TSTP Solution File: SEU262+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU262+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n016.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 17:05:17 EDT 2023
% Result : Theorem 16.31s 3.18s
% Output : CNFRefutation 16.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 96 ( 10 unt; 0 def)
% Number of atoms : 313 ( 28 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 362 ( 145 ~; 146 |; 43 &)
% ( 13 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 3 con; 0-2 aty)
% Number of variables : 269 ( 6 sgn; 172 !; 35 ?)
% Comments :
%------------------------------------------------------------------------------
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(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,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(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f18,axiom,
! [X0,X1,X2] :
( 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(f26,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f28,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f29,conjecture,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( subset(relation_rng(X2),X1)
& subset(relation_dom(X2),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( subset(relation_rng(X2),X1)
& subset(relation_dom(X2),X0) ) ),
inference(negated_conjecture,[],[f29]) ).
fof(f33,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f41,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f42,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
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,[],[f5]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f45,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f46,plain,
? [X0,X1,X2] :
( ( ~ subset(relation_rng(X2),X1)
| ~ subset(relation_dom(X2),X0) )
& relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f56,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f57,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f57,f58]) ).
fof(f60,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(f61,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,[],[f60]) ).
fof(f62,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(sK1(X0,X1),X3),X0)
| ~ in(sK1(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK1(X0,X1),X4),X0)
| in(sK1(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK1(X0,X1),X4),X0)
=> in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK3(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK1(X0,X1),X3),X0)
| ~ in(sK1(X0,X1),X1) )
& ( in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X0)
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK3(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f61,f64,f63,f62]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f44]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(X3,sK4(X0,X1)),X0)
| ~ in(sK4(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK4(X0,X1)),X0)
| in(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK4(X0,X1)),X0)
=> in(ordered_pair(sK5(X0,X1),sK4(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK6(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK4(X0,X1)),X0)
| ~ in(sK4(X0,X1),X1) )
& ( in(ordered_pair(sK5(X0,X1),sK4(X0,X1)),X0)
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK6(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f67,f70,f69,f68]) ).
fof(f82,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(f83,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f84,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
( ? [X0,X1,X2] :
( ( ~ subset(relation_rng(X2),X1)
| ~ subset(relation_dom(X2),X0) )
& relation_of2_as_subset(X2,X0,X1) )
=> ( ( ~ subset(relation_rng(sK14),sK13)
| ~ subset(relation_dom(sK14),sK12) )
& relation_of2_as_subset(sK14,sK12,sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
( ( ~ subset(relation_rng(sK14),sK13)
| ~ subset(relation_dom(sK14),sK12) )
& relation_of2_as_subset(sK14,sK12,sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f46,f85]) ).
fof(f87,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f89,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f41]) ).
fof(f91,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f92,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f93,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f94,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK3(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f98,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK6(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f102,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f103,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f111,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f112,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f114,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f115,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f117,plain,
relation_of2_as_subset(sK14,sK12,sK13),
inference(cnf_transformation,[],[f86]) ).
fof(f118,plain,
( ~ subset(relation_rng(sK14),sK13)
| ~ subset(relation_dom(sK14),sK12) ),
inference(cnf_transformation,[],[f86]) ).
fof(f121,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f131,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK3(X0,X5)),singleton(X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f94,f102]) ).
fof(f135,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK6(X0,X5),X5),singleton(sK6(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f98,f102]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f115,f102]) ).
fof(f139,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f114,f102]) ).
fof(f141,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK3(X0,X5)),singleton(X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f131]) ).
fof(f143,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(sK6(X0,X5),X5),singleton(sK6(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f135]) ).
cnf(c_50,plain,
( ~ element(X0,powerset(cartesian_product2(X1,X2)))
| relation(X0) ),
inference(cnf_transformation,[],[f89]) ).
cnf(c_52,plain,
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
cnf(c_53,plain,
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
cnf(c_54,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f91]) ).
cnf(c_58,plain,
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,sK3(X1,X0)),singleton(X0)),X1) ),
inference(cnf_transformation,[],[f141]) ).
cnf(c_62,plain,
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK6(X1,X0),X0),singleton(sK6(X1,X0))),X1) ),
inference(cnf_transformation,[],[f143]) ).
cnf(c_63,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[],[f103]) ).
cnf(c_71,plain,
( ~ relation_of2(X0,X1,X2)
| relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_72,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f111]) ).
cnf(c_75,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f138]) ).
cnf(c_76,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f139]) ).
cnf(c_77,negated_conjecture,
( ~ subset(relation_dom(sK14),sK12)
| ~ subset(relation_rng(sK14),sK13) ),
inference(cnf_transformation,[],[f118]) ).
cnf(c_78,negated_conjecture,
relation_of2_as_subset(sK14,sK12,sK13),
inference(cnf_transformation,[],[f117]) ).
cnf(c_82,plain,
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
cnf(c_114,plain,
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_72]) ).
cnf(c_115,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_114]) ).
cnf(c_132,plain,
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_71,c_63]) ).
cnf(c_133,plain,
( ~ relation_of2(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(renaming,[status(thm)],[c_132]) ).
cnf(c_431,plain,
( X0 != sK14
| X1 != sK12
| X2 != sK13
| relation_of2(X0,X1,X2) ),
inference(resolution_lifted,[status(thm)],[c_115,c_78]) ).
cnf(c_432,plain,
relation_of2(sK14,sK12,sK13),
inference(unflattening,[status(thm)],[c_431]) ).
cnf(c_450,plain,
( X0 != sK14
| X1 != sK12
| X2 != sK13
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(resolution_lifted,[status(thm)],[c_133,c_432]) ).
cnf(c_451,plain,
element(sK14,powerset(cartesian_product2(sK12,sK13))),
inference(unflattening,[status(thm)],[c_450]) ).
cnf(c_2175,plain,
( ~ element(sK14,powerset(cartesian_product2(sK12,sK13)))
| relation(sK14) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_3738,plain,
subset(sK14,cartesian_product2(sK12,sK13)),
inference(resolution,[status(thm)],[c_82,c_451]) ).
cnf(c_3753,plain,
( ~ in(X0,sK14)
| in(X0,cartesian_product2(sK12,sK13)) ),
inference(resolution,[status(thm)],[c_54,c_3738]) ).
cnf(c_6120,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK14)
| in(X1,sK13) ),
inference(resolution,[status(thm)],[c_75,c_3753]) ).
cnf(c_6126,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK14)
| in(X0,sK12) ),
inference(resolution,[status(thm)],[c_76,c_3753]) ).
cnf(c_8399,plain,
( ~ in(X0,relation_dom(sK14))
| ~ relation(sK14)
| in(X0,sK12) ),
inference(resolution,[status(thm)],[c_6126,c_58]) ).
cnf(c_8450,plain,
( ~ in(X0,relation_dom(sK14))
| in(X0,sK12) ),
inference(global_subsumption_just,[status(thm)],[c_8399,c_451,c_2175,c_8399]) ).
cnf(c_8461,plain,
( in(sK0(relation_dom(sK14),X0),sK12)
| subset(relation_dom(sK14),X0) ),
inference(resolution,[status(thm)],[c_8450,c_53]) ).
cnf(c_8596,plain,
subset(relation_dom(sK14),sK12),
inference(resolution,[status(thm)],[c_8461,c_52]) ).
cnf(c_9427,plain,
( ~ in(X0,relation_rng(sK14))
| ~ relation(sK14)
| in(X0,sK13) ),
inference(resolution,[status(thm)],[c_62,c_6120]) ).
cnf(c_10244,plain,
( ~ in(X0,relation_rng(sK14))
| in(X0,sK13) ),
inference(global_subsumption_just,[status(thm)],[c_9427,c_451,c_2175,c_9427]) ).
cnf(c_10255,plain,
( in(sK0(relation_rng(sK14),X0),sK13)
| subset(relation_rng(sK14),X0) ),
inference(resolution,[status(thm)],[c_10244,c_53]) ).
cnf(c_10403,plain,
subset(relation_rng(sK14),sK13),
inference(resolution,[status(thm)],[c_10255,c_52]) ).
cnf(c_10404,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10403,c_8596,c_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU262+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 01:58:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 16.31/3.18 % SZS status Started for theBenchmark.p
% 16.31/3.18 % SZS status Theorem for theBenchmark.p
% 16.31/3.18
% 16.31/3.18 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 16.31/3.18
% 16.31/3.18 ------ iProver source info
% 16.31/3.18
% 16.31/3.18 git: date: 2023-05-31 18:12:56 +0000
% 16.31/3.18 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 16.31/3.18 git: non_committed_changes: false
% 16.31/3.18 git: last_make_outside_of_git: false
% 16.31/3.18
% 16.31/3.18 ------ Parsing...
% 16.31/3.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 16.31/3.18
% 16.31/3.18 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e
% 16.31/3.18
% 16.31/3.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 16.31/3.18
% 16.31/3.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 16.31/3.18 ------ Proving...
% 16.31/3.18 ------ Problem Properties
% 16.31/3.18
% 16.31/3.18
% 16.31/3.18 clauses 36
% 16.31/3.18 conjectures 1
% 16.31/3.18 EPR 13
% 16.31/3.18 Horn 32
% 16.31/3.18 unary 10
% 16.31/3.18 binary 12
% 16.31/3.18 lits 80
% 16.31/3.18 lits eq 7
% 16.31/3.18 fd_pure 0
% 16.31/3.18 fd_pseudo 0
% 16.31/3.18 fd_cond 1
% 16.31/3.18 fd_pseudo_cond 5
% 16.31/3.18 AC symbols 0
% 16.31/3.18
% 16.31/3.18 ------ Input Options Time Limit: Unbounded
% 16.31/3.18
% 16.31/3.18
% 16.31/3.18 ------
% 16.31/3.18 Current options:
% 16.31/3.18 ------
% 16.31/3.18
% 16.31/3.18
% 16.31/3.18
% 16.31/3.18
% 16.31/3.18 ------ Proving...
% 16.31/3.18
% 16.31/3.18
% 16.31/3.18 % SZS status Theorem for theBenchmark.p
% 16.31/3.18
% 16.31/3.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.31/3.18
% 16.31/3.19
%------------------------------------------------------------------------------