TSTP Solution File: NUN059+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUN059+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n023.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 : Wed May 31 12:31:12 EDT 2023
% Result : Theorem 10.67s 1.72s
% Output : CNFRefutation 10.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 12
% Syntax : Number of formulae : 90 ( 26 unt; 0 def)
% Number of atoms : 216 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 232 ( 106 ~; 88 |; 35 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-6 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 247 (; 224 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [Y24] :
! [X19] :
( ( id(X19,Y24)
& r1(X19) )
| ( ~ r1(X19)
& ~ id(X19,Y24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( id(X18,Y23)
& r4(X16,X17,X18) )
| ( ~ r4(X16,X17,X18)
& ~ id(X18,Y23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X20] : id(X20,X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X21,X22] :
( ~ id(X21,X22)
| id(X22,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X23,X24,X25] :
( ~ id(X23,X24)
| id(X23,X25)
| ~ id(X24,X25) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X38,X39,X40,X41,X42,X43] :
( ~ id(X38,X41)
| ~ id(X39,X42)
| ~ id(X40,X43)
| ( ~ r4(X38,X39,X40)
& ~ r4(X41,X42,X43) )
| ( r4(X38,X39,X40)
& r4(X41,X42,X43) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X4] :
? [Y9] :
( id(Y9,X4)
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( id(Y8,Y18)
& r1(Y18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
? [Y1,Y3,Y2,Y4] :
( ? [Y5] :
( id(Y4,Y5)
& r4(Y2,Y2,Y5) )
& ? [Y6] :
( r4(Y3,Y3,Y6)
& ? [Y7] :
( r4(Y1,Y1,Y7)
& r3(Y7,Y6,Y4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ? [Y1,Y3,Y2,Y4] :
( ? [Y5] :
( id(Y4,Y5)
& r4(Y2,Y2,Y5) )
& ? [Y6] :
( r4(Y3,Y3,Y6)
& ? [Y7] :
( r4(Y1,Y1,Y7)
& r3(Y7,Y6,Y4) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [Y24,X19] :
( pd0_0(X19,Y24)
=> ( id(X19,Y24)
& r1(X19) ) ),
introduced(predicate_definition,[f1]) ).
fof(f22,plain,
? [Y24] :
! [X19] :
( pd0_0(X19,Y24)
| ( ~ r1(X19)
& ~ id(X19,Y24) ) ),
inference(formula_renaming,[status(thm)],[f1,f21]) ).
fof(f23,plain,
! [X19] :
( pd0_0(X19,sk0_0)
| ( ~ r1(X19)
& ~ id(X19,sk0_0) ) ),
inference(skolemization,[status(esa)],[f22]) ).
fof(f24,plain,
! [X0] :
( pd0_0(X0,sk0_0)
| ~ r1(X0) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f25,plain,
! [X0] :
( pd0_0(X0,sk0_0)
| ~ id(X0,sk0_0) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f36,plain,
! [X16,X17,Y23,X18] :
( pd0_3(X18,Y23,X17,X16)
=> ( id(X18,Y23)
& r4(X16,X17,X18) ) ),
introduced(predicate_definition,[f4]) ).
fof(f37,plain,
! [X16,X17] :
? [Y23] :
! [X18] :
( pd0_3(X18,Y23,X17,X16)
| ( ~ r4(X16,X17,X18)
& ~ id(X18,Y23) ) ),
inference(formula_renaming,[status(thm)],[f4,f36]) ).
fof(f38,plain,
! [X16,X17,X18] :
( pd0_3(X18,sk0_3(X17,X16),X17,X16)
| ( ~ r4(X16,X17,X18)
& ~ id(X18,sk0_3(X17,X16)) ) ),
inference(skolemization,[status(esa)],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( pd0_3(X0,sk0_3(X1,X2),X1,X2)
| ~ r4(X2,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( pd0_3(X0,sk0_3(X1,X2),X1,X2)
| ~ id(X0,sk0_3(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f41,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f42,plain,
! [X0,X1] :
( ~ id(X0,X1)
| id(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f43,plain,
! [X24,X25] :
( ! [X23] :
( ~ id(X23,X24)
| id(X23,X25) )
| ~ id(X24,X25) ),
inference(miniscoping,[status(esa)],[f7]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ id(X0,X1)
| id(X0,X2)
| ~ id(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f57,plain,
! [X38,X39,X40,X41,X42,X43] :
( pd0_7(X43,X42,X41,X40,X39,X38)
=> ( ~ r4(X38,X39,X40)
& ~ r4(X41,X42,X43) ) ),
introduced(predicate_definition,[f11]) ).
fof(f58,plain,
! [X38,X39,X40,X41,X42,X43] :
( ~ id(X38,X41)
| ~ id(X39,X42)
| ~ id(X40,X43)
| pd0_7(X43,X42,X41,X40,X39,X38)
| ( r4(X38,X39,X40)
& r4(X41,X42,X43) ) ),
inference(formula_renaming,[status(thm)],[f11,f57]) ).
fof(f60,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ id(X0,X1)
| ~ id(X2,X3)
| ~ id(X4,X5)
| pd0_7(X5,X3,X1,X4,X2,X0)
| r4(X1,X3,X5) ),
inference(cnf_transformation,[status(esa)],[f58]) ).
fof(f74,plain,
! [X4] :
( id(sk0_12(X4),X4)
& r1(sk0_13(X4))
& r3(X4,sk0_13(X4),sk0_12(X4)) ),
inference(skolemization,[status(esa)],[f15]) ).
fof(f75,plain,
! [X0] : id(sk0_12(X0),X0),
inference(cnf_transformation,[status(esa)],[f74]) ).
fof(f76,plain,
! [X0] : r1(sk0_13(X0)),
inference(cnf_transformation,[status(esa)],[f74]) ).
fof(f77,plain,
! [X0] : r3(X0,sk0_13(X0),sk0_12(X0)),
inference(cnf_transformation,[status(esa)],[f74]) ).
fof(f78,plain,
! [X5] :
( r1(sk0_15(X5))
& r4(X5,sk0_15(X5),sk0_14(X5))
& id(sk0_14(X5),sk0_16(X5))
& r1(sk0_16(X5)) ),
inference(skolemization,[status(esa)],[f16]) ).
fof(f79,plain,
! [X0] : r1(sk0_15(X0)),
inference(cnf_transformation,[status(esa)],[f78]) ).
fof(f80,plain,
! [X0] : r4(X0,sk0_15(X0),sk0_14(X0)),
inference(cnf_transformation,[status(esa)],[f78]) ).
fof(f81,plain,
! [X0] : id(sk0_14(X0),sk0_16(X0)),
inference(cnf_transformation,[status(esa)],[f78]) ).
fof(f82,plain,
! [X0] : r1(sk0_16(X0)),
inference(cnf_transformation,[status(esa)],[f78]) ).
fof(f91,plain,
! [Y1,Y3,Y2,Y4] :
( ! [Y5] :
( ~ id(Y4,Y5)
| ~ r4(Y2,Y2,Y5) )
| ! [Y6] :
( ~ r4(Y3,Y3,Y6)
| ! [Y7] :
( ~ r4(Y1,Y1,Y7)
| ~ r3(Y7,Y6,Y4) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f92,plain,
! [Y4] :
( ! [Y5] :
( ~ id(Y4,Y5)
| ! [Y2] : ~ r4(Y2,Y2,Y5) )
| ! [Y6] :
( ! [Y3] : ~ r4(Y3,Y3,Y6)
| ! [Y7] :
( ! [Y1] : ~ r4(Y1,Y1,Y7)
| ~ r3(Y7,Y6,Y4) ) ) ),
inference(miniscoping,[status(esa)],[f91]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ id(X0,X1)
| ~ r4(X2,X2,X1)
| ~ r4(X3,X3,X4)
| ~ r4(X5,X5,X6)
| ~ r3(X6,X4,X0) ),
inference(cnf_transformation,[status(esa)],[f92]) ).
fof(f94,plain,
! [Y24,X19] :
( ~ pd0_0(X19,Y24)
| ( id(X19,Y24)
& r1(X19) ) ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f95,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| id(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| r1(X0) ),
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f103,plain,
! [X16,X17,Y23,X18] :
( ~ pd0_3(X18,Y23,X17,X16)
| ( id(X18,Y23)
& r4(X16,X17,X18) ) ),
inference(pre_NNF_transformation,[status(esa)],[f36]) ).
fof(f104,plain,
! [X0,X1,X2,X3] :
( ~ pd0_3(X0,X1,X2,X3)
| id(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f103]) ).
fof(f105,plain,
! [X0,X1,X2,X3] :
( ~ pd0_3(X0,X1,X2,X3)
| r4(X3,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f103]) ).
fof(f115,plain,
! [X38,X39,X40,X41,X42,X43] :
( ~ pd0_7(X43,X42,X41,X40,X39,X38)
| ( ~ r4(X38,X39,X40)
& ~ r4(X41,X42,X43) ) ),
inference(pre_NNF_transformation,[status(esa)],[f57]) ).
fof(f116,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ pd0_7(X0,X1,X2,X3,X4,X5)
| ~ r4(X5,X4,X3) ),
inference(cnf_transformation,[status(esa)],[f115]) ).
fof(f124,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r4(X0,X0,X1)
| ~ r4(X2,X2,X3)
| ~ r4(X4,X4,X5)
| ~ r3(X5,X3,sk0_12(X1)) ),
inference(resolution,[status(thm)],[f75,f93]) ).
fof(f356,plain,
! [X0,X1,X2,X3] :
( ~ r4(X0,X0,X1)
| ~ r4(X2,X2,sk0_13(X1))
| ~ r4(X3,X3,X1) ),
inference(resolution,[status(thm)],[f77,f124]) ).
fof(f378,plain,
! [X0,X1,X2] :
( ~ r4(X0,X1,X2)
| id(X2,sk0_3(X1,X0)) ),
inference(resolution,[status(thm)],[f39,f104]) ).
fof(f379,plain,
! [X0] : id(sk0_14(X0),sk0_3(sk0_15(X0),X0)),
inference(resolution,[status(thm)],[f378,f80]) ).
fof(f402,plain,
! [X0,X1,X2] :
( ~ id(X0,sk0_3(X1,X2))
| r4(X2,X1,X0) ),
inference(resolution,[status(thm)],[f40,f105]) ).
fof(f405,plain,
! [X0,X1,X2,X3] :
( r4(X0,X1,X2)
| ~ id(X2,X3)
| ~ id(X3,sk0_3(X1,X0)) ),
inference(resolution,[status(thm)],[f402,f44]) ).
fof(f406,plain,
! [X0,X1,X2] :
( r4(X0,X1,X2)
| ~ id(sk0_3(X1,X0),X2) ),
inference(resolution,[status(thm)],[f402,f42]) ).
fof(f407,plain,
! [X0,X1] : r4(X0,X1,sk0_3(X1,X0)),
inference(resolution,[status(thm)],[f402,f41]) ).
fof(f427,plain,
! [X0,X1,X2,X3] :
( r4(X0,X1,X2)
| ~ id(sk0_3(X1,X0),X3)
| ~ id(X3,X2) ),
inference(resolution,[status(thm)],[f406,f44]) ).
fof(f511,plain,
! [X0,X1] :
( r4(X0,sk0_15(X0),X1)
| ~ id(X1,sk0_14(X0)) ),
inference(resolution,[status(thm)],[f405,f379]) ).
fof(f516,plain,
! [X0,X1] :
( ~ id(X0,sk0_14(X1))
| id(X0,sk0_3(sk0_15(X1),X1)) ),
inference(resolution,[status(thm)],[f511,f378]) ).
fof(f519,plain,
! [X0,X1] :
( id(X0,sk0_3(sk0_15(X1),X1))
| ~ id(sk0_14(X1),X0) ),
inference(resolution,[status(thm)],[f516,f42]) ).
fof(f522,plain,
! [X0] : id(sk0_16(X0),sk0_3(sk0_15(X0),X0)),
inference(resolution,[status(thm)],[f519,f81]) ).
fof(f527,plain,
! [X0,X1] :
( r4(X0,sk0_15(X0),X1)
| ~ id(X1,sk0_16(X0)) ),
inference(resolution,[status(thm)],[f522,f405]) ).
fof(f533,plain,
! [X0,X1] :
( ~ id(X0,sk0_16(X1))
| id(X0,sk0_3(sk0_15(X1),X1)) ),
inference(resolution,[status(thm)],[f527,f378]) ).
fof(f537,plain,
! [X0,X1] :
( id(X0,sk0_3(sk0_15(X1),X1))
| ~ id(sk0_16(X1),X0) ),
inference(resolution,[status(thm)],[f533,f42]) ).
fof(f546,plain,
! [X0,X1,X2,X3] :
( r4(X0,X1,X2)
| ~ id(X3,X2)
| ~ id(X3,sk0_3(X1,X0)) ),
inference(resolution,[status(thm)],[f427,f42]) ).
fof(f575,plain,
! [X0] :
( ~ r1(X0)
| id(X0,sk0_0) ),
inference(resolution,[status(thm)],[f24,f95]) ).
fof(f1121,plain,
! [X0] : id(sk0_16(X0),sk0_0),
inference(resolution,[status(thm)],[f575,f82]) ).
fof(f1122,plain,
! [X0] : id(sk0_15(X0),sk0_0),
inference(resolution,[status(thm)],[f575,f79]) ).
fof(f1123,plain,
! [X0] : id(sk0_13(X0),sk0_0),
inference(resolution,[status(thm)],[f575,f76]) ).
fof(f1124,plain,
! [X0] : id(sk0_0,sk0_3(sk0_15(X0),X0)),
inference(resolution,[status(thm)],[f1121,f537]) ).
fof(f1228,plain,
! [X0,X1] :
( r4(X0,sk0_15(X0),X1)
| ~ id(sk0_0,X1) ),
inference(resolution,[status(thm)],[f1124,f546]) ).
fof(f1267,plain,
! [X0,X1] :
( ~ id(sk0_0,X0)
| id(X0,sk0_3(sk0_15(X1),X1)) ),
inference(resolution,[status(thm)],[f1228,f378]) ).
fof(f1269,plain,
! [X0,X1] : id(sk0_3(sk0_15(X0),X0),sk0_3(sk0_15(X1),X1)),
inference(resolution,[status(thm)],[f1267,f1124]) ).
fof(f1658,plain,
! [X0] :
( r1(X0)
| ~ id(X0,sk0_0) ),
inference(resolution,[status(thm)],[f96,f25]) ).
fof(f2146,plain,
! [X0] :
( r1(X0)
| ~ id(sk0_0,X0) ),
inference(resolution,[status(thm)],[f1658,f42]) ).
fof(f2152,plain,
! [X0] : r1(sk0_3(sk0_15(X0),X0)),
inference(resolution,[status(thm)],[f2146,f1124]) ).
fof(f2160,plain,
! [X0] : id(sk0_3(sk0_15(X0),X0),sk0_0),
inference(resolution,[status(thm)],[f2152,f575]) ).
fof(f2769,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r4(X0,X1,X2)
| ~ id(X0,X3)
| ~ id(X1,X4)
| ~ id(X2,X5)
| r4(X3,X4,X5) ),
inference(resolution,[status(thm)],[f116,f60]) ).
fof(f3533,plain,
! [X0,X1,X2,X3,X4] :
( ~ id(X0,X1)
| ~ id(X2,X3)
| ~ id(sk0_3(X2,X0),X4)
| r4(X1,X3,X4) ),
inference(resolution,[status(thm)],[f2769,f407]) ).
fof(f3537,plain,
! [X0,X1,X2,X3] :
( ~ id(X0,X1)
| ~ id(sk0_15(X0),X2)
| r4(X1,X2,sk0_3(sk0_15(X3),X3)) ),
inference(resolution,[status(thm)],[f3533,f1269]) ).
fof(f3556,plain,
! [X0,X1,X2] :
( ~ id(X0,X1)
| r4(X1,sk0_0,sk0_3(sk0_15(X2),X2)) ),
inference(resolution,[status(thm)],[f3537,f1122]) ).
fof(f3596,plain,
! [X0,X1] : r4(X0,sk0_0,sk0_3(sk0_15(X1),X1)),
inference(resolution,[status(thm)],[f3556,f75]) ).
fof(f3639,plain,
! [X0,X1] : id(sk0_3(sk0_15(X0),X0),sk0_3(sk0_0,X1)),
inference(resolution,[status(thm)],[f3596,f378]) ).
fof(f3669,plain,
! [X0,X1,X2] :
( r4(X0,sk0_0,X1)
| ~ id(sk0_3(sk0_15(X2),X2),X1) ),
inference(resolution,[status(thm)],[f3639,f546]) ).
fof(f3775,plain,
! [X0] : r4(X0,sk0_0,sk0_0),
inference(resolution,[status(thm)],[f3669,f2160]) ).
fof(f3824,plain,
! [X0] : id(sk0_0,sk0_3(sk0_0,X0)),
inference(resolution,[status(thm)],[f3775,f378]) ).
fof(f3857,plain,
! [X0,X1] :
( r4(X0,sk0_0,X1)
| ~ id(X1,sk0_0) ),
inference(resolution,[status(thm)],[f3824,f405]) ).
fof(f4034,plain,
! [X0,X1] : r4(X0,sk0_0,sk0_13(X1)),
inference(resolution,[status(thm)],[f3857,f1123]) ).
fof(f4049,plain,
! [X0,X1,X2] :
( ~ r4(X0,X0,X1)
| ~ r4(X2,X2,X1) ),
inference(resolution,[status(thm)],[f4034,f356]) ).
fof(f4219,plain,
! [X0] : ~ r4(X0,X0,sk0_0),
inference(resolution,[status(thm)],[f4049,f3775]) ).
fof(f4224,plain,
$false,
inference(resolution,[status(thm)],[f4219,f3775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUN059+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 30 11:02:23 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Drodi V3.5.1
% 10.67/1.72 % Refutation found
% 10.67/1.72 % SZS status Theorem for theBenchmark: Theorem is valid
% 10.67/1.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.67/1.74 % Elapsed time: 1.386238 seconds
% 10.67/1.74 % CPU time: 10.931032 seconds
% 10.67/1.74 % Memory used: 56.597 MB
%------------------------------------------------------------------------------