%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU328+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:20:11 PM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 59 ( 14 unt; 6 def)
% Number of atoms : 122 ( 41 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 113 ( 50 ~; 42 |; 5 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 46 ( 44 !; 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(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(C,powerset(A))
& element(B,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(thm)],[f17]) ).
fof(f118,plain,
! [A,B] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f119,plain,
! [X0,X1] :
( subset_complement(X1,X0) = set_difference(X1,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f120,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f125,plain,
! [A,B] :
( element(meet_of_subsets(A,B),powerset(A))
| ~ element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f126,plain,
! [X0,X1] :
( element(meet_of_subsets(X1,X0),powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f185,plain,
! [A,B] :
( meet_of_subsets(A,B) = set_meet(B)
| ~ element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f186,plain,
! [X0,X1] :
( meet_of_subsets(X1,X0) = set_meet(X0)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f187,plain,
! [A,B,C] :
( subset_difference(A,B,C) = set_difference(B,C)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f188,plain,
! [X0,X1,X2] :
( subset_difference(X1,X0,X2) = set_difference(X0,X2)
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f191,plain,
? [A,B] :
( union_of_subsets(A,complements_of_subsets(A,B)) != subset_complement(A,meet_of_subsets(A,B))
& B != empty_set
& element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f192,plain,
( union_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,sK5_skl)) != subset_complement(sK4_skl,meet_of_subsets(sK4_skl,sK5_skl))
& sK5_skl != empty_set
& element(sK5_skl,powerset(powerset(sK4_skl))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl)],[f191]) ).
fof(f193,plain,
element(sK5_skl,powerset(powerset(sK4_skl))),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f194,plain,
sK5_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f195,plain,
union_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,sK5_skl)) != subset_complement(sK4_skl,meet_of_subsets(sK4_skl,sK5_skl)),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f205,plain,
! [A,B] :
( union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B))
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f206,plain,
! [X0,X1] :
( union_of_subsets(X1,complements_of_subsets(X1,X0)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X0))
| X0 = empty_set
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f531,plain,
! [X0] : element(X0,powerset(X0)),
inference(forward_demodulation,[status(thm)],[f117,f120]) ).
fof(f1153,plain,
meet_of_subsets(sK4_skl,sK5_skl) = set_meet(sK5_skl),
inference(resolution,[status(thm)],[f186,f193]) ).
fof(f1158,definition,
( sQ57_spl
<=> element(sK5_skl,powerset(powerset(sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1160,plain,
( sQ57_spl
| ~ element(sK5_skl,powerset(powerset(sK4_skl))) ),
inference(component_clause,[status(thm)],[f1158]) ).
fof(f1165,plain,
( sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1160,f193]) ).
fof(f1166,plain,
sQ57_spl,
inference(contradiction_clause,[status(thm)],[f1165]) ).
fof(f1167,plain,
union_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,sK5_skl)) != subset_complement(sK4_skl,set_meet(sK5_skl)),
inference(backward_demodulation,[status(thm)],[f1153,f195]) ).
fof(f1168,plain,
( element(set_meet(sK5_skl),powerset(sK4_skl))
| ~ element(sK5_skl,powerset(powerset(sK4_skl))) ),
inference(paramodulation,[status(thm)],[f1153,f126]) ).
fof(f1169,definition,
( sQ59_spl
<=> element(set_meet(sK5_skl),powerset(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1170,plain,
( ~ sQ59_spl
| element(set_meet(sK5_skl),powerset(sK4_skl)) ),
inference(component_clause,[status(thm)],[f1169]) ).
fof(f1172,plain,
( sQ59_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f1168,f1158,f1169]) ).
fof(f1252,plain,
! [X0,X1] :
( union_of_subsets(X1,complements_of_subsets(X1,X0)) = subset_difference(X1,X1,meet_of_subsets(X1,X0))
| X0 = empty_set
| ~ element(X0,powerset(powerset(X1))) ),
inference(forward_demodulation,[status(thm)],[f117,f206]) ).
fof(f1253,plain,
( union_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,sK5_skl)) = subset_difference(sK4_skl,sK4_skl,set_meet(sK5_skl))
| sK5_skl = empty_set
| ~ element(sK5_skl,powerset(powerset(sK4_skl))) ),
inference(paramodulation,[status(thm)],[f1153,f1252]) ).
fof(f1255,definition,
( sQ62_spl
<=> sK5_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1256,plain,
( ~ sQ62_spl
| sK5_skl = empty_set ),
inference(component_clause,[status(thm)],[f1255]) ).
fof(f1258,definition,
( sQ63_spl
<=> union_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,sK5_skl)) = subset_difference(sK4_skl,sK4_skl,set_meet(sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1259,plain,
( ~ sQ63_spl
| union_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,sK5_skl)) = subset_difference(sK4_skl,sK4_skl,set_meet(sK5_skl)) ),
inference(component_clause,[status(thm)],[f1258]) ).
fof(f1261,plain,
( sQ63_spl
| sQ62_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f1253,f1158,f1255,f1258]) ).
fof(f1269,plain,
( ~ sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1256,f194]) ).
fof(f1270,plain,
~ sQ62_spl,
inference(contradiction_clause,[status(thm)],[f1269]) ).
fof(f1672,plain,
( ~ sQ63_spl
| union_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,sK5_skl)) = set_difference(sK4_skl,set_meet(sK5_skl))
| ~ element(set_meet(sK5_skl),powerset(sK4_skl))
| ~ element(sK4_skl,powerset(sK4_skl)) ),
inference(paramodulation,[status(thm)],[f1259,f188]) ).
fof(f1674,definition,
( sQ101_spl
<=> element(sK4_skl,powerset(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1676,plain,
( sQ101_spl
| ~ element(sK4_skl,powerset(sK4_skl)) ),
inference(component_clause,[status(thm)],[f1674]) ).
fof(f1677,definition,
( sQ102_spl
<=> union_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,sK5_skl)) = set_difference(sK4_skl,set_meet(sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1678,plain,
( ~ sQ102_spl
| union_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,sK5_skl)) = set_difference(sK4_skl,set_meet(sK5_skl)) ),
inference(component_clause,[status(thm)],[f1677]) ).
fof(f1680,plain,
( ~ sQ63_spl
| sQ102_spl
| ~ sQ59_spl
| ~ sQ101_spl ),
inference(split_clause,[status(thm)],[f1672,f1674,f1169,f1677,f1258]) ).
fof(f1685,plain,
( sQ101_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1676,f531]) ).
fof(f1686,plain,
sQ101_spl,
inference(contradiction_clause,[status(thm)],[f1685]) ).
fof(f1990,plain,
( ~ sQ102_spl
| set_difference(sK4_skl,set_meet(sK5_skl)) != subset_complement(sK4_skl,set_meet(sK5_skl)) ),
inference(backward_demodulation,[status(thm)],[f1678,f1167]) ).
fof(f2087,plain,
( ~ sQ102_spl
| ~ element(set_meet(sK5_skl),powerset(sK4_skl)) ),
inference(resolution,[status(thm)],[f1990,f119]) ).
fof(f2088,plain,
( ~ sQ102_spl
| ~ sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2087,f1170]) ).
fof(f2089,plain,
( ~ sQ102_spl
| ~ sQ59_spl ),
inference(contradiction_clause,[status(thm)],[f2088]) ).
fof(f2090,plain,
$false,
inference(sat_refutation,[status(thm)],[f1166,f1172,f1261,f1270,f1680,f1686,f2089]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU328+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 06:11:49 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.45 % Refutation found
% 0.13/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.47 % Elapsed time: 0.115229 seconds
% 0.13/0.47 % CPU time: 0.555535 seconds
% 0.13/0.47 % Total memory used: 118.950 MB
% 0.13/0.47 % Net memory used: 117.746 MB
%------------------------------------------------------------------------------