TSTP Solution File: SEU227+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU227+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n028.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 : Fri May 3 03:05:06 EDT 2024
% Result : Theorem 10.18s 2.18s
% Output : CNFRefutation 10.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 22
% Syntax : Number of formulae : 108 ( 14 unt; 0 def)
% Number of atoms : 451 ( 39 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 566 ( 223 ~; 224 |; 83 &)
% ( 15 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 2 con; 0-3 aty)
% Number of variables : 317 ( 3 sgn 207 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f7,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,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(f10,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(f41,conjecture,
! [X0,X1] :
( relation(X1)
=> ( subset(X0,relation_dom(X1))
=> subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_funct_1) ).
fof(f42,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( subset(X0,relation_dom(X1))
=> subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ) ),
inference(negated_conjecture,[],[f41]) ).
fof(f44,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f45,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f46,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f47,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f61,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f62,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f63,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f69,plain,
? [X0,X1] :
( ~ subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
& subset(X0,relation_dom(X1))
& relation(X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f70,plain,
? [X0,X1] :
( ~ subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
& subset(X0,relation_dom(X1))
& relation(X1) ),
inference(flattening,[],[f69]) ).
fof(f72,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f73,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f75,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f47]) ).
fof(f80,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f61]) ).
fof(f81,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,X3),X0) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) ) )
& ( ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,X6),X0) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(rectify,[],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,X3),X0) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,sK0(X0,X1,X2)),X0) )
| in(sK0(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,sK0(X0,X1,X2)),X0) )
=> ( in(sK1(X0,X1,X2),X1)
& in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
! [X0,X1,X6] :
( ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,X6),X0) )
=> ( in(sK2(X0,X1,X6),X1)
& in(ordered_pair(sK2(X0,X1,X6),X6),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),X1)
& in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) ) )
& ( ( in(sK2(X0,X1,X6),X1)
& in(ordered_pair(sK2(X0,X1,X6),X6),X0) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f81,f84,f83,f82]) ).
fof(f86,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f62]) ).
fof(f87,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X3,X5),X0) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) ) )
& ( ? [X8] :
( in(X8,X1)
& in(ordered_pair(X6,X8),X0) )
| ~ in(X6,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(rectify,[],[f86]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X3,X5),X0) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(sK3(X0,X1,X2),X4),X0) )
| ~ in(sK3(X0,X1,X2),X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(sK3(X0,X1,X2),X5),X0) )
| in(sK3(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ? [X5] :
( in(X5,X1)
& in(ordered_pair(sK3(X0,X1,X2),X5),X0) )
=> ( in(sK4(X0,X1,X2),X1)
& in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
! [X0,X1,X6] :
( ? [X8] :
( in(X8,X1)
& in(ordered_pair(X6,X8),X0) )
=> ( in(sK5(X0,X1,X6),X1)
& in(ordered_pair(X6,sK5(X0,X1,X6)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f91,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(sK3(X0,X1,X2),X4),X0) )
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(sK4(X0,X1,X2),X1)
& in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X0) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) ) )
& ( ( in(sK5(X0,X1,X6),X1)
& in(ordered_pair(X6,sK5(X0,X1,X6)),X0) )
| ~ in(X6,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f87,f90,f89,f88]) ).
fof(f92,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,[],[f63]) ).
fof(f93,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,[],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f93,f94]) ).
fof(f96,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,[],[f64]) ).
fof(f97,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,[],[f96]) ).
fof(f98,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(sK7(X0,X1),X3),X0)
| ~ in(sK7(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK7(X0,X1),X4),X0)
| in(sK7(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK7(X0,X1),X4),X0)
=> in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK9(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK7(X0,X1),X3),X0)
| ~ in(sK7(X0,X1),X1) )
& ( in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0)
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK9(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f97,f100,f99,f98]) ).
fof(f124,plain,
( ? [X0,X1] :
( ~ subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
& subset(X0,relation_dom(X1))
& relation(X1) )
=> ( ~ subset(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))
& subset(sK21,relation_dom(sK22))
& relation(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f125,plain,
( ~ subset(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))
& subset(sK21,relation_dom(sK22))
& relation(sK22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f70,f124]) ).
fof(f126,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f132,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f135,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f141,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f146,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f147,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f148,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK9(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f152,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f185,plain,
relation(sK22),
inference(cnf_transformation,[],[f125]) ).
fof(f186,plain,
subset(sK21,relation_dom(sK22)),
inference(cnf_transformation,[],[f125]) ).
fof(f187,plain,
~ subset(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),
inference(cnf_transformation,[],[f125]) ).
fof(f189,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f191,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f192,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f193,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f199,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f135,f152]) ).
fof(f203,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f141,f152]) ).
fof(f208,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK9(X0,X5)),singleton(X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f148,f152]) ).
fof(f210,plain,
! [X0,X1,X6,X7] :
( in(X6,relation_image(X0,X1))
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f199]) ).
fof(f213,plain,
! [X0,X1,X6,X7] :
( in(X6,relation_inverse_image(X0,X1))
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f203]) ).
fof(f217,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK9(X0,X5)),singleton(X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f208]) ).
cnf(c_52,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f132]) ).
cnf(c_56,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ in(X0,X3)
| ~ relation(X2)
| in(X1,relation_image(X2,X3)) ),
inference(cnf_transformation,[],[f210]) ).
cnf(c_62,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ in(X1,X3)
| ~ relation(X2)
| in(X0,relation_inverse_image(X2,X3)) ),
inference(cnf_transformation,[],[f213]) ).
cnf(c_65,plain,
( ~ in(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
cnf(c_66,plain,
( in(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f146]) ).
cnf(c_71,plain,
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,sK9(X1,X0)),singleton(X0)),X1) ),
inference(cnf_transformation,[],[f217]) ).
cnf(c_104,negated_conjecture,
~ subset(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),
inference(cnf_transformation,[],[f187]) ).
cnf(c_105,negated_conjecture,
subset(sK21,relation_dom(sK22)),
inference(cnf_transformation,[],[f186]) ).
cnf(c_106,negated_conjecture,
relation(sK22),
inference(cnf_transformation,[],[f185]) ).
cnf(c_108,plain,
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f189]) ).
cnf(c_109,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f191]) ).
cnf(c_111,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| element(X2,X1) ),
inference(cnf_transformation,[],[f192]) ).
cnf(c_112,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f193]) ).
cnf(c_147,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(prop_impl_just,[status(thm)],[c_109]) ).
cnf(c_175,plain,
( ~ in(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_65]) ).
cnf(c_185,plain,
( subset(X0,X1)
| in(sK6(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_66]) ).
cnf(c_186,plain,
( in(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_185]) ).
cnf(c_292,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| element(X0,X2) ),
inference(bin_hyper_res,[status(thm)],[c_111,c_147]) ).
cnf(c_293,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| ~ empty(X2) ),
inference(bin_hyper_res,[status(thm)],[c_112,c_147]) ).
cnf(c_561,plain,
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(X1,X0))),X1) ),
inference(demodulation,[status(thm)],[c_71,c_52]) ).
cnf(c_563,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| ~ in(X1,X3)
| ~ relation(X2)
| in(X0,relation_inverse_image(X2,X3)) ),
inference(demodulation,[status(thm)],[c_62,c_52]) ).
cnf(c_564,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| ~ in(X0,X3)
| ~ relation(X2)
| in(X1,relation_image(X2,X3)) ),
inference(demodulation,[status(thm)],[c_56,c_52]) ).
cnf(c_836,plain,
( relation_inverse_image(sK22,relation_image(sK22,sK21)) != X1
| X0 != sK21
| in(sK6(X0,X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_186,c_104]) ).
cnf(c_837,plain,
in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK21),
inference(unflattening,[status(thm)],[c_836]) ).
cnf(c_841,plain,
( relation_inverse_image(sK22,relation_image(sK22,sK21)) != X1
| X0 != sK21
| ~ in(sK6(X0,X1),X1) ),
inference(resolution_lifted,[status(thm)],[c_175,c_104]) ).
cnf(c_842,plain,
~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_inverse_image(sK22,relation_image(sK22,sK21))),
inference(unflattening,[status(thm)],[c_841]) ).
cnf(c_6673,plain,
( ~ subset(sK21,relation_dom(sK22))
| ~ in(X0,sK21)
| ~ empty(relation_dom(sK22)) ),
inference(instantiation,[status(thm)],[c_293]) ).
cnf(c_6674,plain,
( ~ element(X0,relation_dom(sK22))
| in(X0,relation_dom(sK22))
| empty(relation_dom(sK22)) ),
inference(instantiation,[status(thm)],[c_108]) ).
cnf(c_6685,plain,
( ~ in(unordered_pair(singleton(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))),unordered_pair(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),X0)),sK22)
| ~ in(X0,relation_image(sK22,sK21))
| ~ relation(sK22)
| in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_inverse_image(sK22,relation_image(sK22,sK21))) ),
inference(instantiation,[status(thm)],[c_563]) ).
cnf(c_6721,plain,
( ~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK21)
| ~ subset(sK21,relation_dom(sK22))
| ~ empty(relation_dom(sK22)) ),
inference(instantiation,[status(thm)],[c_6673]) ).
cnf(c_6789,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK22)
| ~ in(X0,sK21)
| ~ relation(sK22)
| in(X1,relation_image(sK22,sK21)) ),
inference(instantiation,[status(thm)],[c_564]) ).
cnf(c_6956,plain,
( ~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK21)
| ~ subset(sK21,X0)
| element(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),X0) ),
inference(instantiation,[status(thm)],[c_292]) ).
cnf(c_7193,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK22,X0))),sK22)
| ~ in(X0,sK21)
| ~ relation(sK22)
| in(sK9(sK22,X0),relation_image(sK22,sK21)) ),
inference(instantiation,[status(thm)],[c_6789]) ).
cnf(c_7618,plain,
( ~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK21)
| ~ subset(sK21,relation_dom(sK22))
| element(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_dom(sK22)) ),
inference(instantiation,[status(thm)],[c_6956]) ).
cnf(c_8524,plain,
( ~ in(X0,relation_dom(sK22))
| ~ relation(sK22)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK22,X0))),sK22) ),
inference(instantiation,[status(thm)],[c_561]) ).
cnf(c_9286,plain,
( ~ element(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_dom(sK22))
| in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_dom(sK22))
| empty(relation_dom(sK22)) ),
inference(instantiation,[status(thm)],[c_6674]) ).
cnf(c_20431,plain,
( ~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_dom(sK22))
| ~ relation(sK22)
| in(unordered_pair(singleton(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))),unordered_pair(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))))),sK22) ),
inference(instantiation,[status(thm)],[c_8524]) ).
cnf(c_24315,plain,
( ~ in(unordered_pair(singleton(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))),unordered_pair(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))))),sK22)
| ~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK21)
| ~ relation(sK22)
| in(sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))),relation_image(sK22,sK21)) ),
inference(instantiation,[status(thm)],[c_7193]) ).
cnf(c_24320,plain,
( ~ in(unordered_pair(singleton(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))),unordered_pair(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))))),sK22)
| ~ in(sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))),relation_image(sK22,sK21))
| ~ relation(sK22)
| in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_inverse_image(sK22,relation_image(sK22,sK21))) ),
inference(instantiation,[status(thm)],[c_6685]) ).
cnf(c_24321,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_24320,c_24315,c_20431,c_9286,c_7618,c_6721,c_842,c_837,c_105,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU227+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n028.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 May 2 18:04:33 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.19/0.48 Running first-order theorem proving
% 0.19/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.18/2.18 % SZS status Started for theBenchmark.p
% 10.18/2.18 % SZS status Theorem for theBenchmark.p
% 10.18/2.18
% 10.18/2.18 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 10.18/2.18
% 10.18/2.18 ------ iProver source info
% 10.18/2.18
% 10.18/2.18 git: date: 2024-05-02 19:28:25 +0000
% 10.18/2.18 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 10.18/2.18 git: non_committed_changes: false
% 10.18/2.18
% 10.18/2.18 ------ Parsing...
% 10.18/2.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 10.18/2.18
% 10.18/2.18 ------ Preprocessing... sup_sim: 12 sf_s rm: 6 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 10.18/2.18
% 10.18/2.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 10.18/2.18
% 10.18/2.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.18/2.18 ------ Proving...
% 10.18/2.18 ------ Problem Properties
% 10.18/2.18
% 10.18/2.18
% 10.18/2.18 clauses 59
% 10.18/2.18 conjectures 3
% 10.18/2.18 EPR 25
% 10.18/2.18 Horn 51
% 10.18/2.18 unary 24
% 10.18/2.18 binary 13
% 10.18/2.18 lits 128
% 10.18/2.18 lits eq 11
% 10.18/2.18 fd_pure 0
% 10.18/2.18 fd_pseudo 0
% 10.18/2.18 fd_cond 1
% 10.18/2.18 fd_pseudo_cond 9
% 10.18/2.18 AC symbols 0
% 10.18/2.18
% 10.18/2.18 ------ Input Options Time Limit: Unbounded
% 10.18/2.18
% 10.18/2.18
% 10.18/2.18 ------
% 10.18/2.18 Current options:
% 10.18/2.18 ------
% 10.18/2.18
% 10.18/2.18
% 10.18/2.18
% 10.18/2.18
% 10.18/2.18 ------ Proving...
% 10.18/2.18
% 10.18/2.18
% 10.18/2.18 % SZS status Theorem for theBenchmark.p
% 10.18/2.18
% 10.18/2.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.18/2.18
% 10.18/2.19
%------------------------------------------------------------------------------