%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU308+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 02:20:07 PM UTC 2026
% Result : Theorem 0.22s 5.58s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 10 unt; 2 def)
% Number of atoms : 69 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 57 ( 24 ~; 18 |; 5 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 28 ( 26 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f77,axiom,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f130,axiom,
! [A] :
( one_sorted_str(A)
=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f291,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_difference(A,B,C) = set_difference(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f361,conjecture,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f362,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) ),
inference(negated_conjecture,[status(cth)],[f361]) ).
fof(f890,plain,
! [A] :
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f77]) ).
fof(f891,plain,
! [X0] :
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(thm)],[f890]) ).
fof(f1019,plain,
! [A,B] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f94]) ).
fof(f1020,plain,
! [X0,X1] :
( subset_complement(X1,X0) = set_difference(X1,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f1019]) ).
fof(f1139,plain,
! [A] :
( element(cast_as_carrier_subset(A),powerset(the_carrier(A)))
| ~ one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f130]) ).
fof(f1140,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(thm)],[f1139]) ).
fof(f1624,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)],[f291]) ).
fof(f1625,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)],[f1624]) ).
fof(f2065,plain,
? [A] :
( ? [B] :
( subset_complement(the_carrier(A),B) != subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)
& element(B,powerset(the_carrier(A))) )
& one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f362]) ).
fof(f2066,plain,
( subset_complement(the_carrier(sK252_skl),sK253_skl) != subset_difference(the_carrier(sK252_skl),cast_as_carrier_subset(sK252_skl),sK253_skl)
& element(sK253_skl,powerset(the_carrier(sK252_skl)))
& one_sorted_str(sK252_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK252_skl,sK253_skl]),skolemize(A,sK252_skl),skolemize(B,sK253_skl)],[f2065]) ).
fof(f2067,plain,
one_sorted_str(sK252_skl),
inference(cnf_transformation,[status(thm)],[f2066]) ).
fof(f2068,plain,
element(sK253_skl,powerset(the_carrier(sK252_skl))),
inference(cnf_transformation,[status(thm)],[f2066]) ).
fof(f2069,plain,
subset_complement(the_carrier(sK252_skl),sK253_skl) != subset_difference(the_carrier(sK252_skl),cast_as_carrier_subset(sK252_skl),sK253_skl),
inference(cnf_transformation,[status(thm)],[f2066]) ).
fof(f3287,plain,
cast_as_carrier_subset(sK252_skl) = the_carrier(sK252_skl),
inference(resolution,[status(thm)],[f891,f2067]) ).
fof(f3289,plain,
subset_complement(the_carrier(sK252_skl),sK253_skl) != subset_difference(the_carrier(sK252_skl),the_carrier(sK252_skl),sK253_skl),
inference(backward_demodulation,[status(thm)],[f3287,f2069]) ).
fof(f3290,plain,
subset_complement(the_carrier(sK252_skl),sK253_skl) = set_difference(the_carrier(sK252_skl),sK253_skl),
inference(resolution,[status(thm)],[f1020,f2068]) ).
fof(f3292,plain,
set_difference(the_carrier(sK252_skl),sK253_skl) != subset_difference(the_carrier(sK252_skl),the_carrier(sK252_skl),sK253_skl),
inference(forward_demodulation,[status(thm)],[f3290,f3289]) ).
fof(f3294,plain,
( element(the_carrier(sK252_skl),powerset(the_carrier(sK252_skl)))
| ~ one_sorted_str(sK252_skl) ),
inference(paramodulation,[status(thm)],[f3287,f1140]) ).
fof(f3295,definition,
( sQ57_spl
<=> one_sorted_str(sK252_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f3297,plain,
( sQ57_spl
| ~ one_sorted_str(sK252_skl) ),
inference(component_clause,[status(thm)],[f3295]) ).
fof(f3298,definition,
( sQ58_spl
<=> element(the_carrier(sK252_skl),powerset(the_carrier(sK252_skl))) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f3299,plain,
( ~ sQ58_spl
| element(the_carrier(sK252_skl),powerset(the_carrier(sK252_skl))) ),
inference(component_clause,[status(thm)],[f3298]) ).
fof(f3301,plain,
( sQ58_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f3294,f3295,f3298]) ).
fof(f3302,plain,
( sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3297,f2067]) ).
fof(f3303,plain,
sQ57_spl,
inference(contradiction_clause,[status(thm)],[f3302]) ).
fof(f3394,plain,
! [X0] :
( subset_difference(the_carrier(sK252_skl),X0,sK253_skl) = set_difference(X0,sK253_skl)
| ~ element(X0,powerset(the_carrier(sK252_skl))) ),
inference(resolution,[status(thm)],[f1625,f2068]) ).
fof(f3414,plain,
( ~ sQ58_spl
| subset_difference(the_carrier(sK252_skl),the_carrier(sK252_skl),sK253_skl) = set_difference(the_carrier(sK252_skl),sK253_skl) ),
inference(resolution,[status(thm)],[f3394,f3299]) ).
fof(f3418,plain,
( ~ sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3414,f3292]) ).
fof(f3419,plain,
~ sQ58_spl,
inference(contradiction_clause,[status(thm)],[f3418]) ).
fof(f3420,plain,
$false,
inference(sat_refutation,[status(thm)],[f3301,f3303,f3419]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU308+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.45 % Computer : n002.cluster.edu
% 0.16/5.45 % Model : x86_64 x86_64
% 0.16/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.45 % Memory : 8046.5625MB
% 0.16/5.45 % OS : Linux 6.8.0-71-generic
% 0.16/5.45 % CPULimit : 300
% 0.16/5.45 % WCLimit : 300
% 0.16/5.45 % DateTime : Mon Sep 21 06:12:52 UTC 2026
% 0.16/5.46 % CPUTime :
% 0.22/5.55 % Drodi V4.1.1
% 0.22/5.58 % Refutation found
% 0.22/5.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/5.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/5.63 % Elapsed time: 0.162177 seconds
% 0.22/5.63 % CPU time: 0.450830 seconds
% 0.22/5.63 % Total memory used: 115.715 MB
% 0.22/5.63 % Net memory used: 115.049 MB
%------------------------------------------------------------------------------