TSTP Solution File: SEU326+2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU326+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n023.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 0.20s 0.43s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 3 unt; 0 def)
% Number of atoms : 109 ( 43 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 119 ( 54 ~; 40 |; 16 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 39 (; 35 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f167,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(complements_of_subsets(A,B),powerset(powerset(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f258,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> complements_of_subsets(A,complements_of_subsets(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f360,conjecture,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( ~ ( B != empty_set
& complements_of_subsets(A,B) = empty_set )
& ~ ( complements_of_subsets(A,B) != empty_set
& B = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f361,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(powerset(A)))
=> ( ~ ( B != empty_set
& complements_of_subsets(A,B) = empty_set )
& ~ ( complements_of_subsets(A,B) != empty_set
& B = empty_set ) ) ),
inference(negated_conjecture,[status(cth)],[f360]) ).
fof(f476,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( B != empty_set
& complements_of_subsets(A,B) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1274,plain,
! [A,B] :
( ~ element(B,powerset(powerset(A)))
| element(complements_of_subsets(A,B),powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(esa)],[f167]) ).
fof(f1275,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| element(complements_of_subsets(X1,X0),powerset(powerset(X1))) ),
inference(cnf_transformation,[status(esa)],[f1274]) ).
fof(f1542,plain,
! [A,B] :
( ~ element(B,powerset(powerset(A)))
| complements_of_subsets(A,complements_of_subsets(A,B)) = B ),
inference(pre_NNF_transformation,[status(esa)],[f258]) ).
fof(f1543,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| complements_of_subsets(X1,complements_of_subsets(X1,X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f1542]) ).
fof(f2155,plain,
? [A,B] :
( element(B,powerset(powerset(A)))
& ( ( B != empty_set
& complements_of_subsets(A,B) = empty_set )
| ( complements_of_subsets(A,B) != empty_set
& B = empty_set ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f361]) ).
fof(f2156,plain,
! [A,B] :
( pd0_24(B,A)
=> ( B != empty_set
& complements_of_subsets(A,B) = empty_set ) ),
introduced(predicate_definition,[f2155]) ).
fof(f2157,plain,
? [A,B] :
( element(B,powerset(powerset(A)))
& ( pd0_24(B,A)
| ( complements_of_subsets(A,B) != empty_set
& B = empty_set ) ) ),
inference(formula_renaming,[status(thm)],[f2155,f2156]) ).
fof(f2158,plain,
( element(sk0_277,powerset(powerset(sk0_276)))
& ( pd0_24(sk0_277,sk0_276)
| ( complements_of_subsets(sk0_276,sk0_277) != empty_set
& sk0_277 = empty_set ) ) ),
inference(skolemization,[status(esa)],[f2157]) ).
fof(f2159,plain,
element(sk0_277,powerset(powerset(sk0_276))),
inference(cnf_transformation,[status(esa)],[f2158]) ).
fof(f2160,plain,
( pd0_24(sk0_277,sk0_276)
| complements_of_subsets(sk0_276,sk0_277) != empty_set ),
inference(cnf_transformation,[status(esa)],[f2158]) ).
fof(f2161,plain,
( pd0_24(sk0_277,sk0_276)
| sk0_277 = empty_set ),
inference(cnf_transformation,[status(esa)],[f2158]) ).
fof(f2544,plain,
! [A,B] :
( ~ element(B,powerset(powerset(A)))
| B = empty_set
| complements_of_subsets(A,B) != empty_set ),
inference(pre_NNF_transformation,[status(esa)],[f476]) ).
fof(f2545,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| X0 = empty_set
| complements_of_subsets(X1,X0) != empty_set ),
inference(cnf_transformation,[status(esa)],[f2544]) ).
fof(f2948,plain,
! [A,B] :
( ~ pd0_24(B,A)
| ( B != empty_set
& complements_of_subsets(A,B) = empty_set ) ),
inference(pre_NNF_transformation,[status(esa)],[f2156]) ).
fof(f2949,plain,
! [X0,X1] :
( ~ pd0_24(X0,X1)
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f2948]) ).
fof(f2950,plain,
! [X0,X1] :
( ~ pd0_24(X0,X1)
| complements_of_subsets(X1,X0) = empty_set ),
inference(cnf_transformation,[status(esa)],[f2948]) ).
fof(f3116,plain,
( spl0_31
<=> pd0_24(sk0_277,sk0_276) ),
introduced(split_symbol_definition) ).
fof(f3117,plain,
( pd0_24(sk0_277,sk0_276)
| ~ spl0_31 ),
inference(component_clause,[status(thm)],[f3116]) ).
fof(f3119,plain,
( spl0_32
<=> complements_of_subsets(sk0_276,sk0_277) = empty_set ),
introduced(split_symbol_definition) ).
fof(f3121,plain,
( complements_of_subsets(sk0_276,sk0_277) != empty_set
| spl0_32 ),
inference(component_clause,[status(thm)],[f3119]) ).
fof(f3122,plain,
( spl0_31
| ~ spl0_32 ),
inference(split_clause,[status(thm)],[f2160,f3116,f3119]) ).
fof(f3123,plain,
( spl0_33
<=> sk0_277 = empty_set ),
introduced(split_symbol_definition) ).
fof(f3124,plain,
( sk0_277 = empty_set
| ~ spl0_33 ),
inference(component_clause,[status(thm)],[f3123]) ).
fof(f3126,plain,
( spl0_31
| spl0_33 ),
inference(split_clause,[status(thm)],[f2161,f3116,f3123]) ).
fof(f3385,plain,
! [X0] : ~ pd0_24(empty_set,X0),
inference(destructive_equality_resolution,[status(esa)],[f2949]) ).
fof(f3418,plain,
( complements_of_subsets(sk0_276,empty_set) != empty_set
| ~ spl0_33
| spl0_32 ),
inference(backward_demodulation,[status(thm)],[f3124,f3121]) ).
fof(f3421,plain,
( element(empty_set,powerset(powerset(sk0_276)))
| ~ spl0_33 ),
inference(backward_demodulation,[status(thm)],[f3124,f2159]) ).
fof(f3483,plain,
! [X0] :
( ~ element(complements_of_subsets(X0,empty_set),powerset(powerset(X0)))
| complements_of_subsets(X0,empty_set) = empty_set
| ~ element(empty_set,powerset(powerset(X0))) ),
inference(resolution,[status(thm)],[f2545,f1543]) ).
fof(f3484,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| X0 = empty_set
| ~ pd0_24(X0,X1) ),
inference(resolution,[status(thm)],[f2545,f2950]) ).
fof(f3513,plain,
! [X0] :
( complements_of_subsets(X0,empty_set) = empty_set
| ~ element(empty_set,powerset(powerset(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f3483,f1275]) ).
fof(f3514,plain,
( complements_of_subsets(sk0_276,empty_set) = empty_set
| ~ spl0_33 ),
inference(resolution,[status(thm)],[f3513,f3421]) ).
fof(f3515,plain,
( $false
| spl0_32
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[status(thm)],[f3514,f3418]) ).
fof(f3516,plain,
( spl0_32
| ~ spl0_33 ),
inference(contradiction_clause,[status(thm)],[f3515]) ).
fof(f3526,plain,
( sk0_277 = empty_set
| ~ pd0_24(sk0_277,sk0_276) ),
inference(resolution,[status(thm)],[f2159,f3484]) ).
fof(f3527,plain,
( spl0_33
| ~ spl0_31 ),
inference(split_clause,[status(thm)],[f3526,f3123,f3116]) ).
fof(f3564,plain,
( pd0_24(empty_set,sk0_276)
| ~ spl0_33
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f3124,f3117]) ).
fof(f3565,plain,
( $false
| ~ spl0_33
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[status(thm)],[f3564,f3385]) ).
fof(f3566,plain,
( ~ spl0_33
| ~ spl0_31 ),
inference(contradiction_clause,[status(thm)],[f3565]) ).
fof(f3567,plain,
$false,
inference(sat_refutation,[status(thm)],[f3122,f3126,f3516,f3527,f3566]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU326+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 30 09:28:38 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.20/0.40 % Drodi V3.5.1
% 0.20/0.43 % Refutation found
% 0.20/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.47 % Elapsed time: 0.115718 seconds
% 0.20/0.47 % CPU time: 0.320669 seconds
% 0.20/0.47 % Memory used: 55.748 MB
%------------------------------------------------------------------------------