TSTP Solution File: NUN068+2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUN068+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n009.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 20:36:20 EDT 2024
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 77 ( 9 unt; 0 def)
% Number of atoms : 190 ( 86 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 176 ( 63 ~; 85 |; 25 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 139 ( 126 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [Y24] :
! [X19] :
( ( ~ r1(X19)
& X19 != Y24 )
| ( r1(X19)
& X19 = Y24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ r2(X11,X12)
& X12 != Y21 )
| ( r2(X11,X12)
& X12 = Y21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X3,X10] :
( ! [Y12] :
( ! [Y13] :
( ~ r2(X3,Y13)
| Y13 != Y12 )
| ~ r2(X10,Y12) )
| X3 = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X7,Y10] :
( ! [Y20] :
( ~ r1(Y20)
| Y20 != Y10 )
| ~ r2(X7,Y10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
? [Y1] :
( ! [Y2] :
( ! [Y3] :
( ~ r1(Y3)
| ~ r2(Y3,Y2) )
| Y1 != Y2 )
& ! [Y4] :
( ~ r1(Y4)
| Y1 != Y4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ? [Y1] :
( ! [Y2] :
( ! [Y3] :
( ~ r1(Y3)
| ~ r2(Y3,Y2) )
| Y1 != Y2 )
& ! [Y4] :
( ~ r1(Y4)
| Y1 != Y4 ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [Y24,X19] :
( pd0_0(X19,Y24)
=> ( ~ r1(X19)
& X19 != Y24 ) ),
introduced(predicate_definition,[f1]) ).
fof(f15,plain,
? [Y24] :
! [X19] :
( pd0_0(X19,Y24)
| ( r1(X19)
& X19 = Y24 ) ),
inference(formula_renaming,[status(thm)],[f1,f14]) ).
fof(f16,plain,
! [X19] :
( pd0_0(X19,sk0_0)
| ( r1(X19)
& X19 = sk0_0 ) ),
inference(skolemization,[status(esa)],[f15]) ).
fof(f17,plain,
! [X0] :
( pd0_0(X0,sk0_0)
| r1(X0) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f18,plain,
! [X0] :
( pd0_0(X0,sk0_0)
| X0 = sk0_0 ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f19,plain,
! [X11,Y21,X12] :
( pd0_1(X12,Y21,X11)
=> ( ~ r2(X11,X12)
& X12 != Y21 ) ),
introduced(predicate_definition,[f2]) ).
fof(f20,plain,
! [X11] :
? [Y21] :
! [X12] :
( pd0_1(X12,Y21,X11)
| ( r2(X11,X12)
& X12 = Y21 ) ),
inference(formula_renaming,[status(thm)],[f2,f19]) ).
fof(f21,plain,
! [X11,X12] :
( pd0_1(X12,sk0_1(X11),X11)
| ( r2(X11,X12)
& X12 = sk0_1(X11) ) ),
inference(skolemization,[status(esa)],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( pd0_1(X0,sk0_1(X1),X1)
| r2(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( ~ r2(X0,X1)
| X1 != X2
| ~ r2(X3,X2)
| X0 = X3 ),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f62,plain,
! [Y10] :
( ! [Y20] :
( ~ r1(Y20)
| Y20 != Y10 )
| ! [X7] : ~ r2(X7,Y10) ),
inference(miniscoping,[status(esa)],[f11]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ r1(X0)
| X0 != X1
| ~ r2(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f64,plain,
! [Y1] :
( ? [Y2] :
( ? [Y3] :
( r1(Y3)
& r2(Y3,Y2) )
& Y1 = Y2 )
| ? [Y4] :
( r1(Y4)
& Y1 = Y4 ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f65,plain,
! [Y1,Y2] :
( pd0_5(Y2,Y1)
=> ( ? [Y3] :
( r1(Y3)
& r2(Y3,Y2) )
& Y1 = Y2 ) ),
introduced(predicate_definition,[f64]) ).
fof(f66,plain,
! [Y1] :
( ? [Y2] : pd0_5(Y2,Y1)
| ? [Y4] :
( r1(Y4)
& Y1 = Y4 ) ),
inference(formula_renaming,[status(thm)],[f64,f65]) ).
fof(f67,plain,
! [Y1] :
( pd0_5(sk0_20(Y1),Y1)
| ( r1(sk0_21(Y1))
& Y1 = sk0_21(Y1) ) ),
inference(skolemization,[status(esa)],[f66]) ).
fof(f68,plain,
! [X0] :
( pd0_5(sk0_20(X0),X0)
| r1(sk0_21(X0)) ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f69,plain,
! [X0] :
( pd0_5(sk0_20(X0),X0)
| X0 = sk0_21(X0) ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f70,plain,
! [Y24,X19] :
( ~ pd0_0(X19,Y24)
| ( ~ r1(X19)
& X19 != Y24 ) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f71,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| ~ r1(X0) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f73,plain,
! [X11,Y21,X12] :
( ~ pd0_1(X12,Y21,X11)
| ( ~ r2(X11,X12)
& X12 != Y21 ) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ pd0_1(X0,X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f73]) ).
fof(f85,plain,
! [Y1,Y2] :
( ~ pd0_5(Y2,Y1)
| ( ? [Y3] :
( r1(Y3)
& r2(Y3,Y2) )
& Y1 = Y2 ) ),
inference(pre_NNF_transformation,[status(esa)],[f65]) ).
fof(f86,plain,
! [Y1,Y2] :
( ~ pd0_5(Y2,Y1)
| ( r1(sk0_22(Y2,Y1))
& r2(sk0_22(Y2,Y1),Y2)
& Y1 = Y2 ) ),
inference(skolemization,[status(esa)],[f85]) ).
fof(f87,plain,
! [X0,X1] :
( ~ pd0_5(X0,X1)
| r1(sk0_22(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( ~ pd0_5(X0,X1)
| r2(sk0_22(X0,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f86]) ).
fof(f89,plain,
! [X0,X1] :
( ~ pd0_5(X0,X1)
| X1 = X0 ),
inference(cnf_transformation,[status(esa)],[f86]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ r2(X0,X1)
| ~ r2(X2,X1)
| X0 = X2 ),
inference(destructive_equality_resolution,[status(esa)],[f46]) ).
fof(f91,plain,
! [X0,X1] :
( ~ r1(X0)
| ~ r2(X1,X0) ),
inference(destructive_equality_resolution,[status(esa)],[f63]) ).
fof(f92,plain,
! [X0] : ~ pd0_0(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f72]) ).
fof(f93,plain,
! [X0,X1] : ~ pd0_1(X0,X0,X1),
inference(destructive_equality_resolution,[status(esa)],[f75]) ).
fof(f96,plain,
! [X0] :
( X0 = sk0_21(X0)
| X0 = sk0_20(X0) ),
inference(resolution,[status(thm)],[f69,f89]) ).
fof(f97,plain,
! [X0] :
( r1(sk0_22(sk0_20(X0),X0))
| X0 = sk0_21(X0) ),
inference(resolution,[status(thm)],[f87,f69]) ).
fof(f98,plain,
! [X0] :
( r1(sk0_21(X0))
| r1(sk0_22(sk0_20(X0),X0)) ),
inference(resolution,[status(thm)],[f68,f87]) ).
fof(f99,plain,
! [X0] :
( r1(sk0_21(X0))
| X0 = sk0_20(X0) ),
inference(resolution,[status(thm)],[f68,f89]) ).
fof(f100,plain,
! [X0] :
( r2(sk0_22(sk0_20(X0),X0),sk0_20(X0))
| r1(sk0_21(X0)) ),
inference(resolution,[status(thm)],[f88,f68]) ).
fof(f101,plain,
! [X0] :
( r2(sk0_22(sk0_20(X0),X0),sk0_20(X0))
| X0 = sk0_21(X0) ),
inference(resolution,[status(thm)],[f88,f69]) ).
fof(f102,plain,
! [X0] :
( r1(X0)
| X0 = sk0_20(X0)
| X0 = sk0_20(X0) ),
inference(paramodulation,[status(thm)],[f96,f99]) ).
fof(f103,plain,
! [X0] :
( r1(X0)
| X0 = sk0_20(X0) ),
inference(duplicate_literals_removal,[status(esa)],[f102]) ).
fof(f127,plain,
r1(sk0_0),
inference(resolution,[status(thm)],[f17,f92]) ).
fof(f128,plain,
! [X0] : r2(X0,sk0_1(X0)),
inference(resolution,[status(thm)],[f22,f93]) ).
fof(f568,plain,
! [X0,X1] :
( ~ r2(X0,sk0_1(X1))
| X1 = X0 ),
inference(resolution,[status(thm)],[f128,f90]) ).
fof(f569,plain,
! [X0] : ~ r1(sk0_1(X0)),
inference(resolution,[status(thm)],[f128,f91]) ).
fof(f570,plain,
! [X0] : sk0_1(X0) = sk0_20(sk0_1(X0)),
inference(resolution,[status(thm)],[f569,f103]) ).
fof(f571,plain,
! [X0] :
( ~ r1(X0)
| X0 = sk0_0 ),
inference(resolution,[status(thm)],[f71,f18]) ).
fof(f581,plain,
! [X0] :
( sk0_22(sk0_20(X0),X0) = sk0_0
| r1(sk0_21(X0)) ),
inference(resolution,[status(thm)],[f571,f98]) ).
fof(f582,plain,
! [X0] :
( sk0_22(sk0_20(X0),X0) = sk0_0
| X0 = sk0_21(X0) ),
inference(resolution,[status(thm)],[f571,f97]) ).
fof(f839,plain,
! [X0] :
( r2(sk0_0,sk0_20(X0))
| X0 = sk0_21(X0)
| X0 = sk0_21(X0) ),
inference(paramodulation,[status(thm)],[f582,f101]) ).
fof(f840,plain,
! [X0] :
( r2(sk0_0,sk0_20(X0))
| X0 = sk0_21(X0) ),
inference(duplicate_literals_removal,[status(esa)],[f839]) ).
fof(f860,plain,
! [X0] :
( r2(sk0_0,sk0_1(X0))
| sk0_1(X0) = sk0_21(sk0_1(X0)) ),
inference(paramodulation,[status(thm)],[f570,f840]) ).
fof(f865,plain,
! [X0] :
( sk0_22(sk0_20(X0),X0) = sk0_0
| sk0_21(X0) = sk0_0 ),
inference(resolution,[status(thm)],[f581,f571]) ).
fof(f1021,plain,
! [X0] :
( r2(sk0_0,sk0_20(X0))
| r1(sk0_21(X0))
| sk0_21(X0) = sk0_0 ),
inference(paramodulation,[status(thm)],[f865,f100]) ).
fof(f1022,plain,
! [X0] :
( r2(sk0_0,sk0_20(X0))
| sk0_21(X0) = sk0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f1021,f571]) ).
fof(f1039,plain,
! [X0] :
( r2(sk0_0,sk0_1(X0))
| sk0_21(sk0_1(X0)) = sk0_0 ),
inference(paramodulation,[status(thm)],[f570,f1022]) ).
fof(f1377,plain,
! [X0] :
( X0 = sk0_0
| sk0_1(X0) = sk0_21(sk0_1(X0)) ),
inference(resolution,[status(thm)],[f568,f860]) ).
fof(f1378,plain,
! [X0] :
( X0 = sk0_0
| sk0_21(sk0_1(X0)) = sk0_0 ),
inference(resolution,[status(thm)],[f568,f1039]) ).
fof(f1411,plain,
! [X0] :
( X0 = sk0_0
| sk0_1(X0) = sk0_0
| X0 = sk0_0 ),
inference(paramodulation,[status(thm)],[f1378,f1377]) ).
fof(f1412,plain,
! [X0] :
( X0 = sk0_0
| sk0_1(X0) = sk0_0 ),
inference(duplicate_literals_removal,[status(esa)],[f1411]) ).
fof(f1436,plain,
! [X0,X1] :
( ~ r2(X0,sk0_0)
| X1 = X0
| X1 = sk0_0 ),
inference(paramodulation,[status(thm)],[f1412,f568]) ).
fof(f1461,plain,
! [X0] :
( r2(X0,sk0_0)
| X0 = sk0_0 ),
inference(paramodulation,[status(thm)],[f1412,f128]) ).
fof(f1578,plain,
! [X0,X1] :
( X0 = X1
| X0 = sk0_0
| X1 = sk0_0 ),
inference(resolution,[status(thm)],[f1436,f1461]) ).
fof(f1606,plain,
! [X0,X1] :
( r1(X0)
| X0 = X1
| X1 = sk0_0 ),
inference(paramodulation,[status(thm)],[f1578,f127]) ).
fof(f1661,plain,
! [X0,X1] :
( sk0_1(X0) = X1
| X1 = sk0_0 ),
inference(resolution,[status(thm)],[f1606,f569]) ).
fof(f1758,plain,
! [X0,X1] :
( r2(X0,X1)
| X1 = sk0_0 ),
inference(paramodulation,[status(thm)],[f1661,f128]) ).
fof(f1799,plain,
! [X0,X1,X2] :
( X0 = sk0_0
| ~ r2(X1,X0)
| X2 = X1 ),
inference(resolution,[status(thm)],[f1758,f90]) ).
fof(f1800,plain,
! [X0,X1,X2] :
( X0 = sk0_0
| X1 = X2 ),
inference(forward_subsumption_resolution,[status(thm)],[f1799,f1758]) ).
fof(f1851,plain,
! [X0,X1] :
( sk0_0 != X0
| X1 = X0 ),
inference(equality_factoring,[status(esa)],[f1800]) ).
fof(f1852,plain,
! [X0] : X0 = sk0_0,
inference(destructive_equality_resolution,[status(esa)],[f1851]) ).
fof(f1874,plain,
! [X0] : r1(X0),
inference(paramodulation,[status(thm)],[f1852,f127]) ).
fof(f1876,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f569,f1874]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUN068+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.29 % Computer : n009.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Apr 29 22:33:26 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.09/0.30 % Drodi V3.6.0
% 0.13/0.35 % Refutation found
% 0.13/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.37 % Elapsed time: 0.073640 seconds
% 0.13/0.37 % CPU time: 0.466610 seconds
% 0.13/0.37 % Total memory used: 66.998 MB
% 0.13/0.37 % Net memory used: 66.347 MB
%------------------------------------------------------------------------------