TSTP Solution File: NUN066+2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUN066+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 0.19s 0.53s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 6 unt; 0 def)
% Number of atoms : 153 ( 48 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 176 ( 71 ~; 73 |; 31 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 0 con; 1-2 aty)
% Number of variables : 121 (; 102 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
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/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(f9,axiom,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( r1(Y18)
& Y8 = Y18 ) ),
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] :
( ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y3) )
| ~ r2(Y3,Y2) )
| Y1 != Y2 )
& ! [Y5] :
( ~ r1(Y5)
| Y1 != Y5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ? [Y1] :
( ! [Y2] :
( ! [Y3] :
( ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y3) )
| ~ r2(Y3,Y2) )
| Y1 != Y2 )
& ! [Y5] :
( ~ r1(Y5)
| Y1 != Y5 ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
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(f46,plain,
! [X0,X1,X2,X3] :
( ~ r2(X0,X1)
| X1 != X2
| ~ r2(X3,X2)
| X0 = X3 ),
inference(cnf_transformation,[status(esa)],[f7]) ).
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(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(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] :
( ? [Y4] :
( r1(Y4)
& r2(Y4,Y3) )
& r2(Y3,Y2) )
& Y1 = Y2 )
| ? [Y5] :
( r1(Y5)
& Y1 = Y5 ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f65,plain,
! [Y1,Y2] :
( pd0_5(Y2,Y1)
=> ( ? [Y3] :
( ? [Y4] :
( r1(Y4)
& r2(Y4,Y3) )
& r2(Y3,Y2) )
& Y1 = Y2 ) ),
introduced(predicate_definition,[f64]) ).
fof(f66,plain,
! [Y1] :
( ? [Y2] : pd0_5(Y2,Y1)
| ? [Y5] :
( r1(Y5)
& Y1 = Y5 ) ),
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(f85,plain,
! [Y1,Y2] :
( ~ pd0_5(Y2,Y1)
| ( ? [Y3] :
( ? [Y4] :
( r1(Y4)
& r2(Y4,Y3) )
& r2(Y3,Y2) )
& Y1 = Y2 ) ),
inference(pre_NNF_transformation,[status(esa)],[f65]) ).
fof(f86,plain,
! [Y1,Y2] :
( ~ pd0_5(Y2,Y1)
| ( r1(sk0_23(Y2,Y1))
& r2(sk0_23(Y2,Y1),sk0_22(Y2,Y1))
& r2(sk0_22(Y2,Y1),Y2)
& Y1 = Y2 ) ),
inference(skolemization,[status(esa)],[f85]) ).
fof(f88,plain,
! [X0,X1] :
( ~ pd0_5(X0,X1)
| r2(sk0_23(X0,X1),sk0_22(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f86]) ).
fof(f89,plain,
! [X0,X1] :
( ~ pd0_5(X0,X1)
| r2(sk0_22(X0,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f86]) ).
fof(f90,plain,
! [X0,X1] :
( ~ pd0_5(X0,X1)
| X1 = X0 ),
inference(cnf_transformation,[status(esa)],[f86]) ).
fof(f91,plain,
! [X0] :
( X0 = sk0_21(X0)
| X0 = sk0_20(X0) ),
inference(resolution,[status(thm)],[f69,f90]) ).
fof(f92,plain,
! [X0] :
( r1(sk0_21(X0))
| X0 = sk0_20(X0) ),
inference(resolution,[status(thm)],[f68,f90]) ).
fof(f94,plain,
! [X0] :
( r1(X0)
| X0 = sk0_20(X0)
| X0 = sk0_20(X0) ),
inference(paramodulation,[status(thm)],[f91,f92]) ).
fof(f95,plain,
! [X0] :
( r1(X0)
| X0 = sk0_20(X0) ),
inference(duplicate_literals_removal,[status(esa)],[f94]) ).
fof(f96,plain,
! [X0] :
( pd0_5(X0,X0)
| r1(sk0_21(X0))
| r1(X0) ),
inference(paramodulation,[status(thm)],[f95,f68]) ).
fof(f97,plain,
! [X0] :
( pd0_5(X0,X0)
| X0 = sk0_21(X0)
| r1(X0) ),
inference(paramodulation,[status(thm)],[f95,f69]) ).
fof(f101,plain,
! [X0,X1,X2,X3] :
( ~ r2(X0,X1)
| X1 != X2
| X0 = sk0_22(X2,X3)
| ~ pd0_5(X2,X3) ),
inference(resolution,[status(thm)],[f46,f89]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ~ pd0_5(X0,X1)
| ~ r1(X2)
| X2 != sk0_22(X0,X1) ),
inference(resolution,[status(thm)],[f88,f63]) ).
fof(f107,plain,
! [X0] : r1(sk0_14(X0)),
inference(paramodulation,[status(thm)],[f55,f54]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ~ r1(X0)
| X0 != sk0_6(X1,X2) ),
inference(resolution,[status(thm)],[f35,f63]) ).
fof(f116,plain,
! [X0,X1,X2,X3] :
( ~ pd0_5(X0,X1)
| ~ r1(X2)
| ~ r2(X2,X3)
| X3 != X0
| ~ pd0_5(X0,X1) ),
inference(resolution,[status(thm)],[f106,f101]) ).
fof(f117,plain,
! [X0,X1,X2,X3] :
( ~ pd0_5(X0,X1)
| ~ r1(X2)
| ~ r2(X2,X3)
| X3 != X0 ),
inference(duplicate_literals_removal,[status(esa)],[f116]) ).
fof(f128,plain,
! [X0,X1,X2] :
( ~ r1(X0)
| ~ r2(X0,X1)
| X1 != X2
| r1(sk0_21(X2))
| r1(X2) ),
inference(resolution,[status(thm)],[f117,f96]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ~ r1(X0)
| ~ r2(X0,X1)
| X1 != X2
| r1(sk0_21(X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f63]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ~ r1(X0)
| ~ r2(X0,X1)
| X1 != X2
| X2 = sk0_21(X2)
| r1(X2) ),
inference(resolution,[status(thm)],[f117,f97]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ~ r1(X0)
| ~ r2(X0,X1)
| X1 != X2
| X2 = sk0_21(X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f130,f63]) ).
fof(f136,plain,
! [X0,X1,X2] :
( ~ r1(X0)
| sk0_6(X0,X1) != X2
| X2 = sk0_21(X2) ),
inference(resolution,[status(thm)],[f131,f35]) ).
fof(f141,plain,
! [X0,X1,X2] :
( ~ r1(X0)
| sk0_6(X0,X1) != X2
| r1(sk0_21(X2)) ),
inference(resolution,[status(thm)],[f129,f35]) ).
fof(f156,plain,
! [X0,X1] :
( ~ r1(X0)
| r1(sk0_21(sk0_6(X0,X1))) ),
inference(equality_resolution,[status(esa)],[f141]) ).
fof(f179,plain,
! [X0,X1] :
( ~ r1(X0)
| sk0_6(X0,X1) = sk0_21(sk0_6(X0,X1)) ),
inference(equality_resolution,[status(esa)],[f136]) ).
fof(f323,plain,
! [X0,X1] :
( ~ r1(sk0_21(sk0_6(X0,X1)))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f109,f179]) ).
fof(f324,plain,
! [X0] : ~ r1(X0),
inference(forward_subsumption_resolution,[status(thm)],[f323,f156]) ).
fof(f337,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f107,f324]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUN066+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 : n029.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 : Tue May 30 11:00:07 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.5.1
% 0.19/0.53 % Refutation found
% 0.19/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.55 % Elapsed time: 0.199658 seconds
% 0.19/0.55 % CPU time: 1.441175 seconds
% 0.19/0.55 % Memory used: 72.193 MB
%------------------------------------------------------------------------------