%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU359+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 : n026.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 02:20:17 PM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 34
% Syntax : Number of formulae : 173 ( 7 unt; 31 def)
% Number of atoms : 927 ( 90 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 1344 ( 590 ~; 603 |; 92 &)
% ( 35 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 31 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 229 ( 207 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( ex_sup_of_relstr_set(A,B)
=> ( C = join_on_relstr(A,B)
<=> ( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,B,D)
=> related(A,C,D) ) )
& relstr_set_smaller(A,B,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A) )
=> ! [B] :
( ex_sup_of_relstr_set(A,B)
<=> ? [C] :
( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,B,D)
=> related(A,C,D) ) )
& relstr_set_smaller(A,B,C)
& element(C,the_carrier(A)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( ( ( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) )
& relstr_set_smaller(A,C,B) )
=> ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) ) )
& ( ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) )
=> ( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) )
& relstr_set_smaller(A,C,B) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( ( ( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) )
& relstr_set_smaller(A,C,B) )
=> ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) ) )
& ( ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) )
=> ( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) )
& relstr_set_smaller(A,C,B) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [A] :
( ! [B,C] :
( ( C = join_on_relstr(A,B)
<=> ( ! [D] :
( related(A,C,D)
| ~ relstr_set_smaller(A,B,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,B,C) ) )
| ~ ex_sup_of_relstr_set(A,B)
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
! [A] :
( ! [B,C] :
( ( ( ? [D] :
( ~ related(A,C,D)
& relstr_set_smaller(A,B,D)
& element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B) )
& ( ( ! [D] :
( related(A,C,D)
| ~ relstr_set_smaller(A,B,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,B,C) )
| C != join_on_relstr(A,B) ) )
| ~ ex_sup_of_relstr_set(A,B)
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [A] :
( ! [C] :
( ! [B] :
( ( ( ? [D] :
( ~ related(A,C,D)
& relstr_set_smaller(A,B,D)
& element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B) )
& ( ( ! [D] :
( related(A,C,D)
| ~ relstr_set_smaller(A,B,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,B,C) )
| C != join_on_relstr(A,B) ) )
| ~ ex_sup_of_relstr_set(A,B) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f16,plain,
! [A] :
( ! [C] :
( ! [B] :
( ( ( ( ~ related(A,C,sK0_skl(B,C,A))
& relstr_set_smaller(A,B,sK0_skl(B,C,A))
& element(sK0_skl(B,C,A),the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B) )
& ( ( ! [D] :
( related(A,C,D)
| ~ relstr_set_smaller(A,B,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,B,C) )
| C != join_on_relstr(A,B) ) )
| ~ ex_sup_of_relstr_set(A,B) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(B,C,A))],[f15]) ).
fof(f19,plain,
! [X0,X1,X2] :
( element(sK0_skl(X2,X1,X0),the_carrier(X0))
| ~ relstr_set_smaller(X0,X2,X1)
| X1 = join_on_relstr(X0,X2)
| ~ ex_sup_of_relstr_set(X0,X2)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f20,plain,
! [X0,X1,X2] :
( relstr_set_smaller(X0,X2,sK0_skl(X2,X1,X0))
| ~ relstr_set_smaller(X0,X2,X1)
| X1 = join_on_relstr(X0,X2)
| ~ ex_sup_of_relstr_set(X0,X2)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ related(X0,X1,sK0_skl(X2,X1,X0))
| ~ relstr_set_smaller(X0,X2,X1)
| X1 = join_on_relstr(X0,X2)
| ~ ex_sup_of_relstr_set(X0,X2)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f33,plain,
! [A] :
( ! [B] :
( ex_sup_of_relstr_set(A,B)
<=> ? [C] :
( ! [D] :
( related(A,C,D)
| ~ relstr_set_smaller(A,B,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,B,C)
& element(C,the_carrier(A)) ) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f34,plain,
! [A] :
( ! [B] :
( ( ! [C] :
( ? [D] :
( ~ related(A,C,D)
& relstr_set_smaller(A,B,D)
& element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C)
| ~ element(C,the_carrier(A)) )
| ex_sup_of_relstr_set(A,B) )
& ( ? [C] :
( ! [D] :
( related(A,C,D)
| ~ relstr_set_smaller(A,B,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,B,C)
& element(C,the_carrier(A)) )
| ~ ex_sup_of_relstr_set(A,B) ) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(NNF_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [A] :
( ( ! [B] :
( ! [C] :
( ? [D] :
( ~ related(A,C,D)
& relstr_set_smaller(A,B,D)
& element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C)
| ~ element(C,the_carrier(A)) )
| ex_sup_of_relstr_set(A,B) )
& ! [B] :
( ? [C] :
( ! [D] :
( related(A,C,D)
| ~ relstr_set_smaller(A,B,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,B,C)
& element(C,the_carrier(A)) )
| ~ ex_sup_of_relstr_set(A,B) ) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,plain,
! [A] :
( ( ! [B] :
( ! [C] :
( ( ~ related(A,C,sK5_skl(C,B,A))
& relstr_set_smaller(A,B,sK5_skl(C,B,A))
& element(sK5_skl(C,B,A),the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C)
| ~ element(C,the_carrier(A)) )
| ex_sup_of_relstr_set(A,B) )
& ! [B] :
( ( ! [D] :
( related(A,sK4_skl(B,A),D)
| ~ relstr_set_smaller(A,B,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,B,sK4_skl(B,A))
& element(sK4_skl(B,A),the_carrier(A)) )
| ~ ex_sup_of_relstr_set(A,B) ) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(C,sK4_skl(B,A)),skolemize(D,sK5_skl(C,B,A))],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( element(sK4_skl(X1,X0),the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( relstr_set_smaller(X0,X1,sK4_skl(X1,X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
! [X0,X1,X2] :
( related(X0,sK4_skl(X1,X0),X2)
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f40,plain,
! [X0,X1,X2] :
( element(sK5_skl(X2,X1,X0),the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1)
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f41,plain,
! [X0,X1,X2] :
( relstr_set_smaller(X0,X1,sK5_skl(X2,X1,X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1)
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ related(X0,X2,sK5_skl(X2,X1,X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1)
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f43,plain,
? [A] :
( ? [B] :
( ? [C] :
( ( ( ~ ex_sup_of_relstr_set(A,C)
| B != join_on_relstr(A,C) )
& ! [D] :
( related(A,B,D)
| ~ relstr_set_smaller(A,C,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,C,B) )
| ( ( ? [D] :
( ~ related(A,B,D)
& relstr_set_smaller(A,C,D)
& element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,C,B) )
& ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) ) )
& element(B,the_carrier(A)) )
& rel_str(A)
& antisymmetric_relstr(A) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f44,definition,
! [A,B,C] :
( sP0_prd(C,B,A)
<=> ( ( ? [D] :
( ~ related(A,B,D)
& relstr_set_smaller(A,C,D)
& element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,C,B) )
& ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f45,plain,
? [A] :
( ? [B] :
( ? [C] :
( ( ( ~ ex_sup_of_relstr_set(A,C)
| B != join_on_relstr(A,C) )
& ! [D] :
( related(A,B,D)
| ~ relstr_set_smaller(A,C,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,C,B) )
| sP0_prd(C,B,A) )
& element(B,the_carrier(A)) )
& rel_str(A)
& antisymmetric_relstr(A) ),
inference(formula_renaming,[status(thm)],[f43,f44]) ).
fof(f46,plain,
? [A] :
( ? [B] :
( ( ? [C] :
( ( ~ ex_sup_of_relstr_set(A,C)
| B != join_on_relstr(A,C) )
& ! [D] :
( related(A,B,D)
| ~ relstr_set_smaller(A,C,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,C,B) )
| ? [C] : sP0_prd(C,B,A) )
& element(B,the_carrier(A)) )
& rel_str(A)
& antisymmetric_relstr(A) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
( ( ( ( ~ ex_sup_of_relstr_set(sK6_skl,sK9_skl)
| sK7_skl != join_on_relstr(sK6_skl,sK9_skl) )
& ! [D] :
( related(sK6_skl,sK7_skl,D)
| ~ relstr_set_smaller(sK6_skl,sK9_skl,D)
| ~ element(D,the_carrier(sK6_skl)) )
& relstr_set_smaller(sK6_skl,sK9_skl,sK7_skl) )
| sP0_prd(sK8_skl,sK7_skl,sK6_skl) )
& element(sK7_skl,the_carrier(sK6_skl))
& rel_str(sK6_skl)
& antisymmetric_relstr(sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl,sK8_skl,sK9_skl]),skolemize(A,sK6_skl),skolemize(B,sK7_skl),skolemize(C,sK8_skl),skolemize(C,sK9_skl)],[f46]) ).
fof(f48,plain,
antisymmetric_relstr(sK6_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
rel_str(sK6_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
element(sK7_skl,the_carrier(sK6_skl)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
( relstr_set_smaller(sK6_skl,sK9_skl,sK7_skl)
| sP0_prd(sK8_skl,sK7_skl,sK6_skl) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f52,plain,
! [X0] :
( related(sK6_skl,sK7_skl,X0)
| ~ relstr_set_smaller(sK6_skl,sK9_skl,X0)
| ~ element(X0,the_carrier(sK6_skl))
| sP0_prd(sK8_skl,sK7_skl,sK6_skl) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f53,plain,
( ~ ex_sup_of_relstr_set(sK6_skl,sK9_skl)
| sK7_skl != join_on_relstr(sK6_skl,sK9_skl)
| sP0_prd(sK8_skl,sK7_skl,sK6_skl) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f54,plain,
! [A,B,C] :
( ( ( ! [D] :
( related(A,B,D)
| ~ relstr_set_smaller(A,C,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,C,B) )
| ~ ex_sup_of_relstr_set(A,C)
| B != join_on_relstr(A,C)
| sP0_prd(C,B,A) )
& ( ( ( ? [D] :
( ~ related(A,B,D)
& relstr_set_smaller(A,C,D)
& element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,C,B) )
& ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) )
| ~ sP0_prd(C,B,A) ) ),
inference(NNF_transformation,[status(thm)],[f44]) ).
fof(f55,plain,
( ! [A,B,C] :
( ( ! [D] :
( related(A,B,D)
| ~ relstr_set_smaller(A,C,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,C,B) )
| ~ ex_sup_of_relstr_set(A,C)
| B != join_on_relstr(A,C)
| sP0_prd(C,B,A) )
& ! [A,B,C] :
( ( ( ? [D] :
( ~ related(A,B,D)
& relstr_set_smaller(A,C,D)
& element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,C,B) )
& ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) )
| ~ sP0_prd(C,B,A) ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f56,plain,
( ! [A,B,C] :
( ( ! [D] :
( related(A,B,D)
| ~ relstr_set_smaller(A,C,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,C,B) )
| ~ ex_sup_of_relstr_set(A,C)
| B != join_on_relstr(A,C)
| sP0_prd(C,B,A) )
& ! [A,B,C] :
( ( ( ( ~ related(A,B,sK10_skl(C,B,A))
& relstr_set_smaller(A,C,sK10_skl(C,B,A))
& element(sK10_skl(C,B,A),the_carrier(A)) )
| ~ relstr_set_smaller(A,C,B) )
& ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) )
| ~ sP0_prd(C,B,A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(D,sK10_skl(C,B,A))],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( X1 = join_on_relstr(X2,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ex_sup_of_relstr_set(X2,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f59,plain,
! [X0,X1,X2] :
( element(sK10_skl(X0,X1,X2),the_carrier(X2))
| ~ relstr_set_smaller(X2,X0,X1)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f60,plain,
! [X0,X1,X2] :
( relstr_set_smaller(X2,X0,sK10_skl(X0,X1,X2))
| ~ relstr_set_smaller(X2,X0,X1)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ related(X2,X1,sK10_skl(X0,X1,X2))
| ~ relstr_set_smaller(X2,X0,X1)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f64,definition,
( sQ0_spl
<=> sP0_prd(sK8_skl,sK7_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( ~ sQ0_spl
| sP0_prd(sK8_skl,sK7_skl,sK6_skl) ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,definition,
( sQ1_spl
<=> relstr_set_smaller(sK6_skl,sK9_skl,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ1_spl
| relstr_set_smaller(sK6_skl,sK9_skl,sK7_skl) ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f51,f64,f67]) ).
fof(f71,definition,
! [X0] :
( sQ2_spl
<=> ( related(sK6_skl,sK7_skl,X0)
| ~ relstr_set_smaller(sK6_skl,sK9_skl,X0)
| ~ element(X0,the_carrier(sK6_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f72,plain,
! [X0] :
( ~ sQ2_spl
| related(sK6_skl,sK7_skl,X0)
| ~ relstr_set_smaller(sK6_skl,sK9_skl,X0)
| ~ element(X0,the_carrier(sK6_skl)) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f64,f71]) ).
fof(f75,definition,
( sQ3_spl
<=> sK7_skl = join_on_relstr(sK6_skl,sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f78,definition,
( sQ4_spl
<=> ex_sup_of_relstr_set(sK6_skl,sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( sQ4_spl
| ~ ex_sup_of_relstr_set(sK6_skl,sK9_skl) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f53,f64,f75,f78]) ).
fof(f88,plain,
( ~ sQ0_spl
| sK7_skl = join_on_relstr(sK6_skl,sK8_skl) ),
inference(resolution,[status(thm)],[f57,f65]) ).
fof(f89,plain,
! [X0,X1] :
( related(sK6_skl,sK4_skl(X0,sK6_skl),X1)
| ~ relstr_set_smaller(sK6_skl,X0,X1)
| ~ element(X1,the_carrier(sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ rel_str(sK6_skl) ),
inference(resolution,[status(thm)],[f39,f48]) ).
fof(f90,definition,
( sQ5_spl
<=> rel_str(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( sQ5_spl
| ~ rel_str(sK6_skl) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,definition,
! [X0,X1] :
( sQ6_spl
<=> ( related(sK6_skl,sK4_skl(X0,sK6_skl),X1)
| ~ relstr_set_smaller(sK6_skl,X0,X1)
| ~ element(X1,the_carrier(sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
! [X0,X1] :
( ~ sQ6_spl
| related(sK6_skl,sK4_skl(X0,sK6_skl),X1)
| ~ relstr_set_smaller(sK6_skl,X0,X1)
| ~ element(X1,the_carrier(sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f89,f90,f93]) ).
fof(f97,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f92,f49]) ).
fof(f98,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f97]) ).
fof(f103,definition,
( sQ7_spl
<=> ex_sup_of_relstr_set(sK6_skl,sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f105,plain,
( sQ7_spl
| ~ ex_sup_of_relstr_set(sK6_skl,sK8_skl) ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f113,definition,
( sQ10_spl
<=> relstr_set_smaller(sK6_skl,sK8_skl,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f117,definition,
( sQ11_spl
<=> element(sK7_skl,the_carrier(sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( sQ11_spl
| ~ element(sK7_skl,the_carrier(sK6_skl)) ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f121,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| ~ sP0_prd(X1,sK4_skl(X0,sK6_skl),sK6_skl)
| ~ relstr_set_smaller(sK6_skl,X0,sK10_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ element(sK10_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl),the_carrier(sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f94,f61]) ).
fof(f122,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ element(sK4_skl(X0,sK6_skl),the_carrier(sK6_skl))
| ~ rel_str(sK6_skl)
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ element(sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl),the_carrier(sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f94,f21]) ).
fof(f123,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| ~ sP0_prd(X1,sK4_skl(X0,sK6_skl),sK6_skl)
| ~ relstr_set_smaller(sK6_skl,X0,sK10_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f121,f59]) ).
fof(f124,definition,
! [X0,X1] :
( sQ12_spl
<=> ( ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ element(sK4_skl(X0,sK6_skl),the_carrier(sK6_skl))
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ element(sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl),the_carrier(sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f125,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ element(sK4_skl(X0,sK6_skl),the_carrier(sK6_skl))
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ element(sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl),the_carrier(sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f122,f124,f90,f93]) ).
fof(f128,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ rel_str(sK6_skl)
| ~ antisymmetric_relstr(sK6_skl)
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ element(sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl),the_carrier(sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f125,f37]) ).
fof(f129,definition,
! [X0,X1] :
( sQ13_spl
<=> ( ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ element(sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl),the_carrier(sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f130,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ element(sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl),the_carrier(sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,definition,
( sQ14_spl
<=> antisymmetric_relstr(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( sQ14_spl
| ~ antisymmetric_relstr(sK6_skl) ),
inference(component_clause,[status(thm)],[f132]) ).
fof(f135,plain,
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f128,f129,f132,f90,f124]) ).
fof(f136,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ element(sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl),the_carrier(sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f130]) ).
fof(f137,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f134,f48]) ).
fof(f138,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f137]) ).
fof(f139,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ element(sK4_skl(X0,sK6_skl),the_carrier(sK6_skl))
| ~ rel_str(sK6_skl)
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f136,f19]) ).
fof(f140,definition,
! [X0,X1] :
( sQ15_spl
<=> ( ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ element(sK4_skl(X0,sK6_skl),the_carrier(sK6_skl))
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f141,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ element(sK4_skl(X0,sK6_skl),the_carrier(sK6_skl))
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f139,f140,f90,f129]) ).
fof(f144,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ element(sK4_skl(X0,sK6_skl),the_carrier(sK6_skl))
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f141]) ).
fof(f145,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ rel_str(sK6_skl)
| ~ antisymmetric_relstr(sK6_skl)
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f144,f37]) ).
fof(f146,definition,
! [X0,X1] :
( sQ16_spl
<=> ( ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f147,plain,
! [X0,X1] :
( ~ sQ16_spl
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,plain,
( ~ sQ15_spl
| ~ sQ5_spl
| ~ sQ14_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f145,f146,f132,f90,f140]) ).
fof(f150,plain,
! [X0,X1] :
( ~ sQ16_spl
| ~ relstr_set_smaller(sK6_skl,X1,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X1)
| ~ ex_sup_of_relstr_set(sK6_skl,X1)
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X1,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f147]) ).
fof(f151,plain,
! [X0] :
( ~ sQ16_spl
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ rel_str(sK6_skl)
| ~ antisymmetric_relstr(sK6_skl)
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X0,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f150,f38]) ).
fof(f152,definition,
! [X0] :
( sQ17_spl
<=> ( ~ ex_sup_of_relstr_set(sK6_skl,X0)
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X0,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f153,plain,
! [X0] :
( ~ sQ17_spl
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X0,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,plain,
( ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ14_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f151,f152,f132,f90,f146]) ).
fof(f156,plain,
! [X0] :
( ~ sQ17_spl
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,X0,sK0_skl(X0,sK4_skl(X0,sK6_skl),sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f153]) ).
fof(f157,plain,
! [X0] :
( ~ sQ17_spl
| ~ relstr_set_smaller(sK6_skl,X0,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ element(sK4_skl(X0,sK6_skl),the_carrier(sK6_skl))
| ~ rel_str(sK6_skl)
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f156,f20]) ).
fof(f158,definition,
! [X0] :
( sQ18_spl
<=> ( ~ relstr_set_smaller(sK6_skl,X0,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ element(sK4_skl(X0,sK6_skl),the_carrier(sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f159,plain,
! [X0] :
( ~ sQ18_spl
| ~ relstr_set_smaller(sK6_skl,X0,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ element(sK4_skl(X0,sK6_skl),the_carrier(sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( ~ sQ17_spl
| ~ sQ5_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f157,f158,f90,f152]) ).
fof(f162,plain,
! [X0] :
( ~ sQ18_spl
| ~ relstr_set_smaller(sK6_skl,X0,sK4_skl(X0,sK6_skl))
| ~ element(sK4_skl(X0,sK6_skl),the_carrier(sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f159]) ).
fof(f163,plain,
! [X0] :
( ~ sQ18_spl
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ rel_str(sK6_skl)
| ~ antisymmetric_relstr(sK6_skl)
| ~ relstr_set_smaller(sK6_skl,X0,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f162,f37]) ).
fof(f164,definition,
! [X0] :
( sQ19_spl
<=> ( ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,X0,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f165,plain,
! [X0] :
( ~ sQ19_spl
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,X0,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f167,plain,
( ~ sQ18_spl
| ~ sQ5_spl
| ~ sQ14_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f163,f164,f132,f90,f158]) ).
fof(f168,plain,
! [X0] :
( ~ sQ19_spl
| ~ relstr_set_smaller(sK6_skl,X0,sK4_skl(X0,sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f165]) ).
fof(f169,plain,
! [X0] :
( ~ sQ19_spl
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ rel_str(sK6_skl)
| ~ antisymmetric_relstr(sK6_skl)
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f168,f38]) ).
fof(f170,definition,
! [X0] :
( sQ20_spl
<=> ( ~ ex_sup_of_relstr_set(sK6_skl,X0)
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f171,plain,
! [X0] :
( ~ sQ20_spl
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,plain,
( ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ14_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f169,f170,f132,f90,f164]) ).
fof(f174,plain,
! [X0] :
( ~ sQ20_spl
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f171]) ).
fof(f175,plain,
! [X0,X1] :
( ~ sQ20_spl
| relstr_set_smaller(sK6_skl,X0,sK5_skl(X1,X0,sK6_skl))
| ~ relstr_set_smaller(sK6_skl,X0,X1)
| ~ element(X1,the_carrier(sK6_skl))
| ~ rel_str(sK6_skl)
| ~ antisymmetric_relstr(sK6_skl)
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f174,f41]) ).
fof(f176,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ related(sK6_skl,X1,sK5_skl(X1,X0,sK6_skl))
| ~ relstr_set_smaller(sK6_skl,X0,X1)
| ~ element(X1,the_carrier(sK6_skl))
| ~ rel_str(sK6_skl)
| ~ antisymmetric_relstr(sK6_skl)
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f174,f42]) ).
fof(f177,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sP0_prd(X0,X1,sK6_skl)
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f174,f58]) ).
fof(f178,definition,
! [X0,X1] :
( sQ21_spl
<=> ( relstr_set_smaller(sK6_skl,X0,sK5_skl(X1,X0,sK6_skl))
| ~ relstr_set_smaller(sK6_skl,X0,X1)
| ~ element(X1,the_carrier(sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( ~ sQ20_spl
| ~ sQ5_spl
| ~ sQ14_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f175,f178,f132,f90,f170]) ).
fof(f182,definition,
! [X0,X1] :
( sQ22_spl
<=> ( ~ related(sK6_skl,X1,sK5_skl(X1,X0,sK6_skl))
| ~ relstr_set_smaller(sK6_skl,X0,X1)
| ~ element(X1,the_carrier(sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f183,plain,
! [X0,X1] :
( ~ sQ22_spl
| ~ related(sK6_skl,X1,sK5_skl(X1,X0,sK6_skl))
| ~ relstr_set_smaller(sK6_skl,X0,X1)
| ~ element(X1,the_carrier(sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,plain,
( ~ sQ20_spl
| ~ sQ5_spl
| ~ sQ14_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f176,f182,f132,f90,f170]) ).
fof(f186,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| sK4_skl(sK8_skl,sK6_skl) = join_on_relstr(sK6_skl,sK8_skl) ),
inference(resolution,[status(thm)],[f177,f65]) ).
fof(f188,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| sK4_skl(sK8_skl,sK6_skl) = sK7_skl ),
inference(forward_demodulation,[status(thm)],[f88,f186]) ).
fof(f191,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ6_spl
| ~ relstr_set_smaller(sK6_skl,X0,sK4_skl(sK8_skl,sK6_skl))
| ~ sP0_prd(X0,sK7_skl,sK6_skl)
| ~ relstr_set_smaller(sK6_skl,sK8_skl,sK10_skl(X0,sK4_skl(sK8_skl,sK6_skl),sK6_skl))
| ~ ex_sup_of_relstr_set(sK6_skl,sK8_skl) ),
inference(paramodulation,[status(thm)],[f188,f123]) ).
fof(f193,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| relstr_set_smaller(sK6_skl,sK8_skl,sK7_skl)
| ~ ex_sup_of_relstr_set(sK6_skl,sK8_skl)
| ~ rel_str(sK6_skl)
| ~ antisymmetric_relstr(sK6_skl) ),
inference(paramodulation,[status(thm)],[f188,f38]) ).
fof(f199,definition,
! [X0] :
( sQ24_spl
<=> ( ~ relstr_set_smaller(sK6_skl,X0,sK4_skl(sK8_skl,sK6_skl))
| ~ sP0_prd(X0,sK7_skl,sK6_skl)
| ~ relstr_set_smaller(sK6_skl,sK8_skl,sK10_skl(X0,sK4_skl(sK8_skl,sK6_skl),sK6_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f200,plain,
! [X0] :
( ~ sQ24_spl
| ~ relstr_set_smaller(sK6_skl,X0,sK4_skl(sK8_skl,sK6_skl))
| ~ sP0_prd(X0,sK7_skl,sK6_skl)
| ~ relstr_set_smaller(sK6_skl,sK8_skl,sK10_skl(X0,sK4_skl(sK8_skl,sK6_skl),sK6_skl)) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ6_spl
| sQ24_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f191,f103,f199,f93,f170,f64]) ).
fof(f207,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| sQ10_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f193,f132,f90,f103,f113,f170,f64]) ).
fof(f209,plain,
! [X0] :
( ~ sQ22_spl
| ~ sQ2_spl
| ~ relstr_set_smaller(sK6_skl,X0,sK7_skl)
| ~ element(sK7_skl,the_carrier(sK6_skl))
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,sK9_skl,sK5_skl(sK7_skl,X0,sK6_skl))
| ~ element(sK5_skl(sK7_skl,X0,sK6_skl),the_carrier(sK6_skl)) ),
inference(resolution,[status(thm)],[f72,f183]) ).
fof(f211,plain,
! [X0] :
( ~ sQ2_spl
| ~ relstr_set_smaller(sK6_skl,X0,sK7_skl)
| sK7_skl = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ element(sK7_skl,the_carrier(sK6_skl))
| ~ rel_str(sK6_skl)
| ~ relstr_set_smaller(sK6_skl,sK9_skl,sK0_skl(X0,sK7_skl,sK6_skl))
| ~ element(sK0_skl(X0,sK7_skl,sK6_skl),the_carrier(sK6_skl)) ),
inference(resolution,[status(thm)],[f72,f21]) ).
fof(f212,definition,
! [X0] :
( sQ26_spl
<=> ( ~ relstr_set_smaller(sK6_skl,X0,sK7_skl)
| sK4_skl(X0,sK6_skl) = join_on_relstr(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,sK9_skl,sK5_skl(sK7_skl,X0,sK6_skl))
| ~ element(sK5_skl(sK7_skl,X0,sK6_skl),the_carrier(sK6_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f215,plain,
( ~ sQ22_spl
| ~ sQ2_spl
| ~ sQ11_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f209,f212,f117,f71,f182]) ).
fof(f217,definition,
! [X0] :
( sQ27_spl
<=> ( ~ relstr_set_smaller(sK6_skl,X0,sK7_skl)
| sK7_skl = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,sK9_skl,sK0_skl(X0,sK7_skl,sK6_skl))
| ~ element(sK0_skl(X0,sK7_skl,sK6_skl),the_carrier(sK6_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f218,plain,
! [X0] :
( ~ sQ27_spl
| ~ relstr_set_smaller(sK6_skl,X0,sK7_skl)
| sK7_skl = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,sK9_skl,sK0_skl(X0,sK7_skl,sK6_skl))
| ~ element(sK0_skl(X0,sK7_skl,sK6_skl),the_carrier(sK6_skl)) ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ5_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f211,f217,f90,f117,f71]) ).
fof(f221,plain,
! [X0] :
( ~ sQ27_spl
| ~ relstr_set_smaller(sK6_skl,X0,sK7_skl)
| sK7_skl = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ element(sK7_skl,the_carrier(sK6_skl))
| ~ rel_str(sK6_skl)
| ~ relstr_set_smaller(sK6_skl,X0,sK7_skl)
| sK7_skl = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,sK9_skl,sK0_skl(X0,sK7_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f218,f19]) ).
fof(f222,definition,
! [X0] :
( sQ28_spl
<=> ( ~ relstr_set_smaller(sK6_skl,X0,sK7_skl)
| sK7_skl = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,X0,sK7_skl)
| sK7_skl = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,sK9_skl,sK0_skl(X0,sK7_skl,sK6_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f223,plain,
! [X0] :
( ~ sQ28_spl
| ~ relstr_set_smaller(sK6_skl,X0,sK7_skl)
| sK7_skl = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,X0,sK7_skl)
| sK7_skl = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,sK9_skl,sK0_skl(X0,sK7_skl,sK6_skl)) ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f225,plain,
( ~ sQ27_spl
| ~ sQ11_spl
| ~ sQ5_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f221,f222,f90,f117,f217]) ).
fof(f226,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f50]) ).
fof(f227,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f226]) ).
fof(f228,plain,
! [X0] :
( ~ sQ28_spl
| ~ relstr_set_smaller(sK6_skl,X0,sK7_skl)
| sK7_skl = join_on_relstr(sK6_skl,X0)
| ~ ex_sup_of_relstr_set(sK6_skl,X0)
| ~ relstr_set_smaller(sK6_skl,sK9_skl,sK0_skl(X0,sK7_skl,sK6_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f223]) ).
fof(f240,plain,
! [X0] :
( sQ7_spl
| ~ sP0_prd(sK8_skl,X0,sK6_skl) ),
inference(resolution,[status(thm)],[f105,f58]) ).
fof(f249,plain,
( ~ sQ0_spl
| sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f65,f240]) ).
fof(f250,plain,
( ~ sQ0_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f249]) ).
fof(f253,plain,
! [X0] :
( ~ sQ24_spl
| ~ sQ0_spl
| ~ sQ20_spl
| ~ relstr_set_smaller(sK6_skl,X0,sK4_skl(sK8_skl,sK6_skl))
| ~ sP0_prd(X0,sK7_skl,sK6_skl)
| ~ relstr_set_smaller(sK6_skl,sK8_skl,sK10_skl(X0,sK7_skl,sK6_skl)) ),
inference(forward_demodulation,[status(thm)],[f188,f200]) ).
fof(f254,plain,
! [X0] :
( ~ sQ24_spl
| ~ sQ0_spl
| ~ sQ20_spl
| ~ relstr_set_smaller(sK6_skl,X0,sK7_skl)
| ~ sP0_prd(X0,sK7_skl,sK6_skl)
| ~ relstr_set_smaller(sK6_skl,sK8_skl,sK10_skl(X0,sK7_skl,sK6_skl)) ),
inference(forward_demodulation,[status(thm)],[f188,f253]) ).
fof(f289,plain,
( ~ sQ24_spl
| ~ sQ0_spl
| ~ sQ20_spl
| ~ relstr_set_smaller(sK6_skl,sK8_skl,sK7_skl)
| ~ sP0_prd(sK8_skl,sK7_skl,sK6_skl)
| ~ relstr_set_smaller(sK6_skl,sK8_skl,sK7_skl)
| ~ sP0_prd(sK8_skl,sK7_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f254,f60]) ).
fof(f290,plain,
( ~ sQ24_spl
| ~ sQ20_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f289,f64,f113,f170,f199]) ).
fof(f293,plain,
( ~ sQ28_spl
| ~ sQ1_spl
| sK7_skl = join_on_relstr(sK6_skl,sK9_skl)
| ~ ex_sup_of_relstr_set(sK6_skl,sK9_skl)
| ~ relstr_set_smaller(sK6_skl,sK9_skl,sK0_skl(sK9_skl,sK7_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f68,f228]) ).
fof(f294,definition,
( sQ35_spl
<=> relstr_set_smaller(sK6_skl,sK9_skl,sK0_skl(sK9_skl,sK7_skl,sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f296,plain,
( sQ35_spl
| ~ relstr_set_smaller(sK6_skl,sK9_skl,sK0_skl(sK9_skl,sK7_skl,sK6_skl)) ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f297,plain,
( ~ sQ28_spl
| ~ sQ1_spl
| sQ3_spl
| ~ sQ4_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f293,f294,f78,f75,f67,f222]) ).
fof(f298,plain,
! [X0] :
( sQ4_spl
| relstr_set_smaller(sK6_skl,sK9_skl,sK5_skl(X0,sK9_skl,sK6_skl))
| ~ relstr_set_smaller(sK6_skl,sK9_skl,X0)
| ~ element(X0,the_carrier(sK6_skl))
| ~ rel_str(sK6_skl)
| ~ antisymmetric_relstr(sK6_skl) ),
inference(resolution,[status(thm)],[f80,f41]) ).
fof(f299,plain,
! [X0] :
( sQ4_spl
| ~ related(sK6_skl,X0,sK5_skl(X0,sK9_skl,sK6_skl))
| ~ relstr_set_smaller(sK6_skl,sK9_skl,X0)
| ~ element(X0,the_carrier(sK6_skl))
| ~ rel_str(sK6_skl)
| ~ antisymmetric_relstr(sK6_skl) ),
inference(resolution,[status(thm)],[f80,f42]) ).
fof(f301,definition,
! [X0] :
( sQ36_spl
<=> ( relstr_set_smaller(sK6_skl,sK9_skl,sK5_skl(X0,sK9_skl,sK6_skl))
| ~ relstr_set_smaller(sK6_skl,sK9_skl,X0)
| ~ element(X0,the_carrier(sK6_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f302,plain,
! [X0] :
( ~ sQ36_spl
| relstr_set_smaller(sK6_skl,sK9_skl,sK5_skl(X0,sK9_skl,sK6_skl))
| ~ relstr_set_smaller(sK6_skl,sK9_skl,X0)
| ~ element(X0,the_carrier(sK6_skl)) ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f304,plain,
( sQ4_spl
| sQ36_spl
| ~ sQ5_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f298,f132,f90,f301,f78]) ).
fof(f305,definition,
! [X0] :
( sQ37_spl
<=> ( ~ related(sK6_skl,X0,sK5_skl(X0,sK9_skl,sK6_skl))
| ~ relstr_set_smaller(sK6_skl,sK9_skl,X0)
| ~ element(X0,the_carrier(sK6_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f306,plain,
! [X0] :
( ~ sQ37_spl
| ~ related(sK6_skl,X0,sK5_skl(X0,sK9_skl,sK6_skl))
| ~ relstr_set_smaller(sK6_skl,sK9_skl,X0)
| ~ element(X0,the_carrier(sK6_skl)) ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f308,plain,
( sQ4_spl
| sQ37_spl
| ~ sQ5_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f299,f132,f90,f305,f78]) ).
fof(f338,plain,
( sQ35_spl
| ~ relstr_set_smaller(sK6_skl,sK9_skl,sK7_skl)
| sK7_skl = join_on_relstr(sK6_skl,sK9_skl)
| ~ ex_sup_of_relstr_set(sK6_skl,sK9_skl)
| ~ element(sK7_skl,the_carrier(sK6_skl))
| ~ rel_str(sK6_skl) ),
inference(resolution,[status(thm)],[f296,f20]) ).
fof(f339,plain,
( sQ35_spl
| ~ sQ1_spl
| sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f338,f90,f117,f78,f75,f67,f294]) ).
fof(f350,plain,
( ~ sQ2_spl
| ~ sQ37_spl
| ~ relstr_set_smaller(sK6_skl,sK9_skl,sK5_skl(sK7_skl,sK9_skl,sK6_skl))
| ~ element(sK5_skl(sK7_skl,sK9_skl,sK6_skl),the_carrier(sK6_skl))
| ~ relstr_set_smaller(sK6_skl,sK9_skl,sK7_skl)
| ~ element(sK7_skl,the_carrier(sK6_skl)) ),
inference(resolution,[status(thm)],[f306,f72]) ).
fof(f352,definition,
( sQ42_spl
<=> element(sK5_skl(sK7_skl,sK9_skl,sK6_skl),the_carrier(sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f354,plain,
( sQ42_spl
| ~ element(sK5_skl(sK7_skl,sK9_skl,sK6_skl),the_carrier(sK6_skl)) ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f355,definition,
( sQ43_spl
<=> relstr_set_smaller(sK6_skl,sK9_skl,sK5_skl(sK7_skl,sK9_skl,sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f357,plain,
( sQ43_spl
| ~ relstr_set_smaller(sK6_skl,sK9_skl,sK5_skl(sK7_skl,sK9_skl,sK6_skl)) ),
inference(component_clause,[status(thm)],[f355]) ).
fof(f358,plain,
( ~ sQ2_spl
| ~ sQ37_spl
| ~ sQ43_spl
| ~ sQ42_spl
| ~ sQ1_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f350,f117,f67,f352,f355,f305,f71]) ).
fof(f376,plain,
( sQ42_spl
| ~ relstr_set_smaller(sK6_skl,sK9_skl,sK7_skl)
| ~ element(sK7_skl,the_carrier(sK6_skl))
| ex_sup_of_relstr_set(sK6_skl,sK9_skl)
| ~ rel_str(sK6_skl)
| ~ antisymmetric_relstr(sK6_skl) ),
inference(resolution,[status(thm)],[f354,f40]) ).
fof(f377,plain,
( sQ42_spl
| ~ sQ1_spl
| ~ sQ11_spl
| sQ4_spl
| ~ sQ5_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f376,f132,f90,f78,f117,f67,f352]) ).
fof(f400,plain,
( ~ sQ36_spl
| sQ43_spl
| ~ relstr_set_smaller(sK6_skl,sK9_skl,sK7_skl)
| ~ element(sK7_skl,the_carrier(sK6_skl)) ),
inference(resolution,[status(thm)],[f357,f302]) ).
fof(f402,plain,
( ~ sQ36_spl
| sQ43_spl
| ~ sQ1_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f400,f117,f67,f355,f301]) ).
fof(f407,plain,
$false,
inference(sat_refutation,[status(thm)],[f70,f74,f81,f96,f98,f127,f135,f138,f143,f149,f155,f161,f167,f173,f181,f185,f202,f207,f215,f220,f225,f227,f250,f290,f297,f304,f308,f339,f358,f377,f402]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU359+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n026.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 06:17:51 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.45 % 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
% 0.16/0.53 % Elapsed time: 0.088422 seconds
% 0.16/0.53 % CPU time: 0.128126 seconds
% 0.16/0.53 % Total memory used: 10.853 MB
% 0.16/0.53 % Net memory used: 10.835 MB
%------------------------------------------------------------------------------