TSTP Solution File: SEU214+3 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU214+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:04:47 EDT 2023
% Result : Theorem 9.85s 2.19s
% Output : CNFRefutation 9.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 108 ( 23 unt; 0 def)
% Number of atoms : 490 ( 71 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 644 ( 262 ~; 260 |; 85 &)
% ( 14 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 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 : 278 ( 1 sgn; 177 !; 40 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
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(f114,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
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(f136,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f58]) ).
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_52,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f114]) ).
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_74,plain,
( ~ function(X0)
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1)
| relation(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f136]) ).
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_150,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation(relation_composition(X1,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_74,c_67]) ).
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_297,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X0,sK6(X2,X3,X0,X1)),singleton(X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_66,c_150]) ).
cnf(c_298,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),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(backward_subsumption_resolution,[status(thm)],[c_65,c_150]) ).
cnf(c_568,plain,
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X1,X0))),X1) ),
inference(demodulation,[status(thm)],[c_60,c_52]) ).
cnf(c_575,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| ~ function(X2)
| ~ relation(X2)
| apply(X2,X0) = X1 ),
inference(demodulation,[status(thm)],[c_152,c_52]) ).
cnf(c_584,plain,
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,apply(X1,X0))),X1) ),
inference(demodulation,[status(thm)],[c_56,c_52]) ).
cnf(c_611,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_composition(X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X0,X1))),X2) ),
inference(demodulation,[status(thm)],[c_297,c_52]) ).
cnf(c_620,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_composition(X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| in(unordered_pair(singleton(sK6(X2,X3,X0,X1)),unordered_pair(X1,sK6(X2,X3,X0,X1))),X3) ),
inference(demodulation,[status(thm)],[c_298,c_52]) ).
cnf(c_2267,plain,
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| apply(X1,X0) = sK2(X1,X0) ),
inference(superposition,[status(thm)],[c_568,c_575]) ).
cnf(c_2623,plain,
( ~ in(sK16,relation_dom(relation_composition(sK18,sK17)))
| ~ relation(relation_composition(sK18,sK17))
| in(unordered_pair(singleton(sK16),unordered_pair(sK16,sK2(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17)) ),
inference(instantiation,[status(thm)],[c_568]) ).
cnf(c_2628,plain,
( ~ in(sK16,relation_dom(relation_composition(sK18,sK17)))
| ~ function(relation_composition(sK18,sK17))
| ~ relation(relation_composition(sK18,sK17))
| in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17)) ),
inference(instantiation,[status(thm)],[c_584]) ).
cnf(c_2679,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_composition(X2,X3))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X3)
| sK6(X2,X3,X0,X1) = apply(X2,X0) ),
inference(superposition,[status(thm)],[c_611,c_575]) ).
cnf(c_3104,plain,
( ~ relation(sK18)
| ~ relation(sK17)
| relation(relation_composition(sK18,sK17)) ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_3375,plain,
( ~ function(sK18)
| ~ function(sK17)
| ~ relation(sK18)
| ~ relation(sK17)
| function(relation_composition(sK18,sK17)) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_3571,plain,
( ~ in(unordered_pair(singleton(sK16),unordered_pair(sK16,X0)),relation_composition(sK18,sK17))
| ~ function(relation_composition(sK18,sK17))
| ~ relation(relation_composition(sK18,sK17))
| apply(relation_composition(sK18,sK17),sK16) = X0 ),
inference(instantiation,[status(thm)],[c_575]) ).
cnf(c_5974,plain,
( ~ in(unordered_pair(singleton(sK16),unordered_pair(sK16,sK2(relation_composition(sK18,sK17),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_3571]) ).
cnf(c_6395,plain,
( ~ function(relation_composition(sK18,sK17))
| ~ relation(relation_composition(sK18,sK17))
| apply(relation_composition(sK18,sK17),sK16) = sK2(relation_composition(sK18,sK17),sK16) ),
inference(superposition,[status(thm)],[c_103,c_2267]) ).
cnf(c_7169,plain,
apply(relation_composition(sK18,sK17),sK16) = sK2(relation_composition(sK18,sK17),sK16),
inference(global_subsumption_just,[status(thm)],[c_6395,c_107,c_106,c_105,c_104,c_103,c_2623,c_3104,c_3375,c_5974]) ).
cnf(c_7171,plain,
( ~ in(sK16,relation_dom(relation_composition(sK18,sK17)))
| ~ relation(relation_composition(sK18,sK17))
| in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17)) ),
inference(superposition,[status(thm)],[c_7169,c_568]) ).
cnf(c_7173,plain,
( ~ relation(relation_composition(sK18,sK17))
| in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7171,c_103]) ).
cnf(c_7179,plain,
in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17)),
inference(global_subsumption_just,[status(thm)],[c_7173,c_107,c_106,c_105,c_104,c_103,c_2628,c_3104,c_3375]) ).
cnf(c_32118,plain,
( ~ function(sK18)
| ~ relation(sK18)
| ~ relation(sK17)
| sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16)) = apply(sK18,sK16) ),
inference(superposition,[status(thm)],[c_7179,c_2679]) ).
cnf(c_32187,plain,
sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16)) = apply(sK18,sK16),
inference(forward_subsumption_resolution,[status(thm)],[c_32118,c_107,c_105,c_104]) ).
cnf(c_34040,plain,
( ~ in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17))
| ~ relation(sK18)
| ~ relation(sK17)
| in(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(apply(relation_composition(sK18,sK17),sK16),apply(sK18,sK16))),sK17) ),
inference(superposition,[status(thm)],[c_32187,c_620]) ).
cnf(c_34045,plain,
in(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(apply(relation_composition(sK18,sK17),sK16),apply(sK18,sK16))),sK17),
inference(forward_subsumption_resolution,[status(thm)],[c_34040,c_107,c_105,c_7179]) ).
cnf(c_39296,plain,
in(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(apply(sK18,sK16),apply(relation_composition(sK18,sK17),sK16))),sK17),
inference(demodulation,[status(thm)],[c_34045,c_52]) ).
cnf(c_39304,plain,
( ~ function(sK17)
| ~ relation(sK17)
| apply(relation_composition(sK18,sK17),sK16) = apply(sK17,apply(sK18,sK16)) ),
inference(superposition,[status(thm)],[c_39296,c_575]) ).
cnf(c_39307,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_39304,c_102,c_107,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU214+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 17:47:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.46 Running first-order theorem proving
% 0.20/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.85/2.19 % SZS status Started for theBenchmark.p
% 9.85/2.19 % SZS status Theorem for theBenchmark.p
% 9.85/2.19
% 9.85/2.19 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 9.85/2.19
% 9.85/2.19 ------ iProver source info
% 9.85/2.19
% 9.85/2.19 git: date: 2023-05-31 18:12:56 +0000
% 9.85/2.19 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 9.85/2.19 git: non_committed_changes: false
% 9.85/2.19 git: last_make_outside_of_git: false
% 9.85/2.19
% 9.85/2.19 ------ Parsing...
% 9.85/2.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 9.85/2.19
% 9.85/2.19 ------ Preprocessing... sup_sim: 12 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 9.85/2.19
% 9.85/2.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 9.85/2.19
% 9.85/2.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 9.85/2.19 ------ Proving...
% 9.85/2.19 ------ Problem Properties
% 9.85/2.19
% 9.85/2.19
% 9.85/2.19 clauses 59
% 9.85/2.19 conjectures 6
% 9.85/2.19 EPR 23
% 9.85/2.19 Horn 53
% 9.85/2.19 unary 25
% 9.85/2.19 binary 10
% 9.85/2.19 lits 138
% 9.85/2.19 lits eq 11
% 9.85/2.19 fd_pure 0
% 9.85/2.19 fd_pseudo 0
% 9.85/2.19 fd_cond 1
% 9.85/2.19 fd_pseudo_cond 7
% 9.85/2.19 AC symbols 0
% 9.85/2.19
% 9.85/2.19 ------ Schedule dynamic 5 is on
% 9.85/2.19
% 9.85/2.19 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 9.85/2.19
% 9.85/2.19
% 9.85/2.19 ------
% 9.85/2.19 Current options:
% 9.85/2.19 ------
% 9.85/2.19
% 9.85/2.19
% 9.85/2.19
% 9.85/2.19
% 9.85/2.19 ------ Proving...
% 9.85/2.19
% 9.85/2.19
% 9.85/2.19 % SZS status Theorem for theBenchmark.p
% 9.85/2.19
% 9.85/2.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.85/2.19
% 9.85/2.19
%------------------------------------------------------------------------------