%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET935+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 02:11:01 PM UTC 2026
% Result : Theorem 0.14s 0.63s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 72 ( 19 unt; 4 def)
% Number of atoms : 216 ( 40 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 235 ( 91 ~; 97 |; 35 &)
% ( 10 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 124 ( 118 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( inclusion_comparable(A,B)
<=> ( subset(B,A)
| subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] : set_union2(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,conjecture,
! [A,B] :
( set_union2(powerset(A),powerset(B)) = powerset(set_union2(A,B))
=> inclusion_comparable(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ ! [A,B] :
( set_union2(powerset(A),powerset(B)) = powerset(set_union2(A,B))
=> inclusion_comparable(A,B) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f20,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f26,plain,
! [A,B] :
( ( ? [C] :
( ( subset(C,A)
| in(C,B) )
& ( ~ subset(C,A)
| ~ in(C,B) ) )
| B = powerset(A) )
& ( ! [C] :
( ( ~ subset(C,A)
| in(C,B) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f27,plain,
( ! [A,B] :
( ? [C] :
( ( subset(C,A)
| in(C,B) )
& ( ~ subset(C,A)
| ~ in(C,B) ) )
| B = powerset(A) )
& ! [A,B] :
( ( ! [C] :
( ~ subset(C,A)
| in(C,B) )
& ! [C] :
( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f28,plain,
( ! [A,B] :
( ( ( subset(sK0_skl(B,A),A)
| in(sK0_skl(B,A),B) )
& ( ~ subset(sK0_skl(B,A),A)
| ~ in(sK0_skl(B,A),B) ) )
| B = powerset(A) )
& ! [A,B] :
( ( ! [C] :
( ~ subset(C,A)
| in(C,B) )
& ! [C] :
( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f33,plain,
! [A,B,C] :
( ( ? [D] :
( ( in(D,B)
| in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) ) )
| C = set_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f34,plain,
( ! [A,B,C] :
( ? [D] :
( ( in(D,B)
| in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) ) )
| C = set_union2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ! [D] :
( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f35,plain,
( ! [A,B,C] :
( ( ( in(sK1_skl(C,B,A),B)
| in(sK1_skl(C,B,A),A)
| in(sK1_skl(C,B,A),C) )
& ( ( ~ in(sK1_skl(C,B,A),B)
& ~ in(sK1_skl(C,B,A),A) )
| ~ in(sK1_skl(C,B,A),C) ) )
| C = set_union2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ! [D] :
( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f34]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f42,plain,
! [A,B] :
( ( ( ~ subset(B,A)
& ~ subset(A,B) )
| inclusion_comparable(A,B) )
& ( subset(B,A)
| subset(A,B)
| ~ inclusion_comparable(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f43,plain,
( ! [A,B] :
( ( ~ subset(B,A)
& ~ subset(A,B) )
| inclusion_comparable(A,B) )
& ! [A,B] :
( subset(B,A)
| subset(A,B)
| ~ inclusion_comparable(A,B) ) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f45,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| inclusion_comparable(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f46,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| inclusion_comparable(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f53,plain,
! [A] : set_union2(A,A) = A,
inference(miniscoping,[status(thm)],[f9]) ).
fof(f54,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f65,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f66,plain,
? [A,B] :
( ~ inclusion_comparable(A,B)
& set_union2(powerset(A),powerset(B)) = powerset(set_union2(A,B)) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f67,plain,
( ~ inclusion_comparable(sK4_skl,sK5_skl)
& set_union2(powerset(sK4_skl),powerset(sK5_skl)) = powerset(set_union2(sK4_skl,sK5_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl)],[f66]) ).
fof(f68,plain,
set_union2(powerset(sK4_skl),powerset(sK5_skl)) = powerset(set_union2(sK4_skl,sK5_skl)),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
~ inclusion_comparable(sK4_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f72,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f29]) ).
fof(f73,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f30]) ).
fof(f74,plain,
! [X0,X1,X2] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f36]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f37]) ).
fof(f82,plain,
! [X0] : subset(X0,X0),
inference(paramodulation,[status(thm)],[f54,f65]) ).
fof(f83,plain,
! [X0,X1] : subset(X0,set_union2(X1,X0)),
inference(paramodulation,[status(thm)],[f20,f65]) ).
fof(f89,plain,
~ subset(sK4_skl,sK5_skl),
inference(resolution,[status(thm)],[f45,f69]) ).
fof(f92,plain,
~ subset(sK5_skl,sK4_skl),
inference(resolution,[status(thm)],[f46,f69]) ).
fof(f94,plain,
! [X0,X1] :
( ~ subset(set_union2(X0,X1),X0)
| set_union2(X0,X1) = X0 ),
inference(resolution,[status(thm)],[f25,f65]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| in(X0,set_union2(powerset(X1),X2)) ),
inference(resolution,[status(thm)],[f75,f73]) ).
fof(f128,plain,
! [X0] :
( in(X0,powerset(sK5_skl))
| in(X0,powerset(sK4_skl))
| ~ in(X0,powerset(set_union2(sK4_skl,sK5_skl))) ),
inference(paramodulation,[status(thm)],[f68,f74]) ).
fof(f237,plain,
! [X0,X1] :
( ~ subset(set_union2(X1,X0),X0)
| set_union2(X0,X1) = X0 ),
inference(paramodulation,[status(thm)],[f20,f94]) ).
fof(f296,plain,
! [X0,X1] : in(X0,set_union2(powerset(X0),X1)),
inference(resolution,[status(thm)],[f126,f82]) ).
fof(f307,plain,
! [X0] : in(X0,powerset(X0)),
inference(paramodulation,[status(thm)],[f54,f296]) ).
fof(f339,plain,
( in(set_union2(sK4_skl,sK5_skl),powerset(sK5_skl))
| in(set_union2(sK4_skl,sK5_skl),powerset(sK4_skl)) ),
inference(resolution,[status(thm)],[f128,f307]) ).
fof(f343,definition,
( sQ9_spl
<=> in(set_union2(sK4_skl,sK5_skl),powerset(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f344,plain,
( ~ sQ9_spl
| in(set_union2(sK4_skl,sK5_skl),powerset(sK4_skl)) ),
inference(component_clause,[status(thm)],[f343]) ).
fof(f346,definition,
( sQ10_spl
<=> in(set_union2(sK4_skl,sK5_skl),powerset(sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f347,plain,
( ~ sQ10_spl
| in(set_union2(sK4_skl,sK5_skl),powerset(sK5_skl)) ),
inference(component_clause,[status(thm)],[f346]) ).
fof(f349,plain,
( sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f339,f343,f346]) ).
fof(f490,plain,
( ~ sQ9_spl
| subset(set_union2(sK4_skl,sK5_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f344,f72]) ).
fof(f546,plain,
( ~ sQ9_spl
| ~ subset(sK4_skl,set_union2(sK4_skl,sK5_skl))
| sK4_skl = set_union2(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f490,f25]) ).
fof(f547,definition,
( sQ16_spl
<=> sK4_skl = set_union2(sK4_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f548,plain,
( ~ sQ16_spl
| sK4_skl = set_union2(sK4_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f547]) ).
fof(f550,definition,
( sQ17_spl
<=> subset(sK4_skl,set_union2(sK4_skl,sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f552,plain,
( sQ17_spl
| ~ subset(sK4_skl,set_union2(sK4_skl,sK5_skl)) ),
inference(component_clause,[status(thm)],[f550]) ).
fof(f553,plain,
( ~ sQ9_spl
| ~ sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f546,f547,f550,f343]) ).
fof(f554,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f552,f65]) ).
fof(f555,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f554]) ).
fof(f575,plain,
( ~ sQ16_spl
| subset(sK5_skl,sK4_skl) ),
inference(paramodulation,[status(thm)],[f548,f83]) ).
fof(f613,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f575,f92]) ).
fof(f614,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f613]) ).
fof(f725,plain,
( ~ sQ10_spl
| subset(set_union2(sK4_skl,sK5_skl),sK5_skl) ),
inference(resolution,[status(thm)],[f347,f72]) ).
fof(f748,plain,
( ~ sQ10_spl
| set_union2(sK5_skl,sK4_skl) = sK5_skl ),
inference(resolution,[status(thm)],[f725,f237]) ).
fof(f777,plain,
( ~ sQ10_spl
| subset(sK4_skl,sK5_skl) ),
inference(paramodulation,[status(thm)],[f748,f83]) ).
fof(f807,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f777,f89]) ).
fof(f808,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f807]) ).
fof(f809,plain,
$false,
inference(sat_refutation,[status(thm)],[f349,f553,f555,f614,f808]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET935+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 05:44:05 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.63 % Refutation found
% 0.14/0.63 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.65 % Elapsed time: 0.269796 seconds
% 0.14/0.65 % CPU time: 1.883034 seconds
% 0.14/0.65 % Total memory used: 122.510 MB
% 0.14/0.65 % Net memory used: 119.873 MB
%------------------------------------------------------------------------------