TSTP Solution File: NUN085+2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUN085+2 : 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 12:31:18 EDT 2023
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 68 ( 29 unt; 0 def)
% Number of atoms : 150 ( 46 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 143 ( 61 ~; 43 |; 36 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 120 (; 105 !; 15 ?)
% 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(f11,axiom,
! [X7,Y10] :
( ! [Y20] :
( ~ r1(Y20)
| Y20 != Y10 )
| ~ r2(X7,Y10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [Y1] :
( ! [Y2] :
( ! [Y3] :
( ~ r1(Y3)
| ~ r3(Y3,Y2,Y1) )
| ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y2) ) )
| ! [Y5] :
( Y1 != Y5
| ~ r1(Y5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [Y1] :
( ! [Y2] :
( ! [Y3] :
( ~ r1(Y3)
| ~ r3(Y3,Y2,Y1) )
| ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y2) ) )
| ! [Y5] :
( Y1 != Y5
| ~ r1(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(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(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] :
( r1(Y3)
& r3(Y3,Y2,Y1) )
& ? [Y4] :
( r1(Y4)
& r2(Y4,Y2) ) )
& ? [Y5] :
( Y1 = Y5
& r1(Y5) ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f65,plain,
( r1(sk0_22)
& r3(sk0_22,sk0_21,sk0_20)
& r1(sk0_23)
& r2(sk0_23,sk0_21)
& sk0_20 = sk0_24
& r1(sk0_24) ),
inference(skolemization,[status(esa)],[f64]) ).
fof(f66,plain,
r1(sk0_22),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f67,plain,
r3(sk0_22,sk0_21,sk0_20),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f68,plain,
r1(sk0_23),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f69,plain,
r2(sk0_23,sk0_21),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f70,plain,
sk0_20 = sk0_24,
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f71,plain,
r1(sk0_24),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f72,plain,
! [Y24,X19] :
( ~ pd0_0(X19,Y24)
| ( ~ r1(X19)
& X19 != Y24 ) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f73,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| ~ r1(X0) ),
inference(cnf_transformation,[status(esa)],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f72]) ).
fof(f75,plain,
! [X11,Y21,X12] :
( ~ pd0_1(X12,Y21,X11)
| ( ~ r2(X11,X12)
& X12 != Y21 ) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ pd0_1(X0,X1,X2)
| ~ r2(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f75]) ).
fof(f78,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(f79,plain,
! [X0,X1,X2,X3] :
( ~ pd0_2(X0,X1,X2,X3)
| ~ r3(X3,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f78]) ).
fof(f88,plain,
! [X0,X1] :
( ~ r1(X0)
| ~ r2(X1,X0) ),
inference(destructive_equality_resolution,[status(esa)],[f63]) ).
fof(f89,plain,
! [X0] : ~ pd0_0(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f74]) ).
fof(f93,plain,
r1(sk0_20),
inference(forward_demodulation,[status(thm)],[f70,f71]) ).
fof(f96,plain,
r1(sk0_0),
inference(resolution,[status(thm)],[f17,f89]) ).
fof(f102,plain,
! [X0] :
( ~ r1(X0)
| X0 = sk0_0 ),
inference(resolution,[status(thm)],[f73,f18]) ).
fof(f106,plain,
sk0_20 = sk0_0,
inference(resolution,[status(thm)],[f102,f93]) ).
fof(f107,plain,
sk0_23 = sk0_0,
inference(resolution,[status(thm)],[f102,f68]) ).
fof(f108,plain,
sk0_22 = sk0_0,
inference(resolution,[status(thm)],[f102,f66]) ).
fof(f109,plain,
r3(sk0_22,sk0_21,sk0_0),
inference(backward_demodulation,[status(thm)],[f106,f67]) ).
fof(f113,plain,
r2(sk0_0,sk0_21),
inference(backward_demodulation,[status(thm)],[f107,f69]) ).
fof(f120,plain,
r3(sk0_0,sk0_21,sk0_0),
inference(forward_demodulation,[status(thm)],[f108,f109]) ).
fof(f132,plain,
! [X0,X1] :
( ~ r2(X0,X1)
| X1 = sk0_1(X0) ),
inference(resolution,[status(thm)],[f76,f23]) ).
fof(f133,plain,
sk0_21 = sk0_1(sk0_0),
inference(resolution,[status(thm)],[f132,f113]) ).
fof(f139,plain,
! [X0] :
( pd0_1(X0,sk0_21,sk0_0)
| X0 = sk0_1(sk0_0) ),
inference(paramodulation,[status(thm)],[f133,f23]) ).
fof(f140,plain,
! [X0] :
( pd0_1(X0,sk0_21,sk0_0)
| X0 = sk0_21 ),
inference(forward_demodulation,[status(thm)],[f133,f139]) ).
fof(f142,plain,
! [X0] :
( X0 = sk0_21
| ~ r2(sk0_0,X0) ),
inference(resolution,[status(thm)],[f140,f76]) ).
fof(f145,plain,
! [X0] : sk0_6(sk0_0,X0) = sk0_21,
inference(resolution,[status(thm)],[f142,f35]) ).
fof(f153,plain,
! [X0,X1] : r3(X0,sk0_6(X1,X0),sk0_4(X1,X0)),
inference(forward_demodulation,[status(thm)],[f37,f36]) ).
fof(f154,plain,
! [X0] : r3(X0,sk0_21,sk0_4(sk0_0,X0)),
inference(paramodulation,[status(thm)],[f145,f153]) ).
fof(f166,plain,
! [X0,X1] : ~ r1(sk0_4(X0,X1)),
inference(resolution,[status(thm)],[f38,f88]) ).
fof(f181,plain,
! [X0,X1,X2] :
( ~ r3(X0,X1,X2)
| X2 = sk0_2(X1,X0) ),
inference(resolution,[status(thm)],[f79,f28]) ).
fof(f183,plain,
sk0_0 = sk0_2(sk0_21,sk0_0),
inference(resolution,[status(thm)],[f181,f120]) ).
fof(f185,plain,
! [X0] : sk0_4(sk0_0,X0) = sk0_2(sk0_21,X0),
inference(resolution,[status(thm)],[f181,f154]) ).
fof(f213,plain,
! [X0] : ~ r1(sk0_2(sk0_21,X0)),
inference(paramodulation,[status(thm)],[f185,f166]) ).
fof(f214,plain,
~ r1(sk0_0),
inference(paramodulation,[status(thm)],[f183,f213]) ).
fof(f215,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f214,f96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUN085+2 : TPTP v8.1.2. Released v7.3.0.
% 0.06/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 10:11:40 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 0.12/0.36 % Refutation found
% 0.12/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.63 % Elapsed time: 0.066823 seconds
% 0.19/0.63 % CPU time: 0.025080 seconds
% 0.19/0.63 % Memory used: 3.752 MB
%------------------------------------------------------------------------------