%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU297+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 02:20:04 PM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 84 ( 9 unt; 12 def)
% Number of atoms : 352 ( 40 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 421 ( 153 ~; 182 |; 63 &)
% ( 17 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 12 prp; 0-5 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 162 ( 126 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C)
& element(B,powerset(powerset(A))) )
=> ? [D] :
! [E] :
( in(E,D)
<=> ( in(relation_image(C,E),B)
& in(E,powerset(relation_dom(C))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C)
& element(B,powerset(powerset(A))) )
=> ? [D] :
! [E] :
( in(E,D)
<=> ( in(relation_image(C,E),B)
& in(E,powerset(relation_dom(C))) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f38,axiom,
! [A,B,C] :
( ( function(C)
& relation(C)
& element(B,powerset(powerset(A))) )
=> ( ! [D,E,F] :
( ( in(relation_image(C,F),B)
& D = F
& in(relation_image(C,E),B)
& D = E )
=> E = F )
=> ? [D] :
! [E] :
( in(E,D)
<=> ? [F] :
( in(relation_image(C,E),B)
& F = E
& in(F,powerset(relation_dom(C))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,plain,
? [A,B,C] :
( ! [D] :
? [E] :
( in(E,D)
<~> ( in(relation_image(C,E),B)
& in(E,powerset(relation_dom(C))) ) )
& function(C)
& relation(C)
& element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f40,plain,
? [A,B,C] :
( ! [D] :
? [E] :
( ( ~ in(relation_image(C,E),B)
| ~ in(E,powerset(relation_dom(C)))
| ~ in(E,D) )
& ( ( in(relation_image(C,E),B)
& in(E,powerset(relation_dom(C))) )
| in(E,D) ) )
& function(C)
& relation(C)
& element(B,powerset(powerset(A))) ),
inference(NNF_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
? [B,C] :
( ! [D] :
? [E] :
( ( ~ in(relation_image(C,E),B)
| ~ in(E,powerset(relation_dom(C)))
| ~ in(E,D) )
& ( ( in(relation_image(C,E),B)
& in(E,powerset(relation_dom(C))) )
| in(E,D) ) )
& function(C)
& relation(C)
& ? [A] : element(B,powerset(powerset(A))) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,plain,
( ! [D] :
( ( ~ in(relation_image(sK1_skl,sK3_skl(D)),sK0_skl)
| ~ in(sK3_skl(D),powerset(relation_dom(sK1_skl)))
| ~ in(sK3_skl(D),D) )
& ( ( in(relation_image(sK1_skl,sK3_skl(D)),sK0_skl)
& in(sK3_skl(D),powerset(relation_dom(sK1_skl))) )
| in(sK3_skl(D),D) ) )
& function(sK1_skl)
& relation(sK1_skl)
& element(sK0_skl,powerset(powerset(sK2_skl))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(B,sK0_skl),skolemize(C,sK1_skl),skolemize(A,sK2_skl),skolemize(E,sK3_skl(D))],[f41]) ).
fof(f43,plain,
element(sK0_skl,powerset(powerset(sK2_skl))),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
relation(sK1_skl),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
function(sK1_skl),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f46,plain,
! [X0] :
( in(sK3_skl(X0),powerset(relation_dom(sK1_skl)))
| in(sK3_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f47,plain,
! [X0] :
( in(relation_image(sK1_skl,sK3_skl(X0)),sK0_skl)
| in(sK3_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f48,plain,
! [X0] :
( ~ in(relation_image(sK1_skl,sK3_skl(X0)),sK0_skl)
| ~ in(sK3_skl(X0),powerset(relation_dom(sK1_skl)))
| ~ in(sK3_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f159,plain,
! [A,B,C] :
( ? [D] :
! [E] :
( in(E,D)
<=> ? [F] :
( in(relation_image(C,E),B)
& F = E
& in(F,powerset(relation_dom(C))) ) )
| ? [D,E,F] :
( E != F
& in(relation_image(C,F),B)
& D = F
& in(relation_image(C,E),B)
& D = E )
| ~ function(C)
| ~ relation(C)
| ~ element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f160,definition,
! [B,C,D,E,F] :
( sP0_prd(F,E,D,C,B)
<=> ( E != F
& in(relation_image(C,F),B)
& D = F
& in(relation_image(C,E),B)
& D = E ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f161,plain,
! [A,B,C] :
( ? [D] :
! [E] :
( in(E,D)
<=> ? [F] :
( in(relation_image(C,E),B)
& F = E
& in(F,powerset(relation_dom(C))) ) )
| ? [D,E,F] : sP0_prd(F,E,D,C,B)
| ~ function(C)
| ~ relation(C)
| ~ element(B,powerset(powerset(A))) ),
inference(formula_renaming,[status(thm)],[f159,f160]) ).
fof(f162,plain,
! [A,B,C] :
( ? [D] :
! [E] :
( ( ! [F] :
( ~ in(relation_image(C,E),B)
| F != E
| ~ in(F,powerset(relation_dom(C))) )
| in(E,D) )
& ( ? [F] :
( in(relation_image(C,E),B)
& F = E
& in(F,powerset(relation_dom(C))) )
| ~ in(E,D) ) )
| ? [D,E,F] : sP0_prd(F,E,D,C,B)
| ~ function(C)
| ~ relation(C)
| ~ element(B,powerset(powerset(A))) ),
inference(NNF_transformation,[status(thm)],[f161]) ).
fof(f163,plain,
! [B,C] :
( ? [D] :
( ! [E] :
( ~ in(relation_image(C,E),B)
| ! [F] :
( F != E
| ~ in(F,powerset(relation_dom(C))) )
| in(E,D) )
& ! [E] :
( ( in(relation_image(C,E),B)
& ? [F] :
( F = E
& in(F,powerset(relation_dom(C))) ) )
| ~ in(E,D) ) )
| ? [D,E,F] : sP0_prd(F,E,D,C,B)
| ~ function(C)
| ~ relation(C)
| ! [A] : ~ element(B,powerset(powerset(A))) ),
inference(miniscoping,[status(thm)],[f162]) ).
fof(f164,plain,
! [B,C] :
( ( ! [E] :
( ~ in(relation_image(C,E),B)
| ! [F] :
( F != E
| ~ in(F,powerset(relation_dom(C))) )
| in(E,sK23_skl(C,B)) )
& ! [E] :
( ( in(relation_image(C,E),B)
& sK24_skl(E,C,B) = E
& in(sK24_skl(E,C,B),powerset(relation_dom(C))) )
| ~ in(E,sK23_skl(C,B)) ) )
| sP0_prd(sK22_skl(C,B),sK21_skl(C,B),sK20_skl(C,B),C,B)
| ~ function(C)
| ~ relation(C)
| ! [A] : ~ element(B,powerset(powerset(A))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl]),skolemize(D,sK20_skl(C,B)),skolemize(E,sK21_skl(C,B)),skolemize(F,sK22_skl(C,B)),skolemize(D,sK23_skl(C,B)),skolemize(F,sK24_skl(E,C,B))],[f163]) ).
fof(f165,plain,
! [X0,X1,X2,X3] :
( in(sK24_skl(X3,X2,X0),powerset(relation_dom(X2)))
| ~ in(X3,sK23_skl(X2,X0))
| sP0_prd(sK22_skl(X2,X0),sK21_skl(X2,X0),sK20_skl(X2,X0),X2,X0)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f166,plain,
! [X0,X1,X2,X3] :
( sK24_skl(X3,X2,X0) = X3
| ~ in(X3,sK23_skl(X2,X0))
| sP0_prd(sK22_skl(X2,X0),sK21_skl(X2,X0),sK20_skl(X2,X0),X2,X0)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f167,plain,
! [X0,X1,X2,X3] :
( in(relation_image(X2,X3),X0)
| ~ in(X3,sK23_skl(X2,X0))
| sP0_prd(sK22_skl(X2,X0),sK21_skl(X2,X0),sK20_skl(X2,X0),X2,X0)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f168,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(relation_image(X2,X3),X0)
| X4 != X3
| ~ in(X4,powerset(relation_dom(X2)))
| in(X3,sK23_skl(X2,X0))
| sP0_prd(sK22_skl(X2,X0),sK21_skl(X2,X0),sK20_skl(X2,X0),X2,X0)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f169,plain,
! [B,C,D,E,F] :
( ( E = F
| ~ in(relation_image(C,F),B)
| D != F
| ~ in(relation_image(C,E),B)
| D != E
| sP0_prd(F,E,D,C,B) )
& ( ( E != F
& in(relation_image(C,F),B)
& D = F
& in(relation_image(C,E),B)
& D = E )
| ~ sP0_prd(F,E,D,C,B) ) ),
inference(NNF_transformation,[status(thm)],[f160]) ).
fof(f170,plain,
( ! [B,C,D,E,F] :
( E = F
| ~ in(relation_image(C,F),B)
| D != F
| ~ in(relation_image(C,E),B)
| D != E
| sP0_prd(F,E,D,C,B) )
& ! [B,C,D,E,F] :
( ( E != F
& in(relation_image(C,F),B)
& D = F
& in(relation_image(C,E),B)
& D = E )
| ~ sP0_prd(F,E,D,C,B) ) ),
inference(miniscoping,[status(thm)],[f169]) ).
fof(f171,plain,
! [X0,X1,X2,X3,X4] :
( X2 = X1
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f173,plain,
! [X0,X1,X2,X3,X4] :
( X2 = X0
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f175,plain,
! [X0,X1,X2,X3,X4] :
( X1 != X0
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f177,plain,
! [X0,X1,X2,X3] :
( ~ in(relation_image(X2,X3),X0)
| ~ in(X3,powerset(relation_dom(X2)))
| in(X3,sK23_skl(X2,X0))
| sP0_prd(sK22_skl(X2,X0),sK21_skl(X2,X0),sK20_skl(X2,X0),X2,X0)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X0,powerset(powerset(X1))) ),
inference(destructive_equality_resolution,[status(thm)],[f168]) ).
fof(f178,plain,
! [X0,X1,X2,X3] : ~ sP0_prd(X0,X0,X1,X2,X3),
inference(destructive_equality_resolution,[status(thm)],[f175]) ).
fof(f185,plain,
! [X0,X1,X2] :
( in(sK3_skl(X2),X2)
| ~ in(relation_image(sK1_skl,sK3_skl(X2)),X0)
| in(sK3_skl(X2),sK23_skl(sK1_skl,X0))
| sP0_prd(sK22_skl(sK1_skl,X0),sK21_skl(sK1_skl,X0),sK20_skl(sK1_skl,X0),sK1_skl,X0)
| ~ function(sK1_skl)
| ~ relation(sK1_skl)
| ~ element(X0,powerset(powerset(X1))) ),
inference(resolution,[status(thm)],[f177,f46]) ).
fof(f186,definition,
! [X0,X1,X2] :
( sQ0_spl
<=> ( in(sK3_skl(X2),X2)
| ~ in(relation_image(sK1_skl,sK3_skl(X2)),X0)
| in(sK3_skl(X2),sK23_skl(sK1_skl,X0))
| sP0_prd(sK22_skl(sK1_skl,X0),sK21_skl(sK1_skl,X0),sK20_skl(sK1_skl,X0),sK1_skl,X0)
| ~ element(X0,powerset(powerset(X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f187,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| in(sK3_skl(X2),X2)
| ~ in(relation_image(sK1_skl,sK3_skl(X2)),X0)
| in(sK3_skl(X2),sK23_skl(sK1_skl,X0))
| sP0_prd(sK22_skl(sK1_skl,X0),sK21_skl(sK1_skl,X0),sK20_skl(sK1_skl,X0),sK1_skl,X0)
| ~ element(X0,powerset(powerset(X1))) ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,definition,
( sQ1_spl
<=> relation(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( sQ1_spl
| ~ relation(sK1_skl) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,definition,
( sQ2_spl
<=> function(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( sQ2_spl
| ~ function(sK1_skl) ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f185,f186,f189,f192]) ).
fof(f196,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f194,f45]) ).
fof(f197,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f196]) ).
fof(f198,plain,
! [X0,X1] :
( ~ sQ0_spl
| in(sK3_skl(X1),X1)
| in(sK3_skl(X1),X1)
| in(sK3_skl(X1),sK23_skl(sK1_skl,sK0_skl))
| sP0_prd(sK22_skl(sK1_skl,sK0_skl),sK21_skl(sK1_skl,sK0_skl),sK20_skl(sK1_skl,sK0_skl),sK1_skl,sK0_skl)
| ~ element(sK0_skl,powerset(powerset(X0))) ),
inference(resolution,[status(thm)],[f187,f47]) ).
fof(f199,definition,
! [X0] :
( sQ3_spl
<=> ~ element(sK0_skl,powerset(powerset(X0))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f200,plain,
! [X0] :
( ~ sQ3_spl
| ~ element(sK0_skl,powerset(powerset(X0))) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,definition,
( sQ4_spl
<=> sP0_prd(sK22_skl(sK1_skl,sK0_skl),sK21_skl(sK1_skl,sK0_skl),sK20_skl(sK1_skl,sK0_skl),sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( ~ sQ4_spl
| sP0_prd(sK22_skl(sK1_skl,sK0_skl),sK21_skl(sK1_skl,sK0_skl),sK20_skl(sK1_skl,sK0_skl),sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,definition,
! [X1] :
( sQ5_spl
<=> ( in(sK3_skl(X1),X1)
| in(sK3_skl(X1),X1)
| in(sK3_skl(X1),sK23_skl(sK1_skl,sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0] :
( ~ sQ5_spl
| in(sK3_skl(X0),X0)
| in(sK3_skl(X0),X0)
| in(sK3_skl(X0),sK23_skl(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( ~ sQ0_spl
| sQ5_spl
| sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f198,f199,f202,f205,f186]) ).
fof(f209,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f44]) ).
fof(f210,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f209]) ).
fof(f211,plain,
! [X0] :
( ~ sQ5_spl
| in(sK3_skl(X0),X0)
| in(sK3_skl(X0),sK23_skl(sK1_skl,sK0_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f206]) ).
fof(f230,plain,
( ~ sQ4_spl
| sK20_skl(sK1_skl,sK0_skl) = sK22_skl(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f203,f173]) ).
fof(f231,plain,
( ~ sQ4_spl
| sK20_skl(sK1_skl,sK0_skl) = sK21_skl(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f203,f171]) ).
fof(f234,plain,
( ~ sQ4_spl
| sP0_prd(sK20_skl(sK1_skl,sK0_skl),sK21_skl(sK1_skl,sK0_skl),sK20_skl(sK1_skl,sK0_skl),sK1_skl,sK0_skl) ),
inference(backward_demodulation,[status(thm)],[f230,f203]) ).
fof(f237,plain,
( ~ sQ4_spl
| sP0_prd(sK20_skl(sK1_skl,sK0_skl),sK20_skl(sK1_skl,sK0_skl),sK20_skl(sK1_skl,sK0_skl),sK1_skl,sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f231,f234]) ).
fof(f238,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f237,f178]) ).
fof(f239,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f240,plain,
( ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f43,f200]) ).
fof(f241,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f240]) ).
fof(f270,definition,
( sQ10_spl
<=> sK24_skl(sK3_skl(sK23_skl(sK1_skl,sK0_skl)),sK1_skl,sK0_skl) = sK3_skl(sK23_skl(sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f271,plain,
( ~ sQ10_spl
| sK24_skl(sK3_skl(sK23_skl(sK1_skl,sK0_skl)),sK1_skl,sK0_skl) = sK3_skl(sK23_skl(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f270]) ).
fof(f273,definition,
( sQ11_spl
<=> in(sK3_skl(sK23_skl(sK1_skl,sK0_skl)),sK23_skl(sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f274,plain,
( ~ sQ11_spl
| in(sK3_skl(sK23_skl(sK1_skl,sK0_skl)),sK23_skl(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f275,plain,
( sQ11_spl
| ~ in(sK3_skl(sK23_skl(sK1_skl,sK0_skl)),sK23_skl(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f276,definition,
( sQ12_spl
<=> in(sK3_skl(sK23_skl(sK1_skl,sK0_skl)),powerset(relation_dom(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( sQ12_spl
| ~ in(sK3_skl(sK23_skl(sK1_skl,sK0_skl)),powerset(relation_dom(sK1_skl))) ),
inference(component_clause,[status(thm)],[f276]) ).
fof(f288,plain,
! [X0] :
( ~ sQ11_spl
| in(sK24_skl(sK3_skl(sK23_skl(sK1_skl,sK0_skl)),sK1_skl,sK0_skl),powerset(relation_dom(sK1_skl)))
| sP0_prd(sK22_skl(sK1_skl,sK0_skl),sK21_skl(sK1_skl,sK0_skl),sK20_skl(sK1_skl,sK0_skl),sK1_skl,sK0_skl)
| ~ function(sK1_skl)
| ~ relation(sK1_skl)
| ~ element(sK0_skl,powerset(powerset(X0))) ),
inference(resolution,[status(thm)],[f274,f165]) ).
fof(f289,plain,
! [X0] :
( ~ sQ11_spl
| in(relation_image(sK1_skl,sK3_skl(sK23_skl(sK1_skl,sK0_skl))),sK0_skl)
| sP0_prd(sK22_skl(sK1_skl,sK0_skl),sK21_skl(sK1_skl,sK0_skl),sK20_skl(sK1_skl,sK0_skl),sK1_skl,sK0_skl)
| ~ function(sK1_skl)
| ~ relation(sK1_skl)
| ~ element(sK0_skl,powerset(powerset(X0))) ),
inference(resolution,[status(thm)],[f274,f167]) ).
fof(f290,plain,
! [X0] :
( ~ sQ11_spl
| sK24_skl(sK3_skl(sK23_skl(sK1_skl,sK0_skl)),sK1_skl,sK0_skl) = sK3_skl(sK23_skl(sK1_skl,sK0_skl))
| sP0_prd(sK22_skl(sK1_skl,sK0_skl),sK21_skl(sK1_skl,sK0_skl),sK20_skl(sK1_skl,sK0_skl),sK1_skl,sK0_skl)
| ~ function(sK1_skl)
| ~ relation(sK1_skl)
| ~ element(sK0_skl,powerset(powerset(X0))) ),
inference(resolution,[status(thm)],[f274,f166]) ).
fof(f292,definition,
( sQ14_spl
<=> in(sK24_skl(sK3_skl(sK23_skl(sK1_skl,sK0_skl)),sK1_skl,sK0_skl),powerset(relation_dom(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f293,plain,
( ~ sQ14_spl
| in(sK24_skl(sK3_skl(sK23_skl(sK1_skl,sK0_skl)),sK1_skl,sK0_skl),powerset(relation_dom(sK1_skl))) ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f295,plain,
( ~ sQ11_spl
| sQ14_spl
| sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f288,f199,f189,f192,f202,f292,f273]) ).
fof(f296,definition,
( sQ15_spl
<=> in(relation_image(sK1_skl,sK3_skl(sK23_skl(sK1_skl,sK0_skl))),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( ~ sQ15_spl
| in(relation_image(sK1_skl,sK3_skl(sK23_skl(sK1_skl,sK0_skl))),sK0_skl) ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f299,plain,
( ~ sQ11_spl
| sQ15_spl
| sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f289,f199,f189,f192,f202,f296,f273]) ).
fof(f300,plain,
( ~ sQ11_spl
| sQ10_spl
| sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f290,f199,f189,f192,f202,f270,f273]) ).
fof(f301,plain,
( ~ sQ14_spl
| ~ sQ10_spl
| in(sK3_skl(sK23_skl(sK1_skl,sK0_skl)),powerset(relation_dom(sK1_skl))) ),
inference(forward_demodulation,[status(thm)],[f271,f293]) ).
fof(f308,plain,
( ~ sQ15_spl
| ~ in(sK3_skl(sK23_skl(sK1_skl,sK0_skl)),powerset(relation_dom(sK1_skl)))
| ~ in(sK3_skl(sK23_skl(sK1_skl,sK0_skl)),sK23_skl(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f297,f48]) ).
fof(f311,plain,
( ~ sQ15_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f308,f273,f276,f296]) ).
fof(f313,plain,
( sQ12_spl
| ~ sQ14_spl
| ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f278,f301]) ).
fof(f314,plain,
( sQ12_spl
| ~ sQ14_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f313]) ).
fof(f338,plain,
( ~ sQ5_spl
| sQ11_spl
| in(sK3_skl(sK23_skl(sK1_skl,sK0_skl)),sK23_skl(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f275,f211]) ).
fof(f340,plain,
( ~ sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f338,f273,f205]) ).
fof(f341,plain,
$false,
inference(sat_refutation,[status(thm)],[f195,f197,f208,f210,f239,f241,f295,f299,f300,f311,f314,f340]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU297+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n015.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 06:12:06 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.46 % Refutation found
% 0.16/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.50 % Elapsed time: 0.066311 seconds
% 0.16/0.50 % CPU time: 0.185079 seconds
% 0.16/0.50 % Total memory used: 35.263 MB
% 0.16/0.50 % Net memory used: 35.178 MB
%------------------------------------------------------------------------------