TSTP Solution File: SEU327+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU327+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 12:36:43 EDT 2023
% Result : Theorem 1.93s 0.63s
% Output : CNFRefutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 19 unt; 0 def)
% Number of atoms : 110 ( 47 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 94 ( 41 ~; 33 |; 7 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 61 (; 59 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [A] : cast_to_subset(A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(union_of_subsets(A,B),powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [A,B,C] :
( ( element(B,powerset(A))
& element(C,powerset(A)) )
=> subset_difference(A,B,C) = set_difference(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,conjecture,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> meet_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,union_of_subsets(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> meet_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,union_of_subsets(A,B)) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f53,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f117,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f118,plain,
! [A,B] :
( ~ element(B,powerset(A))
| subset_complement(A,B) = set_difference(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f119,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset_complement(X1,X0) = set_difference(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f118]) ).
fof(f123,plain,
! [A,B] :
( ~ element(B,powerset(powerset(A)))
| element(union_of_subsets(A,B),powerset(A)) ),
inference(pre_NNF_transformation,[status(esa)],[f26]) ).
fof(f124,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| element(union_of_subsets(X1,X0),powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f123]) ).
fof(f183,plain,
! [A,B] :
( ~ element(B,powerset(powerset(A)))
| union_of_subsets(A,B) = union(B) ),
inference(pre_NNF_transformation,[status(esa)],[f44]) ).
fof(f184,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| union_of_subsets(X1,X0) = union(X0) ),
inference(cnf_transformation,[status(esa)],[f183]) ).
fof(f187,plain,
! [A,B,C] :
( ~ element(B,powerset(A))
| ~ element(C,powerset(A))
| subset_difference(A,B,C) = set_difference(B,C) ),
inference(pre_NNF_transformation,[status(esa)],[f46]) ).
fof(f188,plain,
! [X0,X1,X2] :
( ~ element(X0,powerset(X1))
| ~ element(X2,powerset(X1))
| subset_difference(X1,X0,X2) = set_difference(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f187]) ).
fof(f189,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(esa)],[f47]) ).
fof(f190,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f189]) ).
fof(f191,plain,
? [A,B] :
( element(B,powerset(powerset(A)))
& B != empty_set
& meet_of_subsets(A,complements_of_subsets(A,B)) != subset_complement(A,union_of_subsets(A,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f49]) ).
fof(f192,plain,
( element(sk0_5,powerset(powerset(sk0_4)))
& sk0_5 != empty_set
& meet_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5)) != subset_complement(sk0_4,union_of_subsets(sk0_4,sk0_5)) ),
inference(skolemization,[status(esa)],[f191]) ).
fof(f193,plain,
element(sk0_5,powerset(powerset(sk0_4))),
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f194,plain,
sk0_5 != empty_set,
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f195,plain,
meet_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5)) != subset_complement(sk0_4,union_of_subsets(sk0_4,sk0_5)),
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f201,plain,
! [A,B] :
( ( ~ element(A,powerset(B))
| subset(A,B) )
& ( element(A,powerset(B))
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f53]) ).
fof(f202,plain,
( ! [A,B] :
( ~ element(A,powerset(B))
| subset(A,B) )
& ! [A,B] :
( element(A,powerset(B))
| ~ subset(A,B) ) ),
inference(miniscoping,[status(esa)],[f201]) ).
fof(f204,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f202]) ).
fof(f205,plain,
! [A,B] :
( ~ element(B,powerset(powerset(A)))
| B = empty_set
| subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f54]) ).
fof(f206,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| X0 = empty_set
| subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X0)) = meet_of_subsets(X1,complements_of_subsets(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f205]) ).
fof(f233,plain,
element(union_of_subsets(sk0_4,sk0_5),powerset(sk0_4)),
inference(resolution,[status(thm)],[f124,f193]) ).
fof(f236,plain,
subset_complement(sk0_4,union_of_subsets(sk0_4,sk0_5)) = set_difference(sk0_4,union_of_subsets(sk0_4,sk0_5)),
inference(resolution,[status(thm)],[f233,f119]) ).
fof(f1491,plain,
! [X0] : element(X0,powerset(X0)),
inference(resolution,[status(thm)],[f204,f190]) ).
fof(f3244,plain,
union_of_subsets(sk0_4,sk0_5) = union(sk0_5),
inference(resolution,[status(thm)],[f184,f193]) ).
fof(f3284,plain,
! [X0] :
( ~ element(X0,powerset(sk0_4))
| subset_difference(sk0_4,X0,union_of_subsets(sk0_4,sk0_5)) = set_difference(X0,union_of_subsets(sk0_4,sk0_5)) ),
inference(resolution,[status(thm)],[f188,f233]) ).
fof(f3694,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| X0 = empty_set
| subset_difference(X1,X1,union_of_subsets(X1,X0)) = meet_of_subsets(X1,complements_of_subsets(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f117,f206]) ).
fof(f3779,plain,
( spl0_478
<=> sk0_5 = empty_set ),
introduced(split_symbol_definition) ).
fof(f3780,plain,
( sk0_5 = empty_set
| ~ spl0_478 ),
inference(component_clause,[status(thm)],[f3779]) ).
fof(f3782,plain,
( spl0_479
<=> subset_difference(sk0_4,sk0_4,union_of_subsets(sk0_4,sk0_5)) = meet_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f3783,plain,
( subset_difference(sk0_4,sk0_4,union_of_subsets(sk0_4,sk0_5)) = meet_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5))
| ~ spl0_479 ),
inference(component_clause,[status(thm)],[f3782]) ).
fof(f3785,plain,
( sk0_5 = empty_set
| subset_difference(sk0_4,sk0_4,union_of_subsets(sk0_4,sk0_5)) = meet_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5)) ),
inference(resolution,[status(thm)],[f3694,f193]) ).
fof(f3786,plain,
( spl0_478
| spl0_479 ),
inference(split_clause,[status(thm)],[f3785,f3779,f3782]) ).
fof(f3788,plain,
( $false
| ~ spl0_478 ),
inference(forward_subsumption_resolution,[status(thm)],[f3780,f194]) ).
fof(f3789,plain,
~ spl0_478,
inference(contradiction_clause,[status(thm)],[f3788]) ).
fof(f4197,plain,
subset_complement(sk0_4,union_of_subsets(sk0_4,sk0_5)) = set_difference(sk0_4,union(sk0_5)),
inference(backward_demodulation,[status(thm)],[f3244,f236]) ).
fof(f4198,plain,
subset_complement(sk0_4,union(sk0_5)) = set_difference(sk0_4,union(sk0_5)),
inference(forward_demodulation,[status(thm)],[f3244,f4197]) ).
fof(f4629,plain,
( subset_difference(sk0_4,sk0_4,union(sk0_5)) = meet_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5))
| ~ spl0_479 ),
inference(forward_demodulation,[status(thm)],[f3244,f3783]) ).
fof(f5339,plain,
meet_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5)) != subset_complement(sk0_4,union(sk0_5)),
inference(forward_demodulation,[status(thm)],[f3244,f195]) ).
fof(f7192,plain,
! [X0] :
( ~ element(X0,powerset(sk0_4))
| subset_difference(sk0_4,X0,union(sk0_5)) = set_difference(X0,union_of_subsets(sk0_4,sk0_5)) ),
inference(forward_demodulation,[status(thm)],[f3244,f3284]) ).
fof(f7193,plain,
! [X0] :
( ~ element(X0,powerset(sk0_4))
| subset_difference(sk0_4,X0,union(sk0_5)) = set_difference(X0,union(sk0_5)) ),
inference(forward_demodulation,[status(thm)],[f3244,f7192]) ).
fof(f7218,plain,
subset_difference(sk0_4,sk0_4,union(sk0_5)) = set_difference(sk0_4,union(sk0_5)),
inference(resolution,[status(thm)],[f7193,f1491]) ).
fof(f7219,plain,
( meet_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5)) = set_difference(sk0_4,union(sk0_5))
| ~ spl0_479 ),
inference(forward_demodulation,[status(thm)],[f4629,f7218]) ).
fof(f7220,plain,
( meet_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5)) = subset_complement(sk0_4,union(sk0_5))
| ~ spl0_479 ),
inference(forward_demodulation,[status(thm)],[f4198,f7219]) ).
fof(f7221,plain,
( $false
| ~ spl0_479 ),
inference(forward_subsumption_resolution,[status(thm)],[f7220,f5339]) ).
fof(f7222,plain,
~ spl0_479,
inference(contradiction_clause,[status(thm)],[f7221]) ).
fof(f7223,plain,
$false,
inference(sat_refutation,[status(thm)],[f3786,f3789,f7222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU327+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 09:26:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.35 % Drodi V3.5.1
% 1.93/0.63 % Refutation found
% 1.93/0.63 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.93/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.93/0.66 % Elapsed time: 0.309532 seconds
% 1.93/0.66 % CPU time: 2.257284 seconds
% 1.93/0.66 % Memory used: 95.393 MB
%------------------------------------------------------------------------------