TSTP Solution File: NUN072+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUN072+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.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 : Tue Apr 30 14:40:21 EDT 2024
% Result : Theorem 0.21s 0.47s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 35
% Syntax : Number of formulae : 168 ( 79 unt; 0 def)
% Number of atoms : 459 ( 106 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 462 ( 171 ~; 113 |; 156 &)
% ( 5 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 1 con; 0-2 aty)
% Number of variables : 442 ( 339 !; 103 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5296,plain,
$false,
inference(subsumption_resolution,[],[f5285,f400]) ).
fof(f400,plain,
! [X0,X1] : ~ sP1(sK13(X0),X1,X0),
inference(unit_resulting_resolution,[],[f390,f87]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| ~ r2(X2,X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( X0 != X1
& ~ r2(X2,X0) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f49]) ).
fof(f49,plain,
! [X2,X1,X0] :
( ( X1 != X2
& ~ r2(X0,X2) )
| ~ sP1(X2,X1,X0) ),
inference(nnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X2,X1,X0] :
( ( X1 != X2
& ~ r2(X0,X2) )
| ~ sP1(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f390,plain,
! [X0] : r2(X0,sK13(X0)),
inference(unit_resulting_resolution,[],[f116,f89]) ).
fof(f89,plain,
! [X2,X0] :
( sP1(X2,sK13(X0),X0)
| r2(X0,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X2] :
( ( sK13(X0) = X2
& r2(X0,X2) )
| sP1(X2,sK13(X0),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f29,f51]) ).
fof(f51,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( X1 = X2
& r2(X0,X2) )
| sP1(X2,X1,X0) )
=> ! [X2] :
( ( sK13(X0) = X2
& r2(X0,X2) )
| sP1(X2,sK13(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0] :
? [X1] :
! [X2] :
( ( X1 = X2
& r2(X0,X2) )
| sP1(X2,X1,X0) ),
inference(definition_folding,[],[f18,f28]) ).
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',axiom_2) ).
fof(f116,plain,
! [X2,X1] : ~ sP1(X1,X1,X2),
inference(equality_resolution,[],[f88]) ).
fof(f88,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f5285,plain,
sP1(sK13(sK13(sK24)),sK13(sK13(sK24)),sK13(sK24)),
inference(superposition,[],[f2084,f4533]) ).
fof(f4533,plain,
sK13(sK13(sK24)) = sK14(sK13(sK24),sK13(sK24)),
inference(forward_demodulation,[],[f4532,f3565]) ).
fof(f3565,plain,
! [X0] : sK13(X0) = sK18(X0,sK24),
inference(superposition,[],[f591,f3550]) ).
fof(f3550,plain,
! [X0] : sK19(X0,sK24) = X0,
inference(superposition,[],[f3529,f3525]) ).
fof(f3525,plain,
! [X0] : sK23(X0,sK24) = X0,
inference(unit_resulting_resolution,[],[f694,f110]) ).
fof(f110,plain,
! [X3,X0,X1] :
( sP3(X3,sK23(X0,X1),X1,X0)
| sK23(X0,X1) = X3 ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X3] :
( ( sK23(X0,X1) = X3
& r3(X0,X1,X3) )
| sP3(X3,sK23(X0,X1),X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f33,f69]) ).
fof(f69,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( X2 = X3
& r3(X0,X1,X3) )
| sP3(X3,X2,X1,X0) )
=> ! [X3] :
( ( sK23(X0,X1) = X3
& r3(X0,X1,X3) )
| sP3(X3,sK23(X0,X1),X1,X0) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( X2 = X3
& r3(X0,X1,X3) )
| sP3(X3,X2,X1,X0) ),
inference(definition_folding,[],[f24,f32]) ).
fof(f32,plain,
! [X3,X2,X1,X0] :
( ( X2 != X3
& ~ r3(X0,X1,X3) )
| ~ sP3(X3,X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
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',axiom_3) ).
fof(f694,plain,
! [X0,X1] : ~ sP3(X0,X1,sK24,X0),
inference(unit_resulting_resolution,[],[f188,f107]) ).
fof(f107,plain,
! [X2,X3,X0,X1] :
( ~ sP3(X0,X1,X2,X3)
| ~ r3(X3,X2,X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( ( X0 != X1
& ~ r3(X3,X2,X0) )
| ~ sP3(X0,X1,X2,X3) ),
inference(rectify,[],[f67]) ).
fof(f67,plain,
! [X3,X2,X1,X0] :
( ( X2 != X3
& ~ r3(X0,X1,X3) )
| ~ sP3(X3,X2,X1,X0) ),
inference(nnf_transformation,[],[f32]) ).
fof(f188,plain,
! [X0] : r3(X0,sK24,X0),
inference(superposition,[],[f133,f170]) ).
fof(f170,plain,
! [X0] : sK12(X0) = sK24,
inference(unit_resulting_resolution,[],[f137,f114]) ).
fof(f114,plain,
! [X1] :
( sP4(X1,sK24)
| sK24 = X1 ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X1] :
( ( sK24 = X1
& r1(X1) )
| sP4(X1,sK24) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f35,f73]) ).
fof(f73,plain,
( ? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| sP4(X1,X0) )
=> ! [X1] :
( ( sK24 = X1
& r1(X1) )
| sP4(X1,sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| sP4(X1,X0) ),
inference(definition_folding,[],[f1,f34]) ).
fof(f34,plain,
! [X1,X0] :
( ( X0 != X1
& ~ r1(X1) )
| ~ sP4(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f1,axiom,
? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| ( X0 != X1
& ~ r1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f137,plain,
! [X0,X1] : ~ sP4(sK12(X0),X1),
inference(unit_resulting_resolution,[],[f84,f111]) ).
fof(f111,plain,
! [X0,X1] :
( ~ sP4(X0,X1)
| ~ r1(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ( X0 != X1
& ~ r1(X0) )
| ~ sP4(X0,X1) ),
inference(rectify,[],[f71]) ).
fof(f71,plain,
! [X1,X0] :
( ( X0 != X1
& ~ r1(X1) )
| ~ sP4(X1,X0) ),
inference(nnf_transformation,[],[f34]) ).
fof(f84,plain,
! [X0] : r1(sK12(X0)),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( sK11(X0) = X0
& r3(X0,sK12(X0),sK11(X0))
& r1(sK12(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f17,f47,f46]) ).
fof(f46,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r3(X0,X2,X1)
& r1(X2) ) )
=> ( sK11(X0) = X0
& ? [X2] :
( r3(X0,X2,sK11(X0))
& r1(X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
! [X0] :
( ? [X2] :
( r3(X0,X2,sK11(X0))
& r1(X2) )
=> ( r3(X0,sK12(X0),sK11(X0))
& r1(sK12(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',axiom_4a) ).
fof(f133,plain,
! [X0] : r3(X0,sK12(X0),X0),
inference(forward_demodulation,[],[f85,f86]) ).
fof(f86,plain,
! [X0] : sK11(X0) = X0,
inference(cnf_transformation,[],[f48]) ).
fof(f85,plain,
! [X0] : r3(X0,sK12(X0),sK11(X0)),
inference(cnf_transformation,[],[f48]) ).
fof(f3529,plain,
! [X0,X1] : sK19(X0,X1) = sK23(X0,X1),
inference(unit_resulting_resolution,[],[f690,f110]) ).
fof(f690,plain,
! [X2,X0,X1] : ~ sP3(sK19(X0,X1),X2,X1,X0),
inference(unit_resulting_resolution,[],[f102,f107]) ).
fof(f102,plain,
! [X0,X1] : r3(X0,X1,sK19(X0,X1)),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( r3(X0,X1,sK19(X0,X1))
& r2(sK19(X0,X1),sK18(X0,X1))
& sK18(X0,X1) = sK20(X0,X1)
& r3(X0,sK21(X0,X1),sK20(X0,X1))
& r2(X1,sK21(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21])],[f22,f61,f60,f59,f58]) ).
fof(f58,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,sK18(X0,X1)) )
& ? [X4] :
( sK18(X0,X1) = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0,X1] :
( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,sK18(X0,X1)) )
=> ( r3(X0,X1,sK19(X0,X1))
& r2(sK19(X0,X1),sK18(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
! [X0,X1] :
( ? [X4] :
( sK18(X0,X1) = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) )
=> ( sK18(X0,X1) = sK20(X0,X1)
& ? [X5] :
( r3(X0,X5,sK20(X0,X1))
& r2(X1,X5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
! [X0,X1] :
( ? [X5] :
( r3(X0,X5,sK20(X0,X1))
& r2(X1,X5) )
=> ( r3(X0,sK21(X0,X1),sK20(X0,X1))
& r2(X1,sK21(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',axiom_1a) ).
fof(f591,plain,
! [X0,X1] : sK18(X0,X1) = sK13(sK19(X0,X1)),
inference(unit_resulting_resolution,[],[f368,f90]) ).
fof(f90,plain,
! [X2,X0] :
( sP1(X2,sK13(X0),X0)
| sK13(X0) = X2 ),
inference(cnf_transformation,[],[f52]) ).
fof(f368,plain,
! [X2,X0,X1] : ~ sP1(sK18(X0,X1),X2,sK19(X0,X1)),
inference(unit_resulting_resolution,[],[f101,f87]) ).
fof(f101,plain,
! [X0,X1] : r2(sK19(X0,X1),sK18(X0,X1)),
inference(cnf_transformation,[],[f62]) ).
fof(f4532,plain,
sK14(sK13(sK24),sK13(sK24)) = sK18(sK13(sK24),sK24),
inference(forward_demodulation,[],[f4515,f3527]) ).
fof(f3527,plain,
! [X0,X1] : sK18(X0,X1) = sK23(X0,sK13(X1)),
inference(unit_resulting_resolution,[],[f696,f110]) ).
fof(f696,plain,
! [X2,X0,X1] : ~ sP3(sK18(X0,X1),X2,sK13(X1),X0),
inference(forward_demodulation,[],[f693,f589]) ).
fof(f589,plain,
! [X0,X1] : sK13(X0) = sK21(X1,X0),
inference(unit_resulting_resolution,[],[f367,f90]) ).
fof(f367,plain,
! [X2,X0,X1] : ~ sP1(sK21(X0,X1),X2,X1),
inference(unit_resulting_resolution,[],[f98,f87]) ).
fof(f98,plain,
! [X0,X1] : r2(X1,sK21(X0,X1)),
inference(cnf_transformation,[],[f62]) ).
fof(f693,plain,
! [X2,X0,X1] : ~ sP3(sK18(X0,X1),X2,sK21(X0,X1),X0),
inference(unit_resulting_resolution,[],[f135,f107]) ).
fof(f135,plain,
! [X0,X1] : r3(X0,sK21(X0,X1),sK18(X0,X1)),
inference(forward_demodulation,[],[f99,f100]) ).
fof(f100,plain,
! [X0,X1] : sK18(X0,X1) = sK20(X0,X1),
inference(cnf_transformation,[],[f62]) ).
fof(f99,plain,
! [X0,X1] : r3(X0,sK21(X0,X1),sK20(X0,X1)),
inference(cnf_transformation,[],[f62]) ).
fof(f4515,plain,
sK14(sK13(sK24),sK13(sK24)) = sK23(sK13(sK24),sK13(sK24)),
inference(superposition,[],[f3526,f4343]) ).
fof(f4343,plain,
sK13(sK24) = sK15(sK13(sK24),sK13(sK24)),
inference(superposition,[],[f4330,f3494]) ).
fof(f3494,plain,
! [X0,X1] : sK15(X0,X1) = sK22(X0,X1),
inference(unit_resulting_resolution,[],[f681,f106]) ).
fof(f106,plain,
! [X3,X0,X1] :
( sP2(X3,sK22(X0,X1),X1,X0)
| sK22(X0,X1) = X3 ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X3] :
( ( sK22(X0,X1) = X3
& r4(X0,X1,X3) )
| sP2(X3,sK22(X0,X1),X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f31,f65]) ).
fof(f65,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( X2 = X3
& r4(X0,X1,X3) )
| sP2(X3,X2,X1,X0) )
=> ! [X3] :
( ( sK22(X0,X1) = X3
& r4(X0,X1,X3) )
| sP2(X3,sK22(X0,X1),X1,X0) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( X2 = X3
& r4(X0,X1,X3) )
| sP2(X3,X2,X1,X0) ),
inference(definition_folding,[],[f23,f30]) ).
fof(f30,plain,
! [X3,X2,X1,X0] :
( ( X2 != X3
& ~ r4(X0,X1,X3) )
| ~ sP2(X3,X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f23,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( X2 = X3
& r4(X0,X1,X3) )
| ( X2 != X3
& ~ r4(X0,X1,X3) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X9,X10] :
? [X11] :
! [X12] :
( ( X11 = X12
& r4(X9,X10,X12) )
| ( X11 != X12
& ~ r4(X9,X10,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f681,plain,
! [X2,X0,X1] : ~ sP2(sK15(X0,X1),X2,X1,X0),
inference(unit_resulting_resolution,[],[f97,f103]) ).
fof(f103,plain,
! [X2,X3,X0,X1] :
( ~ sP2(X0,X1,X2,X3)
| ~ r4(X3,X2,X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( ( X0 != X1
& ~ r4(X3,X2,X0) )
| ~ sP2(X0,X1,X2,X3) ),
inference(rectify,[],[f63]) ).
fof(f63,plain,
! [X3,X2,X1,X0] :
( ( X2 != X3
& ~ r4(X0,X1,X3) )
| ~ sP2(X3,X2,X1,X0) ),
inference(nnf_transformation,[],[f30]) ).
fof(f97,plain,
! [X0,X1] : r4(X0,X1,sK15(X0,X1)),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( r4(X0,X1,sK15(X0,X1))
& r3(sK15(X0,X1),X0,sK14(X0,X1))
& sK14(X0,X1) = sK16(X0,X1)
& r4(X0,sK17(X0,X1),sK16(X0,X1))
& r2(X1,sK17(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17])],[f21,f56,f55,f54,f53]) ).
fof(f53,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,sK14(X0,X1)) )
& ? [X4] :
( sK14(X0,X1) = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X0,X1] :
( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,sK14(X0,X1)) )
=> ( r4(X0,X1,sK15(X0,X1))
& r3(sK15(X0,X1),X0,sK14(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
! [X0,X1] :
( ? [X4] :
( sK14(X0,X1) = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) )
=> ( sK14(X0,X1) = sK16(X0,X1)
& ? [X5] :
( r4(X0,X5,sK16(X0,X1))
& r2(X1,X5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
! [X0,X1] :
( ? [X5] :
( r4(X0,X5,sK16(X0,X1))
& r2(X1,X5) )
=> ( r4(X0,sK17(X0,X1),sK16(X0,X1))
& r2(X1,sK17(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',axiom_2a) ).
fof(f4330,plain,
sK13(sK24) = sK22(sK13(sK24),sK13(sK24)),
inference(unit_resulting_resolution,[],[f3914,f106]) ).
fof(f3914,plain,
! [X0] : ~ sP2(sK13(sK24),X0,sK13(sK24),sK13(sK24)),
inference(superposition,[],[f686,f3863]) ).
fof(f3863,plain,
sK13(sK24) = sK14(sK13(sK24),sK24),
inference(superposition,[],[f3814,f3810]) ).
fof(f3810,plain,
! [X0] : sK14(X0,sK24) = sK23(sK24,X0),
inference(unit_resulting_resolution,[],[f3545,f110]) ).
fof(f3545,plain,
! [X0,X1] : ~ sP3(sK14(X0,sK24),X1,X0,sK24),
inference(superposition,[],[f695,f3511]) ).
fof(f3511,plain,
! [X0] : sK24 = sK15(X0,sK24),
inference(superposition,[],[f3494,f3493]) ).
fof(f3493,plain,
! [X0] : sK24 = sK22(X0,sK24),
inference(unit_resulting_resolution,[],[f685,f106]) ).
fof(f685,plain,
! [X0,X1] : ~ sP2(sK24,X0,sK24,X1),
inference(unit_resulting_resolution,[],[f182,f103]) ).
fof(f182,plain,
! [X0] : r4(X0,sK24,sK24),
inference(forward_demodulation,[],[f178,f169]) ).
fof(f169,plain,
! [X0] : sK10(X0) = sK24,
inference(unit_resulting_resolution,[],[f136,f114]) ).
fof(f136,plain,
! [X0,X1] : ~ sP4(sK10(X0),X1),
inference(unit_resulting_resolution,[],[f80,f111]) ).
fof(f80,plain,
! [X0] : r1(sK10(X0)),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( sK8(X0) = sK9(X0)
& r1(sK9(X0))
& r4(X0,sK10(X0),sK8(X0))
& r1(sK10(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f16,f44,f43,f42]) ).
fof(f42,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( X1 = X2
& r1(X2) )
& ? [X3] :
( r4(X0,X3,X1)
& r1(X3) ) )
=> ( ? [X2] :
( sK8(X0) = X2
& r1(X2) )
& ? [X3] :
( r4(X0,X3,sK8(X0))
& r1(X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
! [X0] :
( ? [X2] :
( sK8(X0) = X2
& r1(X2) )
=> ( sK8(X0) = sK9(X0)
& r1(sK9(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
! [X0] :
( ? [X3] :
( r4(X0,X3,sK8(X0))
& r1(X3) )
=> ( r4(X0,sK10(X0),sK8(X0))
& r1(sK10(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0] :
? [X1] :
( ? [X2] :
( X1 = X2
& r1(X2) )
& ? [X3] :
( r4(X0,X3,X1)
& r1(X3) ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X32] :
? [X33] :
( ? [X35] :
( X33 = X35
& r1(X35) )
& ? [X34] :
( r4(X32,X34,X33)
& r1(X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).
fof(f178,plain,
! [X0] : r4(X0,sK10(X0),sK24),
inference(superposition,[],[f81,f168]) ).
fof(f168,plain,
! [X0] : sK8(X0) = sK24,
inference(unit_resulting_resolution,[],[f138,f114]) ).
fof(f138,plain,
! [X0,X1] : ~ sP4(sK8(X0),X1),
inference(unit_resulting_resolution,[],[f132,f111]) ).
fof(f132,plain,
! [X0] : r1(sK8(X0)),
inference(forward_demodulation,[],[f82,f83]) ).
fof(f83,plain,
! [X0] : sK8(X0) = sK9(X0),
inference(cnf_transformation,[],[f45]) ).
fof(f82,plain,
! [X0] : r1(sK9(X0)),
inference(cnf_transformation,[],[f45]) ).
fof(f81,plain,
! [X0] : r4(X0,sK10(X0),sK8(X0)),
inference(cnf_transformation,[],[f45]) ).
fof(f695,plain,
! [X2,X0,X1] : ~ sP3(sK14(X0,X1),X2,X0,sK15(X0,X1)),
inference(unit_resulting_resolution,[],[f96,f107]) ).
fof(f96,plain,
! [X0,X1] : r3(sK15(X0,X1),X0,sK14(X0,X1)),
inference(cnf_transformation,[],[f57]) ).
fof(f3814,plain,
! [X0] : sK13(X0) = sK23(X0,sK13(sK24)),
inference(unit_resulting_resolution,[],[f3789,f110]) ).
fof(f3789,plain,
! [X0,X1] : ~ sP3(sK13(X0),X1,sK13(sK24),X0),
inference(superposition,[],[f696,f3565]) ).
fof(f686,plain,
! [X2,X0,X1] : ~ sP2(sK14(X0,X1),X2,sK13(X1),X0),
inference(forward_demodulation,[],[f684,f588]) ).
fof(f588,plain,
! [X0,X1] : sK13(X0) = sK17(X1,X0),
inference(unit_resulting_resolution,[],[f366,f90]) ).
fof(f366,plain,
! [X2,X0,X1] : ~ sP1(sK17(X0,X1),X2,X1),
inference(unit_resulting_resolution,[],[f93,f87]) ).
fof(f93,plain,
! [X0,X1] : r2(X1,sK17(X0,X1)),
inference(cnf_transformation,[],[f57]) ).
fof(f684,plain,
! [X2,X0,X1] : ~ sP2(sK14(X0,X1),X2,sK17(X0,X1),X0),
inference(unit_resulting_resolution,[],[f134,f103]) ).
fof(f134,plain,
! [X0,X1] : r4(X0,sK17(X0,X1),sK14(X0,X1)),
inference(forward_demodulation,[],[f94,f95]) ).
fof(f95,plain,
! [X0,X1] : sK14(X0,X1) = sK16(X0,X1),
inference(cnf_transformation,[],[f57]) ).
fof(f94,plain,
! [X0,X1] : r4(X0,sK17(X0,X1),sK16(X0,X1)),
inference(cnf_transformation,[],[f57]) ).
fof(f3526,plain,
! [X0,X1] : sK14(X0,X1) = sK23(sK15(X0,X1),X0),
inference(unit_resulting_resolution,[],[f695,f110]) ).
fof(f2084,plain,
sP1(sK14(sK13(sK24),sK13(sK24)),sK13(sK13(sK24)),sK13(sK24)),
inference(unit_resulting_resolution,[],[f1958,f89]) ).
fof(f1958,plain,
~ r2(sK13(sK24),sK14(sK13(sK24),sK13(sK24))),
inference(unit_resulting_resolution,[],[f405,f1059,f124]) ).
fof(f124,plain,
! [X2,X1] :
( ~ r2(X2,X1)
| ~ sP25(X2)
| sP26(X1) ),
inference(cnf_transformation,[],[f124_D]) ).
fof(f124_D,plain,
! [X1] :
( ! [X2] :
( ~ r2(X2,X1)
| ~ sP25(X2) )
<=> ~ sP26(X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP26])]) ).
fof(f1059,plain,
~ sP26(sK14(sK13(sK24),sK13(sK24))),
inference(unit_resulting_resolution,[],[f415,f442,f134,f131]) ).
fof(f131,plain,
! [X1,X4,X5] :
( ~ r4(X5,X4,X1)
| ~ sP26(X1)
| ~ sP28(X5)
| ~ sP29(X4) ),
inference(general_splitting,[],[f129,f130_D]) ).
fof(f130,plain,
! [X7,X4] :
( ~ r2(X7,X4)
| ~ sP27(X7)
| sP29(X4) ),
inference(cnf_transformation,[],[f130_D]) ).
fof(f130_D,plain,
! [X4] :
( ! [X7] :
( ~ r2(X7,X4)
| ~ sP27(X7) )
<=> ~ sP29(X4) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP29])]) ).
fof(f129,plain,
! [X1,X7,X4,X5] :
( ~ r4(X5,X4,X1)
| ~ r2(X7,X4)
| ~ sP26(X1)
| ~ sP27(X7)
| ~ sP28(X5) ),
inference(general_splitting,[],[f127,f128_D]) ).
fof(f128,plain,
! [X6,X5] :
( ~ r2(X6,X5)
| ~ r1(X6)
| sP28(X5) ),
inference(cnf_transformation,[],[f128_D]) ).
fof(f128_D,plain,
! [X5] :
( ! [X6] :
( ~ r2(X6,X5)
| ~ r1(X6) )
<=> ~ sP28(X5) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP28])]) ).
fof(f127,plain,
! [X1,X6,X7,X4,X5] :
( ~ r2(X6,X5)
| ~ r1(X6)
| ~ r4(X5,X4,X1)
| ~ r2(X7,X4)
| ~ sP26(X1)
| ~ sP27(X7) ),
inference(general_splitting,[],[f125,f126_D]) ).
fof(f126,plain,
! [X8,X7] :
( ~ r2(X8,X7)
| ~ r1(X8)
| sP27(X7) ),
inference(cnf_transformation,[],[f126_D]) ).
fof(f126_D,plain,
! [X7] :
( ! [X8] :
( ~ r2(X8,X7)
| ~ r1(X8) )
<=> ~ sP27(X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP27])]) ).
fof(f125,plain,
! [X1,X8,X6,X7,X4,X5] :
( ~ r2(X6,X5)
| ~ r1(X6)
| ~ r4(X5,X4,X1)
| ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X4)
| ~ sP26(X1) ),
inference(general_splitting,[],[f123,f124_D]) ).
fof(f123,plain,
! [X2,X1,X8,X6,X7,X4,X5] :
( ~ r2(X2,X1)
| ~ r2(X6,X5)
| ~ r1(X6)
| ~ r4(X5,X4,X1)
| ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X4)
| ~ sP25(X2) ),
inference(general_splitting,[],[f115,f122_D]) ).
fof(f122,plain,
! [X2,X3] :
( ~ r2(X3,X2)
| ~ r1(X3)
| sP25(X2) ),
inference(cnf_transformation,[],[f122_D]) ).
fof(f122_D,plain,
! [X2] :
( ! [X3] :
( ~ r2(X3,X2)
| ~ r1(X3) )
<=> ~ sP25(X2) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP25])]) ).
fof(f115,plain,
! [X2,X3,X1,X8,X6,X7,X4,X5] :
( ~ r2(X3,X2)
| ~ r1(X3)
| ~ r2(X2,X1)
| ~ r2(X6,X5)
| ~ r1(X6)
| ~ r4(X5,X4,X1)
| ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X4) ),
inference(equality_resolution,[],[f75]) ).
fof(f75,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( ~ r2(X3,X2)
| ~ r1(X3)
| ~ r2(X2,X1)
| X0 != X1
| ~ r2(X6,X5)
| ~ r1(X6)
| ~ r4(X5,X4,X0)
| ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X4) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ r2(X3,X2)
| ~ r1(X3) )
| ~ r2(X2,X1) )
| X0 != X1 )
| ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ r2(X6,X5)
| ~ r1(X6) )
| ~ r4(X5,X4,X0) )
| ! [X7] :
( ! [X8] :
( ~ r2(X8,X7)
| ~ r1(X8) )
| ~ r2(X7,X4) ) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
~ ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( r2(X3,X2)
& r1(X3) )
& r2(X2,X1) )
& X0 = X1 )
& ? [X4] :
( ? [X5] :
( ? [X6] :
( r2(X6,X5)
& r1(X6) )
& r4(X5,X4,X0) )
& ? [X7] :
( ? [X8] :
( r2(X8,X7)
& r1(X8) )
& r2(X7,X4) ) ) ),
inference(rectify,[],[f13]) ).
fof(f13,negated_conjecture,
~ ? [X38] :
( ? [X22] :
( ? [X24] :
( ? [X30] :
( r2(X30,X24)
& r1(X30) )
& r2(X24,X22) )
& X22 = X38 )
& ? [X21] :
( ? [X16] :
( ? [X33] :
( r2(X33,X16)
& r1(X33) )
& r4(X16,X21,X38) )
& ? [X15] :
( ? [X18] :
( r2(X18,X15)
& r1(X18) )
& r2(X15,X21) ) ) ),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
? [X38] :
( ? [X22] :
( ? [X24] :
( ? [X30] :
( r2(X30,X24)
& r1(X30) )
& r2(X24,X22) )
& X22 = X38 )
& ? [X21] :
( ? [X16] :
( ? [X33] :
( r2(X33,X16)
& r1(X33) )
& r4(X16,X21,X38) )
& ? [X15] :
( ? [X18] :
( r2(X18,X15)
& r1(X18) )
& r2(X15,X21) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',onetimestwoeqtwo) ).
fof(f442,plain,
! [X0] : sP29(sK17(X0,sK13(sK24))),
inference(unit_resulting_resolution,[],[f93,f411,f130]) ).
fof(f411,plain,
sP27(sK13(sK24)),
inference(unit_resulting_resolution,[],[f139,f390,f126]) ).
fof(f139,plain,
r1(sK24),
inference(unit_resulting_resolution,[],[f121,f113]) ).
fof(f113,plain,
! [X1] :
( sP4(X1,sK24)
| r1(X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f121,plain,
! [X1] : ~ sP4(X1,X1),
inference(equality_resolution,[],[f112]) ).
fof(f112,plain,
! [X0,X1] :
( X0 != X1
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f415,plain,
sP28(sK13(sK24)),
inference(unit_resulting_resolution,[],[f139,f390,f128]) ).
fof(f405,plain,
sP25(sK13(sK24)),
inference(unit_resulting_resolution,[],[f139,f390,f122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUN072+2 : TPTP v8.1.2. Released v7.3.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n013.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 : Tue Apr 30 02:23:49 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % (1739)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (1740)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (1746)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.38 % (1742)WARNING: value z3 for option sas not known
% 0.21/0.38 % (1744)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.38 TRYING [1]
% 0.21/0.38 % (1741)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 TRYING [2]
% 0.21/0.38 % (1742)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.38 % (1745)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.38 % (1743)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [2]
% 0.21/0.39 TRYING [3]
% 0.21/0.39 TRYING [3]
% 0.21/0.39 TRYING [4]
% 0.21/0.40 TRYING [5]
% 0.21/0.42 TRYING [4]
% 0.21/0.43 TRYING [6]
% 0.21/0.46 % (1746)First to succeed.
% 0.21/0.47 % (1746)Refutation found. Thanks to Tanya!
% 0.21/0.47 % SZS status Theorem for theBenchmark
% 0.21/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.47 % (1746)------------------------------
% 0.21/0.47 % (1746)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.47 % (1746)Termination reason: Refutation
% 0.21/0.47
% 0.21/0.47 % (1746)Memory used [KB]: 1578
% 0.21/0.47 % (1746)Time elapsed: 0.091 s
% 0.21/0.47 % (1746)Instructions burned: 166 (million)
% 0.21/0.47 % (1746)------------------------------
% 0.21/0.47 % (1746)------------------------------
% 0.21/0.47 % (1739)Success in time 0.113 s
%------------------------------------------------------------------------------