TSTP Solution File: SET726+4 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET726+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n005.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 15:09:19 EDT 2023
% Result : Theorem 3.10s 1.19s
% Output : CNFRefutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 112 ( 18 unt; 0 def)
% Number of atoms : 471 ( 64 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 547 ( 188 ~; 193 |; 120 &)
% ( 14 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-5 aty)
% Number of variables : 437 ( 0 sgn; 250 !; 37 ?)
% 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/sandbox/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/sandbox/benchmark/theBenchmark.p',compose_function) ).
fof(f15,axiom,
! [X5,X9,X0,X1] :
( equal_maps(X5,X9,X0,X1)
<=> ! [X2,X6,X7] :
( ( member(X7,X1)
& member(X6,X1)
& member(X2,X0) )
=> ( ( apply(X9,X2,X7)
& apply(X5,X2,X6) )
=> X6 = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_maps) ).
fof(f16,axiom,
! [X5,X0] :
( identity(X5,X0)
<=> ! [X2] :
( member(X2,X0)
=> apply(X5,X2,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f21,axiom,
! [X5,X0,X1,X2,X4] :
( ( member(X4,X1)
& member(X2,X0) )
=> ( apply(X5,X2,X4)
<=> apply(inverse_function(X5,X0,X1),X4,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_function) ).
fof(f29,conjecture,
! [X5,X9,X8,X0,X1] :
( ( identity(compose_function(X5,X8,X1,X0,X1),X1)
& identity(compose_function(X9,X5,X0,X1,X0),X0)
& maps(X8,X1,X0)
& maps(X9,X1,X0)
& maps(X5,X0,X1) )
=> equal_maps(inverse_function(X5,X0,X1),X9,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII17) ).
fof(f30,negated_conjecture,
~ ! [X5,X9,X8,X0,X1] :
( ( identity(compose_function(X5,X8,X1,X0,X1),X1)
& identity(compose_function(X9,X5,X0,X1,X0),X0)
& maps(X8,X1,X0)
& maps(X9,X1,X0)
& maps(X5,X0,X1) )
=> equal_maps(inverse_function(X5,X0,X1),X9,X1,X0) ),
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(f43,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
<=> ! [X4,X5,X6] :
( ( member(X6,X3)
& member(X5,X3)
& member(X4,X2) )
=> ( ( apply(X1,X4,X6)
& apply(X0,X4,X5) )
=> X5 = X6 ) ) ),
inference(rectify,[],[f15]) ).
fof(f44,plain,
! [X0,X1] :
( identity(X0,X1)
<=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
inference(rectify,[],[f16]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4] :
( ( member(X4,X2)
& member(X3,X1) )
=> ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) ) ),
inference(rectify,[],[f21]) ).
fof(f57,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( identity(compose_function(X0,X2,X4,X3,X4),X4)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& maps(X2,X4,X3)
& maps(X1,X4,X3)
& maps(X0,X3,X4) )
=> equal_maps(inverse_function(X0,X3,X4),X1,X4,X3) ),
inference(rectify,[],[f30]) ).
fof(f58,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(f59,plain,
! [X0,X1] :
( identity(X0,X1)
=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
inference(unused_predicate_definition_removal,[],[f44]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( ! [X4,X5,X6] :
( ( member(X6,X3)
& member(X5,X3)
& member(X4,X2) )
=> ( ( apply(X1,X4,X6)
& apply(X0,X4,X5) )
=> X5 = X6 ) )
=> equal_maps(X0,X1,X2,X3) ),
inference(unused_predicate_definition_removal,[],[f43]) ).
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,[],[f58]) ).
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,X3] :
( equal_maps(X0,X1,X2,X3)
| ? [X4,X5,X6] :
( X5 != X6
& apply(X1,X4,X6)
& apply(X0,X4,X5)
& member(X6,X3)
& member(X5,X3)
& member(X4,X2) ) ),
inference(ennf_transformation,[],[f60]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| ? [X4,X5,X6] :
( X5 != X6
& apply(X1,X4,X6)
& apply(X0,X4,X5)
& member(X6,X3)
& member(X5,X3)
& member(X4,X2) ) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
| ~ identity(X0,X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f70,plain,
! [X0,X1,X2,X3,X4] :
( ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) )
| ~ member(X4,X2)
| ~ member(X3,X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f71,plain,
! [X0,X1,X2,X3,X4] :
( ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) )
| ~ member(X4,X2)
| ~ member(X3,X1) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
? [X0,X1,X2,X3,X4] :
( ~ equal_maps(inverse_function(X0,X3,X4),X1,X4,X3)
& identity(compose_function(X0,X2,X4,X3,X4),X4)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& maps(X2,X4,X3)
& maps(X1,X4,X3)
& maps(X0,X3,X4) ),
inference(ennf_transformation,[],[f57]) ).
fof(f73,plain,
? [X0,X1,X2,X3,X4] :
( ~ equal_maps(inverse_function(X0,X3,X4),X1,X4,X3)
& identity(compose_function(X0,X2,X4,X3,X4),X4)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& maps(X2,X4,X3)
& maps(X1,X4,X3)
& maps(X0,X3,X4) ),
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,X6] :
( X5 != X6
& apply(X1,X4,X6)
& apply(X0,X4,X5)
& member(X6,X3)
& member(X5,X3)
& member(X4,X2) )
=> ( sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3)
& apply(X1,sK5(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
& apply(X0,sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
& member(sK7(X0,X1,X2,X3),X3)
& member(sK6(X0,X1,X2,X3),X3)
& member(sK5(X0,X1,X2,X3),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| ( sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3)
& apply(X1,sK5(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
& apply(X0,sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
& member(sK7(X0,X1,X2,X3),X3)
& member(sK6(X0,X1,X2,X3),X3)
& member(sK5(X0,X1,X2,X3),X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f68,f102]) ).
fof(f104,plain,
! [X0,X1,X2,X3,X4] :
( ( ( apply(X0,X3,X4)
| ~ apply(inverse_function(X0,X1,X2),X4,X3) )
& ( apply(inverse_function(X0,X1,X2),X4,X3)
| ~ apply(X0,X3,X4) ) )
| ~ member(X4,X2)
| ~ member(X3,X1) ),
inference(nnf_transformation,[],[f71]) ).
fof(f123,plain,
( ? [X0,X1,X2,X3,X4] :
( ~ equal_maps(inverse_function(X0,X3,X4),X1,X4,X3)
& identity(compose_function(X0,X2,X4,X3,X4),X4)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& maps(X2,X4,X3)
& maps(X1,X4,X3)
& maps(X0,X3,X4) )
=> ( ~ equal_maps(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15)
& identity(compose_function(sK12,sK14,sK16,sK15,sK16),sK16)
& identity(compose_function(sK13,sK12,sK15,sK16,sK15),sK15)
& maps(sK14,sK16,sK15)
& maps(sK13,sK16,sK15)
& maps(sK12,sK15,sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f124,plain,
( ~ equal_maps(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15)
& identity(compose_function(sK12,sK14,sK16,sK15,sK16),sK16)
& identity(compose_function(sK13,sK12,sK15,sK16,sK15),sK15)
& maps(sK14,sK16,sK15)
& maps(sK13,sK16,sK15)
& maps(sK12,sK15,sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15,sK16])],[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,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| member(sK5(X0,X1,X2,X3),X2) ),
inference(cnf_transformation,[],[f103]) ).
fof(f159,plain,
! [X2,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| member(sK6(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f103]) ).
fof(f160,plain,
! [X2,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| member(sK7(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f103]) ).
fof(f161,plain,
! [X2,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| apply(X0,sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f162,plain,
! [X2,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| apply(X1,sK5(X0,X1,X2,X3),sK7(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f163,plain,
! [X2,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f103]) ).
fof(f164,plain,
! [X2,X0,X1] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ identity(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f166,plain,
! [X2,X3,X0,X1,X4] :
( apply(X0,X3,X4)
| ~ apply(inverse_function(X0,X1,X2),X4,X3)
| ~ member(X4,X2)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f181,plain,
maps(sK12,sK15,sK16),
inference(cnf_transformation,[],[f124]) ).
fof(f182,plain,
maps(sK13,sK16,sK15),
inference(cnf_transformation,[],[f124]) ).
fof(f184,plain,
identity(compose_function(sK13,sK12,sK15,sK16,sK15),sK15),
inference(cnf_transformation,[],[f124]) ).
fof(f186,plain,
~ equal_maps(inverse_function(sK12,sK15,sK16),sK13,sK16,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,
( sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f163]) ).
cnf(c_83,plain,
( apply(X0,sK5(X1,X0,X2,X3),sK7(X1,X0,X2,X3))
| equal_maps(X1,X0,X2,X3) ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_84,plain,
( apply(X0,sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_85,plain,
( member(sK7(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f160]) ).
cnf(c_86,plain,
( member(sK6(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_87,plain,
( member(sK5(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_88,plain,
( ~ member(X0,X1)
| ~ identity(X2,X1)
| apply(X2,X0,X0) ),
inference(cnf_transformation,[],[f164]) ).
cnf(c_89,plain,
( ~ apply(inverse_function(X0,X1,X2),X3,X4)
| ~ member(X3,X2)
| ~ member(X4,X1)
| apply(X0,X4,X3) ),
inference(cnf_transformation,[],[f166]) ).
cnf(c_105,negated_conjecture,
~ equal_maps(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),
inference(cnf_transformation,[],[f186]) ).
cnf(c_107,negated_conjecture,
identity(compose_function(sK13,sK12,sK15,sK16,sK15),sK15),
inference(cnf_transformation,[],[f184]) ).
cnf(c_109,negated_conjecture,
maps(sK13,sK16,sK15),
inference(cnf_transformation,[],[f182]) ).
cnf(c_110,negated_conjecture,
maps(sK12,sK15,sK16),
inference(cnf_transformation,[],[f181]) ).
cnf(c_209,plain,
( sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_82]) ).
cnf(c_247,plain,
( member(sK5(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_87]) ).
cnf(c_251,plain,
( equal_maps(X0,X1,X2,X3)
| apply(X0,sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3)) ),
inference(prop_impl_just,[status(thm)],[c_84]) ).
cnf(c_252,plain,
( apply(X0,sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(renaming,[status(thm)],[c_251]) ).
cnf(c_253,plain,
( equal_maps(X0,X1,X2,X3)
| member(sK7(X0,X1,X2,X3),X3) ),
inference(prop_impl_just,[status(thm)],[c_85]) ).
cnf(c_254,plain,
( member(sK7(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(renaming,[status(thm)],[c_253]) ).
cnf(c_255,plain,
( equal_maps(X0,X1,X2,X3)
| member(sK6(X0,X1,X2,X3),X3) ),
inference(prop_impl_just,[status(thm)],[c_86]) ).
cnf(c_256,plain,
( member(sK6(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(renaming,[status(thm)],[c_255]) ).
cnf(c_277,plain,
( apply(X0,sK5(X1,X0,X2,X3),sK7(X1,X0,X2,X3))
| equal_maps(X1,X0,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_83]) ).
cnf(c_976,plain,
( compose_function(sK13,sK12,sK15,sK16,sK15) != X1
| X0 != sK15
| ~ member(X2,X0)
| apply(X1,X2,X2) ),
inference(resolution_lifted,[status(thm)],[c_88,c_107]) ).
cnf(c_977,plain,
( ~ member(X0,sK15)
| apply(compose_function(sK13,sK12,sK15,sK16,sK15),X0,X0) ),
inference(unflattening,[status(thm)],[c_976]) ).
cnf(c_989,plain,
( inverse_function(sK12,sK15,sK16) != X0
| X1 != sK13
| X2 != sK16
| X3 != sK15
| member(sK5(X0,X1,X2,X3),X2) ),
inference(resolution_lifted,[status(thm)],[c_247,c_105]) ).
cnf(c_990,plain,
member(sK5(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK16),
inference(unflattening,[status(thm)],[c_989]) ).
cnf(c_994,plain,
( inverse_function(sK12,sK15,sK16) != X0
| X1 != sK13
| X2 != sK16
| X3 != sK15
| member(sK6(X0,X1,X2,X3),X3) ),
inference(resolution_lifted,[status(thm)],[c_256,c_105]) ).
cnf(c_995,plain,
member(sK6(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK15),
inference(unflattening,[status(thm)],[c_994]) ).
cnf(c_999,plain,
( inverse_function(sK12,sK15,sK16) != X0
| X1 != sK13
| X2 != sK16
| X3 != sK15
| member(sK7(X0,X1,X2,X3),X3) ),
inference(resolution_lifted,[status(thm)],[c_254,c_105]) ).
cnf(c_1000,plain,
member(sK7(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK15),
inference(unflattening,[status(thm)],[c_999]) ).
cnf(c_1004,plain,
( inverse_function(sK12,sK15,sK16) != X0
| X1 != sK13
| X2 != sK16
| X3 != sK15
| apply(X0,sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3)) ),
inference(resolution_lifted,[status(thm)],[c_252,c_105]) ).
cnf(c_1005,plain,
apply(inverse_function(sK12,sK15,sK16),sK5(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK6(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15)),
inference(unflattening,[status(thm)],[c_1004]) ).
cnf(c_1009,plain,
( sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3)
| inverse_function(sK12,sK15,sK16) != X0
| X1 != sK13
| X2 != sK16
| X3 != sK15 ),
inference(resolution_lifted,[status(thm)],[c_209,c_105]) ).
cnf(c_1010,plain,
sK6(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15) != sK7(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),
inference(unflattening,[status(thm)],[c_1009]) ).
cnf(c_1014,plain,
( inverse_function(sK12,sK15,sK16) != X1
| X0 != sK13
| X2 != sK16
| X3 != sK15
| apply(X0,sK5(X1,X0,X2,X3),sK7(X1,X0,X2,X3)) ),
inference(resolution_lifted,[status(thm)],[c_277,c_105]) ).
cnf(c_1015,plain,
apply(sK13,sK5(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK7(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15)),
inference(unflattening,[status(thm)],[c_1014]) ).
cnf(c_1112,plain,
( X0 != sK13
| X1 != sK16
| 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_109]) ).
cnf(c_1113,plain,
( ~ apply(sK13,X0,X1)
| ~ apply(sK13,X0,X2)
| ~ member(X0,sK16)
| ~ member(X1,sK15)
| ~ member(X2,sK15)
| X1 = X2 ),
inference(unflattening,[status(thm)],[c_1112]) ).
cnf(c_1133,plain,
( X0 != sK12
| X1 != sK15
| X2 != sK16
| ~ 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_110]) ).
cnf(c_1134,plain,
( ~ apply(sK12,X0,X1)
| ~ apply(sK12,X0,X2)
| ~ member(X0,sK15)
| ~ member(X1,sK16)
| ~ member(X2,sK16)
| X1 = X2 ),
inference(unflattening,[status(thm)],[c_1133]) ).
cnf(c_2620,plain,
( ~ apply(sK13,sK5(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),X0)
| ~ member(sK7(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK15)
| ~ member(sK5(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK16)
| ~ member(X0,sK15)
| sK7(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15) = X0 ),
inference(superposition,[status(thm)],[c_1015,c_1113]) ).
cnf(c_2627,plain,
( ~ apply(sK13,sK5(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),X0)
| ~ member(X0,sK15)
| sK7(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[c_2620,c_990,c_1000]) ).
cnf(c_6141,plain,
( ~ member(sK6(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK15)
| ~ member(sK5(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK16)
| apply(sK12,sK6(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK5(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15)) ),
inference(superposition,[status(thm)],[c_1005,c_89]) ).
cnf(c_6150,plain,
apply(sK12,sK6(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK5(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15)),
inference(forward_subsumption_resolution,[status(thm)],[c_6141,c_990,c_995]) ).
cnf(c_6223,plain,
( ~ member(X0,sK15)
| member(sK4(sK13,sK12,sK16,X0,X0),sK16) ),
inference(superposition,[status(thm)],[c_977,c_81]) ).
cnf(c_7235,plain,
( ~ member(X0,sK15)
| apply(sK13,sK4(sK13,sK12,sK16,X0,X0),X0) ),
inference(superposition,[status(thm)],[c_977,c_79]) ).
cnf(c_7263,plain,
( ~ member(X0,sK15)
| apply(sK12,X0,sK4(sK13,sK12,sK16,X0,X0)) ),
inference(superposition,[status(thm)],[c_977,c_80]) ).
cnf(c_7656,plain,
( ~ member(sK4(sK13,sK12,sK16,X0,X0),sK16)
| ~ apply(sK12,X0,X1)
| ~ member(X0,sK15)
| ~ member(X1,sK16)
| sK4(sK13,sK12,sK16,X0,X0) = X1 ),
inference(superposition,[status(thm)],[c_7263,c_1134]) ).
cnf(c_9353,plain,
( ~ apply(sK12,X0,X1)
| ~ member(X0,sK15)
| ~ member(X1,sK16)
| sK4(sK13,sK12,sK16,X0,X0) = X1 ),
inference(global_subsumption_just,[status(thm)],[c_7656,c_6223,c_7656]) ).
cnf(c_9367,plain,
( ~ member(sK6(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK15)
| ~ member(sK5(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK16)
| sK4(sK13,sK12,sK16,sK6(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK6(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15)) = sK5(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15) ),
inference(superposition,[status(thm)],[c_6150,c_9353]) ).
cnf(c_9384,plain,
sK4(sK13,sK12,sK16,sK6(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK6(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15)) = sK5(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),
inference(forward_subsumption_resolution,[status(thm)],[c_9367,c_990,c_995]) ).
cnf(c_9916,plain,
( ~ member(sK6(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK15)
| apply(sK13,sK5(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK6(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15)) ),
inference(superposition,[status(thm)],[c_9384,c_7235]) ).
cnf(c_9918,plain,
apply(sK13,sK5(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK6(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15)),
inference(forward_subsumption_resolution,[status(thm)],[c_9916,c_995]) ).
cnf(c_9931,plain,
( ~ member(sK6(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15),sK15)
| sK6(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15) = sK7(inverse_function(sK12,sK15,sK16),sK13,sK16,sK15) ),
inference(superposition,[status(thm)],[c_9918,c_2627]) ).
cnf(c_9936,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9931,c_1010,c_995]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SET726+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.13/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 11:51:53 EDT 2023
% 0.13/0.35 % 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 --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.10/1.19 % SZS status Started for theBenchmark.p
% 3.10/1.19 % SZS status Theorem for theBenchmark.p
% 3.10/1.19
% 3.10/1.19 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.10/1.19
% 3.10/1.19 ------ iProver source info
% 3.10/1.19
% 3.10/1.19 git: date: 2023-05-31 18:12:56 +0000
% 3.10/1.19 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.10/1.19 git: non_committed_changes: false
% 3.10/1.19 git: last_make_outside_of_git: false
% 3.10/1.19
% 3.10/1.19 ------ Parsing...
% 3.10/1.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.10/1.19
% 3.10/1.19 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e
% 3.10/1.19
% 3.10/1.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.10/1.19
% 3.10/1.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.10/1.19 ------ Proving...
% 3.10/1.19 ------ Problem Properties
% 3.10/1.19
% 3.10/1.19
% 3.10/1.19 clauses 63
% 3.10/1.19 conjectures 0
% 3.10/1.19 EPR 5
% 3.10/1.19 Horn 58
% 3.10/1.19 unary 10
% 3.10/1.19 binary 33
% 3.10/1.19 lits 155
% 3.10/1.19 lits eq 7
% 3.10/1.19 fd_pure 0
% 3.10/1.19 fd_pseudo 0
% 3.10/1.19 fd_cond 0
% 3.10/1.19 fd_pseudo_cond 5
% 3.10/1.19 AC symbols 0
% 3.10/1.19
% 3.10/1.19 ------ Schedule dynamic 5 is on
% 3.10/1.19
% 3.10/1.19 ------ no conjectures: strip conj schedule
% 3.10/1.19
% 3.10/1.19 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.10/1.19
% 3.10/1.19
% 3.10/1.19 ------
% 3.10/1.19 Current options:
% 3.10/1.19 ------
% 3.10/1.19
% 3.10/1.19
% 3.10/1.19
% 3.10/1.19
% 3.10/1.19 ------ Proving...
% 3.10/1.19
% 3.10/1.19
% 3.10/1.19 % SZS status Theorem for theBenchmark.p
% 3.10/1.19
% 3.10/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.10/1.19
% 3.10/1.20
%------------------------------------------------------------------------------