TSTP Solution File: SET755+4 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET755+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 : Theorem 134.20s 17.33s
% Output : CNFRefutation 134.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 42 ( 6 unt; 0 def)
% Number of atoms : 148 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 173 ( 67 ~; 69 |; 31 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 142 (; 127 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
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,X,Y] :
( ( maps(F,A,B)
& subset(X,B)
& subset(Y,B)
& subset(X,Y) )
=> subset(inverse_image2(F,X),inverse_image2(F,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [F,A,B,X,Y] :
( ( maps(F,A,B)
& subset(X,B)
& subset(Y,B)
& subset(X,Y) )
=> subset(inverse_image2(F,X),inverse_image2(F,Y)) ),
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(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(f193,plain,
! [X0,X1,X2] :
( ~ member(X0,inverse_image2(X1,X2))
| apply(X1,X0,sk0_25(X0,X2,X1)) ),
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,X,Y] :
( maps(F,A,B)
& subset(X,B)
& subset(Y,B)
& subset(X,Y)
& ~ subset(inverse_image2(F,X),inverse_image2(F,Y)) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f245,plain,
? [F,X,Y] :
( ? [B] :
( ? [A] : maps(F,A,B)
& subset(X,B)
& subset(Y,B) )
& subset(X,Y)
& ~ subset(inverse_image2(F,X),inverse_image2(F,Y)) ),
inference(miniscoping,[status(esa)],[f244]) ).
fof(f246,plain,
( maps(sk0_39,sk0_43,sk0_42)
& subset(sk0_40,sk0_42)
& subset(sk0_41,sk0_42)
& subset(sk0_40,sk0_41)
& ~ subset(inverse_image2(sk0_39,sk0_40),inverse_image2(sk0_39,sk0_41)) ),
inference(skolemization,[status(esa)],[f245]) ).
fof(f250,plain,
subset(sk0_40,sk0_41),
inference(cnf_transformation,[status(esa)],[f246]) ).
fof(f251,plain,
~ subset(inverse_image2(sk0_39,sk0_40),inverse_image2(sk0_39,sk0_41)),
inference(cnf_transformation,[status(esa)],[f246]) ).
fof(f271,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| ~ subset(X0,X2)
| member(sk0_0(X1,X0),X2) ),
inference(resolution,[status(thm)],[f36,f35]) ).
fof(f272,plain,
! [X0,X1,X2,X3] :
( subset(X0,X1)
| ~ subset(X0,X2)
| ~ subset(X2,X3)
| member(sk0_0(X1,X0),X3) ),
inference(resolution,[status(thm)],[f271,f35]) ).
fof(f273,plain,
! [X0,X1,X2,X3,X4] :
( subset(X0,X1)
| ~ subset(X0,X2)
| ~ subset(X2,X3)
| ~ subset(X3,X4)
| member(sk0_0(X1,X0),X4) ),
inference(resolution,[status(thm)],[f272,f35]) ).
fof(f302,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,inverse_image2(X1,X2))
| ~ subset(X2,X3)
| member(sk0_25(X0,X2,X1),X3) ),
inference(resolution,[status(thm)],[f192,f35]) ).
fof(f310,plain,
! [X0,X1,X2,X3,X4,X5] :
( subset(X0,X1)
| ~ subset(X0,X2)
| ~ subset(X2,X3)
| ~ subset(X3,X4)
| ~ subset(X4,X5)
| member(sk0_0(X1,X0),X5) ),
inference(resolution,[status(thm)],[f273,f35]) ).
fof(f315,plain,
! [X0] :
( subset(X0,X0)
| subset(X0,X0) ),
inference(resolution,[status(thm)],[f37,f36]) ).
fof(f316,plain,
! [X0] : subset(X0,X0),
inference(duplicate_literals_removal,[status(esa)],[f315]) ).
fof(f321,plain,
! [X0,X1,X2,X3] :
( subset(X0,inverse_image2(X1,X2))
| ~ member(X3,X2)
| ~ apply(X1,sk0_0(inverse_image2(X1,X2),X0),X3) ),
inference(resolution,[status(thm)],[f37,f194]) ).
fof(f352,plain,
! [X0,X1,X2,X3] :
( subset(X0,inverse_image2(X1,X2))
| ~ member(sk0_25(sk0_0(inverse_image2(X1,X2),X0),X3,X1),X2)
| ~ member(sk0_0(inverse_image2(X1,X2),X0),inverse_image2(X1,X3)) ),
inference(resolution,[status(thm)],[f321,f193]) ).
fof(f370,plain,
! [X0,X1,X2,X3,X4] :
( subset(X0,X1)
| ~ subset(X0,X2)
| ~ subset(X2,X3)
| ~ subset(X3,X4)
| ~ subset(X4,X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f310,f37]) ).
fof(f371,plain,
! [X0,X1,X2,X3,X4] :
( subset(X0,X1)
| ~ subset(X0,X2)
| ~ subset(X2,X3)
| ~ subset(X3,X4)
| ~ subset(X4,X1) ),
inference(duplicate_literals_removal,[status(esa)],[f370]) ).
fof(f397,plain,
! [X0,X1,X2] :
( subset(X0,sk0_41)
| ~ subset(X0,X1)
| ~ subset(X1,X2)
| ~ subset(X2,sk0_40) ),
inference(resolution,[status(thm)],[f371,f250]) ).
fof(f7309,plain,
! [X0,X1,X2,X3] :
( subset(X0,inverse_image2(X1,X2))
| ~ member(sk0_0(inverse_image2(X1,X2),X0),inverse_image2(X1,X3))
| ~ member(sk0_0(inverse_image2(X1,X2),X0),inverse_image2(X1,X3))
| ~ subset(X3,X2) ),
inference(resolution,[status(thm)],[f352,f302]) ).
fof(f7310,plain,
! [X0,X1,X2,X3] :
( subset(X0,inverse_image2(X1,X2))
| ~ member(sk0_0(inverse_image2(X1,X2),X0),inverse_image2(X1,X3))
| ~ subset(X3,X2) ),
inference(duplicate_literals_removal,[status(esa)],[f7309]) ).
fof(f10434,plain,
! [X0] :
( subset(X0,sk0_41)
| ~ subset(X0,sk0_40) ),
inference(resolution,[status(thm)],[f397,f316]) ).
fof(f11625,plain,
subset(sk0_40,sk0_41),
inference(resolution,[status(thm)],[f10434,f316]) ).
fof(f21703,plain,
! [X0,X1,X2] :
( subset(inverse_image2(X0,X1),inverse_image2(X0,X2))
| ~ subset(X1,X2)
| subset(inverse_image2(X0,X1),inverse_image2(X0,X2)) ),
inference(resolution,[status(thm)],[f7310,f36]) ).
fof(f21704,plain,
! [X0,X1,X2] :
( subset(inverse_image2(X0,X1),inverse_image2(X0,X2))
| ~ subset(X1,X2) ),
inference(duplicate_literals_removal,[status(esa)],[f21703]) ).
fof(f21718,plain,
~ subset(sk0_40,sk0_41),
inference(resolution,[status(thm)],[f21704,f251]) ).
fof(f21719,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f21718,f11625]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SET755+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.09/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n003.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue May 30 10:16:23 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % Drodi V3.5.1
% 134.20/17.33 % Refutation found
% 134.20/17.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 134.20/17.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 135.27/17.42 % Elapsed time: 17.086179 seconds
% 135.27/17.42 % CPU time: 135.403099 seconds
% 135.27/17.42 % Memory used: 545.395 MB
%------------------------------------------------------------------------------