TSTP Solution File: SET763+4 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET763+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 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 12:35:08 EDT 2023
% Result : Timeout 295.52s 37.68s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 71 ( 13 unt; 0 def)
% Number of atoms : 279 ( 17 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 335 ( 127 ~; 121 |; 72 &)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-4 aty)
% Number of variables : 239 (; 213 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [F,A,B] :
( maps(F,A,B)
<=> ( ! [X] :
( member(X,A)
=> ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) )
& ! [X,Y1,Y2] :
( ( member(X,A)
& member(Y1,B)
& member(Y2,B) )
=> ( ( apply(F,X,Y1)
& apply(F,X,Y2) )
=> Y1 = Y2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [F,A,Y] :
( member(Y,image2(F,A))
<=> ? [X] :
( member(X,A)
& apply(F,X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [F,A,B,X] :
( ( maps(F,A,B)
& subset(X,A)
& equal_set(image2(F,X),empty_set) )
=> equal_set(X,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [F,A,B,X] :
( ( maps(F,A,B)
& subset(X,A)
& equal_set(image2(F,X),empty_set) )
=> equal_set(X,empty_set) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( ~ member(X,A)
| member(X,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f32,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(miniscoping,[status(esa)],[f32]) ).
fof(f34,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ( member(sk0_0(B,A),A)
& ~ member(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f37,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f38,plain,
! [A,B] :
( ( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) )
& ( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f39,plain,
( ! [A,B] :
( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) )
& ! [A,B] :
( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(miniscoping,[status(esa)],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f42,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f57,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f63,plain,
! [X,A] :
( ( ~ member(X,singleton(A))
| X = A )
& ( member(X,singleton(A))
| X != A ) ),
inference(NNF_transformation,[status(esa)],[f8]) ).
fof(f64,plain,
( ! [X,A] :
( ~ member(X,singleton(A))
| X = A )
& ! [X,A] :
( member(X,singleton(A))
| X != A ) ),
inference(miniscoping,[status(esa)],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( member(X0,singleton(X1))
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f85,plain,
! [F,A,B] :
( maps(F,A,B)
<=> ( ! [X] :
( ~ member(X,A)
| ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) )
& ! [X,Y1,Y2] :
( ~ member(X,A)
| ~ member(Y1,B)
| ~ member(Y2,B)
| ~ apply(F,X,Y1)
| ~ apply(F,X,Y2)
| Y1 = Y2 ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f86,plain,
! [F,A,B,X] :
( pd0_0(X,B,A,F)
<=> ( ~ member(X,A)
| ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) ) ),
introduced(predicate_definition,[f85]) ).
fof(f87,plain,
! [F,A,B] :
( maps(F,A,B)
<=> ( ! [X] : pd0_0(X,B,A,F)
& ! [X,Y1,Y2] :
( ~ member(X,A)
| ~ member(Y1,B)
| ~ member(Y2,B)
| ~ apply(F,X,Y1)
| ~ apply(F,X,Y2)
| Y1 = Y2 ) ) ),
inference(formula_renaming,[status(thm)],[f85,f86]) ).
fof(f88,plain,
! [F,A,B] :
( ( ~ maps(F,A,B)
| ( ! [X] : pd0_0(X,B,A,F)
& ! [X,Y1,Y2] :
( ~ member(X,A)
| ~ member(Y1,B)
| ~ member(Y2,B)
| ~ apply(F,X,Y1)
| ~ apply(F,X,Y2)
| Y1 = Y2 ) ) )
& ( maps(F,A,B)
| ? [X] : ~ pd0_0(X,B,A,F)
| ? [X,Y1,Y2] :
( member(X,A)
& member(Y1,B)
& member(Y2,B)
& apply(F,X,Y1)
& apply(F,X,Y2)
& Y1 != Y2 ) ) ),
inference(NNF_transformation,[status(esa)],[f87]) ).
fof(f89,plain,
( ! [F,A,B] :
( ~ maps(F,A,B)
| ( ! [X] : pd0_0(X,B,A,F)
& ! [X,Y1,Y2] :
( ~ member(X,A)
| ~ member(Y1,B)
| ~ member(Y2,B)
| ~ apply(F,X,Y1)
| ~ apply(F,X,Y2)
| Y1 = Y2 ) ) )
& ! [F,A,B] :
( maps(F,A,B)
| ? [X] : ~ pd0_0(X,B,A,F)
| ? [X,Y1,Y2] :
( member(X,A)
& member(Y1,B)
& member(Y2,B)
& apply(F,X,Y1)
& apply(F,X,Y2)
& Y1 != Y2 ) ) ),
inference(miniscoping,[status(esa)],[f88]) ).
fof(f90,plain,
( ! [F,A,B] :
( ~ maps(F,A,B)
| ( ! [X] : pd0_0(X,B,A,F)
& ! [X,Y1,Y2] :
( ~ member(X,A)
| ~ member(Y1,B)
| ~ member(Y2,B)
| ~ apply(F,X,Y1)
| ~ apply(F,X,Y2)
| Y1 = Y2 ) ) )
& ! [F,A,B] :
( maps(F,A,B)
| ~ pd0_0(sk0_3(B,A,F),B,A,F)
| ( member(sk0_4(B,A,F),A)
& member(sk0_5(B,A,F),B)
& member(sk0_6(B,A,F),B)
& apply(F,sk0_4(B,A,F),sk0_5(B,A,F))
& apply(F,sk0_4(B,A,F),sk0_6(B,A,F))
& sk0_5(B,A,F) != sk0_6(B,A,F) ) ) ),
inference(skolemization,[status(esa)],[f89]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( ~ maps(X0,X1,X2)
| pd0_0(X3,X2,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f90]) ).
fof(f176,plain,
! [F,A,Y] :
( ( ~ member(Y,image2(F,A))
| ? [X] :
( member(X,A)
& apply(F,X,Y) ) )
& ( member(Y,image2(F,A))
| ! [X] :
( ~ member(X,A)
| ~ apply(F,X,Y) ) ) ),
inference(NNF_transformation,[status(esa)],[f22]) ).
fof(f177,plain,
( ! [F,A,Y] :
( ~ member(Y,image2(F,A))
| ? [X] :
( member(X,A)
& apply(F,X,Y) ) )
& ! [F,A,Y] :
( member(Y,image2(F,A))
| ! [X] :
( ~ member(X,A)
| ~ apply(F,X,Y) ) ) ),
inference(miniscoping,[status(esa)],[f176]) ).
fof(f178,plain,
( ! [F,A,Y] :
( ~ member(Y,image2(F,A))
| ( member(sk0_23(Y,A,F),A)
& apply(F,sk0_23(Y,A,F),Y) ) )
& ! [F,A,Y] :
( member(Y,image2(F,A))
| ! [X] :
( ~ member(X,A)
| ~ apply(F,X,Y) ) ) ),
inference(skolemization,[status(esa)],[f177]) ).
fof(f181,plain,
! [X0,X1,X2,X3] :
( member(X0,image2(X1,X2))
| ~ member(X3,X2)
| ~ apply(X1,X3,X0) ),
inference(cnf_transformation,[status(esa)],[f178]) ).
fof(f244,plain,
? [F,A,B,X] :
( maps(F,A,B)
& subset(X,A)
& equal_set(image2(F,X),empty_set)
& ~ equal_set(X,empty_set) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f245,plain,
? [X] :
( ? [F] :
( ? [A] :
( ? [B] : maps(F,A,B)
& subset(X,A) )
& equal_set(image2(F,X),empty_set) )
& ~ equal_set(X,empty_set) ),
inference(miniscoping,[status(esa)],[f244]) ).
fof(f246,plain,
( maps(sk0_40,sk0_41,sk0_42)
& subset(sk0_39,sk0_41)
& equal_set(image2(sk0_40,sk0_39),empty_set)
& ~ equal_set(sk0_39,empty_set) ),
inference(skolemization,[status(esa)],[f245]) ).
fof(f247,plain,
maps(sk0_40,sk0_41,sk0_42),
inference(cnf_transformation,[status(esa)],[f246]) ).
fof(f248,plain,
subset(sk0_39,sk0_41),
inference(cnf_transformation,[status(esa)],[f246]) ).
fof(f249,plain,
equal_set(image2(sk0_40,sk0_39),empty_set),
inference(cnf_transformation,[status(esa)],[f246]) ).
fof(f250,plain,
~ equal_set(sk0_39,empty_set),
inference(cnf_transformation,[status(esa)],[f246]) ).
fof(f251,plain,
! [F,A,B,X] :
( ( ~ pd0_0(X,B,A,F)
| ~ member(X,A)
| ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) )
& ( pd0_0(X,B,A,F)
| ( member(X,A)
& ! [Y] :
( ~ member(Y,B)
| ~ apply(F,X,Y) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f86]) ).
fof(f252,plain,
( ! [F,A,B,X] :
( ~ pd0_0(X,B,A,F)
| ~ member(X,A)
| ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) )
& ! [F,A,B,X] :
( pd0_0(X,B,A,F)
| ( member(X,A)
& ! [Y] :
( ~ member(Y,B)
| ~ apply(F,X,Y) ) ) ) ),
inference(miniscoping,[status(esa)],[f251]) ).
fof(f253,plain,
( ! [F,A,B,X] :
( ~ pd0_0(X,B,A,F)
| ~ member(X,A)
| ( member(sk0_43(X,B,A,F),B)
& apply(F,X,sk0_43(X,B,A,F)) ) )
& ! [F,A,B,X] :
( pd0_0(X,B,A,F)
| ( member(X,A)
& ! [Y] :
( ~ member(Y,B)
| ~ apply(F,X,Y) ) ) ) ),
inference(skolemization,[status(esa)],[f252]) ).
fof(f255,plain,
! [X0,X1,X2,X3] :
( ~ pd0_0(X0,X1,X2,X3)
| ~ member(X0,X2)
| apply(X3,X0,sk0_43(X0,X1,X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f253]) ).
fof(f264,plain,
! [X0] : member(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(esa)],[f66]) ).
fof(f267,plain,
subset(image2(sk0_40,sk0_39),empty_set),
inference(resolution,[status(thm)],[f40,f249]) ).
fof(f297,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(X0,X1)
| ~ apply(X2,X0,X3)
| ~ subset(image2(X2,X1),X4)
| member(X3,X4) ),
inference(resolution,[status(thm)],[f181,f35]) ).
fof(f298,plain,
! [X0,X1] :
( ~ member(X0,sk0_39)
| ~ apply(sk0_40,X0,X1)
| member(X1,empty_set) ),
inference(resolution,[status(thm)],[f297,f267]) ).
fof(f299,plain,
! [X0,X1] :
( ~ member(X0,sk0_39)
| ~ apply(sk0_40,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f57]) ).
fof(f300,plain,
! [X0,X1] :
( ~ subset(singleton(X0),X1)
| member(X0,X1) ),
inference(resolution,[status(thm)],[f264,f35]) ).
fof(f301,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[status(thm)],[f36,f57]) ).
fof(f302,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| ~ subset(X0,X2)
| member(sk0_0(X1,X0),X2) ),
inference(resolution,[status(thm)],[f36,f35]) ).
fof(f303,plain,
! [X0] :
( equal_set(X0,empty_set)
| ~ subset(X0,empty_set) ),
inference(resolution,[status(thm)],[f301,f42]) ).
fof(f306,plain,
! [X0,X1] :
( sk0_0(X0,singleton(X1)) = X1
| subset(singleton(X1),X0) ),
inference(resolution,[status(thm)],[f65,f36]) ).
fof(f340,plain,
! [X0,X1,X2,X3] :
( subset(X0,X1)
| ~ subset(X0,X2)
| ~ subset(X2,X3)
| member(sk0_0(X1,X0),X3) ),
inference(resolution,[status(thm)],[f302,f35]) ).
fof(f378,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| ~ subset(X0,X2)
| ~ subset(X2,X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f340,f37]) ).
fof(f379,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| ~ subset(X0,X2)
| ~ subset(X2,X1) ),
inference(duplicate_literals_removal,[status(esa)],[f378]) ).
fof(f391,plain,
! [X0] :
( subset(X0,sk0_41)
| ~ subset(X0,sk0_39) ),
inference(resolution,[status(thm)],[f379,f248]) ).
fof(f2634,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ member(X0,X1)
| subset(singleton(X0),X1) ),
inference(paramodulation,[status(thm)],[f306,f37]) ).
fof(f2635,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ member(X0,X1) ),
inference(duplicate_literals_removal,[status(esa)],[f2634]) ).
fof(f2649,plain,
! [X0] :
( ~ member(X0,sk0_39)
| subset(singleton(X0),sk0_41) ),
inference(resolution,[status(thm)],[f2635,f391]) ).
fof(f2665,plain,
! [X0] :
( ~ member(X0,sk0_39)
| member(X0,sk0_41) ),
inference(resolution,[status(thm)],[f2649,f300]) ).
fof(f27369,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1,X2,sk0_40)
| ~ member(X0,X2)
| ~ member(X0,sk0_39) ),
inference(resolution,[status(thm)],[f255,f299]) ).
fof(f29014,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| ~ member(X0,sk0_39)
| ~ maps(sk0_40,X1,X2) ),
inference(resolution,[status(thm)],[f27369,f91]) ).
fof(f29015,plain,
! [X0] :
( ~ member(X0,sk0_41)
| ~ member(X0,sk0_39) ),
inference(resolution,[status(thm)],[f29014,f247]) ).
fof(f29016,plain,
! [X0] : ~ member(X0,sk0_39),
inference(forward_subsumption_resolution,[status(thm)],[f29015,f2665]) ).
fof(f29063,plain,
! [X0] : subset(sk0_39,X0),
inference(resolution,[status(thm)],[f29016,f36]) ).
fof(f29114,plain,
equal_set(sk0_39,empty_set),
inference(resolution,[status(thm)],[f29063,f303]) ).
fof(f29115,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f29114,f250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SET763+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.04/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n017.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 09:41:10 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.5.1
% 295.52/37.68 % Refutation found
% 295.52/37.68 % SZS status Theorem for theBenchmark: Theorem is valid
% 295.52/37.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 296.63/37.88 % Elapsed time: 37.570711 seconds
% 296.63/37.88 % CPU time: 296.603770 seconds
% 296.63/37.88 % Memory used: 822.207 MB
%------------------------------------------------------------------------------