%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET889+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 02:10:54 PM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 26
% Syntax : Number of formulae : 113 ( 14 unt; 19 def)
% Number of atoms : 327 ( 101 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 345 ( 131 ~; 157 |; 30 &)
% ( 25 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 23 ( 21 usr; 20 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 114 ( 107 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(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,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A] : powerset(singleton(A)) = unordered_pair(empty_set,singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A] : powerset(singleton(A)) = unordered_pair(empty_set,singleton(A)),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f15,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,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(f17,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)],[f16]) ).
fof(f18,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))],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f21,plain,
! [X0,X1] :
( ~ subset(sK0_skl(X0,X1),X1)
| ~ in(sK0_skl(X0,X1),X0)
| X0 = powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f22,plain,
! [X0,X1] :
( subset(sK0_skl(X0,X1),X1)
| in(sK0_skl(X0,X1),X0)
| X0 = powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f23,plain,
! [A,B,C] :
( ( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ( ! [D] :
( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f24,plain,
( ! [A,B,C] :
( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
( ! [A,B,C] :
( ( ( sK1_skl(C,B,A) = B
| sK1_skl(C,B,A) = A
| in(sK1_skl(C,B,A),C) )
& ( ( sK1_skl(C,B,A) != B
& sK1_skl(C,B,A) != A )
| ~ in(sK1_skl(C,B,A),C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f24]) ).
fof(f29,plain,
! [X0,X1,X2] :
( sK1_skl(X0,X2,X1) != X1
| ~ in(sK1_skl(X0,X2,X1),X0)
| X0 = unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f30,plain,
! [X0,X1,X2] :
( sK1_skl(X0,X2,X1) != X2
| ~ in(sK1_skl(X0,X2,X1),X0)
| X0 = unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f31,plain,
! [X0,X1,X2] :
( sK1_skl(X0,X2,X1) = X2
| sK1_skl(X0,X2,X1) = X1
| in(sK1_skl(X0,X2,X1),X0)
| X0 = unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f33,plain,
! [A,B] :
( ( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f34,plain,
( ! [A,B] :
( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ! [A,B] :
( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( X0 = singleton(X1)
| X0 = empty_set
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( X0 != empty_set
| subset(X0,singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f42,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f43,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [A,B] :
( A = B
| ? [C] :
( in(C,A)
<~> in(C,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,B)
| ~ in(C,A) )
& ( in(C,B)
| in(C,A) ) ) ),
inference(NNF_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [A,B] :
( A = B
| ( ( ~ in(sK4_skl(B,A),B)
| ~ in(sK4_skl(B,A),A) )
& ( in(sK4_skl(B,A),B)
| in(sK4_skl(B,A),A) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(C,sK4_skl(B,A))],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( X1 = X0
| in(sK4_skl(X0,X1),X0)
| in(sK4_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( X1 = X0
| ~ in(sK4_skl(X0,X1),X0)
| ~ in(sK4_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
? [A] : powerset(singleton(A)) != unordered_pair(empty_set,singleton(A)),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f50,plain,
powerset(singleton(sK5_skl)) != unordered_pair(empty_set,singleton(sK5_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f49]) ).
fof(f51,plain,
powerset(singleton(sK5_skl)) != unordered_pair(empty_set,singleton(sK5_skl)),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f19]) ).
fof(f53,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f20]) ).
fof(f57,plain,
! [X0] : subset(empty_set,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f36]) ).
fof(f74,plain,
( ~ subset(sK0_skl(unordered_pair(empty_set,singleton(sK5_skl)),singleton(sK5_skl)),singleton(sK5_skl))
| ~ in(sK0_skl(unordered_pair(empty_set,singleton(sK5_skl)),singleton(sK5_skl)),unordered_pair(empty_set,singleton(sK5_skl))) ),
inference(resolution,[status(thm)],[f21,f51]) ).
fof(f75,definition,
( sQ0_spl
<=> in(sK0_skl(unordered_pair(empty_set,singleton(sK5_skl)),singleton(sK5_skl)),unordered_pair(empty_set,singleton(sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( sQ0_spl
| ~ in(sK0_skl(unordered_pair(empty_set,singleton(sK5_skl)),singleton(sK5_skl)),unordered_pair(empty_set,singleton(sK5_skl))) ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,definition,
( sQ1_spl
<=> subset(sK0_skl(unordered_pair(empty_set,singleton(sK5_skl)),singleton(sK5_skl)),singleton(sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f74,f75,f78]) ).
fof(f83,plain,
! [X0,X1,X2] :
( sK1_skl(X0,X1,X2) != X2
| ~ in(sK1_skl(X0,X1,X2),X0)
| X0 = unordered_pair(X1,X2) ),
inference(paramodulation,[status(thm)],[f15,f29]) ).
fof(f112,definition,
( sQ4_spl
<=> powerset(singleton(sK5_skl)) = unordered_pair(empty_set,singleton(sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( ~ sQ4_spl
| powerset(singleton(sK5_skl)) = unordered_pair(empty_set,singleton(sK5_skl)) ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f130,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f113,f51]) ).
fof(f131,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f130]) ).
fof(f145,definition,
( sQ7_spl
<=> subset(empty_set,singleton(sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( sQ7_spl
| ~ subset(empty_set,singleton(sK5_skl)) ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f158,plain,
( sQ0_spl
| subset(sK0_skl(unordered_pair(empty_set,singleton(sK5_skl)),singleton(sK5_skl)),singleton(sK5_skl))
| unordered_pair(empty_set,singleton(sK5_skl)) = powerset(singleton(sK5_skl)) ),
inference(resolution,[status(thm)],[f77,f22]) ).
fof(f159,plain,
( sQ0_spl
| sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f158,f112,f78,f75]) ).
fof(f197,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f147,f57]) ).
fof(f198,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f197]) ).
fof(f231,plain,
( sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)) != singleton(sK5_skl)
| ~ in(sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)),powerset(singleton(sK5_skl))) ),
inference(resolution,[status(thm)],[f83,f51]) ).
fof(f234,definition,
( sQ11_spl
<=> in(sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)),powerset(singleton(sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f236,plain,
( sQ11_spl
| ~ in(sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)),powerset(singleton(sK5_skl))) ),
inference(component_clause,[status(thm)],[f234]) ).
fof(f237,definition,
( sQ12_spl
<=> sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)) = singleton(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( ~ sQ12_spl
| sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)) = singleton(sK5_skl) ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f239,plain,
( sQ12_spl
| sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)) != singleton(sK5_skl) ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f240,plain,
( ~ sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f231,f234,f237]) ).
fof(f241,plain,
( sQ11_spl
| sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)) = empty_set
| sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)) = singleton(sK5_skl)
| powerset(singleton(sK5_skl)) = unordered_pair(singleton(sK5_skl),empty_set) ),
inference(resolution,[status(thm)],[f236,f31]) ).
fof(f242,plain,
( sQ11_spl
| ~ subset(sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)),singleton(sK5_skl)) ),
inference(resolution,[status(thm)],[f236,f53]) ).
fof(f243,definition,
( sQ13_spl
<=> powerset(singleton(sK5_skl)) = unordered_pair(singleton(sK5_skl),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f244,plain,
( ~ sQ13_spl
| powerset(singleton(sK5_skl)) = unordered_pair(singleton(sK5_skl),empty_set) ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f245,plain,
( sQ13_spl
| powerset(singleton(sK5_skl)) != unordered_pair(singleton(sK5_skl),empty_set) ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f246,definition,
( sQ14_spl
<=> sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( ~ sQ14_spl
| sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)) = empty_set ),
inference(component_clause,[status(thm)],[f246]) ).
fof(f249,plain,
( sQ11_spl
| sQ14_spl
| sQ12_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f241,f243,f237,f246,f234]) ).
fof(f251,plain,
( sQ11_spl
| ~ sQ14_spl
| ~ subset(empty_set,singleton(sK5_skl)) ),
inference(backward_demodulation,[status(thm)],[f247,f242]) ).
fof(f252,plain,
( sQ11_spl
| ~ sQ14_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f251,f145,f246,f234]) ).
fof(f254,plain,
( sQ12_spl
| sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)) = empty_set
| ~ subset(sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)),singleton(sK5_skl)) ),
inference(resolution,[status(thm)],[f239,f35]) ).
fof(f264,definition,
( sQ16_spl
<=> subset(sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)),singleton(sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f266,plain,
( sQ16_spl
| ~ subset(sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)),singleton(sK5_skl)) ),
inference(component_clause,[status(thm)],[f264]) ).
fof(f267,plain,
( sQ12_spl
| sQ14_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f254,f264,f246,f237]) ).
fof(f272,plain,
( ~ sQ13_spl
| powerset(singleton(sK5_skl)) = unordered_pair(empty_set,singleton(sK5_skl)) ),
inference(paramodulation,[status(thm)],[f15,f244]) ).
fof(f282,plain,
( ~ sQ13_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f272,f112,f243]) ).
fof(f303,plain,
! [X0,X1,X2] :
( sK1_skl(X0,X1,X2) != X1
| ~ in(sK1_skl(X0,X1,X2),X0)
| X0 = unordered_pair(X1,X2) ),
inference(paramodulation,[status(thm)],[f15,f30]) ).
fof(f308,plain,
( ~ in(sK4_skl(unordered_pair(empty_set,singleton(sK5_skl)),powerset(singleton(sK5_skl))),unordered_pair(empty_set,singleton(sK5_skl)))
| ~ in(sK4_skl(unordered_pair(empty_set,singleton(sK5_skl)),powerset(singleton(sK5_skl))),powerset(singleton(sK5_skl))) ),
inference(resolution,[status(thm)],[f48,f51]) ).
fof(f311,plain,
( ~ in(sK4_skl(powerset(singleton(sK5_skl)),unordered_pair(empty_set,singleton(sK5_skl))),powerset(singleton(sK5_skl)))
| ~ in(sK4_skl(powerset(singleton(sK5_skl)),unordered_pair(empty_set,singleton(sK5_skl))),unordered_pair(empty_set,singleton(sK5_skl))) ),
inference(resolution,[status(thm)],[f48,f51]) ).
fof(f326,definition,
( sQ21_spl
<=> in(sK4_skl(unordered_pair(empty_set,singleton(sK5_skl)),powerset(singleton(sK5_skl))),powerset(singleton(sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f328,plain,
( sQ21_spl
| ~ in(sK4_skl(unordered_pair(empty_set,singleton(sK5_skl)),powerset(singleton(sK5_skl))),powerset(singleton(sK5_skl))) ),
inference(component_clause,[status(thm)],[f326]) ).
fof(f329,definition,
( sQ22_spl
<=> in(sK4_skl(unordered_pair(empty_set,singleton(sK5_skl)),powerset(singleton(sK5_skl))),unordered_pair(empty_set,singleton(sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f308,f326,f329]) ).
fof(f347,definition,
( sQ27_spl
<=> in(sK4_skl(powerset(singleton(sK5_skl)),unordered_pair(empty_set,singleton(sK5_skl))),unordered_pair(empty_set,singleton(sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f349,plain,
( sQ27_spl
| ~ in(sK4_skl(powerset(singleton(sK5_skl)),unordered_pair(empty_set,singleton(sK5_skl))),unordered_pair(empty_set,singleton(sK5_skl))) ),
inference(component_clause,[status(thm)],[f347]) ).
fof(f350,definition,
( sQ28_spl
<=> in(sK4_skl(powerset(singleton(sK5_skl)),unordered_pair(empty_set,singleton(sK5_skl))),powerset(singleton(sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( ~ sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f311,f347,f350]) ).
fof(f355,plain,
( sQ11_spl
| ~ sQ12_spl
| ~ subset(singleton(sK5_skl),singleton(sK5_skl)) ),
inference(forward_demodulation,[status(thm)],[f238,f242]) ).
fof(f356,plain,
( sQ11_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f355,f43]) ).
fof(f357,plain,
( sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f370,plain,
( sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)) != empty_set
| ~ in(sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)),powerset(singleton(sK5_skl))) ),
inference(resolution,[status(thm)],[f303,f51]) ).
fof(f373,plain,
( ~ sQ14_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f370,f234,f246]) ).
fof(f381,plain,
( sQ13_spl
| ~ in(sK4_skl(unordered_pair(singleton(sK5_skl),empty_set),powerset(singleton(sK5_skl))),unordered_pair(singleton(sK5_skl),empty_set))
| ~ in(sK4_skl(unordered_pair(singleton(sK5_skl),empty_set),powerset(singleton(sK5_skl))),powerset(singleton(sK5_skl))) ),
inference(resolution,[status(thm)],[f245,f48]) ).
fof(f384,plain,
( sQ13_spl
| ~ subset(sK0_skl(unordered_pair(singleton(sK5_skl),empty_set),singleton(sK5_skl)),singleton(sK5_skl))
| ~ in(sK0_skl(unordered_pair(singleton(sK5_skl),empty_set),singleton(sK5_skl)),unordered_pair(singleton(sK5_skl),empty_set)) ),
inference(resolution,[status(thm)],[f245,f21]) ).
fof(f385,plain,
( sQ13_spl
| ~ in(sK4_skl(powerset(singleton(sK5_skl)),unordered_pair(singleton(sK5_skl),empty_set)),powerset(singleton(sK5_skl)))
| ~ in(sK4_skl(powerset(singleton(sK5_skl)),unordered_pair(singleton(sK5_skl),empty_set)),unordered_pair(singleton(sK5_skl),empty_set)) ),
inference(resolution,[status(thm)],[f245,f48]) ).
fof(f394,definition,
( sQ29_spl
<=> in(sK4_skl(unordered_pair(singleton(sK5_skl),empty_set),powerset(singleton(sK5_skl))),powerset(singleton(sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f397,definition,
( sQ30_spl
<=> in(sK4_skl(unordered_pair(singleton(sK5_skl),empty_set),powerset(singleton(sK5_skl))),unordered_pair(singleton(sK5_skl),empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f400,plain,
( sQ13_spl
| ~ sQ30_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f381,f394,f397,f243]) ).
fof(f401,definition,
( sQ31_spl
<=> in(sK0_skl(unordered_pair(singleton(sK5_skl),empty_set),singleton(sK5_skl)),unordered_pair(singleton(sK5_skl),empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f404,definition,
( sQ32_spl
<=> subset(sK0_skl(unordered_pair(singleton(sK5_skl),empty_set),singleton(sK5_skl)),singleton(sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f407,plain,
( sQ13_spl
| ~ sQ32_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f384,f401,f404,f243]) ).
fof(f408,definition,
( sQ33_spl
<=> in(sK4_skl(powerset(singleton(sK5_skl)),unordered_pair(singleton(sK5_skl),empty_set)),unordered_pair(singleton(sK5_skl),empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f411,definition,
( sQ34_spl
<=> in(sK4_skl(powerset(singleton(sK5_skl)),unordered_pair(singleton(sK5_skl),empty_set)),powerset(singleton(sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f414,plain,
( sQ13_spl
| ~ sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f385,f408,f411,f243]) ).
fof(f442,plain,
( sQ27_spl
| unordered_pair(empty_set,singleton(sK5_skl)) = powerset(singleton(sK5_skl))
| in(sK4_skl(powerset(singleton(sK5_skl)),unordered_pair(empty_set,singleton(sK5_skl))),powerset(singleton(sK5_skl))) ),
inference(resolution,[status(thm)],[f349,f47]) ).
fof(f443,plain,
( sQ27_spl
| sQ4_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f442,f350,f112,f347]) ).
fof(f444,plain,
( sQ21_spl
| powerset(singleton(sK5_skl)) = unordered_pair(empty_set,singleton(sK5_skl))
| in(sK4_skl(unordered_pair(empty_set,singleton(sK5_skl)),powerset(singleton(sK5_skl))),unordered_pair(empty_set,singleton(sK5_skl))) ),
inference(resolution,[status(thm)],[f328,f47]) ).
fof(f446,plain,
( sQ21_spl
| sQ4_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f444,f329,f112,f326]) ).
fof(f528,plain,
( sQ16_spl
| ~ in(sK1_skl(powerset(singleton(sK5_skl)),empty_set,singleton(sK5_skl)),powerset(singleton(sK5_skl))) ),
inference(resolution,[status(thm)],[f266,f52]) ).
fof(f529,plain,
( sQ16_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f528,f234,f264]) ).
fof(f530,plain,
$false,
inference(sat_refutation,[status(thm)],[f81,f131,f159,f198,f240,f249,f252,f267,f282,f332,f353,f357,f373,f400,f407,f414,f443,f446,f529]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET889+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.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 05:40:50 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.060331 seconds
% 0.13/0.42 % CPU time: 0.195556 seconds
% 0.13/0.42 % Total memory used: 62.929 MB
% 0.13/0.42 % Net memory used: 62.673 MB
%------------------------------------------------------------------------------