TSTP Solution File: SET733+4 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET733+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n004.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 15:09:23 EDT 2023
% Result : Theorem 9.03s 2.14s
% Output : CNFRefutation 9.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 126 ( 19 unt; 0 def)
% Number of atoms : 495 ( 73 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 594 ( 225 ~; 228 |; 101 &)
% ( 10 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-5 aty)
% Number of variables : 382 ( 0 sgn; 204 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X5,X0,X1] :
( maps(X5,X0,X1)
<=> ( ! [X2,X6,X7] :
( ( member(X7,X1)
& member(X6,X1)
& member(X2,X0) )
=> ( ( apply(X5,X2,X7)
& apply(X5,X2,X6) )
=> X6 = X7 ) )
& ! [X2] :
( member(X2,X0)
=> ? [X4] :
( apply(X5,X2,X4)
& member(X4,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps) ).
fof(f14,axiom,
! [X9,X5,X0,X1,X10,X2,X11] :
( ( member(X11,X10)
& member(X2,X0) )
=> ( apply(compose_function(X9,X5,X0,X1,X10),X2,X11)
<=> ? [X4] :
( apply(X9,X4,X11)
& apply(X5,X2,X4)
& member(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_function) ).
fof(f16,axiom,
! [X5,X0] :
( identity(X5,X0)
<=> ! [X2] :
( member(X2,X0)
=> apply(X5,X2,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f17,axiom,
! [X5,X0,X1] :
( injective(X5,X0,X1)
<=> ! [X12,X13,X4] :
( ( member(X4,X1)
& member(X13,X0)
& member(X12,X0) )
=> ( ( apply(X5,X13,X4)
& apply(X5,X12,X4) )
=> X12 = X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injective) ).
fof(f29,conjecture,
! [X5,X9,X0,X1] :
( ( identity(compose_function(X9,X5,X0,X1,X0),X0)
& maps(X9,X1,X0)
& maps(X5,X0,X1) )
=> injective(X5,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII24) ).
fof(f30,negated_conjecture,
~ ! [X5,X9,X0,X1] :
( ( identity(compose_function(X9,X5,X0,X1,X0),X0)
& maps(X9,X1,X0)
& maps(X5,X0,X1) )
=> injective(X5,X0,X1) ),
inference(negated_conjecture,[],[f29]) ).
fof(f40,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X2)
& member(X3,X1) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X3,X4) )
=> X4 = X5 ) )
& ! [X6] :
( member(X6,X1)
=> ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f42,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( member(X6,X4)
& member(X5,X2) )
=> ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) ) ),
inference(rectify,[],[f14]) ).
fof(f44,plain,
! [X0,X1] :
( identity(X0,X1)
<=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
inference(rectify,[],[f16]) ).
fof(f45,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X5)
& apply(X0,X3,X5) )
=> X3 = X4 ) ) ),
inference(rectify,[],[f17]) ).
fof(f57,plain,
~ ! [X0,X1,X2,X3] :
( ( identity(compose_function(X1,X0,X2,X3,X2),X2)
& maps(X1,X3,X2)
& maps(X0,X2,X3) )
=> injective(X0,X2,X3) ),
inference(rectify,[],[f30]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X5)
& apply(X0,X3,X5) )
=> X3 = X4 ) )
=> injective(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f45]) ).
fof(f59,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> ( ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X2)
& member(X3,X1) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X3,X4) )
=> X4 = X5 ) )
& ! [X6] :
( member(X6,X1)
=> ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f40]) ).
fof(f60,plain,
! [X0,X1] :
( identity(X0,X1)
=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
inference(unused_predicate_definition_removal,[],[f44]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( ! [X3,X4,X5] :
( X4 = X5
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1) )
& ! [X6] :
( ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) )
| ~ member(X6,X1) ) )
| ~ maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f59]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( ! [X3,X4,X5] :
( X4 = X5
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1) )
& ! [X6] :
( ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) )
| ~ member(X6,X1) ) )
| ~ maps(X0,X1,X2) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) )
| ~ member(X6,X4)
| ~ member(X5,X2) ),
inference(ennf_transformation,[],[f42]) ).
fof(f66,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) )
| ~ member(X6,X4)
| ~ member(X5,X2) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
| ~ identity(X0,X1) ),
inference(ennf_transformation,[],[f60]) ).
fof(f68,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
| ? [X3,X4,X5] :
( X3 != X4
& apply(X0,X4,X5)
& apply(X0,X3,X5)
& member(X5,X2)
& member(X4,X1)
& member(X3,X1) ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f69,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
| ? [X3,X4,X5] :
( X3 != X4
& apply(X0,X4,X5)
& apply(X0,X3,X5)
& member(X5,X2)
& member(X4,X1)
& member(X3,X1) ) ),
inference(flattening,[],[f68]) ).
fof(f72,plain,
? [X0,X1,X2,X3] :
( ~ injective(X0,X2,X3)
& identity(compose_function(X1,X0,X2,X3,X2),X2)
& maps(X1,X3,X2)
& maps(X0,X2,X3) ),
inference(ennf_transformation,[],[f57]) ).
fof(f73,plain,
? [X0,X1,X2,X3] :
( ~ injective(X0,X2,X3)
& identity(compose_function(X1,X0,X2,X3,X2),X2)
& maps(X1,X3,X2)
& maps(X0,X2,X3) ),
inference(flattening,[],[f72]) ).
fof(f96,plain,
! [X0,X2,X6] :
( ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) )
=> ( apply(X0,X6,sK3(X0,X2,X6))
& member(sK3(X0,X2,X6),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ( ! [X3,X4,X5] :
( X4 = X5
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1) )
& ! [X6] :
( ( apply(X0,X6,sK3(X0,X2,X6))
& member(sK3(X0,X2,X6),X2) )
| ~ member(X6,X1) ) )
| ~ maps(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f64,f96]) ).
fof(f98,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3) ) )
& ( ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X6,X4)
| ~ member(X5,X2) ),
inference(nnf_transformation,[],[f66]) ).
fof(f99,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3) ) )
& ( ? [X8] :
( apply(X0,X8,X6)
& apply(X1,X5,X8)
& member(X8,X3) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X6,X4)
| ~ member(X5,X2) ),
inference(rectify,[],[f98]) ).
fof(f100,plain,
! [X0,X1,X3,X5,X6] :
( ? [X8] :
( apply(X0,X8,X6)
& apply(X1,X5,X8)
& member(X8,X3) )
=> ( apply(X0,sK4(X0,X1,X3,X5,X6),X6)
& apply(X1,X5,sK4(X0,X1,X3,X5,X6))
& member(sK4(X0,X1,X3,X5,X6),X3) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3) ) )
& ( ( apply(X0,sK4(X0,X1,X3,X5,X6),X6)
& apply(X1,X5,sK4(X0,X1,X3,X5,X6))
& member(sK4(X0,X1,X3,X5,X6),X3) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X6,X4)
| ~ member(X5,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f99,f100]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5] :
( X3 != X4
& apply(X0,X4,X5)
& apply(X0,X3,X5)
& member(X5,X2)
& member(X4,X1)
& member(X3,X1) )
=> ( sK5(X0,X1,X2) != sK6(X0,X1,X2)
& apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
& apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2))
& member(sK7(X0,X1,X2),X2)
& member(sK6(X0,X1,X2),X1)
& member(sK5(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
| ( sK5(X0,X1,X2) != sK6(X0,X1,X2)
& apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
& apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2))
& member(sK7(X0,X1,X2),X2)
& member(sK6(X0,X1,X2),X1)
& member(sK5(X0,X1,X2),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f69,f102]) ).
fof(f123,plain,
( ? [X0,X1,X2,X3] :
( ~ injective(X0,X2,X3)
& identity(compose_function(X1,X0,X2,X3,X2),X2)
& maps(X1,X3,X2)
& maps(X0,X2,X3) )
=> ( ~ injective(sK12,sK14,sK15)
& identity(compose_function(sK13,sK12,sK14,sK15,sK14),sK14)
& maps(sK13,sK15,sK14)
& maps(sK12,sK14,sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f124,plain,
( ~ injective(sK12,sK14,sK15)
& identity(compose_function(sK13,sK12,sK14,sK15,sK14),sK14)
& maps(sK13,sK15,sK14)
& maps(sK12,sK14,sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15])],[f73,f123]) ).
fof(f153,plain,
! [X2,X3,X0,X1,X4,X5] :
( X4 = X5
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f154,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( member(sK4(X0,X1,X3,X5,X6),X3)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ~ member(X6,X4)
| ~ member(X5,X2) ),
inference(cnf_transformation,[],[f101]) ).
fof(f155,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( apply(X1,X5,sK4(X0,X1,X3,X5,X6))
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ~ member(X6,X4)
| ~ member(X5,X2) ),
inference(cnf_transformation,[],[f101]) ).
fof(f156,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( apply(X0,sK4(X0,X1,X3,X5,X6),X6)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ~ member(X6,X4)
| ~ member(X5,X2) ),
inference(cnf_transformation,[],[f101]) ).
fof(f158,plain,
! [X2,X0,X1] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ identity(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f159,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| member(sK5(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f160,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| member(sK6(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f161,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| member(sK7(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f103]) ).
fof(f162,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f163,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f164,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| sK5(X0,X1,X2) != sK6(X0,X1,X2) ),
inference(cnf_transformation,[],[f103]) ).
fof(f181,plain,
maps(sK12,sK14,sK15),
inference(cnf_transformation,[],[f124]) ).
fof(f182,plain,
maps(sK13,sK15,sK14),
inference(cnf_transformation,[],[f124]) ).
fof(f183,plain,
identity(compose_function(sK13,sK12,sK14,sK15,sK14),sK14),
inference(cnf_transformation,[],[f124]) ).
fof(f184,plain,
~ injective(sK12,sK14,sK15),
inference(cnf_transformation,[],[f124]) ).
cnf(c_75,plain,
( ~ apply(X0,X1,X2)
| ~ apply(X0,X1,X3)
| ~ maps(X0,X4,X5)
| ~ member(X1,X4)
| ~ member(X2,X5)
| ~ member(X3,X5)
| X2 = X3 ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_79,plain,
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ~ member(X5,X2)
| ~ member(X6,X4)
| apply(X0,sK4(X0,X1,X3,X5,X6),X6) ),
inference(cnf_transformation,[],[f156]) ).
cnf(c_80,plain,
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ~ member(X5,X2)
| ~ member(X6,X4)
| apply(X1,X5,sK4(X0,X1,X3,X5,X6)) ),
inference(cnf_transformation,[],[f155]) ).
cnf(c_81,plain,
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ~ member(X5,X2)
| ~ member(X6,X4)
| member(sK4(X0,X1,X3,X5,X6),X3) ),
inference(cnf_transformation,[],[f154]) ).
cnf(c_82,plain,
( ~ member(X0,X1)
| ~ identity(X2,X1)
| apply(X2,X0,X0) ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_83,plain,
( sK5(X0,X1,X2) != sK6(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f164]) ).
cnf(c_84,plain,
( apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f163]) ).
cnf(c_85,plain,
( apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_86,plain,
( member(sK7(X0,X1,X2),X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_87,plain,
( member(sK6(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f160]) ).
cnf(c_88,plain,
( member(sK5(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_105,negated_conjecture,
~ injective(sK12,sK14,sK15),
inference(cnf_transformation,[],[f184]) ).
cnf(c_106,negated_conjecture,
identity(compose_function(sK13,sK12,sK14,sK15,sK14),sK14),
inference(cnf_transformation,[],[f183]) ).
cnf(c_107,negated_conjecture,
maps(sK13,sK15,sK14),
inference(cnf_transformation,[],[f182]) ).
cnf(c_108,negated_conjecture,
maps(sK12,sK14,sK15),
inference(cnf_transformation,[],[f181]) ).
cnf(c_207,plain,
( sK5(X0,X1,X2) != sK6(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_83]) ).
cnf(c_237,plain,
( member(sK5(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_88]) ).
cnf(c_241,plain,
( injective(X0,X1,X2)
| apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_84]) ).
cnf(c_242,plain,
( apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_241]) ).
cnf(c_243,plain,
( injective(X0,X1,X2)
| apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_85]) ).
cnf(c_244,plain,
( apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_243]) ).
cnf(c_245,plain,
( injective(X0,X1,X2)
| member(sK7(X0,X1,X2),X2) ),
inference(prop_impl_just,[status(thm)],[c_86]) ).
cnf(c_246,plain,
( member(sK7(X0,X1,X2),X2)
| injective(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_245]) ).
cnf(c_247,plain,
( injective(X0,X1,X2)
| member(sK6(X0,X1,X2),X1) ),
inference(prop_impl_just,[status(thm)],[c_87]) ).
cnf(c_248,plain,
( member(sK6(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_247]) ).
cnf(c_681,plain,
( compose_function(sK13,sK12,sK14,sK15,sK14) != X1
| X0 != sK14
| ~ member(X2,X0)
| apply(X1,X2,X2) ),
inference(resolution_lifted,[status(thm)],[c_82,c_106]) ).
cnf(c_682,plain,
( ~ member(X0,sK14)
| apply(compose_function(sK13,sK12,sK14,sK15,sK14),X0,X0) ),
inference(unflattening,[status(thm)],[c_681]) ).
cnf(c_692,plain,
( X0 != sK12
| X1 != sK14
| X2 != sK15
| member(sK5(X0,X1,X2),X1) ),
inference(resolution_lifted,[status(thm)],[c_237,c_105]) ).
cnf(c_693,plain,
member(sK5(sK12,sK14,sK15),sK14),
inference(unflattening,[status(thm)],[c_692]) ).
cnf(c_697,plain,
( X0 != sK12
| X1 != sK14
| X2 != sK15
| member(sK6(X0,X1,X2),X1) ),
inference(resolution_lifted,[status(thm)],[c_248,c_105]) ).
cnf(c_698,plain,
member(sK6(sK12,sK14,sK15),sK14),
inference(unflattening,[status(thm)],[c_697]) ).
cnf(c_702,plain,
( X0 != sK12
| X1 != sK14
| X2 != sK15
| member(sK7(X0,X1,X2),X2) ),
inference(resolution_lifted,[status(thm)],[c_246,c_105]) ).
cnf(c_703,plain,
member(sK7(sK12,sK14,sK15),sK15),
inference(unflattening,[status(thm)],[c_702]) ).
cnf(c_707,plain,
( X0 != sK12
| X1 != sK14
| X2 != sK15
| apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2)) ),
inference(resolution_lifted,[status(thm)],[c_244,c_105]) ).
cnf(c_708,plain,
apply(sK12,sK5(sK12,sK14,sK15),sK7(sK12,sK14,sK15)),
inference(unflattening,[status(thm)],[c_707]) ).
cnf(c_712,plain,
( X0 != sK12
| X1 != sK14
| X2 != sK15
| apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2)) ),
inference(resolution_lifted,[status(thm)],[c_242,c_105]) ).
cnf(c_713,plain,
apply(sK12,sK6(sK12,sK14,sK15),sK7(sK12,sK14,sK15)),
inference(unflattening,[status(thm)],[c_712]) ).
cnf(c_717,plain,
( sK5(X0,X1,X2) != sK6(X0,X1,X2)
| X0 != sK12
| X1 != sK14
| X2 != sK15 ),
inference(resolution_lifted,[status(thm)],[c_207,c_105]) ).
cnf(c_718,plain,
sK5(sK12,sK14,sK15) != sK6(sK12,sK14,sK15),
inference(unflattening,[status(thm)],[c_717]) ).
cnf(c_794,plain,
( X0 != sK13
| X1 != sK15
| X2 != sK14
| ~ apply(X0,X3,X4)
| ~ apply(X0,X3,X5)
| ~ member(X3,X1)
| ~ member(X4,X2)
| ~ member(X5,X2)
| X4 = X5 ),
inference(resolution_lifted,[status(thm)],[c_75,c_107]) ).
cnf(c_795,plain,
( ~ apply(sK13,X0,X1)
| ~ apply(sK13,X0,X2)
| ~ member(X0,sK15)
| ~ member(X1,sK14)
| ~ member(X2,sK14)
| X1 = X2 ),
inference(unflattening,[status(thm)],[c_794]) ).
cnf(c_815,plain,
( X0 != sK12
| X1 != sK14
| X2 != sK15
| ~ apply(X0,X3,X4)
| ~ apply(X0,X3,X5)
| ~ member(X3,X1)
| ~ member(X4,X2)
| ~ member(X5,X2)
| X4 = X5 ),
inference(resolution_lifted,[status(thm)],[c_75,c_108]) ).
cnf(c_816,plain,
( ~ apply(sK12,X0,X1)
| ~ apply(sK12,X0,X2)
| ~ member(X0,sK14)
| ~ member(X1,sK15)
| ~ member(X2,sK15)
| X1 = X2 ),
inference(unflattening,[status(thm)],[c_815]) ).
cnf(c_988,plain,
( ~ member(X0,sK14)
| apply(compose_function(sK13,sK12,sK14,sK15,sK14),X0,X0) ),
inference(prop_impl_just,[status(thm)],[c_682]) ).
cnf(c_1469,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_2767,plain,
( ~ apply(sK12,X0,sK7(sK12,sK14,sK15))
| ~ member(sK7(sK12,sK14,sK15),sK15)
| ~ apply(sK12,X0,X1)
| ~ member(X0,sK14)
| ~ member(X1,sK15)
| X1 = sK7(sK12,sK14,sK15) ),
inference(instantiation,[status(thm)],[c_816]) ).
cnf(c_2772,plain,
( ~ member(sK5(sK12,sK14,sK15),sK14)
| apply(compose_function(sK13,sK12,sK14,sK15,sK14),sK5(sK12,sK14,sK15),sK5(sK12,sK14,sK15)) ),
inference(instantiation,[status(thm)],[c_988]) ).
cnf(c_2773,plain,
( ~ member(sK6(sK12,sK14,sK15),sK14)
| apply(compose_function(sK13,sK12,sK14,sK15,sK14),sK6(sK12,sK14,sK15),sK6(sK12,sK14,sK15)) ),
inference(instantiation,[status(thm)],[c_988]) ).
cnf(c_3275,plain,
( sK5(sK12,sK14,sK15) != X0
| sK6(sK12,sK14,sK15) != X0
| sK5(sK12,sK14,sK15) = sK6(sK12,sK14,sK15) ),
inference(instantiation,[status(thm)],[c_1469]) ).
cnf(c_3754,plain,
( ~ apply(compose_function(sK13,sK12,sK14,sK15,sK14),sK5(sK12,sK14,sK15),sK5(sK12,sK14,sK15))
| ~ member(sK5(sK12,sK14,sK15),sK14)
| apply(sK12,sK5(sK12,sK14,sK15),sK4(sK13,sK12,sK15,sK5(sK12,sK14,sK15),sK5(sK12,sK14,sK15))) ),
inference(instantiation,[status(thm)],[c_80]) ).
cnf(c_3756,plain,
( ~ apply(compose_function(sK13,sK12,sK14,sK15,sK14),sK5(sK12,sK14,sK15),sK5(sK12,sK14,sK15))
| ~ member(sK5(sK12,sK14,sK15),sK14)
| member(sK4(sK13,sK12,sK15,sK5(sK12,sK14,sK15),sK5(sK12,sK14,sK15)),sK15) ),
inference(instantiation,[status(thm)],[c_81]) ).
cnf(c_3817,plain,
( ~ apply(compose_function(sK13,sK12,sK14,sK15,sK14),sK6(sK12,sK14,sK15),sK6(sK12,sK14,sK15))
| ~ member(sK6(sK12,sK14,sK15),sK14)
| apply(sK12,sK6(sK12,sK14,sK15),sK4(sK13,sK12,sK15,sK6(sK12,sK14,sK15),sK6(sK12,sK14,sK15))) ),
inference(instantiation,[status(thm)],[c_80]) ).
cnf(c_3819,plain,
( ~ apply(compose_function(sK13,sK12,sK14,sK15,sK14),sK6(sK12,sK14,sK15),sK6(sK12,sK14,sK15))
| ~ member(sK6(sK12,sK14,sK15),sK14)
| member(sK4(sK13,sK12,sK15,sK6(sK12,sK14,sK15),sK6(sK12,sK14,sK15)),sK15) ),
inference(instantiation,[status(thm)],[c_81]) ).
cnf(c_5578,plain,
( ~ apply(sK12,sK5(sK12,sK14,sK15),sK7(sK12,sK14,sK15))
| ~ apply(sK12,sK5(sK12,sK14,sK15),X0)
| ~ member(sK5(sK12,sK14,sK15),sK14)
| ~ member(sK7(sK12,sK14,sK15),sK15)
| ~ member(X0,sK15)
| X0 = sK7(sK12,sK14,sK15) ),
inference(instantiation,[status(thm)],[c_2767]) ).
cnf(c_5580,plain,
( ~ apply(sK12,sK6(sK12,sK14,sK15),sK7(sK12,sK14,sK15))
| ~ apply(sK12,sK6(sK12,sK14,sK15),X0)
| ~ member(sK6(sK12,sK14,sK15),sK14)
| ~ member(sK7(sK12,sK14,sK15),sK15)
| ~ member(X0,sK15)
| X0 = sK7(sK12,sK14,sK15) ),
inference(instantiation,[status(thm)],[c_2767]) ).
cnf(c_5753,plain,
( ~ apply(compose_function(sK13,sK12,sK14,sK15,sK14),X0,X0)
| ~ member(X0,sK14)
| member(sK4(sK13,sK12,sK15,X0,X0),sK15) ),
inference(instantiation,[status(thm)],[c_81]) ).
cnf(c_9622,plain,
( ~ member(X0,sK14)
| member(sK4(sK13,sK12,sK15,X0,X0),sK15) ),
inference(superposition,[status(thm)],[c_988,c_81]) ).
cnf(c_11325,plain,
( ~ apply(sK12,sK5(sK12,sK14,sK15),sK4(sK13,sK12,sK15,sK5(sK12,sK14,sK15),sK5(sK12,sK14,sK15)))
| ~ member(sK4(sK13,sK12,sK15,sK5(sK12,sK14,sK15),sK5(sK12,sK14,sK15)),sK15)
| ~ apply(sK12,sK5(sK12,sK14,sK15),sK7(sK12,sK14,sK15))
| ~ member(sK5(sK12,sK14,sK15),sK14)
| ~ member(sK7(sK12,sK14,sK15),sK15)
| sK4(sK13,sK12,sK15,sK5(sK12,sK14,sK15),sK5(sK12,sK14,sK15)) = sK7(sK12,sK14,sK15) ),
inference(instantiation,[status(thm)],[c_5578]) ).
cnf(c_11510,plain,
( ~ apply(sK12,sK6(sK12,sK14,sK15),sK4(sK13,sK12,sK15,sK6(sK12,sK14,sK15),sK6(sK12,sK14,sK15)))
| ~ member(sK4(sK13,sK12,sK15,sK6(sK12,sK14,sK15),sK6(sK12,sK14,sK15)),sK15)
| ~ apply(sK12,sK6(sK12,sK14,sK15),sK7(sK12,sK14,sK15))
| ~ member(sK6(sK12,sK14,sK15),sK14)
| ~ member(sK7(sK12,sK14,sK15),sK15)
| sK4(sK13,sK12,sK15,sK6(sK12,sK14,sK15),sK6(sK12,sK14,sK15)) = sK7(sK12,sK14,sK15) ),
inference(instantiation,[status(thm)],[c_5580]) ).
cnf(c_13543,plain,
( ~ member(X0,sK14)
| apply(sK13,sK4(sK13,sK12,sK15,X0,X0),X0) ),
inference(superposition,[status(thm)],[c_988,c_79]) ).
cnf(c_13546,plain,
( ~ member(X0,sK14)
| apply(sK12,X0,sK4(sK13,sK12,sK15,X0,X0)) ),
inference(superposition,[status(thm)],[c_988,c_80]) ).
cnf(c_13564,plain,
( ~ apply(sK13,sK4(sK13,sK12,sK15,X0,X0),X1)
| ~ member(sK4(sK13,sK12,sK15,X0,X0),sK15)
| ~ member(X0,sK14)
| ~ member(X1,sK14)
| X0 = X1 ),
inference(superposition,[status(thm)],[c_13543,c_795]) ).
cnf(c_13577,plain,
( ~ member(sK4(sK13,sK12,sK15,X0,X0),sK15)
| ~ apply(sK12,X0,X1)
| ~ member(X0,sK14)
| ~ member(X1,sK15)
| sK4(sK13,sK12,sK15,X0,X0) = X1 ),
inference(superposition,[status(thm)],[c_13546,c_816]) ).
cnf(c_13589,plain,
( ~ apply(sK13,sK4(sK13,sK12,sK15,X0,X0),X1)
| ~ member(X0,sK14)
| ~ member(X1,sK14)
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_13564,c_682,c_5753,c_13564]) ).
cnf(c_13595,plain,
( ~ apply(sK12,X0,X1)
| ~ member(X0,sK14)
| ~ member(X1,sK15)
| sK4(sK13,sK12,sK15,X0,X0) = X1 ),
inference(global_subsumption_just,[status(thm)],[c_13577,c_9622,c_13577]) ).
cnf(c_13600,plain,
( ~ member(sK5(sK12,sK14,sK15),sK14)
| ~ member(sK7(sK12,sK14,sK15),sK15)
| sK4(sK13,sK12,sK15,sK5(sK12,sK14,sK15),sK5(sK12,sK14,sK15)) = sK7(sK12,sK14,sK15) ),
inference(superposition,[status(thm)],[c_708,c_13595]) ).
cnf(c_13601,plain,
( ~ member(sK6(sK12,sK14,sK15),sK14)
| ~ member(sK7(sK12,sK14,sK15),sK15)
| sK4(sK13,sK12,sK15,sK6(sK12,sK14,sK15),sK6(sK12,sK14,sK15)) = sK7(sK12,sK14,sK15) ),
inference(superposition,[status(thm)],[c_713,c_13595]) ).
cnf(c_13607,plain,
sK4(sK13,sK12,sK15,sK5(sK12,sK14,sK15),sK5(sK12,sK14,sK15)) = sK7(sK12,sK14,sK15),
inference(global_subsumption_just,[status(thm)],[c_13600,c_693,c_703,c_708,c_2772,c_3756,c_3754,c_11325]) ).
cnf(c_13609,plain,
( ~ apply(sK13,sK7(sK12,sK14,sK15),X0)
| ~ member(sK5(sK12,sK14,sK15),sK14)
| ~ member(X0,sK14)
| sK5(sK12,sK14,sK15) = X0 ),
inference(superposition,[status(thm)],[c_13607,c_13589]) ).
cnf(c_13611,plain,
( ~ member(sK5(sK12,sK14,sK15),sK14)
| apply(sK13,sK7(sK12,sK14,sK15),sK5(sK12,sK14,sK15)) ),
inference(superposition,[status(thm)],[c_13607,c_13543]) ).
cnf(c_13614,plain,
sK4(sK13,sK12,sK15,sK6(sK12,sK14,sK15),sK6(sK12,sK14,sK15)) = sK7(sK12,sK14,sK15),
inference(global_subsumption_just,[status(thm)],[c_13601,c_698,c_703,c_713,c_2773,c_3819,c_3817,c_11510]) ).
cnf(c_13616,plain,
( ~ apply(sK13,sK7(sK12,sK14,sK15),X0)
| ~ member(sK6(sK12,sK14,sK15),sK14)
| ~ member(X0,sK14)
| sK6(sK12,sK14,sK15) = X0 ),
inference(superposition,[status(thm)],[c_13614,c_13589]) ).
cnf(c_14092,plain,
apply(sK13,sK7(sK12,sK14,sK15),sK5(sK12,sK14,sK15)),
inference(global_subsumption_just,[status(thm)],[c_13611,c_693,c_13611]) ).
cnf(c_14100,plain,
( ~ apply(sK13,sK7(sK12,sK14,sK15),X0)
| ~ member(sK5(sK12,sK14,sK15),sK14)
| ~ member(sK7(sK12,sK14,sK15),sK15)
| ~ member(X0,sK14)
| sK5(sK12,sK14,sK15) = X0 ),
inference(superposition,[status(thm)],[c_14092,c_795]) ).
cnf(c_14134,plain,
( ~ member(X0,sK14)
| ~ apply(sK13,sK7(sK12,sK14,sK15),X0) ),
inference(global_subsumption_just,[status(thm)],[c_14100,c_693,c_698,c_718,c_3275,c_13609,c_13616]) ).
cnf(c_14135,plain,
( ~ apply(sK13,sK7(sK12,sK14,sK15),X0)
| ~ member(X0,sK14) ),
inference(renaming,[status(thm)],[c_14134]) ).
cnf(c_14139,plain,
~ member(sK5(sK12,sK14,sK15),sK14),
inference(superposition,[status(thm)],[c_14092,c_14135]) ).
cnf(c_14140,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_14139,c_693]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET733+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.11/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n004.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 : Sat Aug 26 11:34:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.03/2.14 % SZS status Started for theBenchmark.p
% 9.03/2.14 % SZS status Theorem for theBenchmark.p
% 9.03/2.14
% 9.03/2.14 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 9.03/2.14
% 9.03/2.14 ------ iProver source info
% 9.03/2.14
% 9.03/2.14 git: date: 2023-05-31 18:12:56 +0000
% 9.03/2.14 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 9.03/2.14 git: non_committed_changes: false
% 9.03/2.14 git: last_make_outside_of_git: false
% 9.03/2.14
% 9.03/2.14 ------ Parsing...
% 9.03/2.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 9.03/2.14
% 9.03/2.14 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e
% 9.03/2.14
% 9.03/2.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 9.03/2.14
% 9.03/2.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 9.03/2.14 ------ Proving...
% 9.03/2.14 ------ Problem Properties
% 9.03/2.14
% 9.03/2.14
% 9.03/2.14 clauses 59
% 9.03/2.14 conjectures 0
% 9.03/2.14 EPR 4
% 9.03/2.14 Horn 54
% 9.03/2.14 unary 10
% 9.03/2.14 binary 30
% 9.03/2.14 lits 143
% 9.03/2.14 lits eq 6
% 9.03/2.14 fd_pure 0
% 9.03/2.14 fd_pseudo 0
% 9.03/2.14 fd_cond 0
% 9.03/2.14 fd_pseudo_cond 4
% 9.03/2.14 AC symbols 0
% 9.03/2.14
% 9.03/2.14 ------ Input Options Time Limit: Unbounded
% 9.03/2.14
% 9.03/2.14
% 9.03/2.14 ------
% 9.03/2.14 Current options:
% 9.03/2.14 ------
% 9.03/2.14
% 9.03/2.14
% 9.03/2.14
% 9.03/2.14
% 9.03/2.14 ------ Proving...
% 9.03/2.14
% 9.03/2.14
% 9.03/2.14 % SZS status Theorem for theBenchmark.p
% 9.03/2.14
% 9.03/2.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.03/2.14
% 9.03/2.14
%------------------------------------------------------------------------------