%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU164+3 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 02:19:29 PM UTC 2026
% Result : Theorem 0.12s 0.82s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 75 ( 12 unt; 8 def)
% Number of atoms : 241 ( 29 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 282 ( 116 ~; 119 |; 31 &)
% ( 14 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-3 aty)
% Number of variables : 123 ( 111 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A] : union(powerset(A)) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A] : union(powerset(A)) = A,
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f22,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)],[f3]) ).
fof(f23,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)],[f22]) ).
fof(f24,plain,
( ! [A,B] :
( ( ( subset(sK1_skl(B,A),A)
| in(sK1_skl(B,A),B) )
& ( ~ subset(sK1_skl(B,A),A)
| ~ in(sK1_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,[sK1_skl]),skolemize(C,sK1_skl(B,A))],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f29,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f30,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f32,plain,
( ! [A,B] :
( ( ~ in(sK2_skl(B,A),B)
& in(sK2_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f36,plain,
! [A,B] :
( ( ? [C] :
( ( ? [D] :
( in(D,A)
& in(C,D) )
| in(C,B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| ~ in(C,B) ) )
| B = union(A) )
& ( ! [C] :
( ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f37,plain,
( ! [A,B] :
( ? [C] :
( ( ? [D] :
( in(D,A)
& in(C,D) )
| in(C,B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| ~ in(C,B) ) )
| B = union(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ! [C] :
( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
( ! [A,B] :
( ( ( ( in(sK5_skl(B,A),A)
& in(sK4_skl(B,A),sK5_skl(B,A)) )
| in(sK4_skl(B,A),B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(sK4_skl(B,A),D) )
| ~ in(sK4_skl(B,A),B) ) )
| B = union(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ! [C] :
( ( in(sK3_skl(C,B,A),A)
& in(C,sK3_skl(C,B,A)) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(D,sK3_skl(C,B,A)),skolemize(C,sK4_skl(B,A)),skolemize(D,sK5_skl(B,A))],[f37]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| ~ in(X2,X3)
| in(X2,X0)
| X0 != union(X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(sK4_skl(X0,X1),X2)
| ~ in(sK4_skl(X0,X1),X0)
| X0 = union(X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f43,plain,
! [X0,X1] :
( in(sK4_skl(X0,X1),sK5_skl(X0,X1))
| in(sK4_skl(X0,X1),X0)
| X0 = union(X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f44,plain,
! [X0,X1] :
( in(sK5_skl(X0,X1),X1)
| in(sK4_skl(X0,X1),X0)
| X0 = union(X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f53,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f54,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f60,plain,
? [A] : union(powerset(A)) != A,
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f61,plain,
union(powerset(sK9_skl)) != sK9_skl,
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(A,sK9_skl)],[f60]) ).
fof(f62,plain,
union(powerset(sK9_skl)) != sK9_skl,
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f65,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f25]) ).
fof(f66,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f26]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(X0,X2)
| in(X0,union(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f41]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(union(X0),X1) ),
inference(resolution,[status(thm)],[f14,f69]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X0)
| ~ in(union(X2),X3)
| ~ in(X1,X2)
| ~ in(union(X0),X1) ),
inference(resolution,[status(thm)],[f72,f69]) ).
fof(f511,plain,
! [X0] :
( ~ in(X0,powerset(sK9_skl))
| ~ in(sK4_skl(sK9_skl,powerset(sK9_skl)),X0)
| ~ in(sK4_skl(sK9_skl,powerset(sK9_skl)),sK9_skl) ),
inference(resolution,[status(thm)],[f42,f62]) ).
fof(f512,definition,
( sQ3_spl
<=> in(sK4_skl(sK9_skl,powerset(sK9_skl)),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( ~ sQ3_spl
| in(sK4_skl(sK9_skl,powerset(sK9_skl)),sK9_skl) ),
inference(component_clause,[status(thm)],[f512]) ).
fof(f514,plain,
( sQ3_spl
| ~ in(sK4_skl(sK9_skl,powerset(sK9_skl)),sK9_skl) ),
inference(component_clause,[status(thm)],[f512]) ).
fof(f515,definition,
! [X0] :
( sQ4_spl
<=> ( ~ in(X0,powerset(sK9_skl))
| ~ in(sK4_skl(sK9_skl,powerset(sK9_skl)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f516,plain,
! [X0] :
( ~ sQ4_spl
| ~ in(X0,powerset(sK9_skl))
| ~ in(sK4_skl(sK9_skl,powerset(sK9_skl)),X0) ),
inference(component_clause,[status(thm)],[f515]) ).
fof(f518,plain,
( sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f511,f512,f515]) ).
fof(f561,plain,
( sQ3_spl
| in(sK5_skl(sK9_skl,powerset(sK9_skl)),powerset(sK9_skl))
| sK9_skl = union(powerset(sK9_skl)) ),
inference(resolution,[status(thm)],[f514,f44]) ).
fof(f562,plain,
! [X0] :
( sQ3_spl
| ~ in(sK4_skl(sK9_skl,powerset(sK9_skl)),X0)
| ~ subset(X0,sK9_skl) ),
inference(resolution,[status(thm)],[f514,f33]) ).
fof(f564,definition,
( sQ5_spl
<=> sK9_skl = union(powerset(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f565,plain,
( ~ sQ5_spl
| sK9_skl = union(powerset(sK9_skl)) ),
inference(component_clause,[status(thm)],[f564]) ).
fof(f567,definition,
( sQ6_spl
<=> in(sK5_skl(sK9_skl,powerset(sK9_skl)),powerset(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f568,plain,
( ~ sQ6_spl
| in(sK5_skl(sK9_skl,powerset(sK9_skl)),powerset(sK9_skl)) ),
inference(component_clause,[status(thm)],[f567]) ).
fof(f570,plain,
( sQ3_spl
| sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f561,f564,f567,f512]) ).
fof(f571,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f565,f62]) ).
fof(f572,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f571]) ).
fof(f600,definition,
( sQ8_spl
<=> in(sK9_skl,powerset(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f601,plain,
( ~ sQ8_spl
| in(sK9_skl,powerset(sK9_skl)) ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f602,plain,
( sQ8_spl
| ~ in(sK9_skl,powerset(sK9_skl)) ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f604,plain,
( sQ8_spl
| ~ subset(sK9_skl,sK9_skl) ),
inference(resolution,[status(thm)],[f602,f66]) ).
fof(f607,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f604,f54]) ).
fof(f608,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f607]) ).
fof(f611,plain,
( ~ sQ8_spl
| ~ in(union(powerset(sK9_skl)),sK9_skl)
| ~ in(union(powerset(sK9_skl)),sK9_skl) ),
inference(resolution,[status(thm)],[f601,f85]) ).
fof(f620,definition,
( sQ9_spl
<=> in(union(powerset(sK9_skl)),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f623,plain,
( ~ sQ8_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f611,f620,f600]) ).
fof(f640,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ in(sK9_skl,powerset(sK9_skl)) ),
inference(resolution,[status(thm)],[f513,f516]) ).
fof(f651,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f640,f600,f512,f515]) ).
fof(f1115,plain,
( sQ3_spl
| in(sK4_skl(sK9_skl,powerset(sK9_skl)),sK9_skl)
| sK9_skl = union(powerset(sK9_skl))
| ~ subset(sK5_skl(sK9_skl,powerset(sK9_skl)),sK9_skl) ),
inference(resolution,[status(thm)],[f562,f43]) ).
fof(f1123,definition,
( sQ19_spl
<=> subset(sK5_skl(sK9_skl,powerset(sK9_skl)),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f1125,plain,
( sQ19_spl
| ~ subset(sK5_skl(sK9_skl,powerset(sK9_skl)),sK9_skl) ),
inference(component_clause,[status(thm)],[f1123]) ).
fof(f1126,plain,
( sQ3_spl
| sQ5_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1115,f1123,f564,f512]) ).
fof(f1127,definition,
( sQ20_spl
<=> subset(sK9_skl,sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f1129,plain,
( sQ20_spl
| ~ subset(sK9_skl,sK9_skl) ),
inference(component_clause,[status(thm)],[f1127]) ).
fof(f1131,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1129,f54]) ).
fof(f1132,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f1131]) ).
fof(f1139,plain,
( sQ19_spl
| ~ in(sK5_skl(sK9_skl,powerset(sK9_skl)),powerset(sK9_skl)) ),
inference(resolution,[status(thm)],[f1125,f65]) ).
fof(f1140,plain,
( sQ19_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1139,f568]) ).
fof(f1141,plain,
( sQ19_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1140]) ).
fof(f1142,plain,
$false,
inference(sat_refutation,[status(thm)],[f518,f570,f572,f608,f623,f651,f1126,f1132,f1141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU164+3 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.53 % Computer : n013.cluster.edu
% 0.07/0.53 % Model : x86_64 x86_64
% 0.07/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.53 % Memory : 8046.5625MB
% 0.07/0.53 % OS : Linux 6.8.0-71-generic
% 0.07/0.53 % CPULimit : 300
% 0.07/0.53 % WCLimit : 300
% 0.07/0.53 % DateTime : Mon Sep 21 05:53:21 UTC 2026
% 0.07/0.53 % CPUTime :
% 0.07/0.54 % Drodi V4.1.1
% 0.12/0.82 % Refutation found
% 0.12/0.82 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.85 % Elapsed time: 0.303293 seconds
% 0.12/0.85 % CPU time: 2.209009 seconds
% 0.12/0.85 % Total memory used: 106.418 MB
% 0.12/0.85 % Net memory used: 100.821 MB
%------------------------------------------------------------------------------