in(sK5(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK5(X0,X1),X4),X0)
| in(sK5(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK5(X0,X1),X4),X0)
=> in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK7(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f70,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,[],[f69]) ).
fof(f69,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,[],[f43]) ).
fof(f43,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/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',d4_relat_1) ).
fof(f488,plain,
! [X0] :
( in(sK9(X0,sF15),X0)
| sF15 = X0
| empty(sK1)
| in(sK9(X0,sF15),sK1) ),
inference(resolution,[],[f454,f106]) ).
fof(f454,plain,
! [X12] :
( element(sK9(X12,sF15),sK1)
| in(sK9(X12,sF15),X12)
| sF15 = X12 ),
inference(resolution,[],[f107,f284]) ).
fof(f284,plain,
! [X0] :
( ~ in(X0,sF15)
| element(X0,sK1) ),
inference(resolution,[],[f283,f120]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',t4_subset) ).
fof(f107,plain,
! [X0,X1] :
( in(sK9(X0,X1),X1)
| X0 = X1
| in(sK9(X0,X1),X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK9(X0,X1),X1)
| ~ in(sK9(X0,X1),X0) )
& ( in(sK9(X0,X1),X1)
| in(sK9(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f77,f78]) ).
fof(f78,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK9(X0,X1),X1)
| ~ in(sK9(X0,X1),X0) )
& ( in(sK9(X0,X1),X1)
| in(sK9(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778',t2_tarski) ).
fof(f547,plain,
( sK1 = sF15
| ~ in(sK9(sK1,sF15),sK1) ),
inference(duplicate_literal_removal,[],[f545]) ).
fof(f545,plain,
( sK1 = sF15
| ~ in(sK9(sK1,sF15),sK1)
| sK1 = sF15 ),
inference(resolution,[],[f108,f520]) ).
fof(f520,plain,
( in(sK9(sK1,sF15),sF15)
| sK1 = sF15 ),
inference(duplicate_literal_removal,[],[f511]) ).
fof(f511,plain,
( sK1 = sF15
| sK1 = sF15
| in(sK9(sK1,sF15),sF15) ),
inference(resolution,[],[f506,f332]) ).
fof(f108,plain,
! [X0,X1] :
( ~ in(sK9(X0,X1),X1)
| X0 = X1
| ~ in(sK9(X0,X1),X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f132,plain,
( sK1 != sF15
| in(sK3,sK1) ),
inference(definition_folding,[],[f91,f130]) ).
fof(f91,plain,
( sK1 != relation_dom_as_subset(sK1,sK0,sK2)
| in(sK3,sK1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f624,plain,
~ in(sK3,sK1),
inference(forward_demodulation,[],[f623,f549]) ).
fof(f623,plain,
~ in(sK3,sF15),
inference(forward_demodulation,[],[f622,f274]) ).
fof(f622,plain,
~ in(sK3,relation_dom(sK2)),
inference(subsumption_resolution,[],[f613,f208]) ).
fof(f613,plain,
( ~ in(sK3,relation_dom(sK2))
| ~ relation(sK2) ),
inference(resolution,[],[f127,f551]) ).
fof(f551,plain,
! [X4] : ~ in(ordered_pair(sK3,X4),sK2),
inference(subsumption_resolution,[],[f131,f549]) ).
fof(f131,plain,
! [X4] :
( sK1 != sF15
| ~ in(ordered_pair(sK3,X4),sK2) ),
inference(definition_folding,[],[f92,f130]) ).
fof(f92,plain,
! [X4] :
( sK1 != relation_dom_as_subset(sK1,sK0,sK2)
| ~ in(ordered_pair(sK3,X4),sK2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f127,plain,
! [X0,X5] :
( in(ordered_pair(X5,sK7(X0,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK7(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SEU265+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.37 % Computer : n023.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Wed Aug 23 20:33:27 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.14/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.n7tGbnab4b/Vampire---4.8_8778
% 0.14/0.38 % (8885)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44 % (8889)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.22/0.44 % (8892)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.22/0.44 % (8891)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.22/0.44 % (8890)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.22/0.44 % (8887)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.22/0.44 % (8888)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.22/0.44 % (8886)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.22/0.44 % (8889)Refutation not found, incomplete strategy% (8889)------------------------------
% 0.22/0.44 % (8889)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.44 % (8889)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.44 % (8889)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.44
% 0.22/0.44 % (8889)Memory used [KB]: 10106
% 0.22/0.44 % (8889)Time elapsed: 0.007 s
% 0.22/0.44 % (8889)------------------------------
% 0.22/0.44 % (8889)------------------------------
% 0.22/0.45 % (8890)First to succeed.
% 0.22/0.46 % (8890)Refutation found. Thanks to Tanya!
% 0.22/0.46 % SZS status Theorem for Vampire---4
% 0.22/0.46 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.46 % (8890)------------------------------
% 0.22/0.46 % (8890)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.46 % (8890)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.46 % (8890)Termination reason: Refutation
% 0.22/0.46
% 0.22/0.46 % (8890)Memory used [KB]: 1279
% 0.22/0.46 % (8890)Time elapsed: 0.021 s
% 0.22/0.46 % (8890)------------------------------
% 0.22/0.46 % (8890)------------------------------
% 0.22/0.46 % (8885)Success in time 0.079 s
% 0.22/0.46 % Vampire---4.8 exiting
%------------------------------------------------------------------------------