TSTP Solution File: SET725+4 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET725+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n021.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 83.98s 12.29s
% Output : CNFRefutation 83.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 197 ( 32 unt; 0 def)
% Number of atoms : 719 ( 99 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 850 ( 328 ~; 333 |; 135 &)
% ( 16 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-5 aty)
% Number of variables : 546 ( 3 sgn; 284 !; 45 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f6,axiom,
! [X2] : ~ member(X2,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
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(f16,axiom,
! [X5,X0] :
( identity(X5,X0)
<=> ! [X2] :
( member(X2,X0)
=> apply(X5,X2,X2) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',injective) ).
fof(f18,axiom,
! [X5,X0,X1] :
( surjective(X5,X0,X1)
<=> ! [X4] :
( member(X4,X1)
=> ? [X3] :
( apply(X5,X3,X4)
& member(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjective) ).
fof(f19,axiom,
! [X5,X0,X1] :
( one_to_one(X5,X0,X1)
<=> ( surjective(X5,X0,X1)
& injective(X5,X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one) ).
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) )
=> one_to_one(X5,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII16) ).
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) )
=> one_to_one(X5,X0,X1) ),
inference(negated_conjecture,[],[f29]) ).
fof(f34,plain,
! [X0] : ~ member(X0,empty_set),
inference(rectify,[],[f6]) ).
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(f46,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ),
inference(rectify,[],[f18]) ).
fof(f47,plain,
! [X0,X1,X2] :
( one_to_one(X0,X1,X2)
<=> ( surjective(X0,X1,X2)
& injective(X0,X1,X2) ) ),
inference(rectify,[],[f19]) ).
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) )
=> one_to_one(X0,X3,X4) ),
inference(rectify,[],[f30]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( surjective(X0,X1,X2)
& injective(X0,X1,X2) )
=> one_to_one(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f47]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) )
=> surjective(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f46]) ).
fof(f60,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(f61,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(f62,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] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f65,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,[],[f61]) ).
fof(f66,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,[],[f65]) ).
fof(f67,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(f68,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,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
| ~ identity(X0,X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f70,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,[],[f60]) ).
fof(f71,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,[],[f70]) ).
fof(f72,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) )
& member(X3,X2) ) ),
inference(ennf_transformation,[],[f59]) ).
fof(f73,plain,
! [X0,X1,X2] :
( one_to_one(X0,X1,X2)
| ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2) ),
inference(ennf_transformation,[],[f58]) ).
fof(f74,plain,
! [X0,X1,X2] :
( one_to_one(X0,X1,X2)
| ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2) ),
inference(flattening,[],[f73]) ).
fof(f77,plain,
? [X0,X1,X2,X3,X4] :
( ~ one_to_one(X0,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) ),
inference(ennf_transformation,[],[f57]) ).
fof(f78,plain,
? [X0,X1,X2,X3,X4] :
( ~ one_to_one(X0,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) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f80,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f80,f81]) ).
fof(f101,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(f102,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])],[f66,f101]) ).
fof(f103,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,[],[f68]) ).
fof(f104,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,[],[f103]) ).
fof(f105,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(f106,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])],[f104,f105]) ).
fof(f107,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(f108,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])],[f71,f107]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ? [X3] :
( ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) )
& member(X3,X2) )
=> ( ! [X4] :
( ~ apply(X0,X4,sK8(X0,X1,X2))
| ~ member(X4,X1) )
& member(sK8(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
| ( ! [X4] :
( ~ apply(X0,X4,sK8(X0,X1,X2))
| ~ member(X4,X1) )
& member(sK8(X0,X1,X2),X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f72,f109]) ).
fof(f130,plain,
( ? [X0,X1,X2,X3,X4] :
( ~ one_to_one(X0,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) )
=> ( ~ one_to_one(sK13,sK16,sK17)
& identity(compose_function(sK13,sK15,sK17,sK16,sK17),sK17)
& identity(compose_function(sK14,sK13,sK16,sK17,sK16),sK16)
& maps(sK15,sK17,sK16)
& maps(sK14,sK17,sK16)
& maps(sK13,sK16,sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f131,plain,
( ~ one_to_one(sK13,sK16,sK17)
& identity(compose_function(sK13,sK15,sK17,sK16,sK17),sK17)
& identity(compose_function(sK14,sK13,sK16,sK17,sK16),sK16)
& maps(sK15,sK17,sK16)
& maps(sK14,sK17,sK16)
& maps(sK13,sK16,sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17])],[f78,f130]) ).
fof(f132,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f143,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f34]) ).
fof(f158,plain,
! [X2,X0,X1,X6] :
( member(sK3(X0,X2,X6),X2)
| ~ member(X6,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f160,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,[],[f102]) ).
fof(f161,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,[],[f106]) ).
fof(f162,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,[],[f106]) ).
fof(f163,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,[],[f106]) ).
fof(f165,plain,
! [X2,X0,X1] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ identity(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f166,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| member(sK5(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f167,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| member(sK6(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f168,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| member(sK7(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f108]) ).
fof(f169,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f170,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f171,plain,
! [X2,X0,X1] :
( injective(X0,X1,X2)
| sK5(X0,X1,X2) != sK6(X0,X1,X2) ),
inference(cnf_transformation,[],[f108]) ).
fof(f172,plain,
! [X2,X0,X1] :
( surjective(X0,X1,X2)
| member(sK8(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f110]) ).
fof(f173,plain,
! [X2,X0,X1,X4] :
( surjective(X0,X1,X2)
| ~ apply(X0,X4,sK8(X0,X1,X2))
| ~ member(X4,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f174,plain,
! [X2,X0,X1] :
( one_to_one(X0,X1,X2)
| ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f74]) ).
fof(f191,plain,
maps(sK13,sK16,sK17),
inference(cnf_transformation,[],[f131]) ).
fof(f192,plain,
maps(sK14,sK17,sK16),
inference(cnf_transformation,[],[f131]) ).
fof(f193,plain,
maps(sK15,sK17,sK16),
inference(cnf_transformation,[],[f131]) ).
fof(f194,plain,
identity(compose_function(sK14,sK13,sK16,sK17,sK16),sK16),
inference(cnf_transformation,[],[f131]) ).
fof(f195,plain,
identity(compose_function(sK13,sK15,sK17,sK16,sK17),sK17),
inference(cnf_transformation,[],[f131]) ).
fof(f196,plain,
~ one_to_one(sK13,sK16,sK17),
inference(cnf_transformation,[],[f131]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f132]) ).
cnf(c_60,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[],[f143]) ).
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,[],[f160]) ).
cnf(c_77,plain,
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK3(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f158]) ).
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,[],[f163]) ).
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,[],[f162]) ).
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,[],[f161]) ).
cnf(c_82,plain,
( ~ member(X0,X1)
| ~ identity(X2,X1)
| apply(X2,X0,X0) ),
inference(cnf_transformation,[],[f165]) ).
cnf(c_83,plain,
( sK5(X0,X1,X2) != sK6(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_84,plain,
( apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f170]) ).
cnf(c_85,plain,
( apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f169]) ).
cnf(c_86,plain,
( member(sK7(X0,X1,X2),X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f168]) ).
cnf(c_87,plain,
( member(sK6(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f167]) ).
cnf(c_88,plain,
( member(sK5(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f166]) ).
cnf(c_89,plain,
( ~ apply(X0,X1,sK8(X0,X2,X3))
| ~ member(X1,X2)
| surjective(X0,X2,X3) ),
inference(cnf_transformation,[],[f173]) ).
cnf(c_90,plain,
( member(sK8(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f172]) ).
cnf(c_91,plain,
( ~ injective(X0,X1,X2)
| ~ surjective(X0,X1,X2)
| one_to_one(X0,X1,X2) ),
inference(cnf_transformation,[],[f174]) ).
cnf(c_108,negated_conjecture,
~ one_to_one(sK13,sK16,sK17),
inference(cnf_transformation,[],[f196]) ).
cnf(c_109,negated_conjecture,
identity(compose_function(sK13,sK15,sK17,sK16,sK17),sK17),
inference(cnf_transformation,[],[f195]) ).
cnf(c_110,negated_conjecture,
identity(compose_function(sK14,sK13,sK16,sK17,sK16),sK16),
inference(cnf_transformation,[],[f194]) ).
cnf(c_111,negated_conjecture,
maps(sK15,sK17,sK16),
inference(cnf_transformation,[],[f193]) ).
cnf(c_112,negated_conjecture,
maps(sK14,sK17,sK16),
inference(cnf_transformation,[],[f192]) ).
cnf(c_113,negated_conjecture,
maps(sK13,sK16,sK17),
inference(cnf_transformation,[],[f191]) ).
cnf(c_215,plain,
( sK5(X0,X1,X2) != sK6(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_83]) ).
cnf(c_219,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_220,plain,
( apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_219]) ).
cnf(c_221,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_222,plain,
( apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_221]) ).
cnf(c_223,plain,
( injective(X0,X1,X2)
| member(sK7(X0,X1,X2),X2) ),
inference(prop_impl_just,[status(thm)],[c_86]) ).
cnf(c_224,plain,
( member(sK7(X0,X1,X2),X2)
| injective(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_223]) ).
cnf(c_225,plain,
( injective(X0,X1,X2)
| member(sK6(X0,X1,X2),X1) ),
inference(prop_impl_just,[status(thm)],[c_87]) ).
cnf(c_226,plain,
( member(sK6(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_225]) ).
cnf(c_227,plain,
( injective(X0,X1,X2)
| member(sK5(X0,X1,X2),X1) ),
inference(prop_impl_just,[status(thm)],[c_88]) ).
cnf(c_228,plain,
( member(sK5(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_227]) ).
cnf(c_229,plain,
( surjective(X0,X1,X2)
| member(sK8(X0,X1,X2),X2) ),
inference(prop_impl_just,[status(thm)],[c_90]) ).
cnf(c_230,plain,
( member(sK8(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_229]) ).
cnf(c_1014,plain,
( X0 != sK13
| X1 != sK16
| X2 != sK17
| ~ injective(X0,X1,X2)
| ~ surjective(X0,X1,X2) ),
inference(resolution_lifted,[status(thm)],[c_91,c_108]) ).
cnf(c_1015,plain,
( ~ injective(sK13,sK16,sK17)
| ~ surjective(sK13,sK16,sK17) ),
inference(unflattening,[status(thm)],[c_1014]) ).
cnf(c_1024,plain,
( compose_function(sK13,sK15,sK17,sK16,sK17) != X1
| X0 != sK17
| ~ member(X2,X0)
| apply(X1,X2,X2) ),
inference(resolution_lifted,[status(thm)],[c_82,c_109]) ).
cnf(c_1025,plain,
( ~ member(X0,sK17)
| apply(compose_function(sK13,sK15,sK17,sK16,sK17),X0,X0) ),
inference(unflattening,[status(thm)],[c_1024]) ).
cnf(c_1033,plain,
( compose_function(sK14,sK13,sK16,sK17,sK16) != X1
| X0 != sK16
| ~ member(X2,X0)
| apply(X1,X2,X2) ),
inference(resolution_lifted,[status(thm)],[c_82,c_110]) ).
cnf(c_1034,plain,
( ~ member(X0,sK16)
| apply(compose_function(sK14,sK13,sK16,sK17,sK16),X0,X0) ),
inference(unflattening,[status(thm)],[c_1033]) ).
cnf(c_1046,plain,
( X0 != sK13
| X1 != sK16
| X2 != sK17
| ~ apply(X0,X3,sK8(X0,X1,X2))
| ~ injective(sK13,sK16,sK17)
| ~ member(X3,X1) ),
inference(resolution_lifted,[status(thm)],[c_89,c_1015]) ).
cnf(c_1047,plain,
( ~ apply(sK13,X0,sK8(sK13,sK16,sK17))
| ~ injective(sK13,sK16,sK17)
| ~ member(X0,sK16) ),
inference(unflattening,[status(thm)],[c_1046]) ).
cnf(c_1058,plain,
( X0 != sK13
| X1 != sK16
| X2 != sK17
| ~ injective(sK13,sK16,sK17)
| member(sK8(X0,X1,X2),X2) ),
inference(resolution_lifted,[status(thm)],[c_230,c_1015]) ).
cnf(c_1059,plain,
( ~ injective(sK13,sK16,sK17)
| member(sK8(sK13,sK16,sK17),sK17) ),
inference(unflattening,[status(thm)],[c_1058]) ).
cnf(c_1158,plain,
( X0 != sK14
| X1 != sK17
| 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_112]) ).
cnf(c_1159,plain,
( ~ apply(sK14,X0,X1)
| ~ apply(sK14,X0,X2)
| ~ member(X0,sK17)
| ~ member(X1,sK16)
| ~ member(X2,sK16)
| X1 = X2 ),
inference(unflattening,[status(thm)],[c_1158]) ).
cnf(c_1179,plain,
( X0 != sK13
| X1 != sK16
| X2 != sK17
| ~ 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_113]) ).
cnf(c_1180,plain,
( ~ apply(sK13,X0,X1)
| ~ apply(sK13,X0,X2)
| ~ member(X0,sK16)
| ~ member(X1,sK17)
| ~ member(X2,sK17)
| X1 = X2 ),
inference(unflattening,[status(thm)],[c_1179]) ).
cnf(c_1200,plain,
( X0 != sK15
| X1 != sK17
| X2 != sK16
| ~ member(X3,X1)
| member(sK3(X0,X2,X3),X2) ),
inference(resolution_lifted,[status(thm)],[c_77,c_111]) ).
cnf(c_1201,plain,
( ~ member(X0,sK17)
| member(sK3(sK15,sK16,X0),sK16) ),
inference(unflattening,[status(thm)],[c_1200]) ).
cnf(c_1236,plain,
( X0 != sK13
| X1 != sK16
| X2 != sK17
| ~ member(X3,X1)
| member(sK3(X0,X2,X3),X2) ),
inference(resolution_lifted,[status(thm)],[c_77,c_113]) ).
cnf(c_1237,plain,
( ~ member(X0,sK16)
| member(sK3(sK13,sK17,X0),sK17) ),
inference(unflattening,[status(thm)],[c_1236]) ).
cnf(c_1284,plain,
( X0 != sK13
| X1 != sK16
| X2 != sK17
| member(sK5(X0,X1,X2),X1)
| member(sK8(sK13,sK16,sK17),sK17) ),
inference(resolution_lifted,[status(thm)],[c_228,c_1059]) ).
cnf(c_1285,plain,
( member(sK5(sK13,sK16,sK17),sK16)
| member(sK8(sK13,sK16,sK17),sK17) ),
inference(unflattening,[status(thm)],[c_1284]) ).
cnf(c_1292,plain,
( X0 != sK13
| X1 != sK16
| X2 != sK17
| ~ apply(sK13,X3,sK8(sK13,sK16,sK17))
| ~ member(X3,sK16)
| member(sK5(X0,X1,X2),X1) ),
inference(resolution_lifted,[status(thm)],[c_228,c_1047]) ).
cnf(c_1293,plain,
( ~ apply(sK13,X0,sK8(sK13,sK16,sK17))
| ~ member(X0,sK16)
| member(sK5(sK13,sK16,sK17),sK16) ),
inference(unflattening,[status(thm)],[c_1292]) ).
cnf(c_1304,plain,
( X0 != sK13
| X1 != sK16
| X2 != sK17
| member(sK6(X0,X1,X2),X1)
| member(sK8(sK13,sK16,sK17),sK17) ),
inference(resolution_lifted,[status(thm)],[c_226,c_1059]) ).
cnf(c_1305,plain,
( member(sK6(sK13,sK16,sK17),sK16)
| member(sK8(sK13,sK16,sK17),sK17) ),
inference(unflattening,[status(thm)],[c_1304]) ).
cnf(c_1312,plain,
( X0 != sK13
| X1 != sK16
| X2 != sK17
| ~ apply(sK13,X3,sK8(sK13,sK16,sK17))
| ~ member(X3,sK16)
| member(sK6(X0,X1,X2),X1) ),
inference(resolution_lifted,[status(thm)],[c_226,c_1047]) ).
cnf(c_1313,plain,
( ~ apply(sK13,X0,sK8(sK13,sK16,sK17))
| ~ member(X0,sK16)
| member(sK6(sK13,sK16,sK17),sK16) ),
inference(unflattening,[status(thm)],[c_1312]) ).
cnf(c_1324,plain,
( X0 != sK13
| X1 != sK16
| X2 != sK17
| member(sK7(X0,X1,X2),X2)
| member(sK8(sK13,sK16,sK17),sK17) ),
inference(resolution_lifted,[status(thm)],[c_224,c_1059]) ).
cnf(c_1325,plain,
( member(sK7(sK13,sK16,sK17),sK17)
| member(sK8(sK13,sK16,sK17),sK17) ),
inference(unflattening,[status(thm)],[c_1324]) ).
cnf(c_1332,plain,
( X0 != sK13
| X1 != sK16
| X2 != sK17
| ~ apply(sK13,X3,sK8(sK13,sK16,sK17))
| ~ member(X3,sK16)
| member(sK7(X0,X1,X2),X2) ),
inference(resolution_lifted,[status(thm)],[c_224,c_1047]) ).
cnf(c_1333,plain,
( ~ apply(sK13,X0,sK8(sK13,sK16,sK17))
| ~ member(X0,sK16)
| member(sK7(sK13,sK16,sK17),sK17) ),
inference(unflattening,[status(thm)],[c_1332]) ).
cnf(c_1344,plain,
( X0 != sK13
| X1 != sK16
| X2 != sK17
| apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2))
| member(sK8(sK13,sK16,sK17),sK17) ),
inference(resolution_lifted,[status(thm)],[c_222,c_1059]) ).
cnf(c_1345,plain,
( apply(sK13,sK5(sK13,sK16,sK17),sK7(sK13,sK16,sK17))
| member(sK8(sK13,sK16,sK17),sK17) ),
inference(unflattening,[status(thm)],[c_1344]) ).
cnf(c_1352,plain,
( X0 != sK13
| X1 != sK16
| X2 != sK17
| ~ apply(sK13,X3,sK8(sK13,sK16,sK17))
| ~ member(X3,sK16)
| apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2)) ),
inference(resolution_lifted,[status(thm)],[c_222,c_1047]) ).
cnf(c_1353,plain,
( ~ apply(sK13,X0,sK8(sK13,sK16,sK17))
| ~ member(X0,sK16)
| apply(sK13,sK5(sK13,sK16,sK17),sK7(sK13,sK16,sK17)) ),
inference(unflattening,[status(thm)],[c_1352]) ).
cnf(c_1364,plain,
( X0 != sK13
| X1 != sK16
| X2 != sK17
| apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
| member(sK8(sK13,sK16,sK17),sK17) ),
inference(resolution_lifted,[status(thm)],[c_220,c_1059]) ).
cnf(c_1365,plain,
( apply(sK13,sK6(sK13,sK16,sK17),sK7(sK13,sK16,sK17))
| member(sK8(sK13,sK16,sK17),sK17) ),
inference(unflattening,[status(thm)],[c_1364]) ).
cnf(c_1372,plain,
( X0 != sK13
| X1 != sK16
| X2 != sK17
| ~ apply(sK13,X3,sK8(sK13,sK16,sK17))
| ~ member(X3,sK16)
| apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2)) ),
inference(resolution_lifted,[status(thm)],[c_220,c_1047]) ).
cnf(c_1373,plain,
( ~ apply(sK13,X0,sK8(sK13,sK16,sK17))
| ~ member(X0,sK16)
| apply(sK13,sK6(sK13,sK16,sK17),sK7(sK13,sK16,sK17)) ),
inference(unflattening,[status(thm)],[c_1372]) ).
cnf(c_1384,plain,
( sK5(X0,X1,X2) != sK6(X0,X1,X2)
| X0 != sK13
| X1 != sK16
| X2 != sK17
| member(sK8(sK13,sK16,sK17),sK17) ),
inference(resolution_lifted,[status(thm)],[c_215,c_1059]) ).
cnf(c_1385,plain,
( sK5(sK13,sK16,sK17) != sK6(sK13,sK16,sK17)
| member(sK8(sK13,sK16,sK17),sK17) ),
inference(unflattening,[status(thm)],[c_1384]) ).
cnf(c_1392,plain,
( sK5(X0,X1,X2) != sK6(X0,X1,X2)
| X0 != sK13
| X1 != sK16
| X2 != sK17
| ~ apply(sK13,X3,sK8(sK13,sK16,sK17))
| ~ member(X3,sK16) ),
inference(resolution_lifted,[status(thm)],[c_215,c_1047]) ).
cnf(c_1393,plain,
( sK5(sK13,sK16,sK17) != sK6(sK13,sK16,sK17)
| ~ apply(sK13,X0,sK8(sK13,sK16,sK17))
| ~ member(X0,sK16) ),
inference(unflattening,[status(thm)],[c_1392]) ).
cnf(c_3593,plain,
( ~ member(sK8(sK13,sK16,sK17),sK17)
| apply(compose_function(sK13,sK15,sK17,sK16,sK17),sK8(sK13,sK16,sK17),sK8(sK13,sK16,sK17)) ),
inference(instantiation,[status(thm)],[c_1025]) ).
cnf(c_6023,plain,
( ~ apply(sK14,X0,sK5(sK13,sK16,sK17))
| ~ apply(sK14,X0,sK6(sK13,sK16,sK17))
| ~ member(sK5(sK13,sK16,sK17),sK16)
| ~ member(sK6(sK13,sK16,sK17),sK16)
| ~ member(X0,sK17)
| sK5(sK13,sK16,sK17) = sK6(sK13,sK16,sK17) ),
inference(instantiation,[status(thm)],[c_1159]) ).
cnf(c_6368,plain,
( ~ apply(compose_function(sK13,sK15,sK17,sK16,sK17),sK8(sK13,sK16,sK17),sK8(sK13,sK16,sK17))
| ~ member(sK8(sK13,sK16,sK17),sK17)
| apply(sK13,sK4(sK13,sK15,sK16,sK8(sK13,sK16,sK17),sK8(sK13,sK16,sK17)),sK8(sK13,sK16,sK17)) ),
inference(instantiation,[status(thm)],[c_79]) ).
cnf(c_6369,plain,
( ~ apply(compose_function(sK13,sK15,sK17,sK16,sK17),sK8(sK13,sK16,sK17),sK8(sK13,sK16,sK17))
| ~ member(sK8(sK13,sK16,sK17),sK17)
| member(sK4(sK13,sK15,sK16,sK8(sK13,sK16,sK17),sK8(sK13,sK16,sK17)),sK16) ),
inference(instantiation,[status(thm)],[c_81]) ).
cnf(c_7185,plain,
( ~ subset(sK17,X0)
| ~ member(X1,sK16)
| member(sK3(sK13,sK17,X1),X0) ),
inference(superposition,[status(thm)],[c_1237,c_51]) ).
cnf(c_8050,plain,
( ~ member(X0,sK16)
| member(sK4(sK14,sK13,sK17,X0,X0),sK17) ),
inference(superposition,[status(thm)],[c_1034,c_81]) ).
cnf(c_8117,plain,
( ~ member(X0,sK17)
| apply(sK13,sK4(sK13,sK15,sK16,X0,X0),X0) ),
inference(superposition,[status(thm)],[c_1025,c_79]) ).
cnf(c_8225,plain,
( ~ member(X0,sK16)
| apply(sK13,X0,sK4(sK14,sK13,sK17,X0,X0)) ),
inference(superposition,[status(thm)],[c_1034,c_80]) ).
cnf(c_8428,plain,
( ~ member(sK4(sK13,sK15,sK16,sK8(sK13,sK16,sK17),sK8(sK13,sK16,sK17)),sK16)
| ~ member(sK8(sK13,sK16,sK17),sK17)
| member(sK7(sK13,sK16,sK17),sK17) ),
inference(superposition,[status(thm)],[c_8117,c_1333]) ).
cnf(c_8429,plain,
( ~ member(sK4(sK13,sK15,sK16,sK8(sK13,sK16,sK17),sK8(sK13,sK16,sK17)),sK16)
| ~ member(sK8(sK13,sK16,sK17),sK17)
| member(sK6(sK13,sK16,sK17),sK16) ),
inference(superposition,[status(thm)],[c_8117,c_1313]) ).
cnf(c_8430,plain,
( ~ member(sK4(sK13,sK15,sK16,sK8(sK13,sK16,sK17),sK8(sK13,sK16,sK17)),sK16)
| ~ member(sK8(sK13,sK16,sK17),sK17)
| member(sK5(sK13,sK16,sK17),sK16) ),
inference(superposition,[status(thm)],[c_8117,c_1293]) ).
cnf(c_8638,plain,
( ~ member(sK4(sK14,sK13,sK17,X0,X0),sK17)
| ~ apply(sK13,X0,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK17)
| sK4(sK14,sK13,sK17,X0,X0) = X1 ),
inference(superposition,[status(thm)],[c_8225,c_1180]) ).
cnf(c_8701,plain,
( ~ member(X0,sK16)
| ~ subset(sK17,empty_set) ),
inference(superposition,[status(thm)],[c_7185,c_60]) ).
cnf(c_9440,plain,
( ~ apply(sK14,sK7(sK13,sK16,sK17),sK5(sK13,sK16,sK17))
| ~ apply(sK14,sK7(sK13,sK16,sK17),sK6(sK13,sK16,sK17))
| ~ member(sK5(sK13,sK16,sK17),sK16)
| ~ member(sK6(sK13,sK16,sK17),sK16)
| ~ member(sK7(sK13,sK16,sK17),sK17)
| sK5(sK13,sK16,sK17) = sK6(sK13,sK16,sK17) ),
inference(instantiation,[status(thm)],[c_6023]) ).
cnf(c_9450,plain,
( ~ member(X0,sK17)
| ~ subset(sK17,empty_set) ),
inference(superposition,[status(thm)],[c_1201,c_8701]) ).
cnf(c_9682,plain,
( ~ subset(sK17,empty_set)
| member(sK7(sK13,sK16,sK17),sK17) ),
inference(superposition,[status(thm)],[c_1325,c_9450]) ).
cnf(c_13905,plain,
member(sK7(sK13,sK16,sK17),sK17),
inference(global_subsumption_just,[status(thm)],[c_9682,c_1325,c_3593,c_6369,c_8428]) ).
cnf(c_29184,plain,
member(sK5(sK13,sK16,sK17),sK16),
inference(global_subsumption_just,[status(thm)],[c_1293,c_1285,c_3593,c_6369,c_8430]) ).
cnf(c_29273,plain,
member(sK6(sK13,sK16,sK17),sK16),
inference(global_subsumption_just,[status(thm)],[c_1305,c_1305,c_3593,c_6369,c_8429]) ).
cnf(c_36237,plain,
( ~ member(X0,sK17)
| apply(sK13,sK4(sK13,sK15,sK16,X0,X0),X0) ),
inference(superposition,[status(thm)],[c_1025,c_79]) ).
cnf(c_38194,plain,
( ~ member(sK4(sK13,sK15,sK16,sK8(sK13,sK16,sK17),sK8(sK13,sK16,sK17)),sK16)
| ~ member(sK8(sK13,sK16,sK17),sK17)
| apply(sK13,sK6(sK13,sK16,sK17),sK7(sK13,sK16,sK17)) ),
inference(superposition,[status(thm)],[c_36237,c_1373]) ).
cnf(c_38195,plain,
( ~ member(sK4(sK13,sK15,sK16,sK8(sK13,sK16,sK17),sK8(sK13,sK16,sK17)),sK16)
| ~ member(sK8(sK13,sK16,sK17),sK17)
| apply(sK13,sK5(sK13,sK16,sK17),sK7(sK13,sK16,sK17)) ),
inference(superposition,[status(thm)],[c_36237,c_1353]) ).
cnf(c_219391,plain,
apply(sK13,sK5(sK13,sK16,sK17),sK7(sK13,sK16,sK17)),
inference(global_subsumption_just,[status(thm)],[c_1345,c_1345,c_3593,c_6369,c_38195]) ).
cnf(c_219401,plain,
apply(sK13,sK6(sK13,sK16,sK17),sK7(sK13,sK16,sK17)),
inference(global_subsumption_just,[status(thm)],[c_1365,c_1365,c_3593,c_6369,c_38194]) ).
cnf(c_219976,plain,
member(sK5(sK13,sK16,sK17),sK16),
inference(global_subsumption_just,[status(thm)],[c_1285,c_29184]) ).
cnf(c_219998,plain,
member(sK6(sK13,sK16,sK17),sK16),
inference(global_subsumption_just,[status(thm)],[c_1305,c_29273]) ).
cnf(c_220756,plain,
member(sK7(sK13,sK16,sK17),sK17),
inference(global_subsumption_just,[status(thm)],[c_1325,c_13905]) ).
cnf(c_220823,plain,
apply(sK13,sK5(sK13,sK16,sK17),sK7(sK13,sK16,sK17)),
inference(global_subsumption_just,[status(thm)],[c_1345,c_219391]) ).
cnf(c_220896,plain,
apply(sK13,sK6(sK13,sK16,sK17),sK7(sK13,sK16,sK17)),
inference(global_subsumption_just,[status(thm)],[c_1365,c_219401]) ).
cnf(c_222986,plain,
( sK5(sK13,sK16,sK17) != sK6(sK13,sK16,sK17)
| ~ apply(sK13,sK4(sK13,sK15,sK16,sK8(sK13,sK16,sK17),sK8(sK13,sK16,sK17)),sK8(sK13,sK16,sK17))
| ~ member(sK4(sK13,sK15,sK16,sK8(sK13,sK16,sK17),sK8(sK13,sK16,sK17)),sK16) ),
inference(instantiation,[status(thm)],[c_1393]) ).
cnf(c_228654,plain,
sK5(sK13,sK16,sK17) != sK6(sK13,sK16,sK17),
inference(global_subsumption_just,[status(thm)],[c_1385,c_1385,c_3593,c_6369,c_6368,c_222986]) ).
cnf(c_239690,plain,
( ~ member(X0,sK16)
| apply(sK14,sK4(sK14,sK13,sK17,X0,X0),X0) ),
inference(superposition,[status(thm)],[c_1034,c_79]) ).
cnf(c_241727,plain,
( ~ member(X0,sK16)
| apply(sK13,X0,sK4(sK14,sK13,sK17,X0,X0)) ),
inference(superposition,[status(thm)],[c_1034,c_80]) ).
cnf(c_243335,plain,
( ~ member(sK4(sK14,sK13,sK17,X0,X0),sK17)
| ~ apply(sK13,X0,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK17)
| sK4(sK14,sK13,sK17,X0,X0) = X1 ),
inference(superposition,[status(thm)],[c_241727,c_1180]) ).
cnf(c_249154,plain,
( ~ apply(sK13,X0,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK17)
| sK4(sK14,sK13,sK17,X0,X0) = X1 ),
inference(global_subsumption_just,[status(thm)],[c_243335,c_8050,c_8638]) ).
cnf(c_249167,plain,
( ~ member(sK5(sK13,sK16,sK17),sK16)
| ~ member(sK7(sK13,sK16,sK17),sK17)
| sK4(sK14,sK13,sK17,sK5(sK13,sK16,sK17),sK5(sK13,sK16,sK17)) = sK7(sK13,sK16,sK17) ),
inference(superposition,[status(thm)],[c_220823,c_249154]) ).
cnf(c_249168,plain,
( ~ member(sK6(sK13,sK16,sK17),sK16)
| ~ member(sK7(sK13,sK16,sK17),sK17)
| sK4(sK14,sK13,sK17,sK6(sK13,sK16,sK17),sK6(sK13,sK16,sK17)) = sK7(sK13,sK16,sK17) ),
inference(superposition,[status(thm)],[c_220896,c_249154]) ).
cnf(c_249181,plain,
sK4(sK14,sK13,sK17,sK6(sK13,sK16,sK17),sK6(sK13,sK16,sK17)) = sK7(sK13,sK16,sK17),
inference(forward_subsumption_resolution,[status(thm)],[c_249168,c_220756,c_219998]) ).
cnf(c_249182,plain,
sK4(sK14,sK13,sK17,sK5(sK13,sK16,sK17),sK5(sK13,sK16,sK17)) = sK7(sK13,sK16,sK17),
inference(forward_subsumption_resolution,[status(thm)],[c_249167,c_220756,c_219976]) ).
cnf(c_250210,plain,
( ~ member(sK6(sK13,sK16,sK17),sK16)
| apply(sK14,sK7(sK13,sK16,sK17),sK6(sK13,sK16,sK17)) ),
inference(superposition,[status(thm)],[c_249181,c_239690]) ).
cnf(c_250212,plain,
apply(sK14,sK7(sK13,sK16,sK17),sK6(sK13,sK16,sK17)),
inference(forward_subsumption_resolution,[status(thm)],[c_250210,c_219998]) ).
cnf(c_252632,plain,
( ~ member(sK5(sK13,sK16,sK17),sK16)
| apply(sK14,sK7(sK13,sK16,sK17),sK5(sK13,sK16,sK17)) ),
inference(superposition,[status(thm)],[c_249182,c_239690]) ).
cnf(c_252634,plain,
apply(sK14,sK7(sK13,sK16,sK17),sK5(sK13,sK16,sK17)),
inference(forward_subsumption_resolution,[status(thm)],[c_252632,c_219976]) ).
cnf(c_252639,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_252634,c_250212,c_228654,c_29273,c_29184,c_13905,c_9440]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET725+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n021.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 12:12:27 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 83.98/12.29 % SZS status Started for theBenchmark.p
% 83.98/12.29 % SZS status Theorem for theBenchmark.p
% 83.98/12.29
% 83.98/12.29 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 83.98/12.29
% 83.98/12.29 ------ iProver source info
% 83.98/12.29
% 83.98/12.29 git: date: 2023-05-31 18:12:56 +0000
% 83.98/12.29 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 83.98/12.29 git: non_committed_changes: false
% 83.98/12.29 git: last_make_outside_of_git: false
% 83.98/12.29
% 83.98/12.29 ------ Parsing...
% 83.98/12.29 ------ Clausification by vclausify_rel & Parsing by iProver...
% 83.98/12.29
% 83.98/12.29 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e
% 83.98/12.29
% 83.98/12.29 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 83.98/12.29
% 83.98/12.29 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 83.98/12.29 ------ Proving...
% 83.98/12.29 ------ Problem Properties
% 83.98/12.29
% 83.98/12.29
% 83.98/12.29 clauses 69
% 83.98/12.29 conjectures 0
% 83.98/12.29 EPR 5
% 83.98/12.29 Horn 59
% 83.98/12.29 unary 4
% 83.98/12.29 binary 39
% 83.98/12.29 lits 179
% 83.98/12.29 lits eq 8
% 83.98/12.29 fd_pure 0
% 83.98/12.29 fd_pseudo 0
% 83.98/12.29 fd_cond 0
% 83.98/12.29 fd_pseudo_cond 5
% 83.98/12.29 AC symbols 0
% 83.98/12.29
% 83.98/12.29 ------ Schedule dynamic 5 is on
% 83.98/12.29
% 83.98/12.29 ------ no conjectures: strip conj schedule
% 83.98/12.29
% 83.98/12.29 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 83.98/12.29
% 83.98/12.29
% 83.98/12.29 ------
% 83.98/12.29 Current options:
% 83.98/12.29 ------
% 83.98/12.29
% 83.98/12.29
% 83.98/12.29
% 83.98/12.29
% 83.98/12.29 ------ Proving...
% 83.98/12.29 Proof_search_loop: time out after: 8609 full_loop iterations
% 83.98/12.29
% 83.98/12.29 ------ Input Options"--res_lit_sel adaptive --res_lit_sel_side num_symb" stripped conjectures Time Limit: 15.
% 83.98/12.29
% 83.98/12.29
% 83.98/12.29 ------
% 83.98/12.29 Current options:
% 83.98/12.29 ------
% 83.98/12.29
% 83.98/12.29
% 83.98/12.29
% 83.98/12.29
% 83.98/12.29 ------ Proving...
% 83.98/12.29
% 83.98/12.29
% 83.98/12.29 % SZS status Theorem for theBenchmark.p
% 83.98/12.29
% 83.98/12.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 83.98/12.29
% 83.98/12.30
%------------------------------------------------------------------------------