TSTP Solution File: NUN082+2 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUN082+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n005.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 20:36:23 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 89 ( 36 unt; 0 def)
% Number of atoms : 196 ( 59 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 182 ( 75 ~; 53 |; 50 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-2 aty)
% Number of variables : 198 ( 171 !; 27 ?)
% 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(f4,axiom,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( ~ r4(X16,X17,X18)
& X18 != Y23 )
| ( r4(X16,X17,X18)
& X18 = Y23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y3] :
( ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) )
& Y3 = Y2 )
& ? [Y6] :
( r3(Y6,X2,Y2)
& r4(X2,X9,Y6) ) ),
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(f9,axiom,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( r1(Y18)
& Y8 = Y18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
? [Y1,Y2] :
( ? [Y3] :
( r4(Y1,Y3,Y2)
& ? [Y4] :
( r1(Y4)
& r2(Y4,Y3) ) )
& ? [Y5] :
( r1(Y5)
& Y2 = Y5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ? [Y1,Y2] :
( ? [Y3] :
( r4(Y1,Y3,Y2)
& ? [Y4] :
( r1(Y4)
& r2(Y4,Y3) ) )
& ? [Y5] :
( r1(Y5)
& Y2 = Y5 ) ),
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(f29,plain,
! [X16,X17,Y23,X18] :
( pd0_3(X18,Y23,X17,X16)
=> ( ~ r4(X16,X17,X18)
& X18 != Y23 ) ),
introduced(predicate_definition,[f4]) ).
fof(f30,plain,
! [X16,X17] :
? [Y23] :
! [X18] :
( pd0_3(X18,Y23,X17,X16)
| ( r4(X16,X17,X18)
& X18 = Y23 ) ),
inference(formula_renaming,[status(thm)],[f4,f29]) ).
fof(f31,plain,
! [X16,X17,X18] :
( pd0_3(X18,sk0_3(X17,X16),X17,X16)
| ( r4(X16,X17,X18)
& X18 = sk0_3(X17,X16) ) ),
inference(skolemization,[status(esa)],[f30]) ).
fof(f33,plain,
! [X0,X1,X2] :
( pd0_3(X0,sk0_3(X1,X2),X1,X2)
| X0 = sk0_3(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f40,plain,
! [X2,X9] :
( r2(X9,sk0_10(X9,X2))
& r4(X2,sk0_10(X9,X2),sk0_9(X9,X2))
& sk0_9(X9,X2) = sk0_8(X9,X2)
& r3(sk0_11(X9,X2),X2,sk0_8(X9,X2))
& r4(X2,X9,sk0_11(X9,X2)) ),
inference(skolemization,[status(esa)],[f6]) ).
fof(f41,plain,
! [X0,X1] : r2(X0,sk0_10(X0,X1)),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f42,plain,
! [X0,X1] : r4(X0,sk0_10(X1,X0),sk0_9(X1,X0)),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f43,plain,
! [X0,X1] : sk0_9(X0,X1) = sk0_8(X0,X1),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f44,plain,
! [X0,X1] : r3(sk0_11(X0,X1),X1,sk0_8(X0,X1)),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f45,plain,
! [X0,X1] : r4(X0,X1,sk0_11(X1,X0)),
inference(cnf_transformation,[status(esa)],[f40]) ).
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(f51,plain,
! [X5] :
( r1(sk0_15(X5))
& r4(X5,sk0_15(X5),sk0_14(X5))
& r1(sk0_16(X5))
& sk0_14(X5) = sk0_16(X5) ),
inference(skolemization,[status(esa)],[f9]) ).
fof(f52,plain,
! [X0] : r1(sk0_15(X0)),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f53,plain,
! [X0] : r4(X0,sk0_15(X0),sk0_14(X0)),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f54,plain,
! [X0] : r1(sk0_16(X0)),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f55,plain,
! [X0] : sk0_14(X0) = sk0_16(X0),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f64,plain,
! [Y1,Y2] :
( ! [Y3] :
( ~ r4(Y1,Y3,Y2)
| ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y3) ) )
| ! [Y5] :
( ~ r1(Y5)
| Y2 != Y5 ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f65,plain,
! [Y2] :
( ! [Y3] :
( ! [Y1] : ~ r4(Y1,Y3,Y2)
| ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y3) ) )
| ! [Y5] :
( ~ r1(Y5)
| Y2 != Y5 ) ),
inference(miniscoping,[status(esa)],[f64]) ).
fof(f66,plain,
! [X0,X1,X2,X3,X4] :
( ~ r4(X0,X1,X2)
| ~ r1(X3)
| ~ r2(X3,X1)
| ~ r1(X4)
| X2 != X4 ),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f67,plain,
! [Y24,X19] :
( ~ pd0_0(X19,Y24)
| ( ~ r1(X19)
& X19 != Y24 ) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f68,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| ~ r1(X0) ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f70,plain,
! [X11,Y21,X12] :
( ~ pd0_1(X12,Y21,X11)
| ( ~ r2(X11,X12)
& X12 != Y21 ) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ pd0_1(X0,X1,X2)
| ~ r2(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ pd0_1(X0,X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f73,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(f74,plain,
! [X0,X1,X2,X3] :
( ~ pd0_2(X0,X1,X2,X3)
| ~ r3(X3,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f73]) ).
fof(f76,plain,
! [X16,X17,Y23,X18] :
( ~ pd0_3(X18,Y23,X17,X16)
| ( ~ r4(X16,X17,X18)
& X18 != Y23 ) ),
inference(pre_NNF_transformation,[status(esa)],[f29]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( ~ pd0_3(X0,X1,X2,X3)
| ~ r4(X3,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f76]) ).
fof(f84,plain,
! [X0,X1,X2,X3] :
( ~ r4(X0,X1,X2)
| ~ r1(X3)
| ~ r2(X3,X1)
| ~ r1(X2) ),
inference(destructive_equality_resolution,[status(esa)],[f66]) ).
fof(f85,plain,
! [X0] : ~ pd0_0(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f69]) ).
fof(f86,plain,
! [X0,X1] : ~ pd0_1(X0,X0,X1),
inference(destructive_equality_resolution,[status(esa)],[f72]) ).
fof(f89,plain,
r1(sk0_0),
inference(resolution,[status(thm)],[f17,f85]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ~ r4(X0,X1,X2)
| ~ r2(sk0_0,X1)
| ~ r1(X2) ),
inference(resolution,[status(thm)],[f89,f84]) ).
fof(f100,plain,
! [X0] : r1(sk0_14(X0)),
inference(backward_demodulation,[status(thm)],[f55,f54]) ).
fof(f111,plain,
! [X0] :
( X0 = sk0_0
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f18,f68]) ).
fof(f112,plain,
! [X0] : sk0_14(X0) = sk0_0,
inference(resolution,[status(thm)],[f111,f100]) ).
fof(f113,plain,
! [X0] : sk0_15(X0) = sk0_0,
inference(resolution,[status(thm)],[f111,f52]) ).
fof(f114,plain,
! [X0] : sk0_13(X0) = sk0_0,
inference(resolution,[status(thm)],[f111,f48]) ).
fof(f118,plain,
! [X0] : r2(X0,sk0_1(X0)),
inference(resolution,[status(thm)],[f22,f86]) ).
fof(f132,plain,
! [X0,X1] :
( ~ r4(X0,sk0_1(sk0_0),X1)
| ~ r1(X1) ),
inference(resolution,[status(thm)],[f118,f91]) ).
fof(f141,plain,
! [X0] : r3(X0,sk0_0,sk0_12(X0)),
inference(forward_demodulation,[status(thm)],[f114,f49]) ).
fof(f142,plain,
! [X0] : r3(X0,sk0_0,X0),
inference(forward_demodulation,[status(thm)],[f50,f141]) ).
fof(f143,plain,
! [X0] : r4(X0,sk0_0,sk0_14(X0)),
inference(forward_demodulation,[status(thm)],[f113,f53]) ).
fof(f144,plain,
! [X0] : r4(X0,sk0_0,sk0_0),
inference(forward_demodulation,[status(thm)],[f112,f143]) ).
fof(f145,plain,
! [X0,X1] :
( ~ r2(X0,X1)
| X1 = sk0_1(X0) ),
inference(resolution,[status(thm)],[f71,f23]) ).
fof(f149,plain,
! [X0,X1] : sk0_10(X0,X1) = sk0_1(X0),
inference(resolution,[status(thm)],[f145,f41]) ).
fof(f164,plain,
! [X0,X1] : r4(X0,sk0_1(X1),sk0_9(X1,X0)),
inference(forward_demodulation,[status(thm)],[f149,f42]) ).
fof(f165,plain,
! [X0,X1] : r4(X0,sk0_1(X1),sk0_8(X1,X0)),
inference(forward_demodulation,[status(thm)],[f43,f164]) ).
fof(f166,plain,
! [X0] : ~ r1(sk0_8(sk0_0,X0)),
inference(resolution,[status(thm)],[f165,f132]) ).
fof(f235,plain,
! [X0,X1,X2] :
( ~ r3(X0,X1,X2)
| X2 = sk0_2(X1,X0) ),
inference(resolution,[status(thm)],[f74,f28]) ).
fof(f238,plain,
! [X0] : X0 = sk0_2(sk0_0,X0),
inference(resolution,[status(thm)],[f235,f142]) ).
fof(f241,plain,
! [X0,X1] :
( pd0_2(X0,X1,sk0_0,X1)
| X0 = sk0_2(sk0_0,X1) ),
inference(paramodulation,[status(thm)],[f238,f28]) ).
fof(f242,plain,
! [X0,X1] :
( pd0_2(X0,X1,sk0_0,X1)
| X0 = X1 ),
inference(forward_demodulation,[status(thm)],[f238,f241]) ).
fof(f248,plain,
! [X0,X1] :
( X0 = X1
| ~ r3(X1,sk0_0,X0) ),
inference(resolution,[status(thm)],[f242,f74]) ).
fof(f249,plain,
! [X0] : sk0_8(X0,sk0_0) = sk0_11(X0,sk0_0),
inference(resolution,[status(thm)],[f248,f44]) ).
fof(f276,plain,
! [X0] : r4(sk0_0,X0,sk0_8(X0,sk0_0)),
inference(paramodulation,[status(thm)],[f249,f45]) ).
fof(f277,plain,
! [X0,X1,X2] :
( ~ r4(X0,X1,X2)
| X2 = sk0_3(X1,X0) ),
inference(resolution,[status(thm)],[f77,f33]) ).
fof(f733,plain,
! [X0] : sk0_8(X0,sk0_0) = sk0_3(X0,sk0_0),
inference(resolution,[status(thm)],[f277,f276]) ).
fof(f735,plain,
! [X0] : sk0_0 = sk0_3(sk0_0,X0),
inference(resolution,[status(thm)],[f277,f144]) ).
fof(f747,plain,
~ r1(sk0_3(sk0_0,sk0_0)),
inference(paramodulation,[status(thm)],[f733,f166]) ).
fof(f748,plain,
~ r1(sk0_0),
inference(forward_demodulation,[status(thm)],[f735,f747]) ).
fof(f749,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f748,f89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUN082+2 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n005.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 : Mon Apr 29 22:34:56 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38 % Elapsed time: 0.029599 seconds
% 0.13/0.38 % CPU time: 0.105418 seconds
% 0.13/0.38 % Total memory used: 21.519 MB
% 0.13/0.38 % Net memory used: 21.386 MB
%------------------------------------------------------------------------------