TSTP Solution File: SEU214+3 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU214+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n019.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 03:05:01 EDT 2024
% Result : Theorem 17.64s 3.18s
% Output : CNFRefutation 17.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 102 ( 17 unt; 0 def)
% Number of atoms : 476 ( 106 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 628 ( 254 ~; 252 |; 85 &)
% ( 14 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-4 aty)
% Number of variables : 256 ( 1 sgn 171 !; 40 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( apply(X0,X1) = X2
<=> empty_set = X2 ) )
& ( in(X1,relation_dom(X0))
=> ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f6,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(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(f8,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(f9,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f13,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f33,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
inference(negated_conjecture,[],[f33]) ).
fof(f49,plain,
! [X0] :
( ! [X1,X2] :
( ( ( apply(X0,X1) = X2
<=> empty_set = X2 )
| in(X1,relation_dom(X0)) )
& ( ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f50,plain,
! [X0] :
( ! [X1,X2] :
( ( ( apply(X0,X1) = X2
<=> empty_set = X2 )
| in(X1,relation_dom(X0)) )
& ( ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f52,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,[],[f8]) ).
fof(f53,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f54,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f53]) ).
fof(f57,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f58,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f57]) ).
fof(f66,plain,
? [X0,X1] :
( ? [X2] :
( apply(relation_composition(X2,X1),X0) != apply(X1,apply(X2,X0))
& in(X0,relation_dom(relation_composition(X2,X1)))
& function(X2)
& relation(X2) )
& function(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f67,plain,
? [X0,X1] :
( ? [X2] :
( apply(relation_composition(X2,X1),X0) != apply(X1,apply(X2,X0))
& in(X0,relation_dom(relation_composition(X2,X1)))
& function(X2)
& relation(X2) )
& function(X1)
& relation(X1) ),
inference(flattening,[],[f66]) ).
fof(f77,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( apply(X0,X1) = X2
| empty_set != X2 )
& ( empty_set = X2
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0)) )
& ( ( ( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0) )
& ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f50]) ).
fof(f78,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,[],[f51]) ).
fof(f79,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,[],[f78]) ).
fof(f80,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(sK0(X0,X1),X3),X0)
| ~ in(sK0(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK0(X0,X1),X4),X0)
| in(sK0(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK0(X0,X1),X4),X0)
=> in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK2(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK0(X0,X1),X3),X0)
| ~ in(sK0(X0,X1),X1) )
& ( in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f79,f82,f81,f80]) ).
fof(f84,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,[],[f52]) ).
fof(f85,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,[],[f84]) ).
fof(f86,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,sK4(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK3(X0,X1,X2),X5),X0) )
| ~ in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,sK4(X0,X1,X2)),X1)
& in(ordered_pair(sK3(X0,X1,X2),X6),X0) )
| in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ? [X6] :
( in(ordered_pair(X6,sK4(X0,X1,X2)),X1)
& in(ordered_pair(sK3(X0,X1,X2),X6),X0) )
=> ( in(ordered_pair(sK5(X0,X1,X2),sK4(X0,X1,X2)),X1)
& in(ordered_pair(sK3(X0,X1,X2),sK5(X0,X1,X2)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
! [X0,X1,X7,X8] :
( ? [X10] :
( in(ordered_pair(X10,X8),X1)
& in(ordered_pair(X7,X10),X0) )
=> ( in(ordered_pair(sK6(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK6(X0,X1,X7,X8)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( relation_composition(X0,X1) = X2
| ( ( ! [X5] :
( ~ in(ordered_pair(X5,sK4(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK3(X0,X1,X2),X5),X0) )
| ~ in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK5(X0,X1,X2),sK4(X0,X1,X2)),X1)
& in(ordered_pair(sK3(X0,X1,X2),sK5(X0,X1,X2)),X0) )
| in(ordered_pair(sK3(X0,X1,X2),sK4(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(sK6(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK6(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,[sK3,sK4,sK5,sK6])],[f85,f88,f87,f86]) ).
fof(f108,plain,
( ? [X0,X1] :
( ? [X2] :
( apply(relation_composition(X2,X1),X0) != apply(X1,apply(X2,X0))
& in(X0,relation_dom(relation_composition(X2,X1)))
& function(X2)
& relation(X2) )
& function(X1)
& relation(X1) )
=> ( ? [X2] :
( apply(relation_composition(X2,sK17),sK16) != apply(sK17,apply(X2,sK16))
& in(sK16,relation_dom(relation_composition(X2,sK17)))
& function(X2)
& relation(X2) )
& function(sK17)
& relation(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
( ? [X2] :
( apply(relation_composition(X2,sK17),sK16) != apply(sK17,apply(X2,sK16))
& in(sK16,relation_dom(relation_composition(X2,sK17)))
& function(X2)
& relation(X2) )
=> ( apply(relation_composition(sK18,sK17),sK16) != apply(sK17,apply(sK18,sK16))
& in(sK16,relation_dom(relation_composition(sK18,sK17)))
& function(sK18)
& relation(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
( apply(relation_composition(sK18,sK17),sK16) != apply(sK17,apply(sK18,sK16))
& in(sK16,relation_dom(relation_composition(sK18,sK17)))
& function(sK18)
& relation(sK18)
& function(sK17)
& relation(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18])],[f67,f109,f108]) ).
fof(f115,plain,
! [X2,X0,X1] :
( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f116,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f119,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f120,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f123,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f124,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(X7,sK6(X0,X1,X7,X8)),X0)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f125,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(sK6(X0,X1,X7,X8),X8),X1)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f130,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f137,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f165,plain,
relation(sK17),
inference(cnf_transformation,[],[f110]) ).
fof(f166,plain,
function(sK17),
inference(cnf_transformation,[],[f110]) ).
fof(f167,plain,
relation(sK18),
inference(cnf_transformation,[],[f110]) ).
fof(f168,plain,
function(sK18),
inference(cnf_transformation,[],[f110]) ).
fof(f169,plain,
in(sK16,relation_dom(relation_composition(sK18,sK17))),
inference(cnf_transformation,[],[f110]) ).
fof(f170,plain,
apply(relation_composition(sK18,sK17),sK16) != apply(sK17,apply(sK18,sK16)),
inference(cnf_transformation,[],[f110]) ).
fof(f178,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f116,f123]) ).
fof(f179,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| apply(X0,X1) != X2
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f115,f123]) ).
fof(f182,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f120,f123]) ).
fof(f183,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK2(X0,X5)),singleton(X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f119,f123]) ).
fof(f188,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK6(X0,X1,X7,X8),X8),singleton(sK6(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f125,f123,f123]) ).
fof(f189,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK6(X0,X1,X7,X8)),singleton(X7)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f124,f123,f123]) ).
fof(f193,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X1,apply(X0,X1)),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f179]) ).
fof(f194,plain,
! [X0,X6,X5] :
( in(X5,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f182]) ).
fof(f195,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK2(X0,X5)),singleton(X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f183]) ).
fof(f197,plain,
! [X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK6(X0,X1,X7,X8),X8),singleton(sK6(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f188]) ).
fof(f198,plain,
! [X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK6(X0,X1,X7,X8)),singleton(X7)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f189]) ).
cnf(c_55,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| apply(X2,X0) = X1 ),
inference(cnf_transformation,[],[f178]) ).
cnf(c_56,plain,
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,apply(X1,X0)),singleton(X0)),X1) ),
inference(cnf_transformation,[],[f193]) ).
cnf(c_59,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2)
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f194]) ).
cnf(c_60,plain,
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,sK2(X1,X0)),singleton(X0)),X1) ),
inference(cnf_transformation,[],[f195]) ).
cnf(c_65,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(X2,X3))
| ~ relation(relation_composition(X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(sK6(X2,X3,X0,X1),X1),singleton(sK6(X2,X3,X0,X1))),X3) ),
inference(cnf_transformation,[],[f197]) ).
cnf(c_66,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(X2,X3))
| ~ relation(relation_composition(X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X0,sK6(X2,X3,X0,X1)),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f198]) ).
cnf(c_67,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f130]) ).
cnf(c_73,plain,
( ~ function(X0)
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1)
| function(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f137]) ).
cnf(c_102,negated_conjecture,
apply(relation_composition(sK18,sK17),sK16) != apply(sK17,apply(sK18,sK16)),
inference(cnf_transformation,[],[f170]) ).
cnf(c_103,negated_conjecture,
in(sK16,relation_dom(relation_composition(sK18,sK17))),
inference(cnf_transformation,[],[f169]) ).
cnf(c_104,negated_conjecture,
function(sK18),
inference(cnf_transformation,[],[f168]) ).
cnf(c_105,negated_conjecture,
relation(sK18),
inference(cnf_transformation,[],[f167]) ).
cnf(c_106,negated_conjecture,
function(sK17),
inference(cnf_transformation,[],[f166]) ).
cnf(c_107,negated_conjecture,
relation(sK17),
inference(cnf_transformation,[],[f165]) ).
cnf(c_152,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ function(X2)
| ~ relation(X2)
| apply(X2,X0) = X1 ),
inference(global_subsumption_just,[status(thm)],[c_55,c_59,c_55]) ).
cnf(c_205,plain,
X0 = X0,
theory(equality) ).
cnf(c_207,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_213,plain,
( X0 != X1
| X2 != X3
| apply(X0,X2) = apply(X1,X3) ),
theory(equality) ).
cnf(c_312,plain,
( apply(relation_composition(sK18,sK17),sK16) != X0
| apply(sK17,apply(sK18,sK16)) != X0
| apply(relation_composition(sK18,sK17),sK16) = apply(sK17,apply(sK18,sK16)) ),
inference(instantiation,[status(thm)],[c_207]) ).
cnf(c_316,plain,
( ~ in(sK16,relation_dom(relation_composition(sK18,sK17)))
| ~ relation(relation_composition(sK18,sK17))
| in(unordered_pair(unordered_pair(sK16,sK2(relation_composition(sK18,sK17),sK16)),singleton(sK16)),relation_composition(sK18,sK17)) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_339,plain,
( ~ in(sK16,relation_dom(relation_composition(sK18,sK17)))
| ~ function(relation_composition(sK18,sK17))
| ~ relation(relation_composition(sK18,sK17))
| in(unordered_pair(unordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16)),singleton(sK16)),relation_composition(sK18,sK17)) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_394,plain,
( ~ relation(sK18)
| ~ relation(sK17)
| relation(relation_composition(sK18,sK17)) ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_410,plain,
( ~ function(sK18)
| ~ function(sK17)
| ~ relation(sK18)
| ~ relation(sK17)
| function(relation_composition(sK18,sK17)) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_451,plain,
( apply(sK17,apply(sK18,sK16)) != X0
| X1 != X0
| apply(sK17,apply(sK18,sK16)) = X1 ),
inference(instantiation,[status(thm)],[c_207]) ).
cnf(c_452,plain,
( apply(relation_composition(sK18,sK17),sK16) != apply(X0,X1)
| apply(sK17,apply(sK18,sK16)) != apply(X0,X1)
| apply(relation_composition(sK18,sK17),sK16) = apply(sK17,apply(sK18,sK16)) ),
inference(instantiation,[status(thm)],[c_312]) ).
cnf(c_453,plain,
( apply(sK18,sK16) != X0
| sK17 != X1
| apply(sK17,apply(sK18,sK16)) = apply(X1,X0) ),
inference(instantiation,[status(thm)],[c_213]) ).
cnf(c_1252,plain,
( ~ in(unordered_pair(unordered_pair(sK16,sK2(relation_composition(sK18,sK17),sK16)),singleton(sK16)),relation_composition(sK18,sK17))
| ~ function(relation_composition(sK18,sK17))
| ~ relation(relation_composition(sK18,sK17))
| apply(relation_composition(sK18,sK17),sK16) = sK2(relation_composition(sK18,sK17),sK16) ),
inference(instantiation,[status(thm)],[c_152]) ).
cnf(c_1256,plain,
( ~ in(unordered_pair(unordered_pair(sK16,sK2(relation_composition(sK18,sK17),sK16)),singleton(sK16)),relation_composition(sK18,sK17))
| ~ relation(relation_composition(sK18,sK17))
| ~ relation(sK18)
| ~ relation(sK17)
| in(unordered_pair(unordered_pair(sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16)),sK2(relation_composition(sK18,sK17),sK16)),singleton(sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16)))),sK17) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_1257,plain,
( ~ in(unordered_pair(unordered_pair(sK16,sK2(relation_composition(sK18,sK17),sK16)),singleton(sK16)),relation_composition(sK18,sK17))
| ~ relation(relation_composition(sK18,sK17))
| ~ relation(sK18)
| ~ relation(sK17)
| in(unordered_pair(unordered_pair(sK16,sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16))),singleton(sK16)),sK18) ),
inference(instantiation,[status(thm)],[c_66]) ).
cnf(c_1339,plain,
( ~ in(unordered_pair(unordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16)),singleton(sK16)),relation_composition(sK18,sK17))
| ~ function(relation_composition(sK18,sK17))
| ~ relation(relation_composition(sK18,sK17))
| apply(relation_composition(sK18,sK17),sK16) = apply(relation_composition(sK18,sK17),sK16) ),
inference(instantiation,[status(thm)],[c_152]) ).
cnf(c_1742,plain,
( apply(relation_composition(sK18,sK17),sK16) != X0
| X1 != X0
| apply(relation_composition(sK18,sK17),sK16) = X1 ),
inference(instantiation,[status(thm)],[c_207]) ).
cnf(c_2357,plain,
( apply(relation_composition(sK18,sK17),sK16) != apply(relation_composition(sK18,sK17),sK16)
| apply(sK17,apply(sK18,sK16)) != apply(relation_composition(sK18,sK17),sK16)
| apply(relation_composition(sK18,sK17),sK16) = apply(sK17,apply(sK18,sK16)) ),
inference(instantiation,[status(thm)],[c_452]) ).
cnf(c_2372,plain,
( apply(sK18,sK16) != X0
| sK17 != sK17
| apply(sK17,apply(sK18,sK16)) = apply(sK17,X0) ),
inference(instantiation,[status(thm)],[c_453]) ).
cnf(c_2373,plain,
sK17 = sK17,
inference(instantiation,[status(thm)],[c_205]) ).
cnf(c_3370,plain,
( ~ in(unordered_pair(unordered_pair(sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16)),sK2(relation_composition(sK18,sK17),sK16)),singleton(sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16)))),sK17)
| ~ function(sK17)
| ~ relation(sK17)
| apply(sK17,sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16))) = sK2(relation_composition(sK18,sK17),sK16) ),
inference(instantiation,[status(thm)],[c_152]) ).
cnf(c_3406,plain,
( ~ in(unordered_pair(unordered_pair(sK16,sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16))),singleton(sK16)),sK18)
| ~ function(sK18)
| ~ relation(sK18)
| apply(sK18,sK16) = sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16)) ),
inference(instantiation,[status(thm)],[c_152]) ).
cnf(c_5036,plain,
( apply(relation_composition(sK18,sK17),sK16) != sK2(relation_composition(sK18,sK17),sK16)
| X0 != sK2(relation_composition(sK18,sK17),sK16)
| apply(relation_composition(sK18,sK17),sK16) = X0 ),
inference(instantiation,[status(thm)],[c_1742]) ).
cnf(c_5577,plain,
( apply(relation_composition(sK18,sK17),sK16) != X0
| apply(sK17,apply(sK18,sK16)) != X0
| apply(sK17,apply(sK18,sK16)) = apply(relation_composition(sK18,sK17),sK16) ),
inference(instantiation,[status(thm)],[c_451]) ).
cnf(c_9692,plain,
( apply(sK18,sK16) != sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16))
| sK17 != sK17
| apply(sK17,apply(sK18,sK16)) = apply(sK17,sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16))) ),
inference(instantiation,[status(thm)],[c_2372]) ).
cnf(c_12021,plain,
( apply(sK17,sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16))) != sK2(relation_composition(sK18,sK17),sK16)
| apply(relation_composition(sK18,sK17),sK16) != sK2(relation_composition(sK18,sK17),sK16)
| apply(relation_composition(sK18,sK17),sK16) = apply(sK17,sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16))) ),
inference(instantiation,[status(thm)],[c_5036]) ).
cnf(c_28619,plain,
( apply(relation_composition(sK18,sK17),sK16) != apply(sK17,sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16)))
| apply(sK17,apply(sK18,sK16)) != apply(sK17,sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16)))
| apply(sK17,apply(sK18,sK16)) = apply(relation_composition(sK18,sK17),sK16) ),
inference(instantiation,[status(thm)],[c_5577]) ).
cnf(c_28629,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_28619,c_12021,c_9692,c_3406,c_3370,c_2373,c_2357,c_1339,c_1256,c_1257,c_1252,c_410,c_394,c_339,c_316,c_102,c_103,c_104,c_105,c_106,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU214+3 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 2 17:42:59 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 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
% 17.64/3.18 % SZS status Started for theBenchmark.p
% 17.64/3.18 % SZS status Theorem for theBenchmark.p
% 17.64/3.18
% 17.64/3.18 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 17.64/3.18
% 17.64/3.18 ------ iProver source info
% 17.64/3.18
% 17.64/3.18 git: date: 2024-05-02 19:28:25 +0000
% 17.64/3.18 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 17.64/3.18 git: non_committed_changes: false
% 17.64/3.18
% 17.64/3.18 ------ Parsing...
% 17.64/3.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 17.64/3.18
% 17.64/3.18 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e
% 17.64/3.18
% 17.64/3.18 ------ Preprocessing...
% 17.64/3.18
% 17.64/3.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.64/3.18 ------ Proving...
% 17.64/3.18 ------ Problem Properties
% 17.64/3.18
% 17.64/3.18
% 17.64/3.18 clauses 61
% 17.64/3.18 conjectures 15
% 17.64/3.18 EPR 24
% 17.64/3.18 Horn 55
% 17.64/3.18 unary 26
% 17.64/3.18 binary 11
% 17.64/3.18 lits 144
% 17.64/3.18 lits eq 11
% 17.64/3.18 fd_pure 0
% 17.64/3.18 fd_pseudo 0
% 17.64/3.18 fd_cond 1
% 17.64/3.18 fd_pseudo_cond 7
% 17.64/3.18 AC symbols 0
% 17.64/3.18
% 17.64/3.18 ------ Input Options Time Limit: Unbounded
% 17.64/3.18
% 17.64/3.18
% 17.64/3.18 ------
% 17.64/3.18 Current options:
% 17.64/3.18 ------
% 17.64/3.18
% 17.64/3.18
% 17.64/3.18
% 17.64/3.18
% 17.64/3.18 ------ Proving...
% 17.64/3.18
% 17.64/3.18
% 17.64/3.18 % SZS status Theorem for theBenchmark.p
% 17.64/3.18
% 17.64/3.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.64/3.18
% 17.64/3.18
%------------------------------------------------------------------------------