TSTP Solution File: SEU328+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU328+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 : Tue Apr 30 20:41:58 EDT 2024
% Result : Theorem 3.13s 0.77s
% Output : CNFRefutation 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 65 ( 17 unt; 0 def)
% Number of atoms : 131 ( 41 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 121 ( 55 ~; 44 |; 5 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 48 ( 46 !; 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(f22,axiom,
! [A] : element(cast_to_subset(A),powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(meet_of_subsets(A,B),powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> meet_of_subsets(A,B) = set_meet(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(f48,conjecture,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,meet_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
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,meet_of_subsets(A,B)) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f54,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_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(f120,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f125,plain,
! [A,B] :
( ~ element(B,powerset(powerset(A)))
| element(meet_of_subsets(A,B),powerset(A)) ),
inference(pre_NNF_transformation,[status(esa)],[f27]) ).
fof(f126,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| element(meet_of_subsets(X1,X0),powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f125]) ).
fof(f133,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f185,plain,
! [A,B] :
( ~ element(B,powerset(powerset(A)))
| meet_of_subsets(A,B) = set_meet(B) ),
inference(pre_NNF_transformation,[status(esa)],[f45]) ).
fof(f186,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| meet_of_subsets(X1,X0) = set_meet(X0) ),
inference(cnf_transformation,[status(esa)],[f185]) ).
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(f191,plain,
? [A,B] :
( element(B,powerset(powerset(A)))
& B != empty_set
& union_of_subsets(A,complements_of_subsets(A,B)) != subset_complement(A,meet_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
& union_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5)) != subset_complement(sk0_4,meet_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,
union_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5)) != subset_complement(sk0_4,meet_of_subsets(sk0_4,sk0_5)),
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f205,plain,
! [A,B] :
( ~ element(B,powerset(powerset(A)))
| B = empty_set
| union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f54]) ).
fof(f206,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| X0 = empty_set
| union_of_subsets(X1,complements_of_subsets(X1,X0)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f205]) ).
fof(f360,plain,
! [X0] : element(X0,powerset(X0)),
inference(forward_demodulation,[status(thm)],[f117,f120]) ).
fof(f2790,plain,
( spl0_104
<=> element(sk0_5,powerset(powerset(sk0_4))) ),
introduced(split_symbol_definition) ).
fof(f2792,plain,
( ~ element(sk0_5,powerset(powerset(sk0_4)))
| spl0_104 ),
inference(component_clause,[status(thm)],[f2790]) ).
fof(f2822,plain,
( $false
| spl0_104 ),
inference(forward_subsumption_resolution,[status(thm)],[f2792,f193]) ).
fof(f2823,plain,
spl0_104,
inference(contradiction_clause,[status(thm)],[f2822]) ).
fof(f2947,plain,
( spl0_120
<=> empty(powerset(sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f2948,plain,
( empty(powerset(sk0_4))
| ~ spl0_120 ),
inference(component_clause,[status(thm)],[f2947]) ).
fof(f3360,plain,
meet_of_subsets(sk0_4,sk0_5) = set_meet(sk0_5),
inference(resolution,[status(thm)],[f186,f193]) ).
fof(f3363,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| X0 = empty_set
| union_of_subsets(X1,complements_of_subsets(X1,X0)) = subset_difference(X1,X1,meet_of_subsets(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f117,f206]) ).
fof(f3365,plain,
union_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5)) != subset_complement(sk0_4,set_meet(sk0_5)),
inference(backward_demodulation,[status(thm)],[f3360,f195]) ).
fof(f3366,plain,
( spl0_138
<=> sk0_5 = empty_set ),
introduced(split_symbol_definition) ).
fof(f3367,plain,
( sk0_5 = empty_set
| ~ spl0_138 ),
inference(component_clause,[status(thm)],[f3366]) ).
fof(f3369,plain,
( spl0_139
<=> union_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5)) = subset_difference(sk0_4,sk0_4,set_meet(sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f3370,plain,
( union_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5)) = subset_difference(sk0_4,sk0_4,set_meet(sk0_5))
| ~ spl0_139 ),
inference(component_clause,[status(thm)],[f3369]) ).
fof(f3372,plain,
( ~ element(sk0_5,powerset(powerset(sk0_4)))
| sk0_5 = empty_set
| union_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5)) = subset_difference(sk0_4,sk0_4,set_meet(sk0_5)) ),
inference(paramodulation,[status(thm)],[f3360,f3363]) ).
fof(f3373,plain,
( ~ spl0_104
| spl0_138
| spl0_139 ),
inference(split_clause,[status(thm)],[f3372,f2790,f3366,f3369]) ).
fof(f3389,plain,
( spl0_143
<=> element(set_meet(sk0_5),powerset(sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f3390,plain,
( element(set_meet(sk0_5),powerset(sk0_4))
| ~ spl0_143 ),
inference(component_clause,[status(thm)],[f3389]) ).
fof(f3392,plain,
( ~ element(sk0_5,powerset(powerset(sk0_4)))
| element(set_meet(sk0_5),powerset(sk0_4)) ),
inference(paramodulation,[status(thm)],[f3360,f126]) ).
fof(f3393,plain,
( ~ spl0_104
| spl0_143 ),
inference(split_clause,[status(thm)],[f3392,f2790,f3389]) ).
fof(f3394,plain,
( $false
| ~ spl0_138 ),
inference(forward_subsumption_resolution,[status(thm)],[f3367,f194]) ).
fof(f3395,plain,
~ spl0_138,
inference(contradiction_clause,[status(thm)],[f3394]) ).
fof(f3523,plain,
( spl0_156
<=> element(sk0_4,powerset(sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f3525,plain,
( ~ element(sk0_4,powerset(sk0_4))
| spl0_156 ),
inference(component_clause,[status(thm)],[f3523]) ).
fof(f3526,plain,
( spl0_157
<=> union_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5)) = set_difference(sk0_4,set_meet(sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f3527,plain,
( union_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5)) = set_difference(sk0_4,set_meet(sk0_5))
| ~ spl0_157 ),
inference(component_clause,[status(thm)],[f3526]) ).
fof(f3529,plain,
( ~ element(sk0_4,powerset(sk0_4))
| ~ element(set_meet(sk0_5),powerset(sk0_4))
| union_of_subsets(sk0_4,complements_of_subsets(sk0_4,sk0_5)) = set_difference(sk0_4,set_meet(sk0_5))
| ~ spl0_139 ),
inference(paramodulation,[status(thm)],[f3370,f188]) ).
fof(f3530,plain,
( ~ spl0_156
| ~ spl0_143
| spl0_157
| ~ spl0_139 ),
inference(split_clause,[status(thm)],[f3529,f3523,f3389,f3526,f3369]) ).
fof(f3536,plain,
( $false
| spl0_156 ),
inference(forward_subsumption_resolution,[status(thm)],[f3525,f360]) ).
fof(f3537,plain,
spl0_156,
inference(contradiction_clause,[status(thm)],[f3536]) ).
fof(f3649,plain,
( $false
| ~ spl0_120 ),
inference(forward_subsumption_resolution,[status(thm)],[f2948,f133]) ).
fof(f3650,plain,
~ spl0_120,
inference(contradiction_clause,[status(thm)],[f3649]) ).
fof(f3900,plain,
( set_difference(sk0_4,set_meet(sk0_5)) != subset_complement(sk0_4,set_meet(sk0_5))
| ~ spl0_157 ),
inference(forward_demodulation,[status(thm)],[f3527,f3365]) ).
fof(f3901,plain,
( ~ element(set_meet(sk0_5),powerset(sk0_4))
| ~ spl0_157 ),
inference(resolution,[status(thm)],[f3900,f119]) ).
fof(f3902,plain,
( $false
| ~ spl0_143
| ~ spl0_157 ),
inference(forward_subsumption_resolution,[status(thm)],[f3901,f3390]) ).
fof(f3903,plain,
( ~ spl0_143
| ~ spl0_157 ),
inference(contradiction_clause,[status(thm)],[f3902]) ).
fof(f3904,plain,
$false,
inference(sat_refutation,[status(thm)],[f2823,f3373,f3393,f3395,f3530,f3537,f3650,f3903]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU328+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % 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 : Mon Apr 29 20:06:34 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 3.13/0.77 % Refutation found
% 3.13/0.77 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.13/0.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.13/0.80 % Elapsed time: 0.441804 seconds
% 3.13/0.80 % CPU time: 3.309328 seconds
% 3.13/0.80 % Total memory used: 121.354 MB
% 3.13/0.80 % Net memory used: 117.794 MB
%------------------------------------------------------------------------------