TSTP Solution File: NUN065+2 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : NUN065+2 : TPTP v8.2.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n006.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 : Mon Jun 24 13:32:46 EDT 2024
% Result : Theorem 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 26
% Syntax : Number of formulae : 120 ( 26 unt; 0 def)
% Number of atoms : 356 ( 128 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 342 ( 106 ~; 100 |; 120 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 1 con; 0-2 aty)
% Number of variables : 262 ( 188 !; 74 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1613,plain,
$false,
inference(subsumption_resolution,[],[f1523,f116]) ).
fof(f116,plain,
r1(sK23),
inference(equality_resolution,[],[f104]) ).
fof(f104,plain,
! [X1] :
( r1(X1)
| sK23 != X1 ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X1] :
( ( sK23 = X1
& r1(X1) )
| ( sK23 != X1
& ~ r1(X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f1,f61]) ).
fof(f61,plain,
( ? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| ( X0 != X1
& ~ r1(X1) ) )
=> ! [X1] :
( ( sK23 = X1
& r1(X1) )
| ( sK23 != X1
& ~ r1(X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1,axiom,
? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| ( X0 != X1
& ~ r1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f1523,plain,
~ r1(sK23),
inference(backward_demodulation,[],[f613,f1230]) ).
fof(f1230,plain,
! [X0] : sK23 = X0,
inference(resolution,[],[f1110,f614]) ).
fof(f614,plain,
! [X0,X1] :
( ~ r2(X1,sK12(X0))
| X0 = X1 ),
inference(forward_demodulation,[],[f606,f604]) ).
fof(f604,plain,
! [X0] : sK12(X0) = sK17(X0,sK23),
inference(resolution,[],[f602,f81]) ).
fof(f81,plain,
! [X2,X0] :
( sK12(X0) = X2
| ~ r2(X0,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X2] :
( ( sK12(X0) = X2
& r2(X0,X2) )
| ( sK12(X0) != X2
& ~ r2(X0,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f18,f45]) ).
fof(f45,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( X1 = X2
& r2(X0,X2) )
| ( X1 != X2
& ~ r2(X0,X2) ) )
=> ! [X2] :
( ( sK12(X0) = X2
& r2(X0,X2) )
| ( sK12(X0) != X2
& ~ r2(X0,X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0] :
? [X1] :
! [X2] :
( ( X1 = X2
& r2(X0,X2) )
| ( X1 != X2
& ~ r2(X0,X2) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2] :
? [X3] :
! [X4] :
( ( X3 = X4
& r2(X2,X4) )
| ( X3 != X4
& ~ r2(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f602,plain,
! [X0] : r2(X0,sK17(X0,sK23)),
inference(superposition,[],[f93,f597]) ).
fof(f597,plain,
! [X0] : sK18(X0,sK23) = X0,
inference(resolution,[],[f537,f94]) ).
fof(f94,plain,
! [X0,X1] : r3(X0,X1,sK18(X0,X1)),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( r3(X0,X1,sK18(X0,X1))
& r2(sK18(X0,X1),sK17(X0,X1))
& sK17(X0,X1) = sK19(X0,X1)
& r3(X0,sK20(X0,X1),sK19(X0,X1))
& r2(X1,sK20(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19,sK20])],[f22,f55,f54,f53,f52]) ).
fof(f52,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,X2) )
& ? [X4] :
( X2 = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) ) )
=> ( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,sK17(X0,X1)) )
& ? [X4] :
( sK17(X0,X1) = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
! [X0,X1] :
( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,sK17(X0,X1)) )
=> ( r3(X0,X1,sK18(X0,X1))
& r2(sK18(X0,X1),sK17(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X0,X1] :
( ? [X4] :
( sK17(X0,X1) = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) )
=> ( sK17(X0,X1) = sK19(X0,X1)
& ? [X5] :
( r3(X0,X5,sK19(X0,X1))
& r2(X1,X5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
! [X0,X1] :
( ? [X5] :
( r3(X0,X5,sK19(X0,X1))
& r2(X1,X5) )
=> ( r3(X0,sK20(X0,X1),sK19(X0,X1))
& r2(X1,sK20(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
? [X2] :
( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,X2) )
& ? [X4] :
( X2 = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X13,X14] :
? [X15] :
( ? [X18] :
( r3(X13,X14,X18)
& r2(X18,X15) )
& ? [X16] :
( X15 = X16
& ? [X17] :
( r3(X13,X17,X16)
& r2(X14,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f537,plain,
! [X0,X1] :
( ~ r3(X0,sK23,X1)
| X0 = X1 ),
inference(superposition,[],[f530,f101]) ).
fof(f101,plain,
! [X3,X0,X1] :
( sK22(X0,X1) = X3
| ~ r3(X0,X1,X3) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1,X3] :
( ( sK22(X0,X1) = X3
& r3(X0,X1,X3) )
| ( sK22(X0,X1) != X3
& ~ r3(X0,X1,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f24,f59]) ).
fof(f59,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( X2 = X3
& r3(X0,X1,X3) )
| ( X2 != X3
& ~ r3(X0,X1,X3) ) )
=> ! [X3] :
( ( sK22(X0,X1) = X3
& r3(X0,X1,X3) )
| ( sK22(X0,X1) != X3
& ~ r3(X0,X1,X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( X2 = X3
& r3(X0,X1,X3) )
| ( X2 != X3
& ~ r3(X0,X1,X3) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X5,X6] :
? [X7] :
! [X8] :
( ( X7 = X8
& r3(X5,X6,X8) )
| ( X7 != X8
& ~ r3(X5,X6,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f530,plain,
! [X0] : sK22(X0,sK23) = X0,
inference(resolution,[],[f527,f101]) ).
fof(f527,plain,
! [X0] : r3(X0,sK23,X0),
inference(forward_demodulation,[],[f525,f78]) ).
fof(f78,plain,
! [X0] : sK10(X0) = X0,
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( sK10(X0) = X0
& r3(X0,sK11(X0),sK10(X0))
& r1(sK11(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f17,f43,f42]) ).
fof(f42,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r3(X0,X2,X1)
& r1(X2) ) )
=> ( sK10(X0) = X0
& ? [X2] :
( r3(X0,X2,sK10(X0))
& r1(X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
! [X0] :
( ? [X2] :
( r3(X0,X2,sK10(X0))
& r1(X2) )
=> ( r3(X0,sK11(X0),sK10(X0))
& r1(sK11(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0] :
? [X1] :
( X0 = X1
& ? [X2] :
( r3(X0,X2,X1)
& r1(X2) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X29] :
? [X30] :
( X29 = X30
& ? [X31] :
( r3(X29,X31,X30)
& r1(X31) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f525,plain,
! [X0] : r3(X0,sK23,sK10(X0)),
inference(backward_demodulation,[],[f77,f521]) ).
fof(f521,plain,
! [X0] : sK11(X0) = sK23,
inference(backward_demodulation,[],[f338,f493]) ).
fof(f493,plain,
! [X0] : sK23 = sK3(sK11(X0)),
inference(resolution,[],[f479,f76]) ).
fof(f76,plain,
! [X0] : r1(sK11(X0)),
inference(cnf_transformation,[],[f44]) ).
fof(f479,plain,
! [X0] :
( ~ r1(X0)
| sK3(X0) = sK23 ),
inference(subsumption_resolution,[],[f474,f117]) ).
fof(f117,plain,
! [X0] :
( sP0(X0)
| sK3(X0) = sK23 ),
inference(resolution,[],[f66,f105]) ).
fof(f105,plain,
! [X1] :
( sK23 = X1
| ~ r1(X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f66,plain,
! [X0] :
( r1(sK3(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0] :
( ( sK3(X0) = X0
& r1(sK3(X0)) )
| sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f27,f33]) ).
fof(f33,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& r1(X1) )
=> ( sK3(X0) = X0
& r1(sK3(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& r1(X1) )
| sP0(X0) ),
inference(definition_folding,[],[f25,f26]) ).
fof(f26,plain,
! [X0] :
( ? [X2] :
( X0 = X2
& ? [X3] :
( r2(X3,X2)
& r1(X3) ) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f25,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& r1(X1) )
| ? [X2] :
( X0 = X2
& ? [X3] :
( r2(X3,X2)
& r1(X3) ) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
~ ? [X0] :
( ! [X1] :
( X0 != X1
| ~ r1(X1) )
& ! [X2] :
( X0 != X2
| ! [X3] :
( ~ r2(X3,X2)
| ~ r1(X3) ) ) ),
inference(rectify,[],[f13]) ).
fof(f13,negated_conjecture,
~ ? [X38] :
( ! [X15] :
( X15 != X38
| ~ r1(X15) )
& ! [X21] :
( X21 != X38
| ! [X22] :
( ~ r2(X22,X21)
| ~ r1(X22) ) ) ),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
? [X38] :
( ! [X15] :
( X15 != X38
| ~ r1(X15) )
& ! [X21] :
( X21 != X38
| ! [X22] :
( ~ r2(X22,X21)
| ~ r1(X22) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f474,plain,
! [X0] :
( ~ r1(X0)
| sK3(X0) = sK23
| ~ sP0(X0) ),
inference(superposition,[],[f443,f65]) ).
fof(f65,plain,
! [X0] :
( sK1(X0) = X0
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0] :
( ( sK1(X0) = X0
& r2(sK2(X0),sK1(X0))
& r1(sK2(X0)) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f29,f31,f30]) ).
fof(f30,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& r1(X2) ) )
=> ( sK1(X0) = X0
& ? [X2] :
( r2(X2,sK1(X0))
& r1(X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0] :
( ? [X2] :
( r2(X2,sK1(X0))
& r1(X2) )
=> ( r2(sK2(X0),sK1(X0))
& r1(sK2(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& r1(X2) ) )
| ~ sP0(X0) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
! [X0] :
( ? [X2] :
( X0 = X2
& ? [X3] :
( r2(X3,X2)
& r1(X3) ) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f26]) ).
fof(f443,plain,
! [X0] :
( ~ r1(sK1(X0))
| sK3(X0) = sK23 ),
inference(resolution,[],[f123,f109]) ).
fof(f109,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ),
inference(equality_resolution,[],[f83]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| X1 != X2
| ~ r1(X2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( ~ r2(X0,X1)
| ! [X2] :
( X1 != X2
| ~ r1(X2) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X40,X41] :
( ~ r2(X40,X41)
| ! [X42] :
( X41 != X42
| ~ r1(X42) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f123,plain,
! [X0] :
( r2(sK2(X0),sK1(X0))
| sK3(X0) = sK23 ),
inference(resolution,[],[f117,f64]) ).
fof(f64,plain,
! [X0] :
( r2(sK2(X0),sK1(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f338,plain,
! [X0] : sK11(X0) = sK3(sK11(X0)),
inference(resolution,[],[f325,f76]) ).
fof(f325,plain,
! [X0] :
( ~ r1(X0)
| sK3(X0) = X0 ),
inference(subsumption_resolution,[],[f320,f67]) ).
fof(f67,plain,
! [X0] :
( sP0(X0)
| sK3(X0) = X0 ),
inference(cnf_transformation,[],[f34]) ).
fof(f320,plain,
! [X0] :
( ~ r1(X0)
| sK3(X0) = X0
| ~ sP0(X0) ),
inference(superposition,[],[f291,f65]) ).
fof(f291,plain,
! [X0] :
( ~ r1(sK1(X0))
| sK3(X0) = X0 ),
inference(resolution,[],[f120,f109]) ).
fof(f120,plain,
! [X0] :
( r2(sK2(X0),sK1(X0))
| sK3(X0) = X0 ),
inference(resolution,[],[f67,f64]) ).
fof(f77,plain,
! [X0] : r3(X0,sK11(X0),sK10(X0)),
inference(cnf_transformation,[],[f44]) ).
fof(f93,plain,
! [X0,X1] : r2(sK18(X0,X1),sK17(X0,X1)),
inference(cnf_transformation,[],[f56]) ).
fof(f606,plain,
! [X0,X1] :
( X0 = X1
| ~ r2(X1,sK17(X0,sK23)) ),
inference(resolution,[],[f602,f110]) ).
fof(f110,plain,
! [X3,X0,X1] :
( X0 = X1
| ~ r2(X1,X3)
| ~ r2(X0,X3) ),
inference(equality_resolution,[],[f84]) ).
fof(f84,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ r2(X1,X2)
| X2 != X3
| ~ r2(X0,X3) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( X0 = X1
| ! [X2] :
( ~ r2(X1,X2)
| ! [X3] :
( X2 != X3
| ~ r2(X0,X3) ) ) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X25,X26] :
( X25 = X26
| ! [X27] :
( ~ r2(X26,X27)
| ! [X28] :
( X27 != X28
| ~ r2(X25,X28) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f1110,plain,
! [X1] : r2(X1,sK12(sK23)),
inference(backward_demodulation,[],[f85,f1095]) ).
fof(f1095,plain,
! [X0,X1] : sK16(X0,X1) = sK12(sK23),
inference(resolution,[],[f1093,f85]) ).
fof(f1093,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| sK12(sK23) = X0 ),
inference(subsumption_resolution,[],[f1085,f241]) ).
fof(f241,plain,
! [X0,X1] :
( ~ sP0(X1)
| sK12(sK23) = X1
| ~ r2(X0,X1) ),
inference(superposition,[],[f228,f81]) ).
fof(f228,plain,
! [X0] :
( ~ sP0(sK12(X0))
| sK12(X0) = sK12(sK23) ),
inference(resolution,[],[f190,f81]) ).
fof(f190,plain,
! [X0] :
( r2(sK23,sK12(X0))
| ~ sP0(sK12(X0)) ),
inference(backward_demodulation,[],[f143,f183]) ).
fof(f183,plain,
! [X0] : sK23 = sK2(sK12(X0)),
inference(resolution,[],[f182,f108]) ).
fof(f108,plain,
! [X0] : r2(X0,sK12(X0)),
inference(equality_resolution,[],[f80]) ).
fof(f80,plain,
! [X2,X0] :
( r2(X0,X2)
| sK12(X0) != X2 ),
inference(cnf_transformation,[],[f46]) ).
fof(f182,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| sK2(X0) = sK23 ),
inference(resolution,[],[f180,f109]) ).
fof(f180,plain,
! [X0] :
( r1(X0)
| sK2(X0) = sK23 ),
inference(subsumption_resolution,[],[f177,f105]) ).
fof(f177,plain,
! [X0] :
( r1(X0)
| sK2(X0) = sK23
| r1(sK2(X0)) ),
inference(resolution,[],[f156,f63]) ).
fof(f63,plain,
! [X0] :
( r1(sK2(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f156,plain,
! [X0] :
( sP0(X0)
| r1(X0)
| sK2(X0) = sK23 ),
inference(superposition,[],[f66,f125]) ).
fof(f125,plain,
! [X0] :
( sK3(X0) = X0
| sK2(X0) = sK23 ),
inference(resolution,[],[f119,f105]) ).
fof(f119,plain,
! [X0] :
( r1(sK2(X0))
| sK3(X0) = X0 ),
inference(resolution,[],[f67,f63]) ).
fof(f143,plain,
! [X0] :
( r2(sK2(sK12(X0)),sK12(X0))
| ~ sP0(sK12(X0)) ),
inference(superposition,[],[f64,f135]) ).
fof(f135,plain,
! [X0] : sK12(X0) = sK1(sK12(X0)),
inference(resolution,[],[f131,f108]) ).
fof(f131,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| sK1(X0) = X0 ),
inference(subsumption_resolution,[],[f129,f65]) ).
fof(f129,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| sP0(X0)
| sK1(X0) = X0 ),
inference(superposition,[],[f118,f121]) ).
fof(f121,plain,
! [X0] :
( sK3(X0) = X0
| sK1(X0) = X0 ),
inference(resolution,[],[f67,f65]) ).
fof(f118,plain,
! [X0,X1] :
( ~ r2(X1,sK3(X0))
| sP0(X0) ),
inference(resolution,[],[f66,f109]) ).
fof(f1085,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| sP0(X0)
| sK12(sK23) = X0 ),
inference(superposition,[],[f118,f1062]) ).
fof(f1062,plain,
! [X0] :
( sK3(X0) = X0
| sK12(sK23) = X0 ),
inference(subsumption_resolution,[],[f1053,f67]) ).
fof(f1053,plain,
! [X0] :
( ~ sP0(X0)
| sK12(sK23) = X0
| sK3(X0) = X0 ),
inference(superposition,[],[f228,f392]) ).
fof(f392,plain,
! [X0] :
( sK12(sK2(X0)) = X0
| sK3(X0) = X0 ),
inference(resolution,[],[f315,f81]) ).
fof(f315,plain,
! [X0] :
( r2(sK2(X0),X0)
| sK3(X0) = X0 ),
inference(subsumption_resolution,[],[f306,f67]) ).
fof(f306,plain,
! [X0] :
( r2(sK2(X0),X0)
| sK3(X0) = X0
| ~ sP0(X0) ),
inference(superposition,[],[f120,f65]) ).
fof(f85,plain,
! [X0,X1] : r2(X1,sK16(X0,X1)),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( r4(X0,X1,sK14(X0,X1))
& r3(sK14(X0,X1),X0,sK13(X0,X1))
& sK13(X0,X1) = sK15(X0,X1)
& r4(X0,sK16(X0,X1),sK15(X0,X1))
& r2(X1,sK16(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f21,f50,f49,f48,f47]) ).
fof(f47,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,X2) )
& ? [X4] :
( X2 = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) ) )
=> ( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,sK13(X0,X1)) )
& ? [X4] :
( sK13(X0,X1) = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
! [X0,X1] :
( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,sK13(X0,X1)) )
=> ( r4(X0,X1,sK14(X0,X1))
& r3(sK14(X0,X1),X0,sK13(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
! [X0,X1] :
( ? [X4] :
( sK13(X0,X1) = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) )
=> ( sK13(X0,X1) = sK15(X0,X1)
& ? [X5] :
( r4(X0,X5,sK15(X0,X1))
& r2(X1,X5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
! [X0,X1] :
( ? [X5] :
( r4(X0,X5,sK15(X0,X1))
& r2(X1,X5) )
=> ( r4(X0,sK16(X0,X1),sK15(X0,X1))
& r2(X1,sK16(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0,X1] :
? [X2] :
( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,X2) )
& ? [X4] :
( X2 = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X19,X20] :
? [X21] :
( ? [X24] :
( r4(X19,X20,X24)
& r3(X24,X19,X21) )
& ? [X22] :
( X21 = X22
& ? [X23] :
( r4(X19,X23,X22)
& r2(X20,X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f613,plain,
! [X0] : ~ r1(sK12(X0)),
inference(forward_demodulation,[],[f605,f604]) ).
fof(f605,plain,
! [X0] : ~ r1(sK17(X0,sK23)),
inference(resolution,[],[f602,f109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUN065+2 : TPTP v8.2.0. Released v7.3.0.
% 0.07/0.13 % Command : run_vampire %s %d THM
% 0.11/0.34 % Computer : n006.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Tue Jun 18 21:18:24 EDT 2024
% 0.11/0.34 % CPUTime :
% 0.11/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.11/0.36 Running first-order theorem proving
% 0.11/0.36 Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.42 % (26218)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.42 % (26223)lrs-1011_37821:262144_bsr=unit_only:sil=2000:fde=none:plsq=on:plsqr=43543,131072:bce=on:rnwc=on:plsql=on:rp=on:nwc=10.0:newcnf=on:i=109:awrs=decay:awrsf=10:ep=R:mep=off:amm=sco_0 on theBenchmark for (2999ds/109Mi)
% 0.19/0.42 % (26218)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.42 % (26222)lrs+21_2461:262144_anc=none:drc=off:sil=2000:sp=occurrence:nwc=6.0:updr=off:st=3.0:i=109:sd=2:afp=4000:erml=3:nm=14:afq=2.0:uhcvi=on:ss=included:er=filter:abs=on:nicw=on:ile=on:sims=off:s2a=on:s2agt=50:s2at=-1.0:plsq=on:plsql=on:plsqc=2:plsqr=1,32:newcnf=on:bd=off:to=lpo_0 on theBenchmark for (2999ds/109Mi)
% 0.19/0.42 % (26218)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.42 % (26225)lrs+1010_1:1_to=lpo:sil=2000:sos=on:fd=off:i=117:bd=off_0 on theBenchmark for (2999ds/117Mi)
% 0.19/0.42 % (26218)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.42 % (26224)ott-1011_16:1_sil=2000:sp=const_max:urr=on:lsd=20:st=3.0:i=117:ss=axioms:gsp=on:rp=on:sos=on:fd=off:aac=none_0 on theBenchmark for (2999ds/117Mi)
% 0.19/0.42 % (26223)Refutation not found, incomplete strategy% (26223)------------------------------
% 0.19/0.42 % (26223)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.19/0.42 % (26223)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.19/0.42 % (26223)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.42
% 0.19/0.42 % (26223)Memory used [KB]: 1149
% 0.19/0.42 % (26223)Time elapsed: 0.003 s
% 0.19/0.42 % (26223)Instructions burned: 3 (million)
% 0.19/0.42 % (26218)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.42 % (26220)lrs+1011_8:1_sil=128000:tgt=ground:fde=unused:sp=frequency:nwc=5.0:lwlo=on:i=105338:awrs=converge:awrsf=1385:av=off_0 on theBenchmark for (2999ds/105338Mi)
% 0.19/0.42 % (26223)------------------------------
% 0.19/0.42 % (26223)------------------------------
% 0.19/0.43 % (26218)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.43 % (26219)ott+4_40_av=off:bce=on:fsd=off:fde=unused:nm=4:nwc=1.1:sos=all:sp=frequency:i=69040_0 on theBenchmark for (2999ds/69040Mi)
% 0.19/0.43 % (26218)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.43 % (26221)dis+1011_1:99_anc=none:fde=unused:plsqc=2:bsd=on:plsq=on:plsqr=109,504:sp=reverse_frequency:spb=intro:rp=on:alpa=random:s2a=on:i=257151:s2at=-1.0:aac=none:nm=16:rawr=on:sil=256000:acc=model_0 on theBenchmark for (2999ds/257151Mi)
% 0.19/0.47 % (26222)Instruction limit reached!
% 0.19/0.47 % (26222)------------------------------
% 0.19/0.47 % (26222)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.19/0.47 % (26222)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.19/0.47 % (26222)Termination reason: Time limit
% 0.19/0.47 % (26222)Termination phase: Saturation
% 0.19/0.47
% 0.19/0.47 % (26222)Memory used [KB]: 1751
% 0.19/0.47 % (26222)Time elapsed: 0.047 s
% 0.19/0.47 % (26222)Instructions burned: 109 (million)
% 0.19/0.47 % (26219)First to succeed.
% 0.19/0.47 % (26219)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26218"
% 0.19/0.47 % (26225)Refutation not found, incomplete strategy% (26225)------------------------------
% 0.19/0.47 % (26225)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.19/0.47 % (26225)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.19/0.47 % (26225)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.47
% 0.19/0.47 % (26225)Memory used [KB]: 1300
% 0.19/0.47 % (26225)Time elapsed: 0.050 s
% 0.19/0.47 % (26225)Instructions burned: 102 (million)
% 0.19/0.47 % (26225)------------------------------
% 0.19/0.47 % (26225)------------------------------
% 0.19/0.47 % (26218)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.47 % (26219)Refutation found. Thanks to Tanya!
% 0.19/0.47 % SZS status Theorem for theBenchmark
% 0.19/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.47 % (26219)------------------------------
% 0.19/0.47 % (26219)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.19/0.47 % (26219)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.19/0.47 % (26219)Termination reason: Refutation
% 0.19/0.47
% 0.19/0.47 % (26219)Memory used [KB]: 1520
% 0.19/0.47 % (26219)Time elapsed: 0.044 s
% 0.19/0.47 % (26219)Instructions burned: 72 (million)
% 0.19/0.47 % (26219)------------------------------
% 0.19/0.47 % (26219)------------------------------
% 0.19/0.47 % (26218)Success in time 0.102 s
%------------------------------------------------------------------------------