TSTP Solution File: SEU216+3 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU216+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 : Thu Aug 31 17:04:48 EDT 2023
% Result : Theorem 29.34s 4.78s
% Output : CNFRefutation 29.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 16
% Syntax : Number of formulae : 137 ( 28 unt; 0 def)
% Number of atoms : 563 ( 248 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 693 ( 267 ~; 312 |; 85 &)
% ( 15 <=>; 12 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 242 ( 5 sgn; 134 !; 26 ?)
% 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,X1] :
( relation(X1)
=> ( identity_relation(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
fof(f6,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(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(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f14,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f33,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( identity_relation(X0) = X1
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( identity_relation(X0) = X1
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(negated_conjecture,[],[f33]) ).
fof(f39,axiom,
! [X0] :
( relation_rng(identity_relation(X0)) = X0
& relation_dom(identity_relation(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
fof(f42,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f50,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f51,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,[],[f6]) ).
fof(f52,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,[],[f51]) ).
fof(f63,plain,
? [X0,X1] :
( ( identity_relation(X0) = X1
<~> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
& function(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f64,plain,
? [X0,X1] :
( ( identity_relation(X0) = X1
<~> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
& function(X1)
& relation(X1) ),
inference(flattening,[],[f63]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<=> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f42]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<=> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) )
& ( ( X2 = X3
& in(X2,X0) )
| ~ in(ordered_pair(X2,X3),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f50]) ).
fof(f75,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) )
& ( ( X2 = X3
& in(X2,X0) )
| ~ in(ordered_pair(X2,X3),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0) )
& ( ( X4 = X5
& in(X4,X0) )
| ~ in(ordered_pair(X4,X5),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) )
=> ( ( sK0(X0,X1) != sK1(X0,X1)
| ~ in(sK0(X0,X1),X0)
| ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) )
& ( ( sK0(X0,X1) = sK1(X0,X1)
& in(sK0(X0,X1),X0) )
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ( ( sK0(X0,X1) != sK1(X0,X1)
| ~ in(sK0(X0,X1),X0)
| ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) )
& ( ( sK0(X0,X1) = sK1(X0,X1)
& in(sK0(X0,X1),X0) )
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0) )
& ( ( X4 = X5
& in(X4,X0) )
| ~ in(ordered_pair(X4,X5),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f76,f77]) ).
fof(f79,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,[],[f52]) ).
fof(f98,plain,
? [X0,X1] :
( ( ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0
| identity_relation(X0) != X1 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) = X1 )
& function(X1)
& relation(X1) ),
inference(nnf_transformation,[],[f64]) ).
fof(f99,plain,
? [X0,X1] :
( ( ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0
| identity_relation(X0) != X1 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) = X1 )
& function(X1)
& relation(X1) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
? [X0,X1] :
( ( ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0
| identity_relation(X0) != X1 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) = X1 )
& function(X1)
& relation(X1) ),
inference(rectify,[],[f99]) ).
fof(f101,plain,
( ? [X0,X1] :
( ( ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0
| identity_relation(X0) != X1 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) = X1 )
& function(X1)
& relation(X1) )
=> ( ( ? [X2] :
( apply(sK12,X2) != X2
& in(X2,sK11) )
| sK11 != relation_dom(sK12)
| sK12 != identity_relation(sK11) )
& ( ( ! [X3] :
( apply(sK12,X3) = X3
| ~ in(X3,sK11) )
& sK11 = relation_dom(sK12) )
| sK12 = identity_relation(sK11) )
& function(sK12)
& relation(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
( ? [X2] :
( apply(sK12,X2) != X2
& in(X2,sK11) )
=> ( sK13 != apply(sK12,sK13)
& in(sK13,sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
( ( ( sK13 != apply(sK12,sK13)
& in(sK13,sK11) )
| sK11 != relation_dom(sK12)
| sK12 != identity_relation(sK11) )
& ( ( ! [X3] :
( apply(sK12,X3) = X3
| ~ in(X3,sK11) )
& sK11 = relation_dom(sK12) )
| sK12 = identity_relation(sK11) )
& function(sK12)
& relation(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f100,f102,f101]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ( ( in(ordered_pair(X0,X1),X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2)) )
& ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2) ) )
| ~ function(X2)
| ~ relation(X2) ),
inference(nnf_transformation,[],[f73]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ( ( in(ordered_pair(X0,X1),X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2)) )
& ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2) ) )
| ~ function(X2)
| ~ relation(X2) ),
inference(flattening,[],[f104]) ).
fof(f109,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f112,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f113,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| in(sK0(X0,X1),X0)
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f114,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| sK0(X0,X1) = sK1(X0,X1)
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f115,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| sK0(X0,X1) != sK1(X0,X1)
| ~ in(sK0(X0,X1),X0)
| ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f116,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,[],[f79]) ).
fof(f117,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,[],[f79]) ).
fof(f120,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f121,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f8]) ).
fof(f128,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f129,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f156,plain,
relation(sK12),
inference(cnf_transformation,[],[f103]) ).
fof(f157,plain,
function(sK12),
inference(cnf_transformation,[],[f103]) ).
fof(f158,plain,
( sK11 = relation_dom(sK12)
| sK12 = identity_relation(sK11) ),
inference(cnf_transformation,[],[f103]) ).
fof(f159,plain,
! [X3] :
( apply(sK12,X3) = X3
| ~ in(X3,sK11)
| sK12 = identity_relation(sK11) ),
inference(cnf_transformation,[],[f103]) ).
fof(f160,plain,
( in(sK13,sK11)
| sK11 != relation_dom(sK12)
| sK12 != identity_relation(sK11) ),
inference(cnf_transformation,[],[f103]) ).
fof(f161,plain,
( sK13 != apply(sK12,sK13)
| sK11 != relation_dom(sK12)
| sK12 != identity_relation(sK11) ),
inference(cnf_transformation,[],[f103]) ).
fof(f166,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f39]) ).
fof(f170,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f105]) ).
fof(f171,plain,
! [X2,X0,X1] :
( apply(X2,X0) = X1
| ~ in(ordered_pair(X0,X1),X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f105]) ).
fof(f173,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| sK0(X0,X1) != sK1(X0,X1)
| ~ in(sK0(X0,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X1)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f115,f120]) ).
fof(f174,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| sK0(X0,X1) = sK1(X0,X1)
| in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X1)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f114,f120]) ).
fof(f175,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| in(sK0(X0,X1),X0)
| in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X1)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f113,f120]) ).
fof(f176,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1)
| X4 != X5
| ~ in(X4,X0)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(definition_unfolding,[],[f112,f120]) ).
fof(f179,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,[],[f117,f120]) ).
fof(f180,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,[],[f116,f120]) ).
fof(f183,plain,
! [X2,X0,X1] :
( apply(X2,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f171,f120]) ).
fof(f184,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f170,f120]) ).
fof(f185,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,X5),singleton(X5)),X1)
| ~ in(X5,X0)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(equality_resolution,[],[f176]) ).
fof(f186,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,X5),singleton(X5)),identity_relation(X0))
| ~ in(X5,X0)
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f185]) ).
fof(f191,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,[],[f180]) ).
cnf(c_52,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f109]) ).
cnf(c_53,plain,
( sK0(X0,X1) != sK1(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X1)
| ~ in(sK0(X0,X1),X0)
| ~ relation(X1)
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f173]) ).
cnf(c_54,plain,
( ~ relation(X0)
| sK0(X1,X0) = sK1(X1,X0)
| identity_relation(X1) = X0
| in(unordered_pair(unordered_pair(sK0(X1,X0),sK1(X1,X0)),singleton(sK0(X1,X0))),X0) ),
inference(cnf_transformation,[],[f174]) ).
cnf(c_55,plain,
( ~ relation(X0)
| identity_relation(X1) = X0
| in(unordered_pair(unordered_pair(sK0(X1,X0),sK1(X1,X0)),singleton(sK0(X1,X0))),X0)
| in(sK0(X1,X0),X1) ),
inference(cnf_transformation,[],[f175]) ).
cnf(c_56,plain,
( ~ in(X0,X1)
| ~ relation(identity_relation(X1))
| in(unordered_pair(unordered_pair(X0,X0),singleton(X0)),identity_relation(X1)) ),
inference(cnf_transformation,[],[f186]) ).
cnf(c_61,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,[],[f179]) ).
cnf(c_62,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,[],[f191]) ).
cnf(c_63,plain,
relation(identity_relation(X0)),
inference(cnf_transformation,[],[f121]) ).
cnf(c_70,plain,
function(identity_relation(X0)),
inference(cnf_transformation,[],[f129]) ).
cnf(c_71,plain,
relation(identity_relation(X0)),
inference(cnf_transformation,[],[f128]) ).
cnf(c_98,negated_conjecture,
( apply(sK12,sK13) != sK13
| identity_relation(sK11) != sK12
| relation_dom(sK12) != sK11 ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_99,negated_conjecture,
( identity_relation(sK11) != sK12
| relation_dom(sK12) != sK11
| in(sK13,sK11) ),
inference(cnf_transformation,[],[f160]) ).
cnf(c_100,negated_conjecture,
( ~ in(X0,sK11)
| apply(sK12,X0) = X0
| identity_relation(sK11) = sK12 ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_101,negated_conjecture,
( identity_relation(sK11) = sK12
| relation_dom(sK12) = sK11 ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_102,negated_conjecture,
function(sK12),
inference(cnf_transformation,[],[f157]) ).
cnf(c_103,negated_conjecture,
relation(sK12),
inference(cnf_transformation,[],[f156]) ).
cnf(c_109,plain,
relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f166]) ).
cnf(c_113,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ function(X2)
| ~ relation(X2)
| apply(X2,X0) = X1 ),
inference(cnf_transformation,[],[f183]) ).
cnf(c_114,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ function(X2)
| ~ relation(X2)
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f184]) ).
cnf(c_154,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_61,c_113]) ).
cnf(c_182,plain,
( ~ in(X0,X1)
| in(unordered_pair(unordered_pair(X0,X0),singleton(X0)),identity_relation(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_63]) ).
cnf(c_481,plain,
( ~ in(X0,X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),identity_relation(X1)) ),
inference(demodulation,[status(thm)],[c_182,c_52]) ).
cnf(c_516,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| ~ function(X2)
| ~ relation(X2)
| in(X0,relation_dom(X2)) ),
inference(demodulation,[status(thm)],[c_114,c_52]) ).
cnf(c_531,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| ~ function(X2)
| ~ relation(X2)
| apply(X2,X0) = X1 ),
inference(demodulation,[status(thm)],[c_154,c_52]) ).
cnf(c_540,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_62,c_52]) ).
cnf(c_549,plain,
( ~ relation(X0)
| identity_relation(X1) = X0
| in(unordered_pair(singleton(sK0(X1,X0)),unordered_pair(sK0(X1,X0),sK1(X1,X0))),X0)
| in(sK0(X1,X0),X1) ),
inference(demodulation,[status(thm)],[c_55,c_52]) ).
cnf(c_558,plain,
( ~ relation(X0)
| sK0(X1,X0) = sK1(X1,X0)
| identity_relation(X1) = X0
| in(unordered_pair(singleton(sK0(X1,X0)),unordered_pair(sK0(X1,X0),sK1(X1,X0))),X0) ),
inference(demodulation,[status(thm)],[c_54,c_52]) ).
cnf(c_567,plain,
( sK0(X0,X1) != sK1(X0,X1)
| ~ in(unordered_pair(singleton(sK0(X0,X1)),unordered_pair(sK0(X0,X1),sK1(X0,X1))),X1)
| ~ in(sK0(X0,X1),X0)
| ~ relation(X1)
| identity_relation(X0) = X1 ),
inference(demodulation,[status(thm)],[c_53,c_52]) ).
cnf(c_3602,plain,
X0 = X0,
theory(equality) ).
cnf(c_3604,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_3605,plain,
( X0 != X1
| X2 != X3
| ~ in(X1,X3)
| in(X0,X2) ),
theory(equality) ).
cnf(c_3613,plain,
( X0 != X1
| relation_dom(X0) = relation_dom(X1) ),
theory(equality) ).
cnf(c_3621,plain,
sK12 = sK12,
inference(instantiation,[status(thm)],[c_3602]) ).
cnf(c_5042,plain,
( relation_dom(sK12) != X0
| sK11 != X0
| relation_dom(sK12) = sK11 ),
inference(instantiation,[status(thm)],[c_3604]) ).
cnf(c_5332,plain,
( X0 != X1
| sK11 != X1
| sK11 = X0 ),
inference(instantiation,[status(thm)],[c_3604]) ).
cnf(c_8496,plain,
( X0 != sK11
| sK11 != sK11
| sK11 = X0 ),
inference(instantiation,[status(thm)],[c_5332]) ).
cnf(c_8497,plain,
sK11 = sK11,
inference(instantiation,[status(thm)],[c_3602]) ).
cnf(c_20345,plain,
( relation_dom(identity_relation(sK11)) != sK11
| sK11 != sK11
| sK11 = relation_dom(identity_relation(sK11)) ),
inference(instantiation,[status(thm)],[c_8496]) ).
cnf(c_20346,plain,
relation_dom(identity_relation(sK11)) = sK11,
inference(instantiation,[status(thm)],[c_109]) ).
cnf(c_27105,plain,
( ~ in(X0,X1)
| ~ function(identity_relation(X1))
| ~ relation(identity_relation(X1))
| apply(identity_relation(X1),X0) = X0 ),
inference(superposition,[status(thm)],[c_481,c_531]) ).
cnf(c_27109,plain,
( ~ in(X0,X1)
| apply(identity_relation(X1),X0) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[c_27105,c_71,c_70]) ).
cnf(c_27361,plain,
( ~ function(X0)
| ~ relation(X0)
| identity_relation(X1) = X0
| in(sK0(X1,X0),relation_dom(X0))
| in(sK0(X1,X0),X1) ),
inference(superposition,[status(thm)],[c_549,c_516]) ).
cnf(c_27420,plain,
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK0(X1,X0)) = sK1(X1,X0)
| sK0(X1,X0) = sK1(X1,X0)
| identity_relation(X1) = X0 ),
inference(superposition,[status(thm)],[c_558,c_531]) ).
cnf(c_34041,plain,
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| apply(identity_relation(X1),unordered_pair(singleton(X0),unordered_pair(X0,apply(X1,X0)))) = unordered_pair(singleton(X0),unordered_pair(X0,apply(X1,X0))) ),
inference(superposition,[status(thm)],[c_540,c_27109]) ).
cnf(c_36405,plain,
( relation_dom(sK12) != relation_dom(identity_relation(sK11))
| sK11 != relation_dom(identity_relation(sK11))
| relation_dom(sK12) = sK11 ),
inference(instantiation,[status(thm)],[c_5042]) ).
cnf(c_48030,plain,
( sK12 != identity_relation(sK11)
| relation_dom(sK12) = relation_dom(identity_relation(sK11)) ),
inference(instantiation,[status(thm)],[c_3613]) ).
cnf(c_65289,plain,
( ~ function(sK12)
| ~ relation(sK12)
| identity_relation(X0) = sK12
| identity_relation(sK11) = sK12
| in(sK0(X0,sK12),X0)
| in(sK0(X0,sK12),sK11) ),
inference(superposition,[status(thm)],[c_101,c_27361]) ).
cnf(c_65409,plain,
( identity_relation(X0) = sK12
| identity_relation(sK11) = sK12
| in(sK0(X0,sK12),X0)
| in(sK0(X0,sK12),sK11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_65289,c_103,c_102]) ).
cnf(c_66547,plain,
( identity_relation(sK11) != X0
| sK12 != X0
| sK12 = identity_relation(sK11) ),
inference(instantiation,[status(thm)],[c_3604]) ).
cnf(c_66548,plain,
( identity_relation(sK11) != sK12
| sK12 != sK12
| sK12 = identity_relation(sK11) ),
inference(instantiation,[status(thm)],[c_66547]) ).
cnf(c_69914,plain,
( apply(sK12,sK0(X0,sK12)) = sK0(X0,sK12)
| identity_relation(X0) = sK12
| identity_relation(sK11) = sK12
| in(sK0(X0,sK12),X0) ),
inference(superposition,[status(thm)],[c_65409,c_100]) ).
cnf(c_69937,plain,
( identity_relation(sK11) = sK12
| in(sK0(sK11,sK12),sK11) ),
inference(equality_factoring,[status(thm)],[c_65409]) ).
cnf(c_70193,plain,
( apply(sK12,sK0(sK11,sK12)) = sK0(sK11,sK12)
| identity_relation(sK11) = sK12 ),
inference(superposition,[status(thm)],[c_69914,c_100]) ).
cnf(c_70601,plain,
( ~ in(sK0(sK11,sK12),relation_dom(sK12))
| ~ function(sK12)
| ~ relation(sK12)
| identity_relation(sK11) = sK12
| in(unordered_pair(singleton(sK0(sK11,sK12)),unordered_pair(sK0(sK11,sK12),sK0(sK11,sK12))),sK12) ),
inference(superposition,[status(thm)],[c_70193,c_540]) ).
cnf(c_70607,plain,
( ~ in(sK0(sK11,sK12),relation_dom(sK12))
| identity_relation(sK11) = sK12
| in(unordered_pair(singleton(sK0(sK11,sK12)),unordered_pair(sK0(sK11,sK12),sK0(sK11,sK12))),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_70601,c_103,c_102]) ).
cnf(c_89742,plain,
( X0 != sK0(sK11,sK12)
| X1 != sK11
| ~ in(sK0(sK11,sK12),sK11)
| in(X0,X1) ),
inference(instantiation,[status(thm)],[c_3605]) ).
cnf(c_107497,plain,
( relation_dom(sK12) != sK11
| X0 != sK0(sK11,sK12)
| ~ in(sK0(sK11,sK12),sK11)
| in(X0,relation_dom(sK12)) ),
inference(instantiation,[status(thm)],[c_89742]) ).
cnf(c_111980,plain,
( ~ relation(sK12)
| apply(sK12,sK0(X0,sK12)) = sK1(X0,sK12)
| sK0(X0,sK12) = sK1(X0,sK12)
| identity_relation(X0) = sK12 ),
inference(superposition,[status(thm)],[c_102,c_27420]) ).
cnf(c_111984,plain,
( apply(sK12,sK0(X0,sK12)) = sK1(X0,sK12)
| sK0(X0,sK12) = sK1(X0,sK12)
| identity_relation(X0) = sK12 ),
inference(forward_subsumption_resolution,[status(thm)],[c_111980,c_103]) ).
cnf(c_112178,plain,
( sK0(sK11,sK12) = sK1(sK11,sK12)
| identity_relation(sK11) = sK12 ),
inference(superposition,[status(thm)],[c_111984,c_70193]) ).
cnf(c_112647,plain,
( sK0(sK11,sK12) != sK0(sK11,sK12)
| relation_dom(sK12) != sK11
| ~ in(sK0(sK11,sK12),sK11)
| in(sK0(sK11,sK12),relation_dom(sK12)) ),
inference(instantiation,[status(thm)],[c_107497]) ).
cnf(c_112648,plain,
sK0(sK11,sK12) = sK0(sK11,sK12),
inference(instantiation,[status(thm)],[c_3602]) ).
cnf(c_115661,plain,
( ~ in(unordered_pair(singleton(sK0(sK11,sK12)),unordered_pair(sK0(sK11,sK12),sK1(sK11,sK12))),sK12)
| ~ in(sK0(sK11,sK12),sK11)
| ~ relation(sK12)
| identity_relation(sK11) = sK12 ),
inference(superposition,[status(thm)],[c_112178,c_567]) ).
cnf(c_115671,plain,
( ~ in(unordered_pair(singleton(sK0(sK11,sK12)),unordered_pair(sK0(sK11,sK12),sK1(sK11,sK12))),sK12)
| ~ in(sK0(sK11,sK12),sK11)
| identity_relation(sK11) = sK12 ),
inference(forward_subsumption_resolution,[status(thm)],[c_115661,c_103]) ).
cnf(c_115731,plain,
( ~ in(X0,sK11)
| ~ function(sK12)
| ~ relation(sK12)
| apply(identity_relation(sK12),unordered_pair(singleton(X0),unordered_pair(X0,apply(sK12,X0)))) = unordered_pair(singleton(X0),unordered_pair(X0,apply(sK12,X0)))
| identity_relation(sK11) = sK12 ),
inference(superposition,[status(thm)],[c_101,c_34041]) ).
cnf(c_115748,plain,
( ~ in(X0,sK11)
| apply(identity_relation(sK12),unordered_pair(singleton(X0),unordered_pair(X0,apply(sK12,X0)))) = unordered_pair(singleton(X0),unordered_pair(X0,apply(sK12,X0)))
| identity_relation(sK11) = sK12 ),
inference(forward_subsumption_resolution,[status(thm)],[c_115731,c_103,c_102]) ).
cnf(c_118425,plain,
( ~ in(unordered_pair(singleton(sK0(sK11,sK12)),unordered_pair(sK0(sK11,sK12),sK1(sK11,sK12))),sK12)
| identity_relation(sK11) = sK12 ),
inference(global_subsumption_just,[status(thm)],[c_115671,c_69937,c_115671]) ).
cnf(c_118436,plain,
( ~ in(unordered_pair(singleton(sK0(sK11,sK12)),unordered_pair(sK0(sK11,sK12),sK0(sK11,sK12))),sK12)
| identity_relation(sK11) = sK12 ),
inference(superposition,[status(thm)],[c_112178,c_118425]) ).
cnf(c_118612,plain,
identity_relation(sK11) = sK12,
inference(global_subsumption_just,[status(thm)],[c_115748,c_101,c_69937,c_70607,c_112647,c_112648,c_118436]) ).
cnf(c_118807,plain,
( relation_dom(sK12) != sK11
| sK12 != sK12
| in(sK13,sK11) ),
inference(demodulation,[status(thm)],[c_99,c_118612]) ).
cnf(c_118808,plain,
( relation_dom(sK12) != sK11
| in(sK13,sK11) ),
inference(equality_resolution_simp,[status(thm)],[c_118807]) ).
cnf(c_119607,plain,
in(sK13,sK11),
inference(global_subsumption_just,[status(thm)],[c_118808,c_99,c_3621,c_8497,c_20345,c_20346,c_36405,c_48030,c_66548,c_118612]) ).
cnf(c_119614,plain,
apply(identity_relation(sK11),sK13) = sK13,
inference(superposition,[status(thm)],[c_119607,c_27109]) ).
cnf(c_119621,plain,
apply(sK12,sK13) = sK13,
inference(light_normalisation,[status(thm)],[c_119614,c_118612]) ).
cnf(c_119628,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_119621,c_118612,c_66548,c_48030,c_36405,c_20346,c_20345,c_8497,c_3621,c_98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU216+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15 % Command : run_iprover %s %d THM
% 0.18/0.36 % Computer : n019.cluster.edu
% 0.18/0.36 % Model : x86_64 x86_64
% 0.18/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.36 % Memory : 8042.1875MB
% 0.18/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36 % CPULimit : 300
% 0.18/0.36 % WCLimit : 300
% 0.18/0.36 % DateTime : Wed Aug 23 17:48:44 EDT 2023
% 0.18/0.37 % CPUTime :
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 29.34/4.78 % SZS status Started for theBenchmark.p
% 29.34/4.78 % SZS status Theorem for theBenchmark.p
% 29.34/4.78
% 29.34/4.78 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 29.34/4.78
% 29.34/4.78 ------ iProver source info
% 29.34/4.78
% 29.34/4.78 git: date: 2023-05-31 18:12:56 +0000
% 29.34/4.78 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 29.34/4.78 git: non_committed_changes: false
% 29.34/4.78 git: last_make_outside_of_git: false
% 29.34/4.78
% 29.34/4.78 ------ Parsing...
% 29.34/4.78 ------ Clausification by vclausify_rel & Parsing by iProver...
% 29.34/4.78
% 29.34/4.78 ------ Preprocessing... sup_sim: 9 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
% 29.34/4.78
% 29.34/4.78 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 29.34/4.78
% 29.34/4.78 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 29.34/4.78 ------ Proving...
% 29.34/4.78 ------ Problem Properties
% 29.34/4.78
% 29.34/4.78
% 29.34/4.78 clauses 57
% 29.34/4.78 conjectures 6
% 29.34/4.78 EPR 21
% 29.34/4.78 Horn 50
% 29.34/4.78 unary 25
% 29.34/4.78 binary 16
% 29.34/4.78 lits 113
% 29.34/4.78 lits eq 22
% 29.34/4.78 fd_pure 0
% 29.34/4.78 fd_pseudo 0
% 29.34/4.78 fd_cond 1
% 29.34/4.78 fd_pseudo_cond 6
% 29.34/4.78 AC symbols 0
% 29.34/4.78
% 29.34/4.78 ------ Schedule dynamic 5 is on
% 29.34/4.78
% 29.34/4.78 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 29.34/4.78
% 29.34/4.78
% 29.34/4.78 ------
% 29.34/4.78 Current options:
% 29.34/4.78 ------
% 29.34/4.78
% 29.34/4.78
% 29.34/4.78
% 29.34/4.78
% 29.34/4.78 ------ Proving...
% 29.34/4.78
% 29.34/4.78
% 29.34/4.78 % SZS status Theorem for theBenchmark.p
% 29.34/4.78
% 29.34/4.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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% 29.34/4.78
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