TSTP Solution File: NUN066+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUN066+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 12:31:14 EDT 2023
% Result : Theorem 18.58s 2.69s
% Output : CNFRefutation 18.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 84 ( 15 unt; 0 def)
% Number of atoms : 214 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 238 ( 108 ~; 92 |; 34 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 164 (; 148 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [Y24] :
! [X19] :
( ( id(X19,Y24)
& r1(X19) )
| ( ~ r1(X19)
& ~ id(X19,Y24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( id(X12,Y21)
& r2(X11,X12) )
| ( ~ r2(X11,X12)
& ~ id(X12,Y21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X20] : id(X20,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X21,X22] :
( ~ id(X21,X22)
| id(X22,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X23,X24,X25] :
( ~ id(X23,X24)
| id(X23,X25)
| ~ id(X24,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X26,X27] :
( ~ id(X26,X27)
| ( ~ r1(X26)
& ~ r1(X27) )
| ( r1(X26)
& r1(X27) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X3,X10] :
( ! [Y12] :
( ! [Y13] :
( ~ id(Y13,Y12)
| ~ r2(X3,Y13) )
| ~ r2(X10,Y12) )
| id(X3,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X7,Y10] :
( ! [Y20] :
( ~ id(Y20,Y10)
| ~ r1(Y20) )
| ~ r2(X7,Y10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
? [Y1] :
( ! [Y2] :
( ! [Y3] :
( ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y3) )
| ~ r2(Y3,Y2) )
| ~ id(Y1,Y2) )
& ! [Y5] :
( ~ id(Y1,Y5)
| ~ r1(Y5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ? [Y1] :
( ! [Y2] :
( ! [Y3] :
( ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y3) )
| ~ r2(Y3,Y2) )
| ~ id(Y1,Y2) )
& ! [Y5] :
( ~ id(Y1,Y5)
| ~ r1(Y5) ) ),
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(f26,plain,
! [X11,Y21,X12] :
( pd0_1(X12,Y21,X11)
=> ( id(X12,Y21)
& r2(X11,X12) ) ),
introduced(predicate_definition,[f2]) ).
fof(f27,plain,
! [X11] :
? [Y21] :
! [X12] :
( pd0_1(X12,Y21,X11)
| ( ~ r2(X11,X12)
& ~ id(X12,Y21) ) ),
inference(formula_renaming,[status(thm)],[f2,f26]) ).
fof(f28,plain,
! [X11,X12] :
( pd0_1(X12,sk0_1(X11),X11)
| ( ~ r2(X11,X12)
& ~ id(X12,sk0_1(X11)) ) ),
inference(skolemization,[status(esa)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( pd0_1(X0,sk0_1(X1),X1)
| ~ r2(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( pd0_1(X0,sk0_1(X1),X1)
| ~ id(X0,sk0_1(X1)) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
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(f45,plain,
! [X26,X27] :
( pd0_4(X27,X26)
=> ( ~ r1(X26)
& ~ r1(X27) ) ),
introduced(predicate_definition,[f8]) ).
fof(f46,plain,
! [X26,X27] :
( ~ id(X26,X27)
| pd0_4(X27,X26)
| ( r1(X26)
& r1(X27) ) ),
inference(formula_renaming,[status(thm)],[f8,f45]) ).
fof(f48,plain,
! [X0,X1] :
( ~ id(X0,X1)
| pd0_4(X1,X0)
| r1(X1) ),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f73,plain,
! [X0,X1,X2,X3] :
( ~ id(X0,X1)
| ~ r2(X2,X0)
| ~ r2(X3,X1)
| id(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f89,plain,
! [Y10] :
( ! [Y20] :
( ~ id(Y20,Y10)
| ~ r1(Y20) )
| ! [X7] : ~ r2(X7,Y10) ),
inference(miniscoping,[status(esa)],[f18]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ id(X0,X1)
| ~ r1(X0)
| ~ r2(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f89]) ).
fof(f91,plain,
! [Y1] :
( ? [Y2] :
( ? [Y3] :
( ? [Y4] :
( r1(Y4)
& r2(Y4,Y3) )
& r2(Y3,Y2) )
& id(Y1,Y2) )
| ? [Y5] :
( id(Y1,Y5)
& r1(Y5) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f92,plain,
! [Y1,Y2] :
( pd0_9(Y2,Y1)
=> ( ? [Y3] :
( ? [Y4] :
( r1(Y4)
& r2(Y4,Y3) )
& r2(Y3,Y2) )
& id(Y1,Y2) ) ),
introduced(predicate_definition,[f91]) ).
fof(f93,plain,
! [Y1] :
( ? [Y2] : pd0_9(Y2,Y1)
| ? [Y5] :
( id(Y1,Y5)
& r1(Y5) ) ),
inference(formula_renaming,[status(thm)],[f91,f92]) ).
fof(f94,plain,
! [Y1] :
( pd0_9(sk0_20(Y1),Y1)
| ( id(Y1,sk0_21(Y1))
& r1(sk0_21(Y1)) ) ),
inference(skolemization,[status(esa)],[f93]) ).
fof(f95,plain,
! [X0] :
( pd0_9(sk0_20(X0),X0)
| id(X0,sk0_21(X0)) ),
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f96,plain,
! [X0] :
( pd0_9(sk0_20(X0),X0)
| r1(sk0_21(X0)) ),
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f97,plain,
! [Y24,X19] :
( ~ pd0_0(X19,Y24)
| ( id(X19,Y24)
& r1(X19) ) ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f98,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| id(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| r1(X0) ),
inference(cnf_transformation,[status(esa)],[f97]) ).
fof(f100,plain,
! [X11,Y21,X12] :
( ~ pd0_1(X12,Y21,X11)
| ( id(X12,Y21)
& r2(X11,X12) ) ),
inference(pre_NNF_transformation,[status(esa)],[f26]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ~ pd0_1(X0,X1,X2)
| id(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f100]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ~ pd0_1(X0,X1,X2)
| r2(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f100]) ).
fof(f109,plain,
! [X26,X27] :
( ~ pd0_4(X27,X26)
| ( ~ r1(X26)
& ~ r1(X27) ) ),
inference(pre_NNF_transformation,[status(esa)],[f45]) ).
fof(f110,plain,
! [X0,X1] :
( ~ pd0_4(X0,X1)
| ~ r1(X1) ),
inference(cnf_transformation,[status(esa)],[f109]) ).
fof(f124,plain,
! [Y1,Y2] :
( ~ pd0_9(Y2,Y1)
| ( ? [Y3] :
( ? [Y4] :
( r1(Y4)
& r2(Y4,Y3) )
& r2(Y3,Y2) )
& id(Y1,Y2) ) ),
inference(pre_NNF_transformation,[status(esa)],[f92]) ).
fof(f125,plain,
! [Y1,Y2] :
( ~ pd0_9(Y2,Y1)
| ( r1(sk0_23(Y2,Y1))
& r2(sk0_23(Y2,Y1),sk0_22(Y2,Y1))
& r2(sk0_22(Y2,Y1),Y2)
& id(Y1,Y2) ) ),
inference(skolemization,[status(esa)],[f124]) ).
fof(f127,plain,
! [X0,X1] :
( ~ pd0_9(X0,X1)
| r2(sk0_23(X0,X1),sk0_22(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f125]) ).
fof(f128,plain,
! [X0,X1] :
( ~ pd0_9(X0,X1)
| r2(sk0_22(X0,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f125]) ).
fof(f129,plain,
! [X0,X1] :
( ~ pd0_9(X0,X1)
| id(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f125]) ).
fof(f130,plain,
! [X0] :
( r1(sk0_21(X0))
| id(X0,sk0_20(X0)) ),
inference(resolution,[status(thm)],[f96,f129]) ).
fof(f131,plain,
! [X0] :
( id(X0,sk0_21(X0))
| id(X0,sk0_20(X0)) ),
inference(resolution,[status(thm)],[f95,f129]) ).
fof(f150,plain,
! [X0] :
( id(X0,sk0_0)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f98,f24]) ).
fof(f151,plain,
! [X0] :
( ~ id(X0,sk0_0)
| r1(X0) ),
inference(resolution,[status(thm)],[f25,f99]) ).
fof(f334,plain,
! [X0,X1,X2] :
( r1(X0)
| ~ id(X1,X2)
| ~ r2(X0,X1)
| ~ r2(sk0_0,X2) ),
inference(resolution,[status(thm)],[f151,f73]) ).
fof(f335,plain,
! [X0,X1] :
( r1(X0)
| ~ id(X0,X1)
| ~ id(X1,sk0_0) ),
inference(resolution,[status(thm)],[f151,f44]) ).
fof(f337,plain,
r1(sk0_0),
inference(resolution,[status(thm)],[f151,f41]) ).
fof(f338,plain,
! [X0,X1] :
( ~ id(sk0_0,X0)
| ~ r2(X1,X0) ),
inference(resolution,[status(thm)],[f337,f90]) ).
fof(f367,plain,
! [X0,X1] :
( id(X0,sk0_1(X1))
| ~ r2(X1,X0) ),
inference(resolution,[status(thm)],[f101,f29]) ).
fof(f368,plain,
! [X0,X1] :
( r2(X0,X1)
| ~ id(X1,sk0_1(X0)) ),
inference(resolution,[status(thm)],[f102,f30]) ).
fof(f562,plain,
! [X0,X1] :
( ~ id(X0,X1)
| r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f48,f110]) ).
fof(f723,plain,
! [X0,X1] :
( r1(X0)
| ~ id(X0,X1)
| ~ r1(X1) ),
inference(resolution,[status(thm)],[f335,f150]) ).
fof(f1115,plain,
! [X0,X1] :
( id(sk0_22(X0,X1),sk0_1(sk0_23(X0,X1)))
| ~ pd0_9(X0,X1) ),
inference(resolution,[status(thm)],[f367,f127]) ).
fof(f1125,plain,
! [X0,X1] :
( r2(X0,X1)
| ~ id(sk0_1(X0),X1) ),
inference(resolution,[status(thm)],[f368,f42]) ).
fof(f1126,plain,
! [X0] : r2(X0,sk0_1(X0)),
inference(resolution,[status(thm)],[f368,f41]) ).
fof(f1129,plain,
! [X0,X1] :
( r1(X0)
| ~ id(X1,sk0_1(sk0_0))
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f1126,f334]) ).
fof(f1137,plain,
! [X0] : ~ id(sk0_0,sk0_1(X0)),
inference(resolution,[status(thm)],[f1126,f338]) ).
fof(f1144,plain,
! [X0] : ~ id(sk0_1(X0),sk0_0),
inference(resolution,[status(thm)],[f1137,f42]) ).
fof(f1145,plain,
! [X0] : ~ r1(sk0_1(X0)),
inference(resolution,[status(thm)],[f1144,f150]) ).
fof(f1147,plain,
! [X0,X1] :
( ~ id(sk0_1(X0),X1)
| ~ id(X1,sk0_0) ),
inference(resolution,[status(thm)],[f1144,f44]) ).
fof(f1331,plain,
! [X0,X1] :
( r1(sk0_1(sk0_23(X0,X1)))
| ~ r1(sk0_22(X0,X1))
| ~ pd0_9(X0,X1) ),
inference(resolution,[status(thm)],[f562,f1115]) ).
fof(f1332,plain,
! [X0,X1] :
( ~ r1(sk0_22(X0,X1))
| ~ pd0_9(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1331,f1145]) ).
fof(f1859,plain,
! [X0] :
( r1(X0)
| ~ r1(sk0_21(X0))
| id(X0,sk0_20(X0)) ),
inference(resolution,[status(thm)],[f723,f131]) ).
fof(f1860,plain,
! [X0] :
( r1(X0)
| id(X0,sk0_20(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1859,f130]) ).
fof(f1877,plain,
! [X0] :
( r1(sk0_1(X0))
| r2(X0,sk0_20(sk0_1(X0))) ),
inference(resolution,[status(thm)],[f1860,f1125]) ).
fof(f1878,plain,
! [X0] : r2(X0,sk0_20(sk0_1(X0))),
inference(forward_subsumption_resolution,[status(thm)],[f1877,f1145]) ).
fof(f1910,plain,
! [X0] : id(sk0_20(sk0_1(X0)),sk0_1(X0)),
inference(resolution,[status(thm)],[f1878,f367]) ).
fof(f13142,plain,
! [X0] :
( r1(X0)
| ~ r2(X0,sk0_20(sk0_1(sk0_0))) ),
inference(resolution,[status(thm)],[f1129,f1910]) ).
fof(f14812,plain,
! [X0] :
( r1(sk0_22(sk0_20(sk0_1(sk0_0)),X0))
| ~ pd0_9(sk0_20(sk0_1(sk0_0)),X0) ),
inference(resolution,[status(thm)],[f13142,f128]) ).
fof(f14813,plain,
! [X0] : ~ pd0_9(sk0_20(sk0_1(sk0_0)),X0),
inference(forward_subsumption_resolution,[status(thm)],[f14812,f1332]) ).
fof(f14847,plain,
r1(sk0_21(sk0_1(sk0_0))),
inference(resolution,[status(thm)],[f14813,f96]) ).
fof(f14848,plain,
id(sk0_1(sk0_0),sk0_21(sk0_1(sk0_0))),
inference(resolution,[status(thm)],[f14813,f95]) ).
fof(f14851,plain,
id(sk0_21(sk0_1(sk0_0)),sk0_0),
inference(resolution,[status(thm)],[f14847,f150]) ).
fof(f14865,plain,
! [X0] : ~ id(sk0_1(X0),sk0_21(sk0_1(sk0_0))),
inference(resolution,[status(thm)],[f14851,f1147]) ).
fof(f16498,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f14848,f14865]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUN066+1 : TPTP v8.1.2. Released v7.3.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33 % Computer : n017.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 May 30 10:11:40 EDT 2023
% 0.20/0.33 % CPUTime :
% 0.20/0.34 % Drodi V3.5.1
% 18.58/2.69 % Refutation found
% 18.58/2.69 % SZS status Theorem for theBenchmark: Theorem is valid
% 18.58/2.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 18.58/2.73 % Elapsed time: 2.374925 seconds
% 18.58/2.73 % CPU time: 18.795786 seconds
% 18.58/2.73 % Memory used: 84.834 MB
%------------------------------------------------------------------------------