%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU164+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 : n017.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 1.37s 0.60s
% Output : CNFRefutation 1.37s
% 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/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A] : union(powerset(A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A] : union(powerset(A)) = A,
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f23,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(f24,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)],[f23]) ).
fof(f25,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))],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f30,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f31,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)],[f30]) ).
fof(f32,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)],[f31]) ).
fof(f33,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))],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
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) )
& ( ! [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(f38,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)],[f37]) ).
fof(f39,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))],[f38]) ).
fof(f42,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| ~ in(X2,X3)
| in(X2,X0)
| X0 != union(X1) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f43,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)],[f39]) ).
fof(f44,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)],[f39]) ).
fof(f45,plain,
! [X0,X1] :
( in(sK5_skl(X0,X1),X1)
| in(sK4_skl(X0,X1),X0)
| X0 = union(X1) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f50,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f51,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f57,plain,
? [A] : union(powerset(A)) != A,
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f58,plain,
union(powerset(sK7_skl)) != sK7_skl,
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(A,sK7_skl)],[f57]) ).
fof(f59,plain,
union(powerset(sK7_skl)) != sK7_skl,
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f62,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f26]) ).
fof(f63,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f27]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(X0,X2)
| in(X0,union(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f42]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(union(X0),X1) ),
inference(resolution,[status(thm)],[f15,f66]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X0)
| ~ in(union(X2),X3)
| ~ in(X1,X2)
| ~ in(union(X0),X1) ),
inference(resolution,[status(thm)],[f69,f66]) ).
fof(f560,plain,
! [X0] :
( ~ in(X0,powerset(sK7_skl))
| ~ in(sK4_skl(sK7_skl,powerset(sK7_skl)),X0)
| ~ in(sK4_skl(sK7_skl,powerset(sK7_skl)),sK7_skl) ),
inference(resolution,[status(thm)],[f43,f59]) ).
fof(f561,definition,
( sQ3_spl
<=> in(sK4_skl(sK7_skl,powerset(sK7_skl)),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f562,plain,
( ~ sQ3_spl
| in(sK4_skl(sK7_skl,powerset(sK7_skl)),sK7_skl) ),
inference(component_clause,[status(thm)],[f561]) ).
fof(f563,plain,
( sQ3_spl
| ~ in(sK4_skl(sK7_skl,powerset(sK7_skl)),sK7_skl) ),
inference(component_clause,[status(thm)],[f561]) ).
fof(f564,definition,
! [X0] :
( sQ4_spl
<=> ( ~ in(X0,powerset(sK7_skl))
| ~ in(sK4_skl(sK7_skl,powerset(sK7_skl)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f565,plain,
! [X0] :
( ~ sQ4_spl
| ~ in(X0,powerset(sK7_skl))
| ~ in(sK4_skl(sK7_skl,powerset(sK7_skl)),X0) ),
inference(component_clause,[status(thm)],[f564]) ).
fof(f567,plain,
( sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f560,f561,f564]) ).
fof(f616,plain,
( sQ3_spl
| in(sK5_skl(sK7_skl,powerset(sK7_skl)),powerset(sK7_skl))
| sK7_skl = union(powerset(sK7_skl)) ),
inference(resolution,[status(thm)],[f563,f45]) ).
fof(f617,plain,
! [X0] :
( sQ3_spl
| ~ in(sK4_skl(sK7_skl,powerset(sK7_skl)),X0)
| ~ subset(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f563,f34]) ).
fof(f619,definition,
( sQ5_spl
<=> sK7_skl = union(powerset(sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f620,plain,
( ~ sQ5_spl
| sK7_skl = union(powerset(sK7_skl)) ),
inference(component_clause,[status(thm)],[f619]) ).
fof(f622,definition,
( sQ6_spl
<=> in(sK5_skl(sK7_skl,powerset(sK7_skl)),powerset(sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f623,plain,
( ~ sQ6_spl
| in(sK5_skl(sK7_skl,powerset(sK7_skl)),powerset(sK7_skl)) ),
inference(component_clause,[status(thm)],[f622]) ).
fof(f625,plain,
( sQ3_spl
| sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f616,f619,f622,f561]) ).
fof(f626,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f620,f59]) ).
fof(f627,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f626]) ).
fof(f657,definition,
( sQ8_spl
<=> in(sK7_skl,powerset(sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f658,plain,
( ~ sQ8_spl
| in(sK7_skl,powerset(sK7_skl)) ),
inference(component_clause,[status(thm)],[f657]) ).
fof(f659,plain,
( sQ8_spl
| ~ in(sK7_skl,powerset(sK7_skl)) ),
inference(component_clause,[status(thm)],[f657]) ).
fof(f661,plain,
( sQ8_spl
| ~ subset(sK7_skl,sK7_skl) ),
inference(resolution,[status(thm)],[f659,f63]) ).
fof(f664,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f661,f51]) ).
fof(f665,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f664]) ).
fof(f670,plain,
( ~ sQ8_spl
| ~ in(union(powerset(sK7_skl)),sK7_skl)
| ~ in(union(powerset(sK7_skl)),sK7_skl) ),
inference(resolution,[status(thm)],[f658,f83]) ).
fof(f679,definition,
( sQ9_spl
<=> in(union(powerset(sK7_skl)),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f682,plain,
( ~ sQ8_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f670,f679,f657]) ).
fof(f706,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ in(sK7_skl,powerset(sK7_skl)) ),
inference(resolution,[status(thm)],[f562,f565]) ).
fof(f719,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f706,f657,f561,f564]) ).
fof(f1243,plain,
( sQ3_spl
| in(sK4_skl(sK7_skl,powerset(sK7_skl)),sK7_skl)
| sK7_skl = union(powerset(sK7_skl))
| ~ subset(sK5_skl(sK7_skl,powerset(sK7_skl)),sK7_skl) ),
inference(resolution,[status(thm)],[f617,f44]) ).
fof(f1251,definition,
( sQ27_spl
<=> subset(sK5_skl(sK7_skl,powerset(sK7_skl)),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f1253,plain,
( sQ27_spl
| ~ subset(sK5_skl(sK7_skl,powerset(sK7_skl)),sK7_skl) ),
inference(component_clause,[status(thm)],[f1251]) ).
fof(f1254,plain,
( sQ3_spl
| sQ5_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f1243,f1251,f619,f561]) ).
fof(f1255,definition,
( sQ28_spl
<=> subset(sK7_skl,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f1257,plain,
( sQ28_spl
| ~ subset(sK7_skl,sK7_skl) ),
inference(component_clause,[status(thm)],[f1255]) ).
fof(f1259,plain,
( sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1257,f51]) ).
fof(f1260,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f1259]) ).
fof(f1270,plain,
( sQ27_spl
| ~ in(sK5_skl(sK7_skl,powerset(sK7_skl)),powerset(sK7_skl)) ),
inference(resolution,[status(thm)],[f1253,f62]) ).
fof(f1271,plain,
( sQ27_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1270,f623]) ).
fof(f1272,plain,
( sQ27_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1271]) ).
fof(f1273,plain,
$false,
inference(sat_refutation,[status(thm)],[f567,f625,f627,f665,f682,f719,f1254,f1260,f1272]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU164+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n017.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 05:49:26 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 1.37/0.60 % Refutation found
% 1.37/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.37/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.37/0.62 % Elapsed time: 0.277309 seconds
% 1.37/0.62 % CPU time: 1.920958 seconds
% 1.37/0.62 % Total memory used: 108.661 MB
% 1.37/0.62 % Net memory used: 102.941 MB
%------------------------------------------------------------------------------