TSTP Solution File: SET764+4 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET764+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n025.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 12:35:09 EDT 2023
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 8 unt; 0 def)
% Number of atoms : 137 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 144 ( 52 ~; 55 |; 27 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 137 (; 124 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [F,A] :
( identity(F,A)
<=> ! [X] :
( member(X,A)
=> apply(F,X,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [F,B,X] :
( member(X,inverse_image2(F,B))
<=> ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [F,A,B] :
( maps(F,A,B)
=> equal_set(inverse_image2(F,empty_set),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [F,A,B] :
( maps(F,A,B)
=> equal_set(inverse_image2(F,empty_set),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(f36,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
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(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(f130,plain,
! [F,A] :
( identity(F,A)
<=> ! [X] :
( ~ member(X,A)
| apply(F,X,X) ) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f131,plain,
! [F,A] :
( ( ~ identity(F,A)
| ! [X] :
( ~ member(X,A)
| apply(F,X,X) ) )
& ( identity(F,A)
| ? [X] :
( member(X,A)
& ~ apply(F,X,X) ) ) ),
inference(NNF_transformation,[status(esa)],[f130]) ).
fof(f132,plain,
( ! [F,A] :
( ~ identity(F,A)
| ! [X] :
( ~ member(X,A)
| apply(F,X,X) ) )
& ! [F,A] :
( identity(F,A)
| ? [X] :
( member(X,A)
& ~ apply(F,X,X) ) ) ),
inference(miniscoping,[status(esa)],[f131]) ).
fof(f133,plain,
( ! [F,A] :
( ~ identity(F,A)
| ! [X] :
( ~ member(X,A)
| apply(F,X,X) ) )
& ! [F,A] :
( identity(F,A)
| ( member(sk0_15(A,F),A)
& ~ apply(F,sk0_15(A,F),sk0_15(A,F)) ) ) ),
inference(skolemization,[status(esa)],[f132]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ~ identity(X0,X1)
| ~ member(X2,X1)
| apply(X0,X2,X2) ),
inference(cnf_transformation,[status(esa)],[f133]) ).
fof(f135,plain,
! [X0,X1] :
( identity(X0,X1)
| member(sk0_15(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f133]) ).
fof(f189,plain,
! [F,B,X] :
( ( ~ member(X,inverse_image2(F,B))
| ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) )
& ( member(X,inverse_image2(F,B))
| ! [Y] :
( ~ member(Y,B)
| ~ apply(F,X,Y) ) ) ),
inference(NNF_transformation,[status(esa)],[f24]) ).
fof(f190,plain,
( ! [F,B,X] :
( ~ member(X,inverse_image2(F,B))
| ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) )
& ! [F,B,X] :
( member(X,inverse_image2(F,B))
| ! [Y] :
( ~ member(Y,B)
| ~ apply(F,X,Y) ) ) ),
inference(miniscoping,[status(esa)],[f189]) ).
fof(f191,plain,
( ! [F,B,X] :
( ~ member(X,inverse_image2(F,B))
| ( member(sk0_25(X,B,F),B)
& apply(F,X,sk0_25(X,B,F)) ) )
& ! [F,B,X] :
( member(X,inverse_image2(F,B))
| ! [Y] :
( ~ member(Y,B)
| ~ apply(F,X,Y) ) ) ),
inference(skolemization,[status(esa)],[f190]) ).
fof(f192,plain,
! [X0,X1,X2] :
( ~ member(X0,inverse_image2(X1,X2))
| member(sk0_25(X0,X2,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f191]) ).
fof(f194,plain,
! [X0,X1,X2,X3] :
( member(X0,inverse_image2(X1,X2))
| ~ member(X3,X2)
| ~ apply(X1,X0,X3) ),
inference(cnf_transformation,[status(esa)],[f191]) ).
fof(f244,plain,
? [F,A,B] :
( maps(F,A,B)
& ~ equal_set(inverse_image2(F,empty_set),empty_set) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f245,plain,
? [F] :
( ? [A,B] : maps(F,A,B)
& ~ equal_set(inverse_image2(F,empty_set),empty_set) ),
inference(miniscoping,[status(esa)],[f244]) ).
fof(f246,plain,
( maps(sk0_39,sk0_40,sk0_41)
& ~ equal_set(inverse_image2(sk0_39,empty_set),empty_set) ),
inference(skolemization,[status(esa)],[f245]) ).
fof(f248,plain,
~ equal_set(inverse_image2(sk0_39,empty_set),empty_set),
inference(cnf_transformation,[status(esa)],[f246]) ).
fof(f266,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[status(thm)],[f36,f57]) ).
fof(f267,plain,
! [X0,X1,X2,X3] :
( subset(X0,X1)
| member(X2,inverse_image2(X3,X0))
| ~ apply(X3,X2,sk0_0(X1,X0)) ),
inference(resolution,[status(thm)],[f36,f194]) ).
fof(f299,plain,
! [X0,X1,X2] :
( member(sk0_25(sk0_15(inverse_image2(X0,X1),X2),X1,X0),X1)
| identity(X2,inverse_image2(X0,X1)) ),
inference(resolution,[status(thm)],[f192,f135]) ).
fof(f311,plain,
! [X0,X1] : identity(X0,inverse_image2(X1,empty_set)),
inference(resolution,[status(thm)],[f299,f57]) ).
fof(f313,plain,
! [X0,X1,X2] :
( ~ member(X0,inverse_image2(X1,empty_set))
| apply(X2,X0,X0) ),
inference(resolution,[status(thm)],[f311,f134]) ).
fof(f316,plain,
! [X0,X1,X2] :
( apply(X0,sk0_0(X1,inverse_image2(X2,empty_set)),sk0_0(X1,inverse_image2(X2,empty_set)))
| subset(inverse_image2(X2,empty_set),X1) ),
inference(resolution,[status(thm)],[f313,f36]) ).
fof(f318,plain,
! [X0,X1,X2] :
( subset(inverse_image2(X0,empty_set),X1)
| subset(inverse_image2(X0,empty_set),X1)
| member(sk0_0(X1,inverse_image2(X0,empty_set)),inverse_image2(X2,inverse_image2(X0,empty_set))) ),
inference(resolution,[status(thm)],[f316,f267]) ).
fof(f319,plain,
! [X0,X1,X2] :
( subset(inverse_image2(X0,empty_set),X1)
| member(sk0_0(X1,inverse_image2(X0,empty_set)),inverse_image2(X2,inverse_image2(X0,empty_set))) ),
inference(duplicate_literals_removal,[status(esa)],[f318]) ).
fof(f323,plain,
! [X0,X1,X2] :
( subset(inverse_image2(X0,empty_set),X1)
| member(sk0_25(sk0_0(X1,inverse_image2(X0,empty_set)),inverse_image2(X0,empty_set),X2),inverse_image2(X0,empty_set)) ),
inference(resolution,[status(thm)],[f319,f192]) ).
fof(f345,plain,
! [X0,X1,X2] :
( subset(inverse_image2(X0,empty_set),X1)
| member(sk0_25(sk0_25(sk0_0(X1,inverse_image2(X0,empty_set)),inverse_image2(X0,empty_set),X2),empty_set,X0),empty_set) ),
inference(resolution,[status(thm)],[f323,f192]) ).
fof(f346,plain,
! [X0,X1] : subset(inverse_image2(X0,empty_set),X1),
inference(forward_subsumption_resolution,[status(thm)],[f345,f57]) ).
fof(f351,plain,
! [X0,X1] :
( equal_set(inverse_image2(X0,empty_set),X1)
| ~ subset(X1,inverse_image2(X0,empty_set)) ),
inference(resolution,[status(thm)],[f346,f42]) ).
fof(f358,plain,
! [X0] : equal_set(inverse_image2(X0,empty_set),empty_set),
inference(resolution,[status(thm)],[f351,f266]) ).
fof(f360,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f248,f358]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET764+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 10:31:57 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.39 % Elapsed time: 0.044288 seconds
% 0.20/0.39 % CPU time: 0.179170 seconds
% 0.20/0.39 % Memory used: 20.385 MB
%------------------------------------------------------------------------------