TSTP Solution File: SET764+4 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% 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 : n013.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 : Tue Apr 30 20:40:18 EDT 2024
% Result : Theorem 0.15s 0.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 95 ( 37 ~; 30 |; 21 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 81 ( 70 !; 11 ?)
% 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(f24,axiom,
! [F,B,X] :
( member(X,inverse_image2(F,B))
<=> ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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(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(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(f265,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[status(thm)],[f36,f57]) ).
fof(f266,plain,
! [X0] :
( equal_set(X0,empty_set)
| ~ subset(X0,empty_set) ),
inference(resolution,[status(thm)],[f265,f42]) ).
fof(f325,plain,
! [X0,X1] : ~ member(X0,inverse_image2(X1,empty_set)),
inference(resolution,[status(thm)],[f192,f57]) ).
fof(f332,plain,
! [X0,X1] : subset(inverse_image2(X0,empty_set),X1),
inference(resolution,[status(thm)],[f325,f36]) ).
fof(f343,plain,
! [X0] : equal_set(inverse_image2(X0,empty_set),empty_set),
inference(resolution,[status(thm)],[f332,f266]) ).
fof(f347,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f248,f343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET764+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.12/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.15/0.35 % Computer : n013.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Apr 29 21:42:04 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.37 % Drodi V3.6.0
% 0.15/0.42 % Refutation found
% 0.15/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.42 % Elapsed time: 0.064051 seconds
% 0.15/0.42 % CPU time: 0.364622 seconds
% 0.15/0.42 % Total memory used: 58.953 MB
% 0.15/0.42 % Net memory used: 58.774 MB
%------------------------------------------------------------------------------