TSTP Solution File: NUN057+2 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUN057+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 20:36:17 EDT 2024
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 73 ( 27 unt; 0 def)
% Number of atoms : 209 ( 44 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 246 ( 110 ~; 85 |; 48 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 199 ( 169 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [Y24] :
! [X19] :
( ( ~ r1(X19)
& X19 != Y24 )
| ( r1(X19)
& X19 = Y24 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ r2(X11,X12)
& X12 != Y21 )
| ( r2(X11,X12)
& X12 = Y21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( ~ r3(X13,X14,X15)
& X15 != Y22 )
| ( r3(X13,X14,X15)
& X15 = Y22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y5] :
( ? [Y15] :
( r2(X8,Y15)
& r3(X1,Y15,Y5) )
& Y5 = Y4 )
& ? [Y7] :
( r2(Y7,Y4)
& r3(X1,X8,Y7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) )
& Y9 = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
? [Y1] :
( ? [Y2] :
( Y1 = Y2
& ? [Y3] :
( r2(Y3,Y2)
& ? [Y4] :
( r2(Y4,Y3)
& ? [Y6] :
( r2(Y6,Y4)
& ? [Y8] :
( r1(Y8)
& r2(Y8,Y6) ) ) ) ) )
& ? [Y5] :
( r3(Y5,Y5,Y1)
& ? [Y7] :
( r2(Y7,Y5)
& ? [Y9] :
( r1(Y9)
& r2(Y9,Y7) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ? [Y1] :
( ? [Y2] :
( Y1 = Y2
& ? [Y3] :
( r2(Y3,Y2)
& ? [Y4] :
( r2(Y4,Y3)
& ? [Y6] :
( r2(Y6,Y4)
& ? [Y8] :
( r1(Y8)
& r2(Y8,Y6) ) ) ) ) )
& ? [Y5] :
( r3(Y5,Y5,Y1)
& ? [Y7] :
( r2(Y7,Y5)
& ? [Y9] :
( r1(Y9)
& r2(Y9,Y7) ) ) ) ),
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(f23,plain,
! [X0,X1] :
( pd0_1(X0,sk0_1(X1),X1)
| X0 = sk0_1(X1) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f24,plain,
! [X13,X14,Y22,X15] :
( pd0_2(X15,Y22,X14,X13)
=> ( ~ r3(X13,X14,X15)
& X15 != Y22 ) ),
introduced(predicate_definition,[f3]) ).
fof(f25,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( pd0_2(X15,Y22,X14,X13)
| ( r3(X13,X14,X15)
& X15 = Y22 ) ),
inference(formula_renaming,[status(thm)],[f3,f24]) ).
fof(f26,plain,
! [X13,X14,X15] :
( pd0_2(X15,sk0_2(X14,X13),X14,X13)
| ( r3(X13,X14,X15)
& X15 = sk0_2(X14,X13) ) ),
inference(skolemization,[status(esa)],[f25]) ).
fof(f28,plain,
! [X0,X1,X2] :
( pd0_2(X0,sk0_2(X1,X2),X1,X2)
| X0 = sk0_2(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f34,plain,
! [X1,X8] :
( r2(X8,sk0_6(X8,X1))
& r3(X1,sk0_6(X8,X1),sk0_5(X8,X1))
& sk0_5(X8,X1) = sk0_4(X8,X1)
& r2(sk0_7(X8,X1),sk0_4(X8,X1))
& r3(X1,X8,sk0_7(X8,X1)) ),
inference(skolemization,[status(esa)],[f5]) ).
fof(f35,plain,
! [X0,X1] : r2(X0,sk0_6(X0,X1)),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f36,plain,
! [X0,X1] : r3(X0,sk0_6(X1,X0),sk0_5(X1,X0)),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f37,plain,
! [X0,X1] : sk0_5(X0,X1) = sk0_4(X0,X1),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f38,plain,
! [X0,X1] : r2(sk0_7(X0,X1),sk0_4(X0,X1)),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f39,plain,
! [X0,X1] : r3(X0,X1,sk0_7(X1,X0)),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f47,plain,
! [X4] :
( r1(sk0_13(X4))
& r3(X4,sk0_13(X4),sk0_12(X4))
& sk0_12(X4) = X4 ),
inference(skolemization,[status(esa)],[f8]) ).
fof(f48,plain,
! [X0] : r1(sk0_13(X0)),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
! [X0] : r3(X0,sk0_13(X0),sk0_12(X0)),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f50,plain,
! [X0] : sk0_12(X0) = X0,
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f64,plain,
! [Y1] :
( ! [Y2] :
( Y1 != Y2
| ! [Y3] :
( ~ r2(Y3,Y2)
| ! [Y4] :
( ~ r2(Y4,Y3)
| ! [Y6] :
( ~ r2(Y6,Y4)
| ! [Y8] :
( ~ r1(Y8)
| ~ r2(Y8,Y6) ) ) ) ) )
| ! [Y5] :
( ~ r3(Y5,Y5,Y1)
| ! [Y7] :
( ~ r2(Y7,Y5)
| ! [Y9] :
( ~ r1(Y9)
| ~ r2(Y9,Y7) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( X0 != X1
| ~ r2(X2,X1)
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r1(X5)
| ~ r2(X5,X4)
| ~ r3(X6,X6,X0)
| ~ r2(X7,X6)
| ~ r1(X8)
| ~ r2(X8,X7) ),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f66,plain,
! [Y24,X19] :
( ~ pd0_0(X19,Y24)
| ( ~ r1(X19)
& X19 != Y24 ) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f67,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| ~ r1(X0) ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f69,plain,
! [X11,Y21,X12] :
( ~ pd0_1(X12,Y21,X11)
| ( ~ r2(X11,X12)
& X12 != Y21 ) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ pd0_1(X0,X1,X2)
| ~ r2(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ pd0_1(X0,X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f72,plain,
! [X13,X14,Y22,X15] :
( ~ pd0_2(X15,Y22,X14,X13)
| ( ~ r3(X13,X14,X15)
& X15 != Y22 ) ),
inference(pre_NNF_transformation,[status(esa)],[f24]) ).
fof(f73,plain,
! [X0,X1,X2,X3] :
( ~ pd0_2(X0,X1,X2,X3)
| ~ r3(X3,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f72]) ).
fof(f83,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ r2(X0,X1)
| ~ r2(X2,X0)
| ~ r2(X3,X2)
| ~ r1(X4)
| ~ r2(X4,X3)
| ~ r3(X5,X5,X1)
| ~ r2(X6,X5)
| ~ r1(X7)
| ~ r2(X7,X6) ),
inference(destructive_equality_resolution,[status(esa)],[f65]) ).
fof(f84,plain,
! [X0] : ~ pd0_0(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f68]) ).
fof(f85,plain,
! [X0,X1] : ~ pd0_1(X0,X0,X1),
inference(destructive_equality_resolution,[status(esa)],[f71]) ).
fof(f88,plain,
r1(sk0_0),
inference(resolution,[status(thm)],[f17,f84]) ).
fof(f90,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ r2(X0,X1)
| ~ r2(X2,X0)
| ~ r2(X3,X2)
| ~ r1(X4)
| ~ r2(X4,X3)
| ~ r3(X5,X5,X1)
| ~ r2(X6,X5)
| ~ r2(sk0_0,X6) ),
inference(resolution,[status(thm)],[f88,f83]) ).
fof(f110,plain,
! [X0] :
( X0 = sk0_0
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f18,f67]) ).
fof(f113,plain,
! [X0] : sk0_13(X0) = sk0_0,
inference(resolution,[status(thm)],[f110,f48]) ).
fof(f117,plain,
! [X0] : r2(X0,sk0_1(X0)),
inference(resolution,[status(thm)],[f22,f85]) ).
fof(f131,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r2(X0,X1)
| ~ r2(X2,X0)
| ~ r2(X3,X2)
| ~ r1(X4)
| ~ r2(X4,X3)
| ~ r3(X5,X5,X1)
| ~ r2(sk0_1(sk0_0),X5) ),
inference(resolution,[status(thm)],[f117,f90]) ).
fof(f140,plain,
! [X0] : r3(X0,sk0_0,sk0_12(X0)),
inference(forward_demodulation,[status(thm)],[f113,f49]) ).
fof(f141,plain,
! [X0] : r3(X0,sk0_0,X0),
inference(forward_demodulation,[status(thm)],[f50,f140]) ).
fof(f162,plain,
! [X0,X1] :
( ~ r2(X0,X1)
| X1 = sk0_1(X0) ),
inference(resolution,[status(thm)],[f70,f23]) ).
fof(f163,plain,
! [X0,X1] : r3(X0,sk0_6(X1,X0),sk0_4(X1,X0)),
inference(forward_demodulation,[status(thm)],[f37,f36]) ).
fof(f165,plain,
! [X0,X1] : sk0_4(X0,X1) = sk0_1(sk0_7(X0,X1)),
inference(resolution,[status(thm)],[f162,f38]) ).
fof(f167,plain,
! [X0,X1] : sk0_6(X0,X1) = sk0_1(X0),
inference(resolution,[status(thm)],[f162,f35]) ).
fof(f176,plain,
! [X0,X1] : r3(X0,sk0_1(X1),sk0_4(X1,X0)),
inference(backward_demodulation,[status(thm)],[f167,f163]) ).
fof(f202,plain,
! [X0,X1,X2,X3,X4] :
( ~ r2(X0,sk0_4(X1,sk0_1(X1)))
| ~ r2(X2,X0)
| ~ r2(X3,X2)
| ~ r1(X4)
| ~ r2(X4,X3)
| ~ r2(sk0_1(sk0_0),sk0_1(X1)) ),
inference(resolution,[status(thm)],[f176,f131]) ).
fof(f204,plain,
! [X0,X1,X2] :
( ~ r3(X0,X1,X2)
| X2 = sk0_2(X1,X0) ),
inference(resolution,[status(thm)],[f73,f28]) ).
fof(f206,plain,
! [X0,X1] : sk0_4(X0,X1) = sk0_2(sk0_1(X0),X1),
inference(resolution,[status(thm)],[f204,f176]) ).
fof(f207,plain,
! [X0] : X0 = sk0_2(sk0_0,X0),
inference(resolution,[status(thm)],[f204,f141]) ).
fof(f208,plain,
! [X0,X1] : sk0_7(X0,X1) = sk0_2(X0,X1),
inference(resolution,[status(thm)],[f204,f39]) ).
fof(f215,plain,
! [X0,X1] : sk0_4(X0,X1) = sk0_1(sk0_2(X0,X1)),
inference(backward_demodulation,[status(thm)],[f208,f165]) ).
fof(f217,plain,
! [X0,X1] : r2(sk0_2(X0,X1),sk0_4(X0,X1)),
inference(backward_demodulation,[status(thm)],[f208,f38]) ).
fof(f229,plain,
! [X0] : sk0_4(sk0_0,X0) = sk0_1(X0),
inference(paramodulation,[status(thm)],[f207,f215]) ).
fof(f256,plain,
! [X0,X1,X2,X3] :
( ~ r2(X0,sk0_4(sk0_1(sk0_0),sk0_1(sk0_1(sk0_0))))
| ~ r2(X1,X0)
| ~ r2(X2,X1)
| ~ r1(X3)
| ~ r2(X3,X2) ),
inference(resolution,[status(thm)],[f202,f117]) ).
fof(f259,plain,
! [X0,X1,X2] :
( ~ r2(X0,sk0_2(sk0_1(sk0_0),sk0_1(sk0_1(sk0_0))))
| ~ r2(X1,X0)
| ~ r1(X2)
| ~ r2(X2,X1) ),
inference(resolution,[status(thm)],[f256,f217]) ).
fof(f260,plain,
! [X0,X1,X2] :
( ~ r2(X0,sk0_4(sk0_0,sk0_1(sk0_1(sk0_0))))
| ~ r2(X1,X0)
| ~ r1(X2)
| ~ r2(X2,X1) ),
inference(forward_demodulation,[status(thm)],[f206,f259]) ).
fof(f261,plain,
! [X0,X1,X2] :
( ~ r2(X0,sk0_1(sk0_1(sk0_1(sk0_0))))
| ~ r2(X1,X0)
| ~ r1(X2)
| ~ r2(X2,X1) ),
inference(forward_demodulation,[status(thm)],[f229,f260]) ).
fof(f262,plain,
! [X0,X1] :
( ~ r2(X0,sk0_1(sk0_1(sk0_0)))
| ~ r1(X1)
| ~ r2(X1,X0) ),
inference(resolution,[status(thm)],[f261,f117]) ).
fof(f263,plain,
! [X0] :
( ~ r1(X0)
| ~ r2(X0,sk0_1(sk0_0)) ),
inference(resolution,[status(thm)],[f262,f117]) ).
fof(f264,plain,
~ r1(sk0_0),
inference(resolution,[status(thm)],[f263,f117]) ).
fof(f265,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f264,f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN057+2 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 22:39:43 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.037108 seconds
% 0.13/0.40 % CPU time: 0.138284 seconds
% 0.13/0.40 % Total memory used: 26.568 MB
% 0.13/0.40 % Net memory used: 26.502 MB
%------------------------------------------------------------------------------