TSTP Solution File: SEU079+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU079+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% 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 : Fri May 3 03:04:28 EDT 2024
% Result : Theorem 72.77s 10.69s
% Output : CNFRefutation 72.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 27
% Syntax : Number of formulae : 117 ( 11 unt; 0 def)
% Number of atoms : 610 ( 55 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 800 ( 307 ~; 313 |; 125 &)
% ( 22 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 3 con; 0-4 aty)
% Number of variables : 421 ( 0 sgn 299 !; 82 ?)
% Comments :
%------------------------------------------------------------------------------
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] :
( 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(f11,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(f12,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( relation_composition(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f13,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f40,conjecture,
! [X0,X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> subset(relation_inverse_image(X1,X0),relation_inverse_image(relation_composition(X1,X2),relation_image(X2,X0))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_funct_1) ).
fof(f41,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> subset(relation_inverse_image(X1,X0),relation_inverse_image(relation_composition(X1,X2),relation_image(X2,X0))) ) ) ),
inference(negated_conjecture,[],[f40]) ).
fof(f60,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(f61,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(f62,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f63,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(f64,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( relation_composition(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f66,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f67,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f66]) ).
fof(f81,plain,
? [X0,X1] :
( ? [X2] :
( ~ subset(relation_inverse_image(X1,X0),relation_inverse_image(relation_composition(X1,X2),relation_image(X2,X0)))
& subset(relation_rng(X1),relation_dom(X2))
& relation(X2) )
& relation(X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f82,plain,
? [X0,X1] :
( ? [X2] :
( ~ subset(relation_inverse_image(X1,X0),relation_inverse_image(relation_composition(X1,X2),relation_image(X2,X0)))
& subset(relation_rng(X1),relation_dom(X2))
& relation(X2) )
& relation(X1) ),
inference(flattening,[],[f81]) ).
fof(f92,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,[],[f60]) ).
fof(f93,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,[],[f92]) ).
fof(f94,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(f95,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(f96,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(f97,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])],[f93,f96,f95,f94]) ).
fof(f98,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,[],[f61]) ).
fof(f99,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,[],[f98]) ).
fof(f100,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(f101,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(f102,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(f103,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])],[f99,f102,f101,f100]) ).
fof(f104,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,[],[f62]) ).
fof(f105,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,[],[f104]) ).
fof(f106,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f107,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])],[f105,f106]) ).
fof(f108,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,[],[f63]) ).
fof(f109,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,[],[f108]) ).
fof(f110,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(f111,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(f112,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK9(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f113,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])],[f109,f112,f111,f110]) ).
fof(f114,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,[],[f64]) ).
fof(f115,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,[],[f114]) ).
fof(f116,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,sK10(X0,X1)),X0)
| ~ in(sK10(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK10(X0,X1)),X0)
| in(sK10(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK10(X0,X1)),X0)
=> in(ordered_pair(sK11(X0,X1),sK10(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f118,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK12(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK10(X0,X1)),X0)
| ~ in(sK10(X0,X1),X1) )
& ( in(ordered_pair(sK11(X0,X1),sK10(X0,X1)),X0)
| in(sK10(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK12(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f115,f118,f117,f116]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( relation_composition(X0,X1) = X2
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) ) )
& ( ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f65]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( relation_composition(X0,X1) = X2
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,X4),X1)
& in(ordered_pair(X3,X6),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) ) )
& ( ? [X10] :
( in(ordered_pair(X10,X8),X1)
& in(ordered_pair(X7,X10),X0) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f120]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,X4),X1)
& in(ordered_pair(X3,X6),X0) )
| in(ordered_pair(X3,X4),X2) ) )
=> ( ( ! [X5] :
( ~ in(ordered_pair(X5,sK14(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK13(X0,X1,X2),X5),X0) )
| ~ in(ordered_pair(sK13(X0,X1,X2),sK14(X0,X1,X2)),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,sK14(X0,X1,X2)),X1)
& in(ordered_pair(sK13(X0,X1,X2),X6),X0) )
| in(ordered_pair(sK13(X0,X1,X2),sK14(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ? [X6] :
( in(ordered_pair(X6,sK14(X0,X1,X2)),X1)
& in(ordered_pair(sK13(X0,X1,X2),X6),X0) )
=> ( in(ordered_pair(sK15(X0,X1,X2),sK14(X0,X1,X2)),X1)
& in(ordered_pair(sK13(X0,X1,X2),sK15(X0,X1,X2)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f124,plain,
! [X0,X1,X7,X8] :
( ? [X10] :
( in(ordered_pair(X10,X8),X1)
& in(ordered_pair(X7,X10),X0) )
=> ( in(ordered_pair(sK16(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK16(X0,X1,X7,X8)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( relation_composition(X0,X1) = X2
| ( ( ! [X5] :
( ~ in(ordered_pair(X5,sK14(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK13(X0,X1,X2),X5),X0) )
| ~ in(ordered_pair(sK13(X0,X1,X2),sK14(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK15(X0,X1,X2),sK14(X0,X1,X2)),X1)
& in(ordered_pair(sK13(X0,X1,X2),sK15(X0,X1,X2)),X0) )
| in(ordered_pair(sK13(X0,X1,X2),sK14(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) ) )
& ( ( in(ordered_pair(sK16(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK16(X0,X1,X7,X8)),X0) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f121,f124,f123,f122]) ).
fof(f148,plain,
( ? [X0,X1] :
( ? [X2] :
( ~ subset(relation_inverse_image(X1,X0),relation_inverse_image(relation_composition(X1,X2),relation_image(X2,X0)))
& subset(relation_rng(X1),relation_dom(X2))
& relation(X2) )
& relation(X1) )
=> ( ? [X2] :
( ~ subset(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,X2),relation_image(X2,sK28)))
& subset(relation_rng(sK29),relation_dom(X2))
& relation(X2) )
& relation(sK29) ) ),
introduced(choice_axiom,[]) ).
fof(f149,plain,
( ? [X2] :
( ~ subset(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,X2),relation_image(X2,sK28)))
& subset(relation_rng(sK29),relation_dom(X2))
& relation(X2) )
=> ( ~ subset(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))
& subset(relation_rng(sK29),relation_dom(sK30))
& relation(sK30) ) ),
introduced(choice_axiom,[]) ).
fof(f150,plain,
( ~ subset(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))
& subset(relation_rng(sK29),relation_dom(sK30))
& relation(sK30)
& relation(sK29) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29,sK30])],[f82,f149,f148]) ).
fof(f160,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,[],[f97]) ).
fof(f164,plain,
! [X2,X0,X1,X6] :
( in(ordered_pair(X6,sK5(X0,X1,X6)),X0)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f165,plain,
! [X2,X0,X1,X6] :
( in(sK5(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f166,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,[],[f103]) ).
fof(f170,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f171,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f172,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f173,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK9(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f178,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f181,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f184,plain,
! [X2,X0,X1,X8,X9,X7] :
( in(ordered_pair(X7,X8),X2)
| ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f188,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f230,plain,
relation(sK29),
inference(cnf_transformation,[],[f150]) ).
fof(f231,plain,
relation(sK30),
inference(cnf_transformation,[],[f150]) ).
fof(f232,plain,
subset(relation_rng(sK29),relation_dom(sK30)),
inference(cnf_transformation,[],[f150]) ).
fof(f233,plain,
~ subset(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),
inference(cnf_transformation,[],[f150]) ).
fof(f245,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,[],[f160,f181]) ).
fof(f249,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,[],[f166,f181]) ).
fof(f250,plain,
! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK5(X0,X1,X6)),singleton(X6)),X0)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f164,f181]) ).
fof(f254,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,[],[f173,f181]) ).
fof(f257,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f178,f181]) ).
fof(f262,plain,
! [X2,X0,X1,X8,X9,X7] :
( in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),X2)
| ~ in(unordered_pair(unordered_pair(X9,X8),singleton(X9)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X9),singleton(X7)),X0)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f184,f181,f181,f181]) ).
fof(f266,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,[],[f245]) ).
fof(f269,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,[],[f249]) ).
fof(f270,plain,
! [X0,X1,X6] :
( in(sK5(X0,X1,X6),X1)
| ~ in(X6,relation_inverse_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f165]) ).
fof(f271,plain,
! [X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK5(X0,X1,X6)),singleton(X6)),X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f250]) ).
fof(f273,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,[],[f254]) ).
fof(f274,plain,
! [X0,X6,X5] :
( in(X5,relation_rng(X0))
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f257]) ).
fof(f276,plain,
! [X0,X1,X8,X9,X7] :
( in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
| ~ in(unordered_pair(unordered_pair(X9,X8),singleton(X9)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X9),singleton(X7)),X0)
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f262]) ).
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,[],[f266]) ).
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,[],[f269]) ).
cnf(c_63,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| in(sK5(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f270]) ).
cnf(c_64,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,sK5(X1,X2,X0)),singleton(X0)),X1) ),
inference(cnf_transformation,[],[f271]) ).
cnf(c_65,plain,
( ~ in(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f172]) ).
cnf(c_66,plain,
( in(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_67,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f170]) ).
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,[],[f273]) ).
cnf(c_74,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(cnf_transformation,[],[f274]) ).
cnf(c_79,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X4)
| ~ relation(relation_composition(X2,X4))
| ~ relation(X2)
| ~ relation(X4)
| in(unordered_pair(unordered_pair(X0,X3),singleton(X0)),relation_composition(X2,X4)) ),
inference(cnf_transformation,[],[f276]) ).
cnf(c_82,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f188]) ).
cnf(c_124,negated_conjecture,
~ subset(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),
inference(cnf_transformation,[],[f233]) ).
cnf(c_125,negated_conjecture,
subset(relation_rng(sK29),relation_dom(sK30)),
inference(cnf_transformation,[],[f232]) ).
cnf(c_126,negated_conjecture,
relation(sK30),
inference(cnf_transformation,[],[f231]) ).
cnf(c_127,negated_conjecture,
relation(sK29),
inference(cnf_transformation,[],[f230]) ).
cnf(c_242,plain,
( in(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),relation_inverse_image(sK29,sK28))
| subset(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))) ),
inference(instantiation,[status(thm)],[c_66]) ).
cnf(c_352,plain,
( ~ in(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),relation_inverse_image(sK29,sK28))
| ~ relation(sK29)
| in(unordered_pair(unordered_pair(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),singleton(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),sK29) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_353,plain,
( ~ in(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),relation_inverse_image(sK29,sK28))
| ~ relation(sK29)
| in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),sK28) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_777,plain,
( ~ in(unordered_pair(unordered_pair(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),singleton(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),sK29)
| ~ relation(sK29)
| in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),relation_rng(sK29)) ),
inference(instantiation,[status(thm)],[c_74]) ).
cnf(c_806,plain,
( ~ in(unordered_pair(unordered_pair(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),X0),singleton(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),X1)
| ~ in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),sK28)
| ~ relation(X1)
| in(X0,relation_image(X1,sK28)) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_2063,plain,
( ~ relation(sK29)
| ~ relation(sK30)
| relation(relation_composition(sK29,sK30)) ),
inference(instantiation,[status(thm)],[c_82]) ).
cnf(c_2319,plain,
( ~ in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),relation_rng(sK29))
| ~ subset(relation_rng(sK29),X0)
| in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),X0) ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_11273,plain,
( ~ in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),relation_rng(sK29))
| ~ subset(relation_rng(sK29),relation_dom(sK30))
| in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),relation_dom(sK30)) ),
inference(instantiation,[status(thm)],[c_2319]) ).
cnf(c_12856,plain,
( ~ in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),relation_dom(sK30))
| ~ relation(sK30)
| in(unordered_pair(unordered_pair(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),singleton(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),sK30) ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_21687,plain,
( ~ in(unordered_pair(unordered_pair(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),singleton(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),sK30)
| ~ in(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),sK28)
| ~ relation(sK30)
| in(sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),relation_image(sK30,sK28)) ),
inference(instantiation,[status(thm)],[c_806]) ).
cnf(c_63714,plain,
( ~ in(unordered_pair(unordered_pair(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),singleton(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),sK30)
| ~ in(unordered_pair(unordered_pair(X0,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),singleton(X0)),X1)
| ~ relation(relation_composition(X1,sK30))
| ~ relation(X1)
| ~ relation(sK30)
| in(unordered_pair(unordered_pair(X0,sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),singleton(X0)),relation_composition(X1,sK30)) ),
inference(instantiation,[status(thm)],[c_79]) ).
cnf(c_68189,plain,
( ~ in(unordered_pair(unordered_pair(X0,sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),singleton(X0)),X1)
| ~ in(sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),relation_image(sK30,sK28))
| ~ relation(X1)
| in(X0,relation_inverse_image(X1,relation_image(sK30,sK28))) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_69942,plain,
( ~ in(unordered_pair(unordered_pair(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))),sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),singleton(sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),sK30)
| ~ in(unordered_pair(unordered_pair(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),singleton(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),sK29)
| ~ relation(relation_composition(sK29,sK30))
| ~ relation(sK29)
| ~ relation(sK30)
| in(unordered_pair(unordered_pair(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),singleton(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),relation_composition(sK29,sK30)) ),
inference(instantiation,[status(thm)],[c_63714]) ).
cnf(c_92879,plain,
( ~ in(unordered_pair(unordered_pair(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))))),singleton(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),relation_composition(sK29,sK30))
| ~ in(sK9(sK30,sK5(sK29,sK28,sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))))),relation_image(sK30,sK28))
| ~ relation(relation_composition(sK29,sK30))
| in(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))) ),
inference(instantiation,[status(thm)],[c_68189]) ).
cnf(c_96309,plain,
( ~ in(sK6(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28)))
| subset(relation_inverse_image(sK29,sK28),relation_inverse_image(relation_composition(sK29,sK30),relation_image(sK30,sK28))) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_96310,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_96309,c_92879,c_69942,c_21687,c_12856,c_11273,c_2063,c_777,c_352,c_353,c_242,c_124,c_125,c_126,c_127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SEU079+1 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.11 % Command : run_iprover %s %d THM
% 0.10/0.31 % Computer : n023.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu May 2 18:00:39 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 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
% 72.77/10.69 % SZS status Started for theBenchmark.p
% 72.77/10.69 % SZS status Theorem for theBenchmark.p
% 72.77/10.69
% 72.77/10.69 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 72.77/10.69
% 72.77/10.69 ------ iProver source info
% 72.77/10.69
% 72.77/10.69 git: date: 2024-05-02 19:28:25 +0000
% 72.77/10.69 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 72.77/10.69 git: non_committed_changes: false
% 72.77/10.69
% 72.77/10.69 ------ Parsing...
% 72.77/10.69 ------ Clausification by vclausify_rel & Parsing by iProver...
% 72.77/10.69
% 72.77/10.69 ------ Preprocessing... sf_s rm: 7 0s sf_e sf_s rm: 2 0s sf_e
% 72.77/10.69
% 72.77/10.69 ------ Preprocessing...
% 72.77/10.69
% 72.77/10.69 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 72.77/10.69 ------ Proving...
% 72.77/10.69 ------ Problem Properties
% 72.77/10.69
% 72.77/10.69
% 72.77/10.69 clauses 79
% 72.77/10.69 conjectures 4
% 72.77/10.69 EPR 24
% 72.77/10.69 Horn 68
% 72.77/10.69 unary 26
% 72.77/10.69 binary 15
% 72.77/10.69 lits 201
% 72.77/10.69 lits eq 16
% 72.77/10.69 fd_pure 0
% 72.77/10.69 fd_pseudo 0
% 72.77/10.69 fd_cond 1
% 72.77/10.69 fd_pseudo_cond 14
% 72.77/10.69 AC symbols 0
% 72.77/10.69
% 72.77/10.69 ------ Input Options Time Limit: Unbounded
% 72.77/10.69
% 72.77/10.69
% 72.77/10.69 ------
% 72.77/10.69 Current options:
% 72.77/10.69 ------
% 72.77/10.69
% 72.77/10.69
% 72.77/10.69
% 72.77/10.69
% 72.77/10.69 ------ Proving...
% 72.77/10.69
% 72.77/10.69
% 72.77/10.69 % SZS status Theorem for theBenchmark.p
% 72.77/10.69
% 72.77/10.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 72.77/10.69
% 72.77/10.69
%------------------------------------------------------------------------------