TSTP Solution File: NUN058+2 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUN058+2 : TPTP v8.2.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n011.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 13:30:45 EDT 2024
% Result : Theorem 137.38s 19.22s
% Output : CNFRefutation 137.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 26
% Syntax : Number of formulae : 164 ( 96 unt; 0 def)
% Number of atoms : 496 ( 126 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 519 ( 187 ~; 151 |; 164 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 1 con; 0-2 aty)
% Number of variables : 484 ( 20 sgn 192 !; 117 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| ( X0 != X1
& ~ r1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
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(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(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(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(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(f8,axiom,
! [X29] :
? [X30] :
( X29 = X30
& ? [X31] :
( r3(X29,X31,X30)
& r1(X31) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).
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(f12,conjecture,
? [X38] :
( ? [X22,X16] :
( ? [X18] :
( ? [X30] :
( ? [X39] :
( ? [X28] :
( ? [X17] :
( r2(X17,X28)
& r1(X17) )
& r2(X28,X39) )
& r2(X39,X30) )
& r2(X30,X18) )
& r3(X22,X18,X16) )
& X16 = X38 )
& ? [X21,X15] :
( ? [X33] :
( X33 = X38
& r3(X21,X15,X33) )
& ? [X24] :
( X24 = X38
& ? [X41] :
( ? [X27] :
( ? [X23] :
( r2(X23,X27)
& r1(X23) )
& r2(X27,X41) )
& r4(X41,X21,X24) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',evengreq4) ).
fof(f13,negated_conjecture,
~ ? [X38] :
( ? [X22,X16] :
( ? [X18] :
( ? [X30] :
( ? [X39] :
( ? [X28] :
( ? [X17] :
( r2(X17,X28)
& r1(X17) )
& r2(X28,X39) )
& r2(X39,X30) )
& r2(X30,X18) )
& r3(X22,X18,X16) )
& X16 = X38 )
& ? [X21,X15] :
( ? [X33] :
( X33 = X38
& r3(X21,X15,X33) )
& ? [X24] :
( X24 = X38
& ? [X41] :
( ? [X27] :
( ? [X23] :
( r2(X23,X27)
& r1(X23) )
& r2(X27,X41) )
& r4(X41,X21,X24) ) ) ) ),
inference(negated_conjecture,[],[f12]) ).
fof(f14,plain,
! [X0] :
? [X1] :
! [X2] :
( ( X1 = X2
& r2(X0,X2) )
| ( X1 != X2
& ~ r2(X0,X2) ) ),
inference(rectify,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( X2 = X3
& r3(X0,X1,X3) )
| ( X2 != X3
& ~ r3(X0,X1,X3) ) ),
inference(rectify,[],[f3]) ).
fof(f16,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( X2 = X3
& r4(X0,X1,X3) )
| ( X2 != X3
& ~ r4(X0,X1,X3) ) ),
inference(rectify,[],[f4]) ).
fof(f17,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(f18,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(f20,plain,
! [X0] :
? [X1] :
( X0 = X1
& ? [X2] :
( r3(X0,X2,X1)
& r1(X2) ) ),
inference(rectify,[],[f8]) ).
fof(f21,plain,
! [X0] :
? [X1] :
( ? [X2] :
( X1 = X2
& r1(X2) )
& ? [X3] :
( r4(X0,X3,X1)
& r1(X3) ) ),
inference(rectify,[],[f9]) ).
fof(f24,plain,
~ ? [X0] :
( ? [X1,X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( r2(X7,X6)
& r1(X7) )
& r2(X6,X5) )
& r2(X5,X4) )
& r2(X4,X3) )
& r3(X1,X3,X2) )
& X0 = X2 )
& ? [X8,X9] :
( ? [X10] :
( X0 = X10
& r3(X8,X9,X10) )
& ? [X11] :
( X0 = X11
& ? [X12] :
( ? [X13] :
( ? [X14] :
( r2(X14,X13)
& r1(X14) )
& r2(X13,X12) )
& r4(X12,X8,X11) ) ) ) ),
inference(rectify,[],[f13]) ).
fof(f25,plain,
! [X0] :
( ! [X1,X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ r2(X7,X6)
| ~ r1(X7) )
| ~ r2(X6,X5) )
| ~ r2(X5,X4) )
| ~ r2(X4,X3) )
| ~ r3(X1,X3,X2) )
| X0 != X2 )
| ! [X8,X9] :
( ! [X10] :
( X0 != X10
| ~ r3(X8,X9,X10) )
| ! [X11] :
( X0 != X11
| ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ r2(X14,X13)
| ~ r1(X14) )
| ~ r2(X13,X12) )
| ~ r4(X12,X8,X11) ) ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f26,plain,
( ? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| ( X0 != X1
& ~ r1(X1) ) )
=> ! [X1] :
( ( sK0 = X1
& r1(X1) )
| ( sK0 != X1
& ~ r1(X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X1] :
( ( sK0 = X1
& r1(X1) )
| ( sK0 != X1
& ~ r1(X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f1,f26]) ).
fof(f28,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( X1 = X2
& r2(X0,X2) )
| ( X1 != X2
& ~ r2(X0,X2) ) )
=> ! [X2] :
( ( sK1(X0) = X2
& r2(X0,X2) )
| ( sK1(X0) != X2
& ~ r2(X0,X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X2] :
( ( sK1(X0) = X2
& r2(X0,X2) )
| ( sK1(X0) != X2
& ~ r2(X0,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f14,f28]) ).
fof(f30,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( X2 = X3
& r3(X0,X1,X3) )
| ( X2 != X3
& ~ r3(X0,X1,X3) ) )
=> ! [X3] :
( ( sK2(X0,X1) = X3
& r3(X0,X1,X3) )
| ( sK2(X0,X1) != X3
& ~ r3(X0,X1,X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X1,X3] :
( ( sK2(X0,X1) = X3
& r3(X0,X1,X3) )
| ( sK2(X0,X1) != X3
& ~ r3(X0,X1,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f15,f30]) ).
fof(f32,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( X2 = X3
& r4(X0,X1,X3) )
| ( X2 != X3
& ~ r4(X0,X1,X3) ) )
=> ! [X3] :
( ( sK3(X0,X1) = X3
& r4(X0,X1,X3) )
| ( sK3(X0,X1) != X3
& ~ r4(X0,X1,X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0,X1,X3] :
( ( sK3(X0,X1) = X3
& r4(X0,X1,X3) )
| ( sK3(X0,X1) != X3
& ~ r4(X0,X1,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f16,f32]) ).
fof(f34,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,sK4(X0,X1)) )
& ? [X4] :
( sK4(X0,X1) = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
! [X0,X1] :
( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,sK4(X0,X1)) )
=> ( r3(X0,X1,sK5(X0,X1))
& r2(sK5(X0,X1),sK4(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
! [X0,X1] :
( ? [X4] :
( sK4(X0,X1) = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) )
=> ( sK4(X0,X1) = sK6(X0,X1)
& ? [X5] :
( r3(X0,X5,sK6(X0,X1))
& r2(X1,X5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
! [X0,X1] :
( ? [X5] :
( r3(X0,X5,sK6(X0,X1))
& r2(X1,X5) )
=> ( r3(X0,sK7(X0,X1),sK6(X0,X1))
& r2(X1,sK7(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
! [X0,X1] :
( r3(X0,X1,sK5(X0,X1))
& r2(sK5(X0,X1),sK4(X0,X1))
& sK4(X0,X1) = sK6(X0,X1)
& r3(X0,sK7(X0,X1),sK6(X0,X1))
& r2(X1,sK7(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f17,f37,f36,f35,f34]) ).
fof(f39,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,sK8(X0,X1)) )
& ? [X4] :
( sK8(X0,X1) = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
! [X0,X1] :
( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,sK8(X0,X1)) )
=> ( r4(X0,X1,sK9(X0,X1))
& r3(sK9(X0,X1),X0,sK8(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f41,plain,
! [X0,X1] :
( ? [X4] :
( sK8(X0,X1) = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) )
=> ( sK8(X0,X1) = sK10(X0,X1)
& ? [X5] :
( r4(X0,X5,sK10(X0,X1))
& r2(X1,X5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
! [X0,X1] :
( ? [X5] :
( r4(X0,X5,sK10(X0,X1))
& r2(X1,X5) )
=> ( r4(X0,sK11(X0,X1),sK10(X0,X1))
& r2(X1,sK11(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
! [X0,X1] :
( r4(X0,X1,sK9(X0,X1))
& r3(sK9(X0,X1),X0,sK8(X0,X1))
& sK8(X0,X1) = sK10(X0,X1)
& r4(X0,sK11(X0,X1),sK10(X0,X1))
& r2(X1,sK11(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f18,f42,f41,f40,f39]) ).
fof(f44,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r3(X0,X2,X1)
& r1(X2) ) )
=> ( sK12(X0) = X0
& ? [X2] :
( r3(X0,X2,sK12(X0))
& r1(X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
! [X0] :
( ? [X2] :
( r3(X0,X2,sK12(X0))
& r1(X2) )
=> ( r3(X0,sK13(X0),sK12(X0))
& r1(sK13(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X0] :
( sK12(X0) = X0
& r3(X0,sK13(X0),sK12(X0))
& r1(sK13(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f20,f45,f44]) ).
fof(f47,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( X1 = X2
& r1(X2) )
& ? [X3] :
( r4(X0,X3,X1)
& r1(X3) ) )
=> ( ? [X2] :
( sK14(X0) = X2
& r1(X2) )
& ? [X3] :
( r4(X0,X3,sK14(X0))
& r1(X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
! [X0] :
( ? [X2] :
( sK14(X0) = X2
& r1(X2) )
=> ( sK14(X0) = sK15(X0)
& r1(sK15(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
! [X0] :
( ? [X3] :
( r4(X0,X3,sK14(X0))
& r1(X3) )
=> ( r4(X0,sK16(X0),sK14(X0))
& r1(sK16(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
! [X0] :
( sK14(X0) = sK15(X0)
& r1(sK15(X0))
& r4(X0,sK16(X0),sK14(X0))
& r1(sK16(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f21,f49,f48,f47]) ).
fof(f55,plain,
! [X1] :
( r1(X1)
| sK0 != X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f56,plain,
! [X1] :
( sK0 = X1
| ~ r1(X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f59,plain,
! [X2,X0] :
( r2(X0,X2)
| sK1(X0) != X2 ),
inference(cnf_transformation,[],[f29]) ).
fof(f60,plain,
! [X2,X0] :
( sK1(X0) = X2
| ~ r2(X0,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f64,plain,
! [X3,X0,X1] :
( sK2(X0,X1) = X3
| ~ r3(X0,X1,X3) ),
inference(cnf_transformation,[],[f31]) ).
fof(f68,plain,
! [X3,X0,X1] :
( sK3(X0,X1) = X3
| ~ r4(X0,X1,X3) ),
inference(cnf_transformation,[],[f33]) ).
fof(f70,plain,
! [X0,X1] : r2(X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f38]) ).
fof(f71,plain,
! [X0,X1] : r3(X0,sK7(X0,X1),sK6(X0,X1)),
inference(cnf_transformation,[],[f38]) ).
fof(f72,plain,
! [X0,X1] : sK4(X0,X1) = sK6(X0,X1),
inference(cnf_transformation,[],[f38]) ).
fof(f73,plain,
! [X0,X1] : r2(sK5(X0,X1),sK4(X0,X1)),
inference(cnf_transformation,[],[f38]) ).
fof(f74,plain,
! [X0,X1] : r3(X0,X1,sK5(X0,X1)),
inference(cnf_transformation,[],[f38]) ).
fof(f75,plain,
! [X0,X1] : r2(X1,sK11(X0,X1)),
inference(cnf_transformation,[],[f43]) ).
fof(f76,plain,
! [X0,X1] : r4(X0,sK11(X0,X1),sK10(X0,X1)),
inference(cnf_transformation,[],[f43]) ).
fof(f77,plain,
! [X0,X1] : sK8(X0,X1) = sK10(X0,X1),
inference(cnf_transformation,[],[f43]) ).
fof(f78,plain,
! [X0,X1] : r3(sK9(X0,X1),X0,sK8(X0,X1)),
inference(cnf_transformation,[],[f43]) ).
fof(f79,plain,
! [X0,X1] : r4(X0,X1,sK9(X0,X1)),
inference(cnf_transformation,[],[f43]) ).
fof(f81,plain,
! [X0] : r1(sK13(X0)),
inference(cnf_transformation,[],[f46]) ).
fof(f82,plain,
! [X0] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f46]) ).
fof(f83,plain,
! [X0] : sK12(X0) = X0,
inference(cnf_transformation,[],[f46]) ).
fof(f84,plain,
! [X0] : r1(sK16(X0)),
inference(cnf_transformation,[],[f50]) ).
fof(f85,plain,
! [X0] : r4(X0,sK16(X0),sK14(X0)),
inference(cnf_transformation,[],[f50]) ).
fof(f86,plain,
! [X0] : r1(sK15(X0)),
inference(cnf_transformation,[],[f50]) ).
fof(f87,plain,
! [X0] : sK14(X0) = sK15(X0),
inference(cnf_transformation,[],[f50]) ).
fof(f93,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X14,X4,X5,X12,X13] :
( ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r3(X1,X3,X2)
| X0 != X2
| X0 != X10
| ~ r3(X8,X9,X10)
| X0 != X11
| ~ r2(X14,X13)
| ~ r1(X14)
| ~ r2(X13,X12)
| ~ r4(X12,X8,X11) ),
inference(cnf_transformation,[],[f25]) ).
fof(f94,plain,
! [X0,X1] : r2(sK5(X0,X1),sK6(X0,X1)),
inference(definition_unfolding,[],[f73,f72]) ).
fof(f95,plain,
! [X0,X1] : r3(sK9(X0,X1),X0,sK10(X0,X1)),
inference(definition_unfolding,[],[f78,f77]) ).
fof(f96,plain,
! [X0] : r4(X0,sK16(X0),sK15(X0)),
inference(definition_unfolding,[],[f85,f87]) ).
fof(f98,plain,
r1(sK0),
inference(equality_resolution,[],[f55]) ).
fof(f100,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f59]) ).
fof(f107,plain,
! [X2,X3,X10,X11,X1,X8,X6,X9,X7,X14,X4,X5,X12,X13] :
( ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r3(X1,X3,X2)
| X2 != X10
| ~ r3(X8,X9,X10)
| X2 != X11
| ~ r2(X14,X13)
| ~ r1(X14)
| ~ r2(X13,X12)
| ~ r4(X12,X8,X11) ),
inference(equality_resolution,[],[f93]) ).
fof(f108,plain,
! [X3,X10,X11,X1,X8,X6,X9,X7,X14,X4,X5,X12,X13] :
( ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r3(X1,X3,X10)
| ~ r3(X8,X9,X10)
| X10 != X11
| ~ r2(X14,X13)
| ~ r1(X14)
| ~ r2(X13,X12)
| ~ r4(X12,X8,X11) ),
inference(equality_resolution,[],[f107]) ).
fof(f109,plain,
! [X3,X11,X1,X8,X6,X9,X7,X14,X4,X5,X12,X13] :
( ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r3(X1,X3,X11)
| ~ r3(X8,X9,X11)
| ~ r2(X14,X13)
| ~ r1(X14)
| ~ r2(X13,X12)
| ~ r4(X12,X8,X11) ),
inference(equality_resolution,[],[f108]) ).
cnf(c_49,plain,
( ~ r1(X0)
| X0 = sK0 ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_50,plain,
r1(sK0),
inference(cnf_transformation,[],[f98]) ).
cnf(c_51,plain,
( ~ r2(X0,X1)
| sK1(X0) = X1 ),
inference(cnf_transformation,[],[f60]) ).
cnf(c_52,plain,
r2(X0,sK1(X0)),
inference(cnf_transformation,[],[f100]) ).
cnf(c_53,plain,
( ~ r3(X0,X1,X2)
| sK2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f64]) ).
cnf(c_55,plain,
( ~ r4(X0,X1,X2)
| sK3(X0,X1) = X2 ),
inference(cnf_transformation,[],[f68]) ).
cnf(c_57,plain,
r3(X0,X1,sK5(X0,X1)),
inference(cnf_transformation,[],[f74]) ).
cnf(c_58,plain,
r2(sK5(X0,X1),sK6(X0,X1)),
inference(cnf_transformation,[],[f94]) ).
cnf(c_59,plain,
r3(X0,sK7(X0,X1),sK6(X0,X1)),
inference(cnf_transformation,[],[f71]) ).
cnf(c_60,plain,
r2(X0,sK7(X1,X0)),
inference(cnf_transformation,[],[f70]) ).
cnf(c_61,plain,
r4(X0,X1,sK9(X0,X1)),
inference(cnf_transformation,[],[f79]) ).
cnf(c_62,plain,
r3(sK9(X0,X1),X0,sK10(X0,X1)),
inference(cnf_transformation,[],[f95]) ).
cnf(c_63,plain,
r4(X0,sK11(X0,X1),sK10(X0,X1)),
inference(cnf_transformation,[],[f76]) ).
cnf(c_64,plain,
r2(X0,sK11(X1,X0)),
inference(cnf_transformation,[],[f75]) ).
cnf(c_66,plain,
sK12(X0) = X0,
inference(cnf_transformation,[],[f83]) ).
cnf(c_67,plain,
r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f82]) ).
cnf(c_68,plain,
r1(sK13(X0)),
inference(cnf_transformation,[],[f81]) ).
cnf(c_69,plain,
r1(sK15(X0)),
inference(cnf_transformation,[],[f86]) ).
cnf(c_70,plain,
r4(X0,sK16(X0),sK15(X0)),
inference(cnf_transformation,[],[f96]) ).
cnf(c_71,plain,
r1(sK16(X0)),
inference(cnf_transformation,[],[f84]) ).
cnf(c_77,negated_conjecture,
( ~ r3(X0,X1,X2)
| ~ r3(X3,X4,X2)
| ~ r4(X5,X3,X2)
| ~ r2(X6,X7)
| ~ r2(X7,X8)
| ~ r2(X8,X9)
| ~ r2(X9,X1)
| ~ r2(X10,X11)
| ~ r2(X11,X5)
| ~ r1(X6)
| ~ r1(X10) ),
inference(cnf_transformation,[],[f109]) ).
cnf(c_81,plain,
r2(sK0,sK1(sK0)),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_205,plain,
r3(X0,sK13(X0),X0),
inference(light_normalisation,[status(thm)],[c_67,c_66]) ).
cnf(c_467,negated_conjecture,
( ~ r3(X0,X1,X2)
| ~ r3(X3,X4,X2)
| ~ r4(X5,X3,X2)
| ~ r2(X6,X7)
| ~ r2(X7,X8)
| ~ r2(X8,X9)
| ~ r2(X9,X1)
| ~ r2(X10,X11)
| ~ r2(X11,X5)
| ~ r1(X6)
| ~ r1(X10) ),
inference(demodulation,[status(thm)],[c_77]) ).
cnf(c_810,plain,
sK13(X0) = sK0,
inference(superposition,[status(thm)],[c_68,c_49]) ).
cnf(c_811,plain,
sK15(X0) = sK0,
inference(superposition,[status(thm)],[c_69,c_49]) ).
cnf(c_812,plain,
sK16(X0) = sK0,
inference(superposition,[status(thm)],[c_71,c_49]) ).
cnf(c_813,plain,
r3(X0,sK0,X0),
inference(demodulation,[status(thm)],[c_205,c_810]) ).
cnf(c_815,plain,
r4(X0,sK16(X0),sK0),
inference(demodulation,[status(thm)],[c_70,c_811]) ).
cnf(c_1321,plain,
sK7(X0,X1) = sK1(X1),
inference(superposition,[status(thm)],[c_60,c_51]) ).
cnf(c_1322,plain,
sK11(X0,X1) = sK1(X1),
inference(superposition,[status(thm)],[c_64,c_51]) ).
cnf(c_1326,plain,
r3(X0,sK1(X1),sK6(X0,X1)),
inference(demodulation,[status(thm)],[c_59,c_1321]) ).
cnf(c_1339,plain,
r4(X0,sK1(X1),sK10(X0,X1)),
inference(demodulation,[status(thm)],[c_63,c_1322]) ).
cnf(c_1348,plain,
r4(X0,sK0,sK0),
inference(light_normalisation,[status(thm)],[c_815,c_812]) ).
cnf(c_1605,plain,
sK2(X0,X1) = sK5(X0,X1),
inference(superposition,[status(thm)],[c_57,c_53]) ).
cnf(c_1607,plain,
sK2(X0,sK0) = X0,
inference(superposition,[status(thm)],[c_813,c_53]) ).
cnf(c_1610,plain,
r2(sK2(X0,X1),sK6(X0,X1)),
inference(demodulation,[status(thm)],[c_58,c_1605]) ).
cnf(c_1637,plain,
sK3(X0,X1) = sK9(X0,X1),
inference(superposition,[status(thm)],[c_61,c_55]) ).
cnf(c_1638,plain,
sK3(X0,sK0) = sK0,
inference(superposition,[status(thm)],[c_1348,c_55]) ).
cnf(c_1639,plain,
r3(sK3(X0,X1),X0,sK10(X0,X1)),
inference(demodulation,[status(thm)],[c_62,c_1637]) ).
cnf(c_1796,plain,
r2(X0,sK6(X0,sK0)),
inference(superposition,[status(thm)],[c_1607,c_1610]) ).
cnf(c_1798,plain,
sK1(sK2(X0,X1)) = sK6(X0,X1),
inference(superposition,[status(thm)],[c_1610,c_51]) ).
cnf(c_1831,plain,
sK2(X0,sK1(X1)) = sK6(X0,X1),
inference(superposition,[status(thm)],[c_1326,c_53]) ).
cnf(c_1835,plain,
sK3(X0,sK1(X1)) = sK10(X0,X1),
inference(superposition,[status(thm)],[c_1339,c_55]) ).
cnf(c_1860,plain,
sK6(X0,sK0) = sK1(X0),
inference(superposition,[status(thm)],[c_1796,c_51]) ).
cnf(c_2103,plain,
r3(sK0,X0,sK10(X0,sK0)),
inference(superposition,[status(thm)],[c_1638,c_1639]) ).
cnf(c_2104,plain,
sK2(sK3(X0,X1),X0) = sK10(X0,X1),
inference(superposition,[status(thm)],[c_1639,c_53]) ).
cnf(c_2109,plain,
sK2(sK0,X0) = sK10(X0,sK0),
inference(superposition,[status(thm)],[c_2103,c_53]) ).
cnf(c_2321,plain,
sK1(sK6(X0,X1)) = sK6(X0,sK1(X1)),
inference(superposition,[status(thm)],[c_1831,c_1798]) ).
cnf(c_3258,plain,
sK6(sK3(sK1(X0),X1),X0) = sK10(sK1(X0),X1),
inference(superposition,[status(thm)],[c_2104,c_1831]) ).
cnf(c_5170,plain,
sK2(X0,X1) = sK5(X0,X1),
inference(superposition,[status(thm)],[c_57,c_53]) ).
cnf(c_33688,plain,
r2(sK2(sK3(sK1(X0),X1),X0),sK10(sK1(X0),X1)),
inference(superposition,[status(thm)],[c_3258,c_1610]) ).
cnf(c_34477,plain,
r2(sK2(sK10(sK1(X0),X1),X0),sK10(sK1(X0),sK1(X1))),
inference(superposition,[status(thm)],[c_1835,c_33688]) ).
cnf(c_60967,plain,
r2(sK2(sK2(sK0,sK1(X0)),X0),sK10(sK1(X0),sK1(sK0))),
inference(superposition,[status(thm)],[c_2109,c_34477]) ).
cnf(c_69334,plain,
r2(sK2(sK6(sK0,X0),X0),sK10(sK1(X0),sK1(sK0))),
inference(demodulation,[status(thm)],[c_60967,c_1831]) ).
cnf(c_69336,plain,
r2(sK6(sK6(sK0,sK1(X0)),X0),sK10(sK1(sK1(X0)),sK1(sK0))),
inference(superposition,[status(thm)],[c_1831,c_69334]) ).
cnf(c_164628,plain,
r2(sK6(sK1(sK6(sK0,X0)),X0),sK10(sK1(sK1(X0)),sK1(sK0))),
inference(demodulation,[status(thm)],[c_69336,c_2321]) ).
cnf(c_164656,plain,
sK1(sK6(sK1(sK6(sK0,X0)),X0)) = sK10(sK1(sK1(X0)),sK1(sK0)),
inference(superposition,[status(thm)],[c_164628,c_51]) ).
cnf(c_172876,plain,
sK1(sK1(sK1(sK6(sK0,sK0)))) = sK10(sK1(sK1(sK0)),sK1(sK0)),
inference(superposition,[status(thm)],[c_1860,c_164656]) ).
cnf(c_243885,plain,
sK13(X0) = sK0,
inference(superposition,[status(thm)],[c_68,c_49]) ).
cnf(c_243888,plain,
r3(X0,sK0,X0),
inference(demodulation,[status(thm)],[c_205,c_243885]) ).
cnf(c_244067,plain,
r2(sK2(X0,X1),sK6(X0,X1)),
inference(light_normalisation,[status(thm)],[c_58,c_5170]) ).
cnf(c_244325,plain,
sK7(X0,X1) = sK1(X1),
inference(superposition,[status(thm)],[c_60,c_51]) ).
cnf(c_244326,plain,
sK11(X0,X1) = sK1(X1),
inference(superposition,[status(thm)],[c_64,c_51]) ).
cnf(c_244328,plain,
sK1(sK2(X0,X1)) = sK6(X0,X1),
inference(superposition,[status(thm)],[c_244067,c_51]) ).
cnf(c_244332,plain,
r3(X0,sK1(X1),sK6(X0,X1)),
inference(demodulation,[status(thm)],[c_59,c_244325]) ).
cnf(c_244365,plain,
r4(X0,sK1(X1),sK10(X0,X1)),
inference(demodulation,[status(thm)],[c_63,c_244326]) ).
cnf(c_244592,plain,
sK2(X0,sK0) = X0,
inference(superposition,[status(thm)],[c_243888,c_53]) ).
cnf(c_244612,plain,
r2(X0,sK6(X0,sK0)),
inference(superposition,[status(thm)],[c_244592,c_244067]) ).
cnf(c_244628,plain,
sK6(X0,sK0) = sK1(X0),
inference(superposition,[status(thm)],[c_244612,c_51]) ).
cnf(c_244661,plain,
sK2(X0,sK1(X1)) = sK6(X0,X1),
inference(superposition,[status(thm)],[c_244332,c_53]) ).
cnf(c_245261,plain,
sK1(sK6(X0,X1)) = sK6(X0,sK1(X1)),
inference(superposition,[status(thm)],[c_244661,c_244328]) ).
cnf(c_249068,plain,
r3(X0,sK1(sK1(X1)),sK1(sK6(X0,X1))),
inference(superposition,[status(thm)],[c_245261,c_244332]) ).
cnf(c_249327,plain,
r3(X0,sK1(sK1(sK0)),sK1(sK1(X0))),
inference(superposition,[status(thm)],[c_244628,c_249068]) ).
cnf(c_249328,plain,
r3(X0,sK1(sK1(sK1(X1))),sK1(sK1(sK6(X0,X1)))),
inference(superposition,[status(thm)],[c_245261,c_249068]) ).
cnf(c_255662,plain,
r3(X0,sK1(sK1(sK1(sK1(X1)))),sK1(sK1(sK1(sK6(X0,X1))))),
inference(superposition,[status(thm)],[c_245261,c_249328]) ).
cnf(c_340536,plain,
r3(X0,sK1(sK1(sK1(sK1(sK0)))),sK1(sK1(sK1(sK1(X0))))),
inference(superposition,[status(thm)],[c_244628,c_255662]) ).
cnf(c_340656,plain,
( ~ r3(X0,X1,sK1(sK1(sK1(sK1(X2)))))
| ~ r4(X3,X0,sK1(sK1(sK1(sK1(X2)))))
| ~ r2(X4,sK1(sK1(sK1(sK1(sK0)))))
| ~ r2(X5,X6)
| ~ r2(X6,X7)
| ~ r2(X7,X4)
| ~ r2(X8,X9)
| ~ r2(X9,X3)
| ~ r1(X5)
| ~ r1(X8) ),
inference(superposition,[status(thm)],[c_340536,c_467]) ).
cnf(c_341292,plain,
( ~ r4(X0,sK1(sK1(X1)),sK1(sK1(sK1(sK1(X1)))))
| ~ r2(X2,sK1(sK1(sK1(sK1(sK0)))))
| ~ r2(X3,X4)
| ~ r2(X4,X5)
| ~ r2(X5,X2)
| ~ r2(X6,X7)
| ~ r2(X7,X0)
| ~ r1(X3)
| ~ r1(X6) ),
inference(superposition,[status(thm)],[c_249327,c_340656]) ).
cnf(c_423309,plain,
sK10(sK1(sK1(sK0)),sK1(sK0)) = sK1(sK1(sK1(sK1(sK0)))),
inference(demodulation,[status(thm)],[c_172876,c_244628]) ).
cnf(c_423318,plain,
r4(sK1(sK1(sK0)),sK1(sK1(sK0)),sK1(sK1(sK1(sK1(sK0))))),
inference(superposition,[status(thm)],[c_423309,c_244365]) ).
cnf(c_426319,plain,
( ~ r2(X0,sK1(sK1(sK1(sK1(sK0)))))
| ~ r2(X1,sK1(sK1(sK0)))
| ~ r2(X2,X3)
| ~ r2(X3,X4)
| ~ r2(X4,X0)
| ~ r2(X5,X1)
| ~ r1(X2)
| ~ r1(X5) ),
inference(superposition,[status(thm)],[c_423318,c_341292]) ).
cnf(c_431645,plain,
( ~ r2(X0,sK1(sK1(sK1(sK0))))
| ~ r2(X1,sK1(sK1(sK0)))
| ~ r2(X2,X3)
| ~ r2(X3,X0)
| ~ r2(X4,X1)
| ~ r1(X2)
| ~ r1(X4) ),
inference(superposition,[status(thm)],[c_52,c_426319]) ).
cnf(c_432629,plain,
( ~ r2(X0,sK1(sK1(sK0)))
| ~ r2(X1,sK1(sK1(sK0)))
| ~ r2(X2,X1)
| ~ r2(X3,X0)
| ~ r1(X2)
| ~ r1(X3) ),
inference(superposition,[status(thm)],[c_52,c_431645]) ).
cnf(c_432683,plain,
( ~ r2(X0,sK1(sK1(sK0)))
| ~ r2(X1,sK1(sK0))
| ~ r2(X2,X0)
| ~ r1(X1)
| ~ r1(X2) ),
inference(superposition,[status(thm)],[c_52,c_432629]) ).
cnf(c_432730,plain,
( ~ r2(X0,sK1(sK0))
| ~ r2(X1,sK1(sK0))
| ~ r1(X0)
| ~ r1(X1) ),
inference(superposition,[status(thm)],[c_52,c_432683]) ).
cnf(c_432762,plain,
( ~ r2(sK0,sK1(sK0))
| ~ r1(sK0) ),
inference(instantiation,[status(thm)],[c_432730]) ).
cnf(c_432763,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_432762,c_81,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : NUN058+2 : TPTP v8.2.0. Released v7.3.0.
% 0.05/0.13 % Command : run_iprover %s %d THM
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Jun 18 20:43:54 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.19/0.44 Running first-order theorem proving
% 0.19/0.44 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 137.38/19.22 % SZS status Started for theBenchmark.p
% 137.38/19.22 % SZS status Theorem for theBenchmark.p
% 137.38/19.22
% 137.38/19.22 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 137.38/19.22
% 137.38/19.22 ------ iProver source info
% 137.38/19.22
% 137.38/19.22 git: date: 2024-06-12 09:56:46 +0000
% 137.38/19.22 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 137.38/19.22 git: non_committed_changes: false
% 137.38/19.22
% 137.38/19.22 ------ Parsing...
% 137.38/19.22 ------ Clausification by vclausify_rel & Parsing by iProver...
% 137.38/19.22
% 137.38/19.22 ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e
% 137.38/19.22
% 137.38/19.22 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 137.38/19.22
% 137.38/19.22 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 137.38/19.22 ------ Proving...
% 137.38/19.22 ------ Problem Properties
% 137.38/19.22
% 137.38/19.22
% 137.38/19.22 clauses 29
% 137.38/19.22 conjectures 1
% 137.38/19.22 EPR 5
% 137.38/19.22 Horn 25
% 137.38/19.22 unary 18
% 137.38/19.22 binary 9
% 137.38/19.22 lits 50
% 137.38/19.22 lits eq 10
% 137.38/19.22 fd_pure 0
% 137.38/19.22 fd_pseudo 0
% 137.38/19.22 fd_cond 1
% 137.38/19.22 fd_pseudo_cond 4
% 137.38/19.22 AC symbols 0
% 137.38/19.22
% 137.38/19.22 ------ Schedule dynamic 5 is on
% 137.38/19.22
% 137.38/19.22 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 137.38/19.22
% 137.38/19.22
% 137.38/19.22 ------
% 137.38/19.22 Current options:
% 137.38/19.22 ------
% 137.38/19.22
% 137.38/19.22
% 137.38/19.22
% 137.38/19.22
% 137.38/19.22 ------ Proving...
% 137.38/19.22 Proof_search_loop: time out after: 5150 full_loop iterations
% 137.38/19.22
% 137.38/19.22 ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 137.38/19.22
% 137.38/19.22
% 137.38/19.22 ------
% 137.38/19.22 Current options:
% 137.38/19.22 ------
% 137.38/19.22
% 137.38/19.22
% 137.38/19.22
% 137.38/19.22
% 137.38/19.22 ------ Proving...
% 137.38/19.22
% 137.38/19.22
% 137.38/19.22 % SZS status Theorem for theBenchmark.p
% 137.38/19.22
% 137.38/19.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 137.38/19.22
% 137.38/19.23
%------------------------------------------------------------------------------