%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU319+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 : n009.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 02:20:09 PM UTC 2026
% Result : Theorem 0.21s 0.69s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 32
% Syntax : Number of formulae : 140 ( 23 unt; 21 def)
% Number of atoms : 323 ( 40 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 310 ( 127 ~; 132 |; 11 &)
% ( 25 <=>; 14 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 28 ( 26 usr; 22 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 75 ( 69 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( closed_subset(B,A)
<=> open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( one_sorted_str(A)
=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> element(subset_difference(A,B,C),powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] :
( top_str(A)
=> one_sorted_str(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
? [A] : top_str(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
? [A] : one_sorted_str(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_difference(A,B,C) = set_difference(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( closed_subset(B,A)
<=> open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( closed_subset(B,A)
<=> open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f21,plain,
! [A] :
( ! [B] :
( ( closed_subset(B,A)
<=> open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [A] :
( ! [B] :
( ( ( ~ open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A)
| closed_subset(B,A) )
& ( open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A)
| ~ closed_subset(B,A) ) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(NNF_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [A] :
( element(cast_as_carrier_subset(A),powerset(the_carrier(A)))
| ~ one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f26,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [A,B] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f28,plain,
! [X0,X1] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [A,B,C] :
( element(subset_difference(A,B,C),powerset(A))
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f30,plain,
! [X0,X1,X2] :
( element(subset_difference(X1,X0,X2),powerset(X1))
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [A] :
( one_sorted_str(A)
| ~ top_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f32,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
top_str(sK0_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(A,sK0_skl)],[f11]) ).
fof(f34,plain,
top_str(sK0_skl),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
one_sorted_str(sK1_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(A,sK1_skl)],[f12]) ).
fof(f36,plain,
one_sorted_str(sK1_skl),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f39,plain,
! [A,B] :
( subset_complement(A,subset_complement(A,B)) = B
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f40,plain,
! [X0,X1] :
( subset_complement(X1,subset_complement(X1,X0)) = X0
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [A,B,C] :
( subset_difference(A,B,C) = set_difference(B,C)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f42,plain,
! [X0,X1,X2] :
( subset_difference(X1,X0,X2) = set_difference(X0,X2)
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f45,plain,
! [A] :
( ! [B] :
( subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)
| ~ element(B,powerset(the_carrier(A))) )
| ~ one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f46,plain,
! [X0,X1] :
( subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
? [A] :
( ? [B] :
( ( closed_subset(B,A)
<~> open_subset(subset_complement(the_carrier(A),B),A) )
& element(B,powerset(the_carrier(A))) )
& top_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f48,plain,
? [A] :
( ? [B] :
( ( ~ open_subset(subset_complement(the_carrier(A),B),A)
| ~ closed_subset(B,A) )
& ( open_subset(subset_complement(the_carrier(A),B),A)
| closed_subset(B,A) )
& element(B,powerset(the_carrier(A))) )
& top_str(A) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
( ( ~ open_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)
| ~ closed_subset(sK4_skl,sK3_skl) )
& ( open_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)
| closed_subset(sK4_skl,sK3_skl) )
& element(sK4_skl,powerset(the_carrier(sK3_skl)))
& top_str(sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f48]) ).
fof(f50,plain,
top_str(sK3_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
element(sK4_skl,powerset(the_carrier(sK3_skl))),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
( open_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)
| closed_subset(sK4_skl,sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
( ~ open_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)
| ~ closed_subset(sK4_skl,sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f58,definition,
( sQ0_spl
<=> closed_subset(sK4_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f60,plain,
( sQ0_spl
| ~ closed_subset(sK4_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,definition,
( sQ1_spl
<=> open_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( ~ sQ1_spl
| open_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f58,f61]) ).
fof(f65,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f53,f58,f61]) ).
fof(f66,plain,
subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl)) = sK4_skl,
inference(resolution,[status(thm)],[f40,f51]) ).
fof(f67,plain,
! [X0,X1] :
( subset_complement(X1,subset_complement(X1,subset_complement(X1,X0))) = subset_complement(X1,X0)
| ~ element(X0,powerset(X1)) ),
inference(resolution,[status(thm)],[f28,f40]) ).
fof(f68,plain,
( element(sK4_skl,powerset(the_carrier(sK3_skl)))
| ~ element(subset_complement(the_carrier(sK3_skl),sK4_skl),powerset(the_carrier(sK3_skl))) ),
inference(paramodulation,[status(thm)],[f66,f28]) ).
fof(f69,definition,
( sQ2_spl
<=> element(subset_complement(the_carrier(sK3_skl),sK4_skl),powerset(the_carrier(sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( ~ sQ2_spl
| element(subset_complement(the_carrier(sK3_skl),sK4_skl),powerset(the_carrier(sK3_skl))) ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f71,plain,
( sQ2_spl
| ~ element(subset_complement(the_carrier(sK3_skl),sK4_skl),powerset(the_carrier(sK3_skl))) ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,definition,
( sQ3_spl
<=> element(sK4_skl,powerset(the_carrier(sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f68,f69,f72]) ).
fof(f76,plain,
( sQ2_spl
| ~ element(sK4_skl,powerset(the_carrier(sK3_skl))) ),
inference(resolution,[status(thm)],[f71,f28]) ).
fof(f77,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f51]) ).
fof(f78,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f77]) ).
fof(f95,plain,
element(cast_as_carrier_subset(sK1_skl),powerset(the_carrier(sK1_skl))),
inference(resolution,[status(thm)],[f26,f36]) ).
fof(f96,plain,
! [X0] :
( ~ top_str(X0)
| element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
inference(resolution,[status(thm)],[f26,f32]) ).
fof(f99,plain,
subset_complement(the_carrier(sK1_skl),subset_complement(the_carrier(sK1_skl),cast_as_carrier_subset(sK1_skl))) = cast_as_carrier_subset(sK1_skl),
inference(resolution,[status(thm)],[f95,f40]) ).
fof(f100,plain,
element(cast_as_carrier_subset(sK0_skl),powerset(the_carrier(sK0_skl))),
inference(resolution,[status(thm)],[f96,f34]) ).
fof(f101,plain,
element(cast_as_carrier_subset(sK3_skl),powerset(the_carrier(sK3_skl))),
inference(resolution,[status(thm)],[f96,f50]) ).
fof(f103,plain,
! [X0,X1,X2] :
( subset_complement(X1,subset_complement(X1,subset_complement(X1,subset_difference(X1,X0,X2)))) = subset_complement(X1,subset_difference(X1,X0,X2))
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(resolution,[status(thm)],[f30,f67]) ).
fof(f104,plain,
! [X0,X1,X2] :
( subset_complement(X1,subset_complement(X1,subset_difference(X1,X0,X2))) = subset_difference(X1,X0,X2)
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(resolution,[status(thm)],[f30,f40]) ).
fof(f105,plain,
! [X0] :
( subset_complement(the_carrier(sK1_skl),X0) = subset_difference(the_carrier(sK1_skl),cast_as_carrier_subset(sK1_skl),X0)
| ~ element(X0,powerset(the_carrier(sK1_skl))) ),
inference(resolution,[status(thm)],[f46,f36]) ).
fof(f106,plain,
! [X0,X1] :
( ~ top_str(X1)
| subset_complement(the_carrier(X1),X0) = subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X0)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(resolution,[status(thm)],[f46,f32]) ).
fof(f109,plain,
subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl))) = cast_as_carrier_subset(sK3_skl),
inference(resolution,[status(thm)],[f101,f40]) ).
fof(f110,plain,
( element(cast_as_carrier_subset(sK3_skl),powerset(the_carrier(sK3_skl)))
| ~ element(subset_complement(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl)),powerset(the_carrier(sK3_skl))) ),
inference(paramodulation,[status(thm)],[f109,f28]) ).
fof(f111,definition,
( sQ4_spl
<=> element(subset_complement(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl)),powerset(the_carrier(sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( sQ4_spl
| ~ element(subset_complement(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl)),powerset(the_carrier(sK3_skl))) ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,definition,
( sQ5_spl
<=> element(cast_as_carrier_subset(sK3_skl),powerset(the_carrier(sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f117,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f110,f111,f114]) ).
fof(f118,plain,
( sQ4_spl
| ~ element(cast_as_carrier_subset(sK3_skl),powerset(the_carrier(sK3_skl))) ),
inference(resolution,[status(thm)],[f113,f28]) ).
fof(f119,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f101]) ).
fof(f120,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f119]) ).
fof(f125,plain,
( element(cast_as_carrier_subset(sK1_skl),powerset(the_carrier(sK1_skl)))
| ~ element(subset_complement(the_carrier(sK1_skl),cast_as_carrier_subset(sK1_skl)),powerset(the_carrier(sK1_skl))) ),
inference(paramodulation,[status(thm)],[f99,f28]) ).
fof(f126,definition,
( sQ6_spl
<=> element(subset_complement(the_carrier(sK1_skl),cast_as_carrier_subset(sK1_skl)),powerset(the_carrier(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( sQ6_spl
| ~ element(subset_complement(the_carrier(sK1_skl),cast_as_carrier_subset(sK1_skl)),powerset(the_carrier(sK1_skl))) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,definition,
( sQ7_spl
<=> element(cast_as_carrier_subset(sK1_skl),powerset(the_carrier(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f125,f126,f129]) ).
fof(f133,plain,
( sQ6_spl
| ~ element(cast_as_carrier_subset(sK1_skl),powerset(the_carrier(sK1_skl))) ),
inference(resolution,[status(thm)],[f128,f28]) ).
fof(f134,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f95]) ).
fof(f135,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f134]) ).
fof(f141,plain,
subset_complement(the_carrier(sK0_skl),subset_complement(the_carrier(sK0_skl),cast_as_carrier_subset(sK0_skl))) = cast_as_carrier_subset(sK0_skl),
inference(resolution,[status(thm)],[f100,f40]) ).
fof(f142,plain,
( element(cast_as_carrier_subset(sK0_skl),powerset(the_carrier(sK0_skl)))
| ~ element(subset_complement(the_carrier(sK0_skl),cast_as_carrier_subset(sK0_skl)),powerset(the_carrier(sK0_skl))) ),
inference(paramodulation,[status(thm)],[f141,f28]) ).
fof(f143,definition,
( sQ8_spl
<=> element(subset_complement(the_carrier(sK0_skl),cast_as_carrier_subset(sK0_skl)),powerset(the_carrier(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( sQ8_spl
| ~ element(subset_complement(the_carrier(sK0_skl),cast_as_carrier_subset(sK0_skl)),powerset(the_carrier(sK0_skl))) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,definition,
( sQ9_spl
<=> element(cast_as_carrier_subset(sK0_skl),powerset(the_carrier(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f149,plain,
( sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f142,f143,f146]) ).
fof(f150,plain,
( sQ8_spl
| ~ element(cast_as_carrier_subset(sK0_skl),powerset(the_carrier(sK0_skl))) ),
inference(resolution,[status(thm)],[f145,f28]) ).
fof(f151,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f150,f100]) ).
fof(f152,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f151]) ).
fof(f157,plain,
! [X0] :
( subset_complement(the_carrier(sK3_skl),X0) = subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),X0)
| ~ element(X0,powerset(the_carrier(sK3_skl))) ),
inference(resolution,[status(thm)],[f106,f50]) ).
fof(f159,plain,
subset_complement(the_carrier(sK1_skl),cast_as_carrier_subset(sK1_skl)) = subset_difference(the_carrier(sK1_skl),cast_as_carrier_subset(sK1_skl),cast_as_carrier_subset(sK1_skl)),
inference(resolution,[status(thm)],[f105,f95]) ).
fof(f166,plain,
( subset_complement(the_carrier(sK1_skl),subset_complement(the_carrier(sK1_skl),subset_complement(the_carrier(sK1_skl),cast_as_carrier_subset(sK1_skl)))) = subset_difference(the_carrier(sK1_skl),cast_as_carrier_subset(sK1_skl),cast_as_carrier_subset(sK1_skl))
| ~ element(cast_as_carrier_subset(sK1_skl),powerset(the_carrier(sK1_skl)))
| ~ element(cast_as_carrier_subset(sK1_skl),powerset(the_carrier(sK1_skl))) ),
inference(paramodulation,[status(thm)],[f159,f104]) ).
fof(f167,plain,
( subset_complement(the_carrier(sK1_skl),cast_as_carrier_subset(sK1_skl)) = set_difference(cast_as_carrier_subset(sK1_skl),cast_as_carrier_subset(sK1_skl))
| ~ element(cast_as_carrier_subset(sK1_skl),powerset(the_carrier(sK1_skl)))
| ~ element(cast_as_carrier_subset(sK1_skl),powerset(the_carrier(sK1_skl))) ),
inference(paramodulation,[status(thm)],[f159,f42]) ).
fof(f179,definition,
( sQ13_spl
<=> subset_complement(the_carrier(sK1_skl),subset_complement(the_carrier(sK1_skl),subset_complement(the_carrier(sK1_skl),cast_as_carrier_subset(sK1_skl)))) = subset_difference(the_carrier(sK1_skl),cast_as_carrier_subset(sK1_skl),cast_as_carrier_subset(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( sQ13_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f166,f129,f179]) ).
fof(f183,definition,
( sQ14_spl
<=> subset_complement(the_carrier(sK1_skl),cast_as_carrier_subset(sK1_skl)) = set_difference(cast_as_carrier_subset(sK1_skl),cast_as_carrier_subset(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( ~ sQ14_spl
| subset_complement(the_carrier(sK1_skl),cast_as_carrier_subset(sK1_skl)) = set_difference(cast_as_carrier_subset(sK1_skl),cast_as_carrier_subset(sK1_skl)) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( sQ14_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f167,f129,f183]) ).
fof(f193,plain,
( ~ sQ14_spl
| element(set_difference(cast_as_carrier_subset(sK1_skl),cast_as_carrier_subset(sK1_skl)),powerset(the_carrier(sK1_skl)))
| ~ element(cast_as_carrier_subset(sK1_skl),powerset(the_carrier(sK1_skl))) ),
inference(paramodulation,[status(thm)],[f184,f28]) ).
fof(f194,definition,
( sQ15_spl
<=> element(set_difference(cast_as_carrier_subset(sK1_skl),cast_as_carrier_subset(sK1_skl)),powerset(the_carrier(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f197,plain,
( ~ sQ14_spl
| sQ15_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f193,f129,f194,f183]) ).
fof(f213,plain,
( ~ sQ2_spl
| subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl)) = subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl)) ),
inference(resolution,[status(thm)],[f157,f70]) ).
fof(f215,plain,
subset_complement(the_carrier(sK3_skl),sK4_skl) = subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),sK4_skl),
inference(resolution,[status(thm)],[f157,f51]) ).
fof(f218,plain,
( ~ sQ2_spl
| sK4_skl = subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f66,f213]) ).
fof(f220,plain,
( ~ sQ2_spl
| subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl))) = subset_complement(the_carrier(sK3_skl),subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl)))
| ~ element(subset_complement(the_carrier(sK3_skl),sK4_skl),powerset(the_carrier(sK3_skl)))
| ~ element(cast_as_carrier_subset(sK3_skl),powerset(the_carrier(sK3_skl))) ),
inference(paramodulation,[status(thm)],[f218,f103]) ).
fof(f221,plain,
( ~ sQ2_spl
| subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl)) = subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl))
| ~ element(subset_complement(the_carrier(sK3_skl),sK4_skl),powerset(the_carrier(sK3_skl)))
| ~ element(cast_as_carrier_subset(sK3_skl),powerset(the_carrier(sK3_skl))) ),
inference(paramodulation,[status(thm)],[f218,f104]) ).
fof(f222,plain,
( ~ sQ2_spl
| sK4_skl = set_difference(cast_as_carrier_subset(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl))
| ~ element(subset_complement(the_carrier(sK3_skl),sK4_skl),powerset(the_carrier(sK3_skl)))
| ~ element(cast_as_carrier_subset(sK3_skl),powerset(the_carrier(sK3_skl))) ),
inference(paramodulation,[status(thm)],[f218,f42]) ).
fof(f224,definition,
( sQ16_spl
<=> top_str(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( sQ16_spl
| ~ top_str(sK3_skl) ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f234,definition,
( sQ19_spl
<=> subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl))) = subset_complement(the_carrier(sK3_skl),subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f237,plain,
( sQ19_spl
| ~ sQ2_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f220,f114,f69,f234]) ).
fof(f238,definition,
( sQ20_spl
<=> subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl)) = subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( sQ20_spl
| ~ sQ2_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f221,f114,f69,f238]) ).
fof(f242,definition,
( sQ21_spl
<=> sK4_skl = set_difference(cast_as_carrier_subset(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f245,plain,
( sQ21_spl
| ~ sQ2_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f222,f114,f69,f242]) ).
fof(f249,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f226,f50]) ).
fof(f250,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f249]) ).
fof(f263,plain,
( open_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)
| ~ closed_subset(sK4_skl,sK3_skl)
| ~ element(sK4_skl,powerset(the_carrier(sK3_skl)))
| ~ top_str(sK3_skl) ),
inference(paramodulation,[status(thm)],[f215,f23]) ).
fof(f264,plain,
( subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl)))) = subset_complement(the_carrier(sK3_skl),subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),sK4_skl))
| ~ element(sK4_skl,powerset(the_carrier(sK3_skl)))
| ~ element(cast_as_carrier_subset(sK3_skl),powerset(the_carrier(sK3_skl))) ),
inference(paramodulation,[status(thm)],[f215,f103]) ).
fof(f265,plain,
( subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl))) = subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),sK4_skl)
| ~ element(sK4_skl,powerset(the_carrier(sK3_skl)))
| ~ element(cast_as_carrier_subset(sK3_skl),powerset(the_carrier(sK3_skl))) ),
inference(paramodulation,[status(thm)],[f215,f104]) ).
fof(f266,plain,
( subset_complement(the_carrier(sK3_skl),sK4_skl) = set_difference(cast_as_carrier_subset(sK3_skl),sK4_skl)
| ~ element(sK4_skl,powerset(the_carrier(sK3_skl)))
| ~ element(cast_as_carrier_subset(sK3_skl),powerset(the_carrier(sK3_skl))) ),
inference(paramodulation,[status(thm)],[f215,f42]) ).
fof(f268,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f263,f224,f72,f58,f61]) ).
fof(f269,definition,
( sQ23_spl
<=> subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl)))) = subset_complement(the_carrier(sK3_skl),subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f272,plain,
( sQ23_spl
| ~ sQ3_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f264,f114,f72,f269]) ).
fof(f273,definition,
( sQ24_spl
<=> subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl))) = subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f276,plain,
( sQ24_spl
| ~ sQ3_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f265,f114,f72,f273]) ).
fof(f277,definition,
( sQ25_spl
<=> subset_complement(the_carrier(sK3_skl),sK4_skl) = set_difference(cast_as_carrier_subset(sK3_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( sQ25_spl
| ~ sQ3_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f266,f114,f72,f277]) ).
fof(f286,plain,
( sQ0_spl
| ~ open_subset(subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),sK4_skl),sK3_skl)
| ~ element(sK4_skl,powerset(the_carrier(sK3_skl)))
| ~ top_str(sK3_skl) ),
inference(resolution,[status(thm)],[f60,f24]) ).
fof(f287,definition,
( sQ26_spl
<=> open_subset(subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),sK4_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f289,plain,
( sQ26_spl
| ~ open_subset(subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),sK4_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f287]) ).
fof(f290,plain,
( sQ0_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f286,f224,f72,f287,f58]) ).
fof(f291,plain,
( sQ26_spl
| ~ open_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f215,f289]) ).
fof(f292,plain,
( sQ26_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f291,f62]) ).
fof(f293,plain,
( sQ26_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f292]) ).
fof(f294,plain,
$false,
inference(sat_refutation,[status(thm)],[f64,f65,f75,f78,f117,f120,f132,f135,f149,f152,f182,f186,f197,f237,f241,f245,f250,f268,f272,f276,f280,f290,f293]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU319+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.63 % Computer : n009.cluster.edu
% 0.16/0.63 % Model : x86_64 x86_64
% 0.16/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.63 % Memory : 8046.5625MB
% 0.16/0.63 % OS : Linux 6.8.0-71-generic
% 0.16/0.63 % CPULimit : 300
% 0.16/0.63 % WCLimit : 300
% 0.16/0.63 % DateTime : Mon Sep 21 06:11:29 UTC 2026
% 0.16/0.64 % CPUTime :
% 0.21/0.65 % Drodi V4.1.1
% 0.21/0.69 % Refutation found
% 0.21/0.69 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.72 % Elapsed time: 0.072749 seconds
% 0.21/0.72 % CPU time: 0.215114 seconds
% 0.21/0.72 % Total memory used: 81.413 MB
% 0.21/0.72 % Net memory used: 81.025 MB
%------------------------------------------------------------------------------