TSTP Solution File: SET708+4 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET708+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n014.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 15:09:14 EDT 2023
% Result : Theorem 3.42s 1.18s
% Output : CNFRefutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 133 ( 24 unt; 0 def)
% Number of atoms : 592 ( 126 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 762 ( 303 ~; 308 |; 112 &)
% ( 11 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-6 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-5 aty)
% Number of variables : 525 ( 0 sgn; 237 !; 44 ?)
% 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(f13,axiom,
! [X8,X9,X5,X0,X1,X10] :
( compose_predicate(X8,X9,X5,X0,X1,X10)
<=> ! [X2,X11] :
( ( member(X11,X10)
& member(X2,X0) )
=> ( apply(X8,X2,X11)
<=> ? [X4] :
( apply(X9,X4,X11)
& apply(X5,X2,X4)
& member(X4,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_predicate) ).
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(f29,conjecture,
! [X5,X9,X16,X17,X0,X1,X10] :
( ( compose_predicate(X17,X9,X5,X0,X1,X10)
& compose_predicate(X16,X9,X5,X0,X1,X10)
& maps(X9,X1,X10)
& maps(X5,X0,X1) )
=> equal_maps(X16,X17,X0,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII01a) ).
fof(f30,negated_conjecture,
~ ! [X5,X9,X16,X17,X0,X1,X10] :
( ( compose_predicate(X17,X9,X5,X0,X1,X10)
& compose_predicate(X16,X9,X5,X0,X1,X10)
& maps(X9,X1,X10)
& maps(X5,X0,X1) )
=> equal_maps(X16,X17,X0,X10) ),
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(f41,plain,
! [X0,X1,X2,X3,X4,X5] :
( compose_predicate(X0,X1,X2,X3,X4,X5)
<=> ! [X6,X7] :
( ( member(X7,X5)
& member(X6,X3) )
=> ( apply(X0,X6,X7)
<=> ? [X8] :
( apply(X1,X8,X7)
& apply(X2,X6,X8)
& member(X8,X4) ) ) ) ),
inference(rectify,[],[f13]) ).
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(f57,plain,
~ ! [X0,X1,X2,X3,X4,X5,X6] :
( ( compose_predicate(X3,X1,X0,X4,X5,X6)
& compose_predicate(X2,X1,X0,X4,X5,X6)
& maps(X1,X5,X6)
& maps(X0,X4,X5) )
=> equal_maps(X2,X3,X4,X6) ),
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,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(f60,plain,
! [X0,X1,X2,X3,X4,X5] :
( compose_predicate(X0,X1,X2,X3,X4,X5)
=> ! [X6,X7] :
( ( member(X7,X5)
& member(X6,X3) )
=> ( apply(X0,X6,X7)
<=> ? [X8] :
( apply(X1,X8,X7)
& apply(X2,X6,X8)
& member(X8,X4) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f41]) ).
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,X7] :
( ( apply(X0,X6,X7)
<=> ? [X8] :
( apply(X1,X8,X7)
& apply(X2,X6,X8)
& member(X8,X4) ) )
| ~ member(X7,X5)
| ~ member(X6,X3) )
| ~ compose_predicate(X0,X1,X2,X3,X4,X5) ),
inference(ennf_transformation,[],[f60]) ).
fof(f66,plain,
! [X0,X1,X2,X3,X4,X5] :
( ! [X6,X7] :
( ( apply(X0,X6,X7)
<=> ? [X8] :
( apply(X1,X8,X7)
& apply(X2,X6,X8)
& member(X8,X4) ) )
| ~ member(X7,X5)
| ~ member(X6,X3) )
| ~ compose_predicate(X0,X1,X2,X3,X4,X5) ),
inference(flattening,[],[f65]) ).
fof(f69,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,[],[f59]) ).
fof(f70,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,[],[f69]) ).
fof(f73,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( ~ equal_maps(X2,X3,X4,X6)
& compose_predicate(X3,X1,X0,X4,X5,X6)
& compose_predicate(X2,X1,X0,X4,X5,X6)
& maps(X1,X5,X6)
& maps(X0,X4,X5) ),
inference(ennf_transformation,[],[f57]) ).
fof(f74,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( ~ equal_maps(X2,X3,X4,X6)
& compose_predicate(X3,X1,X0,X4,X5,X6)
& compose_predicate(X2,X1,X0,X4,X5,X6)
& maps(X1,X5,X6)
& maps(X0,X4,X5) ),
inference(flattening,[],[f73]) ).
fof(f97,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(f98,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,f97]) ).
fof(f99,plain,
! [X0,X1,X2,X3,X4,X5] :
( ! [X6,X7] :
( ( ( apply(X0,X6,X7)
| ! [X8] :
( ~ apply(X1,X8,X7)
| ~ apply(X2,X6,X8)
| ~ member(X8,X4) ) )
& ( ? [X8] :
( apply(X1,X8,X7)
& apply(X2,X6,X8)
& member(X8,X4) )
| ~ apply(X0,X6,X7) ) )
| ~ member(X7,X5)
| ~ member(X6,X3) )
| ~ compose_predicate(X0,X1,X2,X3,X4,X5) ),
inference(nnf_transformation,[],[f66]) ).
fof(f100,plain,
! [X0,X1,X2,X3,X4,X5] :
( ! [X6,X7] :
( ( ( apply(X0,X6,X7)
| ! [X8] :
( ~ apply(X1,X8,X7)
| ~ apply(X2,X6,X8)
| ~ member(X8,X4) ) )
& ( ? [X9] :
( apply(X1,X9,X7)
& apply(X2,X6,X9)
& member(X9,X4) )
| ~ apply(X0,X6,X7) ) )
| ~ member(X7,X5)
| ~ member(X6,X3) )
| ~ compose_predicate(X0,X1,X2,X3,X4,X5) ),
inference(rectify,[],[f99]) ).
fof(f101,plain,
! [X1,X2,X4,X6,X7] :
( ? [X9] :
( apply(X1,X9,X7)
& apply(X2,X6,X9)
& member(X9,X4) )
=> ( apply(X1,sK4(X1,X2,X4,X6,X7),X7)
& apply(X2,X6,sK4(X1,X2,X4,X6,X7))
& member(sK4(X1,X2,X4,X6,X7),X4) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X1,X2,X3,X4,X5] :
( ! [X6,X7] :
( ( ( apply(X0,X6,X7)
| ! [X8] :
( ~ apply(X1,X8,X7)
| ~ apply(X2,X6,X8)
| ~ member(X8,X4) ) )
& ( ( apply(X1,sK4(X1,X2,X4,X6,X7),X7)
& apply(X2,X6,sK4(X1,X2,X4,X6,X7))
& member(sK4(X1,X2,X4,X6,X7),X4) )
| ~ apply(X0,X6,X7) ) )
| ~ member(X7,X5)
| ~ member(X6,X3) )
| ~ compose_predicate(X0,X1,X2,X3,X4,X5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f100,f101]) ).
fof(f107,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) )
=> ( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3)
& apply(X1,sK6(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
& apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
& member(sK8(X0,X1,X2,X3),X3)
& member(sK7(X0,X1,X2,X3),X3)
& member(sK6(X0,X1,X2,X3),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f108,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| ( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3)
& apply(X1,sK6(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
& apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
& member(sK8(X0,X1,X2,X3),X3)
& member(sK7(X0,X1,X2,X3),X3)
& member(sK6(X0,X1,X2,X3),X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f70,f107]) ).
fof(f128,plain,
( ? [X0,X1,X2,X3,X4,X5,X6] :
( ~ equal_maps(X2,X3,X4,X6)
& compose_predicate(X3,X1,X0,X4,X5,X6)
& compose_predicate(X2,X1,X0,X4,X5,X6)
& maps(X1,X5,X6)
& maps(X0,X4,X5) )
=> ( ~ equal_maps(sK15,sK16,sK17,sK19)
& compose_predicate(sK16,sK14,sK13,sK17,sK18,sK19)
& compose_predicate(sK15,sK14,sK13,sK17,sK18,sK19)
& maps(sK14,sK18,sK19)
& maps(sK13,sK17,sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f129,plain,
( ~ equal_maps(sK15,sK16,sK17,sK19)
& compose_predicate(sK16,sK14,sK13,sK17,sK18,sK19)
& compose_predicate(sK15,sK14,sK13,sK17,sK18,sK19)
& maps(sK14,sK18,sK19)
& maps(sK13,sK17,sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17,sK18,sK19])],[f74,f128]) ).
fof(f156,plain,
! [X2,X0,X1,X6] :
( member(sK3(X0,X2,X6),X2)
| ~ member(X6,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f157,plain,
! [X2,X0,X1,X6] :
( apply(X0,X6,sK3(X0,X2,X6))
| ~ member(X6,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f158,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,[],[f98]) ).
fof(f159,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( member(sK4(X1,X2,X4,X6,X7),X4)
| ~ apply(X0,X6,X7)
| ~ member(X7,X5)
| ~ member(X6,X3)
| ~ compose_predicate(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f102]) ).
fof(f160,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( apply(X2,X6,sK4(X1,X2,X4,X6,X7))
| ~ apply(X0,X6,X7)
| ~ member(X7,X5)
| ~ member(X6,X3)
| ~ compose_predicate(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f102]) ).
fof(f161,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( apply(X1,sK4(X1,X2,X4,X6,X7),X7)
| ~ apply(X0,X6,X7)
| ~ member(X7,X5)
| ~ member(X6,X3)
| ~ compose_predicate(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f102]) ).
fof(f167,plain,
! [X2,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| member(sK6(X0,X1,X2,X3),X2) ),
inference(cnf_transformation,[],[f108]) ).
fof(f168,plain,
! [X2,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| member(sK7(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f108]) ).
fof(f169,plain,
! [X2,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| member(sK8(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f108]) ).
fof(f170,plain,
! [X2,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f171,plain,
! [X2,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| apply(X1,sK6(X0,X1,X2,X3),sK8(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f172,plain,
! [X2,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f108]) ).
fof(f189,plain,
maps(sK13,sK17,sK18),
inference(cnf_transformation,[],[f129]) ).
fof(f190,plain,
maps(sK14,sK18,sK19),
inference(cnf_transformation,[],[f129]) ).
fof(f191,plain,
compose_predicate(sK15,sK14,sK13,sK17,sK18,sK19),
inference(cnf_transformation,[],[f129]) ).
fof(f192,plain,
compose_predicate(sK16,sK14,sK13,sK17,sK18,sK19),
inference(cnf_transformation,[],[f129]) ).
fof(f193,plain,
~ equal_maps(sK15,sK16,sK17,sK19),
inference(cnf_transformation,[],[f129]) ).
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,[],[f158]) ).
cnf(c_76,plain,
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK3(X0,X2,X3)) ),
inference(cnf_transformation,[],[f157]) ).
cnf(c_77,plain,
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK3(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f156]) ).
cnf(c_79,plain,
( ~ compose_predicate(X0,X1,X2,X3,X4,X5)
| ~ apply(X0,X6,X7)
| ~ member(X6,X3)
| ~ member(X7,X5)
| apply(X1,sK4(X1,X2,X4,X6,X7),X7) ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_80,plain,
( ~ compose_predicate(X0,X1,X2,X3,X4,X5)
| ~ apply(X0,X6,X7)
| ~ member(X6,X3)
| ~ member(X7,X5)
| apply(X2,X6,sK4(X1,X2,X4,X6,X7)) ),
inference(cnf_transformation,[],[f160]) ).
cnf(c_81,plain,
( ~ compose_predicate(X0,X1,X2,X3,X4,X5)
| ~ apply(X0,X6,X7)
| ~ member(X6,X3)
| ~ member(X7,X5)
| member(sK4(X1,X2,X4,X6,X7),X4) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_86,plain,
( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f172]) ).
cnf(c_87,plain,
( apply(X0,sK6(X1,X0,X2,X3),sK8(X1,X0,X2,X3))
| equal_maps(X1,X0,X2,X3) ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_88,plain,
( apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f170]) ).
cnf(c_89,plain,
( member(sK8(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f169]) ).
cnf(c_90,plain,
( member(sK7(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f168]) ).
cnf(c_91,plain,
( member(sK6(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f167]) ).
cnf(c_108,negated_conjecture,
~ equal_maps(sK15,sK16,sK17,sK19),
inference(cnf_transformation,[],[f193]) ).
cnf(c_109,negated_conjecture,
compose_predicate(sK16,sK14,sK13,sK17,sK18,sK19),
inference(cnf_transformation,[],[f192]) ).
cnf(c_110,negated_conjecture,
compose_predicate(sK15,sK14,sK13,sK17,sK18,sK19),
inference(cnf_transformation,[],[f191]) ).
cnf(c_111,negated_conjecture,
maps(sK14,sK18,sK19),
inference(cnf_transformation,[],[f190]) ).
cnf(c_112,negated_conjecture,
maps(sK13,sK17,sK18),
inference(cnf_transformation,[],[f189]) ).
cnf(c_213,plain,
( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_86]) ).
cnf(c_251,plain,
( member(sK6(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_91]) ).
cnf(c_255,plain,
( equal_maps(X0,X1,X2,X3)
| apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3)) ),
inference(prop_impl_just,[status(thm)],[c_88]) ).
cnf(c_256,plain,
( apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(renaming,[status(thm)],[c_255]) ).
cnf(c_257,plain,
( equal_maps(X0,X1,X2,X3)
| member(sK8(X0,X1,X2,X3),X3) ),
inference(prop_impl_just,[status(thm)],[c_89]) ).
cnf(c_258,plain,
( member(sK8(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(renaming,[status(thm)],[c_257]) ).
cnf(c_259,plain,
( equal_maps(X0,X1,X2,X3)
| member(sK7(X0,X1,X2,X3),X3) ),
inference(prop_impl_just,[status(thm)],[c_90]) ).
cnf(c_260,plain,
( member(sK7(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(renaming,[status(thm)],[c_259]) ).
cnf(c_281,plain,
( apply(X0,sK6(X1,X0,X2,X3),sK8(X1,X0,X2,X3))
| equal_maps(X1,X0,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_87]) ).
cnf(c_1051,plain,
( X0 != sK15
| X1 != sK16
| X2 != sK17
| X3 != sK19
| member(sK6(X0,X1,X2,X3),X2) ),
inference(resolution_lifted,[status(thm)],[c_251,c_108]) ).
cnf(c_1052,plain,
member(sK6(sK15,sK16,sK17,sK19),sK17),
inference(unflattening,[status(thm)],[c_1051]) ).
cnf(c_1056,plain,
( X0 != sK15
| X1 != sK16
| X2 != sK17
| X3 != sK19
| member(sK7(X0,X1,X2,X3),X3) ),
inference(resolution_lifted,[status(thm)],[c_260,c_108]) ).
cnf(c_1057,plain,
member(sK7(sK15,sK16,sK17,sK19),sK19),
inference(unflattening,[status(thm)],[c_1056]) ).
cnf(c_1061,plain,
( X0 != sK15
| X1 != sK16
| X2 != sK17
| X3 != sK19
| member(sK8(X0,X1,X2,X3),X3) ),
inference(resolution_lifted,[status(thm)],[c_258,c_108]) ).
cnf(c_1062,plain,
member(sK8(sK15,sK16,sK17,sK19),sK19),
inference(unflattening,[status(thm)],[c_1061]) ).
cnf(c_1066,plain,
( X0 != sK15
| X1 != sK16
| X2 != sK17
| X3 != sK19
| apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3)) ),
inference(resolution_lifted,[status(thm)],[c_256,c_108]) ).
cnf(c_1067,plain,
apply(sK15,sK6(sK15,sK16,sK17,sK19),sK7(sK15,sK16,sK17,sK19)),
inference(unflattening,[status(thm)],[c_1066]) ).
cnf(c_1071,plain,
( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3)
| X0 != sK15
| X1 != sK16
| X2 != sK17
| X3 != sK19 ),
inference(resolution_lifted,[status(thm)],[c_213,c_108]) ).
cnf(c_1072,plain,
sK7(sK15,sK16,sK17,sK19) != sK8(sK15,sK16,sK17,sK19),
inference(unflattening,[status(thm)],[c_1071]) ).
cnf(c_1076,plain,
( X0 != sK16
| X1 != sK15
| X2 != sK17
| X3 != sK19
| apply(X0,sK6(X1,X0,X2,X3),sK8(X1,X0,X2,X3)) ),
inference(resolution_lifted,[status(thm)],[c_281,c_108]) ).
cnf(c_1077,plain,
apply(sK16,sK6(sK15,sK16,sK17,sK19),sK8(sK15,sK16,sK17,sK19)),
inference(unflattening,[status(thm)],[c_1076]) ).
cnf(c_1153,plain,
( X0 != sK14
| X1 != sK18
| X2 != sK19
| ~ 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_111]) ).
cnf(c_1154,plain,
( ~ apply(sK14,X0,X1)
| ~ apply(sK14,X0,X2)
| ~ member(X0,sK18)
| ~ member(X1,sK19)
| ~ member(X2,sK19)
| X1 = X2 ),
inference(unflattening,[status(thm)],[c_1153]) ).
cnf(c_1174,plain,
( X0 != sK13
| X1 != sK17
| X2 != sK18
| ~ 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_1175,plain,
( ~ apply(sK13,X0,X1)
| ~ apply(sK13,X0,X2)
| ~ member(X0,sK17)
| ~ member(X1,sK18)
| ~ member(X2,sK18)
| X1 = X2 ),
inference(unflattening,[status(thm)],[c_1174]) ).
cnf(c_1195,plain,
( X0 != sK14
| X1 != sK18
| X2 != sK19
| ~ member(X3,X1)
| member(sK3(X0,X2,X3),X2) ),
inference(resolution_lifted,[status(thm)],[c_77,c_111]) ).
cnf(c_1196,plain,
( ~ member(X0,sK18)
| member(sK3(sK14,sK19,X0),sK19) ),
inference(unflattening,[status(thm)],[c_1195]) ).
cnf(c_1204,plain,
( X0 != sK14
| X1 != sK18
| X2 != sK19
| ~ member(X3,X1)
| apply(X0,X3,sK3(X0,X2,X3)) ),
inference(resolution_lifted,[status(thm)],[c_76,c_111]) ).
cnf(c_1205,plain,
( ~ member(X0,sK18)
| apply(sK14,X0,sK3(sK14,sK19,X0)) ),
inference(unflattening,[status(thm)],[c_1204]) ).
cnf(c_1213,plain,
( X0 != sK13
| X1 != sK17
| X2 != sK18
| ~ member(X3,X1)
| member(sK3(X0,X2,X3),X2) ),
inference(resolution_lifted,[status(thm)],[c_77,c_112]) ).
cnf(c_1214,plain,
( ~ member(X0,sK17)
| member(sK3(sK13,sK18,X0),sK18) ),
inference(unflattening,[status(thm)],[c_1213]) ).
cnf(c_1222,plain,
( X0 != sK13
| X1 != sK17
| X2 != sK18
| ~ member(X3,X1)
| apply(X0,X3,sK3(X0,X2,X3)) ),
inference(resolution_lifted,[status(thm)],[c_76,c_112]) ).
cnf(c_1223,plain,
( ~ member(X0,sK17)
| apply(sK13,X0,sK3(sK13,sK18,X0)) ),
inference(unflattening,[status(thm)],[c_1222]) ).
cnf(c_1251,plain,
( X0 != sK16
| X1 != sK14
| X2 != sK13
| X3 != sK17
| X4 != sK18
| X5 != sK19
| ~ apply(X0,X6,X7)
| ~ member(X6,X3)
| ~ member(X7,X5)
| member(sK4(X1,X2,X4,X6,X7),X4) ),
inference(resolution_lifted,[status(thm)],[c_81,c_109]) ).
cnf(c_1252,plain,
( ~ apply(sK16,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK19)
| member(sK4(sK14,sK13,sK18,X0,X1),sK18) ),
inference(unflattening,[status(thm)],[c_1251]) ).
cnf(c_1266,plain,
( X0 != sK16
| X1 != sK14
| X2 != sK13
| X3 != sK17
| X4 != sK18
| X5 != sK19
| ~ apply(X0,X6,X7)
| ~ member(X6,X3)
| ~ member(X7,X5)
| apply(X2,X6,sK4(X1,X2,X4,X6,X7)) ),
inference(resolution_lifted,[status(thm)],[c_80,c_109]) ).
cnf(c_1267,plain,
( ~ apply(sK16,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK19)
| apply(sK13,X0,sK4(sK14,sK13,sK18,X0,X1)) ),
inference(unflattening,[status(thm)],[c_1266]) ).
cnf(c_1281,plain,
( X0 != sK16
| X1 != sK14
| X2 != sK13
| X3 != sK17
| X4 != sK18
| X5 != sK19
| ~ apply(X0,X6,X7)
| ~ member(X6,X3)
| ~ member(X7,X5)
| apply(X1,sK4(X1,X2,X4,X6,X7),X7) ),
inference(resolution_lifted,[status(thm)],[c_79,c_109]) ).
cnf(c_1282,plain,
( ~ apply(sK16,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK19)
| apply(sK14,sK4(sK14,sK13,sK18,X0,X1),X1) ),
inference(unflattening,[status(thm)],[c_1281]) ).
cnf(c_1317,plain,
( X0 != sK15
| X1 != sK14
| X2 != sK13
| X3 != sK17
| X4 != sK18
| X5 != sK19
| ~ apply(X0,X6,X7)
| ~ member(X6,X3)
| ~ member(X7,X5)
| member(sK4(X1,X2,X4,X6,X7),X4) ),
inference(resolution_lifted,[status(thm)],[c_81,c_110]) ).
cnf(c_1318,plain,
( ~ apply(sK15,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK19)
| member(sK4(sK14,sK13,sK18,X0,X1),sK18) ),
inference(unflattening,[status(thm)],[c_1317]) ).
cnf(c_1332,plain,
( X0 != sK15
| X1 != sK14
| X2 != sK13
| X3 != sK17
| X4 != sK18
| X5 != sK19
| ~ apply(X0,X6,X7)
| ~ member(X6,X3)
| ~ member(X7,X5)
| apply(X2,X6,sK4(X1,X2,X4,X6,X7)) ),
inference(resolution_lifted,[status(thm)],[c_80,c_110]) ).
cnf(c_1333,plain,
( ~ apply(sK15,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK19)
| apply(sK13,X0,sK4(sK14,sK13,sK18,X0,X1)) ),
inference(unflattening,[status(thm)],[c_1332]) ).
cnf(c_1347,plain,
( X0 != sK15
| X1 != sK14
| X2 != sK13
| X3 != sK17
| X4 != sK18
| X5 != sK19
| ~ apply(X0,X6,X7)
| ~ member(X6,X3)
| ~ member(X7,X5)
| apply(X1,sK4(X1,X2,X4,X6,X7),X7) ),
inference(resolution_lifted,[status(thm)],[c_79,c_110]) ).
cnf(c_1348,plain,
( ~ apply(sK15,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK19)
| apply(sK14,sK4(sK14,sK13,sK18,X0,X1),X1) ),
inference(unflattening,[status(thm)],[c_1347]) ).
cnf(c_2846,plain,
( ~ member(sK3(sK14,sK19,X0),sK19)
| ~ apply(sK14,X0,X1)
| ~ member(X0,sK18)
| ~ member(X1,sK19)
| sK3(sK14,sK19,X0) = X1 ),
inference(superposition,[status(thm)],[c_1205,c_1154]) ).
cnf(c_2942,plain,
( ~ member(sK3(sK13,sK18,X0),sK18)
| ~ apply(sK13,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK18)
| sK3(sK13,sK18,X0) = X1 ),
inference(superposition,[status(thm)],[c_1223,c_1175]) ).
cnf(c_3039,plain,
( ~ apply(sK14,X0,X1)
| ~ member(X0,sK18)
| ~ member(X1,sK19)
| sK3(sK14,sK19,X0) = X1 ),
inference(global_subsumption_just,[status(thm)],[c_2846,c_1196,c_2846]) ).
cnf(c_3051,plain,
( ~ member(sK4(sK14,sK13,sK18,X0,X1),sK18)
| ~ apply(sK15,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK19)
| sK3(sK14,sK19,sK4(sK14,sK13,sK18,X0,X1)) = X1 ),
inference(superposition,[status(thm)],[c_1348,c_3039]) ).
cnf(c_3052,plain,
( ~ member(sK4(sK14,sK13,sK18,X0,X1),sK18)
| ~ apply(sK16,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK19)
| sK3(sK14,sK19,sK4(sK14,sK13,sK18,X0,X1)) = X1 ),
inference(superposition,[status(thm)],[c_1282,c_3039]) ).
cnf(c_3065,plain,
( ~ apply(sK13,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK18)
| sK3(sK13,sK18,X0) = X1 ),
inference(global_subsumption_just,[status(thm)],[c_2942,c_1214,c_2942]) ).
cnf(c_3077,plain,
( ~ member(sK4(sK14,sK13,sK18,X0,X1),sK18)
| ~ apply(sK15,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK19)
| sK4(sK14,sK13,sK18,X0,X1) = sK3(sK13,sK18,X0) ),
inference(superposition,[status(thm)],[c_1333,c_3065]) ).
cnf(c_3078,plain,
( ~ member(sK4(sK14,sK13,sK18,X0,X1),sK18)
| ~ apply(sK16,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK19)
| sK4(sK14,sK13,sK18,X0,X1) = sK3(sK13,sK18,X0) ),
inference(superposition,[status(thm)],[c_1267,c_3065]) ).
cnf(c_3113,plain,
( ~ apply(sK15,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK19)
| sK3(sK14,sK19,sK4(sK14,sK13,sK18,X0,X1)) = X1 ),
inference(global_subsumption_just,[status(thm)],[c_3051,c_1318,c_3051]) ).
cnf(c_3124,plain,
( ~ member(sK7(sK15,sK16,sK17,sK19),sK19)
| ~ member(sK6(sK15,sK16,sK17,sK19),sK17)
| sK3(sK14,sK19,sK4(sK14,sK13,sK18,sK6(sK15,sK16,sK17,sK19),sK7(sK15,sK16,sK17,sK19))) = sK7(sK15,sK16,sK17,sK19) ),
inference(superposition,[status(thm)],[c_1067,c_3113]) ).
cnf(c_3131,plain,
sK3(sK14,sK19,sK4(sK14,sK13,sK18,sK6(sK15,sK16,sK17,sK19),sK7(sK15,sK16,sK17,sK19))) = sK7(sK15,sK16,sK17,sK19),
inference(forward_subsumption_resolution,[status(thm)],[c_3124,c_1052,c_1057]) ).
cnf(c_3227,plain,
( ~ apply(sK16,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK19)
| sK3(sK14,sK19,sK4(sK14,sK13,sK18,X0,X1)) = X1 ),
inference(global_subsumption_just,[status(thm)],[c_3052,c_1252,c_3052]) ).
cnf(c_3238,plain,
( ~ member(sK8(sK15,sK16,sK17,sK19),sK19)
| ~ member(sK6(sK15,sK16,sK17,sK19),sK17)
| sK3(sK14,sK19,sK4(sK14,sK13,sK18,sK6(sK15,sK16,sK17,sK19),sK8(sK15,sK16,sK17,sK19))) = sK8(sK15,sK16,sK17,sK19) ),
inference(superposition,[status(thm)],[c_1077,c_3227]) ).
cnf(c_3240,plain,
sK3(sK14,sK19,sK4(sK14,sK13,sK18,sK6(sK15,sK16,sK17,sK19),sK8(sK15,sK16,sK17,sK19))) = sK8(sK15,sK16,sK17,sK19),
inference(forward_subsumption_resolution,[status(thm)],[c_3238,c_1052,c_1062]) ).
cnf(c_3257,plain,
( ~ apply(sK15,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK19)
| sK4(sK14,sK13,sK18,X0,X1) = sK3(sK13,sK18,X0) ),
inference(global_subsumption_just,[status(thm)],[c_3077,c_1318,c_3077]) ).
cnf(c_3268,plain,
( ~ member(sK7(sK15,sK16,sK17,sK19),sK19)
| ~ member(sK6(sK15,sK16,sK17,sK19),sK17)
| sK4(sK14,sK13,sK18,sK6(sK15,sK16,sK17,sK19),sK7(sK15,sK16,sK17,sK19)) = sK3(sK13,sK18,sK6(sK15,sK16,sK17,sK19)) ),
inference(superposition,[status(thm)],[c_1067,c_3257]) ).
cnf(c_3275,plain,
sK4(sK14,sK13,sK18,sK6(sK15,sK16,sK17,sK19),sK7(sK15,sK16,sK17,sK19)) = sK3(sK13,sK18,sK6(sK15,sK16,sK17,sK19)),
inference(forward_subsumption_resolution,[status(thm)],[c_3268,c_1052,c_1057]) ).
cnf(c_3276,plain,
sK3(sK14,sK19,sK3(sK13,sK18,sK6(sK15,sK16,sK17,sK19))) = sK7(sK15,sK16,sK17,sK19),
inference(demodulation,[status(thm)],[c_3131,c_3275]) ).
cnf(c_5370,plain,
( ~ apply(sK16,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK19)
| sK4(sK14,sK13,sK18,X0,X1) = sK3(sK13,sK18,X0) ),
inference(global_subsumption_just,[status(thm)],[c_3078,c_1252,c_3078]) ).
cnf(c_5382,plain,
( ~ member(sK8(sK15,sK16,sK17,sK19),sK19)
| ~ member(sK6(sK15,sK16,sK17,sK19),sK17)
| sK4(sK14,sK13,sK18,sK6(sK15,sK16,sK17,sK19),sK8(sK15,sK16,sK17,sK19)) = sK3(sK13,sK18,sK6(sK15,sK16,sK17,sK19)) ),
inference(superposition,[status(thm)],[c_1077,c_5370]) ).
cnf(c_5389,plain,
sK4(sK14,sK13,sK18,sK6(sK15,sK16,sK17,sK19),sK8(sK15,sK16,sK17,sK19)) = sK3(sK13,sK18,sK6(sK15,sK16,sK17,sK19)),
inference(forward_subsumption_resolution,[status(thm)],[c_5382,c_1052,c_1062]) ).
cnf(c_5390,plain,
sK3(sK14,sK19,sK3(sK13,sK18,sK6(sK15,sK16,sK17,sK19))) = sK8(sK15,sK16,sK17,sK19),
inference(demodulation,[status(thm)],[c_3240,c_5389]) ).
cnf(c_5391,plain,
sK7(sK15,sK16,sK17,sK19) = sK8(sK15,sK16,sK17,sK19),
inference(light_normalisation,[status(thm)],[c_5390,c_3276]) ).
cnf(c_5392,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5391,c_1072]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET708+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.15 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 11:24:17 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.42/1.18 % SZS status Started for theBenchmark.p
% 3.42/1.18 % SZS status Theorem for theBenchmark.p
% 3.42/1.18
% 3.42/1.18 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.42/1.18
% 3.42/1.18 ------ iProver source info
% 3.42/1.18
% 3.42/1.18 git: date: 2023-05-31 18:12:56 +0000
% 3.42/1.18 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.42/1.18 git: non_committed_changes: false
% 3.42/1.18 git: last_make_outside_of_git: false
% 3.42/1.18
% 3.42/1.18 ------ Parsing...
% 3.42/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.42/1.18
% 3.42/1.18 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e
% 3.42/1.18
% 3.42/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.42/1.18
% 3.42/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.42/1.18 ------ Proving...
% 3.42/1.18 ------ Problem Properties
% 3.42/1.18
% 3.42/1.18
% 3.42/1.18 clauses 66
% 3.42/1.18 conjectures 0
% 3.42/1.18 EPR 6
% 3.42/1.18 Horn 61
% 3.42/1.18 unary 10
% 3.42/1.18 binary 29
% 3.42/1.18 lits 177
% 3.42/1.18 lits eq 6
% 3.42/1.18 fd_pure 0
% 3.42/1.18 fd_pseudo 0
% 3.42/1.18 fd_cond 0
% 3.42/1.18 fd_pseudo_cond 4
% 3.42/1.18 AC symbols 0
% 3.42/1.18
% 3.42/1.18 ------ Schedule dynamic 5 is on
% 3.42/1.18
% 3.42/1.18 ------ no conjectures: strip conj schedule
% 3.42/1.18
% 3.42/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.42/1.18
% 3.42/1.18
% 3.42/1.18 ------
% 3.42/1.18 Current options:
% 3.42/1.18 ------
% 3.42/1.18
% 3.42/1.18
% 3.42/1.18
% 3.42/1.18
% 3.42/1.18 ------ Proving...
% 3.42/1.18
% 3.42/1.18
% 3.42/1.18 % SZS status Theorem for theBenchmark.p
% 3.42/1.18
% 3.42/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.42/1.19
% 3.42/1.19
%------------------------------------------------------------------------------