TSTP Solution File: SEU361+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU361+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:40:37 EDT 2022
% Result : Theorem 0.18s 0.38s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 80 ( 21 unt; 0 def)
% Number of atoms : 343 ( 32 equ)
% Maximal formula atoms : 50 ( 4 avg)
% Number of connectives : 453 ( 190 ~; 189 |; 55 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 87 ( 0 sgn 50 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d11_yellow_0,axiom,
! [A] :
( rel_str(A)
=> bottom_of_relstr(A) = join_on_relstr(A,empty_set) ) ).
fof(dt_k3_yellow_0,axiom,
! [A] :
( rel_str(A)
=> element(bottom_of_relstr(A),the_carrier(A)) ) ).
fof(t30_yellow_0,axiom,
! [A] :
( ( antisymmetric_relstr(A)
& rel_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( ( ( B = join_on_relstr(A,C)
& ex_sup_of_relstr_set(A,C) )
=> ( relstr_set_smaller(A,C,B)
& ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) ) ) )
& ( ( relstr_set_smaller(A,C,B)
& ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) ) )
=> ( B = join_on_relstr(A,C)
& ex_sup_of_relstr_set(A,C) ) ) ) ) ) ).
fof(t42_yellow_0,axiom,
! [A] :
( ( ~ empty_carrier(A)
& antisymmetric_relstr(A)
& lower_bounded_relstr(A)
& rel_str(A) )
=> ( ex_sup_of_relstr_set(A,empty_set)
& ex_inf_of_relstr_set(A,the_carrier(A)) ) ) ).
fof(t44_yellow_0,conjecture,
! [A] :
( ( ~ empty_carrier(A)
& antisymmetric_relstr(A)
& lower_bounded_relstr(A)
& rel_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> related(A,bottom_of_relstr(A),B) ) ) ).
fof(t6_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_set_smaller(A,empty_set,B)
& relstr_element_smaller(A,empty_set,B) ) ) ) ).
fof(subgoal_0,plain,
! [A] :
( ( ~ empty_carrier(A)
& antisymmetric_relstr(A)
& lower_bounded_relstr(A)
& rel_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> related(A,bottom_of_relstr(A),B) ) ),
inference(strip,[],[t44_yellow_0]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ( ~ empty_carrier(A)
& antisymmetric_relstr(A)
& lower_bounded_relstr(A)
& rel_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> related(A,bottom_of_relstr(A),B) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] :
( ~ empty_carrier(A)
& antisymmetric_relstr(A)
& lower_bounded_relstr(A)
& rel_str(A)
& ? [B] :
( ~ related(A,bottom_of_relstr(A),B)
& element(B,the_carrier(A)) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ empty_carrier(skolemFOFtoCNF_A_6)
& antisymmetric_relstr(skolemFOFtoCNF_A_6)
& lower_bounded_relstr(skolemFOFtoCNF_A_6)
& rel_str(skolemFOFtoCNF_A_6)
& ? [B] :
( ~ related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),B)
& element(B,the_carrier(skolemFOFtoCNF_A_6)) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [B] :
( ~ related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),B)
& element(B,the_carrier(skolemFOFtoCNF_A_6)) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ~ related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_1)
& element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_6)) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_6)),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A] :
( ~ rel_str(A)
| ! [B] :
( ~ element(B,the_carrier(A))
| ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) ) ) ),
inference(canonicalize,[],[t6_yellow_0]) ).
fof(normalize_0_6,plain,
! [A] :
( ~ rel_str(A)
| ! [B] :
( ~ element(B,the_carrier(A))
| ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) ) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ( ~ element(B,the_carrier(A))
| ~ rel_str(A)
| relstr_element_smaller(A,empty_set,B) )
& ( ~ element(B,the_carrier(A))
| ~ rel_str(A)
| relstr_set_smaller(A,empty_set,B) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ element(B,the_carrier(A))
| ~ rel_str(A)
| relstr_set_smaller(A,empty_set,B) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
rel_str(skolemFOFtoCNF_A_6),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_10,plain,
! [A] :
( ~ antisymmetric_relstr(A)
| ~ rel_str(A)
| ! [B] :
( ~ element(B,the_carrier(A))
| ( ! [C] :
( B != join_on_relstr(A,C)
| ~ ex_sup_of_relstr_set(A,C)
| ( relstr_set_smaller(A,C,B)
& ! [D] :
( ~ element(D,the_carrier(A))
| ~ relstr_set_smaller(A,C,D)
| related(A,B,D) ) ) )
& ! [C] :
( ~ relstr_set_smaller(A,C,B)
| ( B = join_on_relstr(A,C)
& ex_sup_of_relstr_set(A,C) )
| ? [D] :
( ~ related(A,B,D)
& element(D,the_carrier(A))
& relstr_set_smaller(A,C,D) ) ) ) ) ),
inference(canonicalize,[],[t30_yellow_0]) ).
fof(normalize_0_11,plain,
! [A] :
( ~ antisymmetric_relstr(A)
| ~ rel_str(A)
| ! [B] :
( ~ element(B,the_carrier(A))
| ( ! [C] :
( B != join_on_relstr(A,C)
| ~ ex_sup_of_relstr_set(A,C)
| ( relstr_set_smaller(A,C,B)
& ! [D] :
( ~ element(D,the_carrier(A))
| ~ relstr_set_smaller(A,C,D)
| related(A,B,D) ) ) )
& ! [C] :
( ~ relstr_set_smaller(A,C,B)
| ( B = join_on_relstr(A,C)
& ex_sup_of_relstr_set(A,C) )
| ? [D] :
( ~ related(A,B,D)
& element(D,the_carrier(A))
& relstr_set_smaller(A,C,D) ) ) ) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B,C,D] :
( ( B != join_on_relstr(A,C)
| ~ antisymmetric_relstr(A)
| ~ element(B,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,C)
| ~ rel_str(A)
| relstr_set_smaller(A,C,B) )
& ( ~ antisymmetric_relstr(A)
| ~ element(B,the_carrier(A))
| ~ rel_str(A)
| ~ related(A,B,skolemFOFtoCNF_D(A,B,C))
| ~ relstr_set_smaller(A,C,B)
| B = join_on_relstr(A,C) )
& ( ~ antisymmetric_relstr(A)
| ~ element(B,the_carrier(A))
| ~ rel_str(A)
| ~ related(A,B,skolemFOFtoCNF_D(A,B,C))
| ~ relstr_set_smaller(A,C,B)
| ex_sup_of_relstr_set(A,C) )
& ( ~ antisymmetric_relstr(A)
| ~ element(B,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_set_smaller(A,C,B)
| B = join_on_relstr(A,C)
| element(skolemFOFtoCNF_D(A,B,C),the_carrier(A)) )
& ( ~ antisymmetric_relstr(A)
| ~ element(B,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_set_smaller(A,C,B)
| B = join_on_relstr(A,C)
| relstr_set_smaller(A,C,skolemFOFtoCNF_D(A,B,C)) )
& ( ~ antisymmetric_relstr(A)
| ~ element(B,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_set_smaller(A,C,B)
| element(skolemFOFtoCNF_D(A,B,C),the_carrier(A))
| ex_sup_of_relstr_set(A,C) )
& ( ~ antisymmetric_relstr(A)
| ~ element(B,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_set_smaller(A,C,B)
| ex_sup_of_relstr_set(A,C)
| relstr_set_smaller(A,C,skolemFOFtoCNF_D(A,B,C)) )
& ( B != join_on_relstr(A,C)
| ~ antisymmetric_relstr(A)
| ~ element(B,the_carrier(A))
| ~ element(D,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,C)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,C,D)
| related(A,B,D) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B,C,D] :
( B != join_on_relstr(A,C)
| ~ antisymmetric_relstr(A)
| ~ element(B,the_carrier(A))
| ~ element(D,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,C)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,C,D)
| related(A,B,D) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A] :
( ~ rel_str(A)
| bottom_of_relstr(A) = join_on_relstr(A,empty_set) ),
inference(canonicalize,[],[d11_yellow_0]) ).
fof(normalize_0_15,plain,
! [A] :
( ~ rel_str(A)
| bottom_of_relstr(A) = join_on_relstr(A,empty_set) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
antisymmetric_relstr(skolemFOFtoCNF_A_6),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_17,plain,
! [A] :
( ~ rel_str(A)
| element(bottom_of_relstr(A),the_carrier(A)) ),
inference(canonicalize,[],[dt_k3_yellow_0]) ).
fof(normalize_0_18,plain,
! [A] :
( ~ rel_str(A)
| element(bottom_of_relstr(A),the_carrier(A)) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A] :
( ~ antisymmetric_relstr(A)
| ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| empty_carrier(A)
| ( ex_inf_of_relstr_set(A,the_carrier(A))
& ex_sup_of_relstr_set(A,empty_set) ) ),
inference(canonicalize,[],[t42_yellow_0]) ).
fof(normalize_0_20,plain,
! [A] :
( ~ antisymmetric_relstr(A)
| ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| empty_carrier(A)
| ( ex_inf_of_relstr_set(A,the_carrier(A))
& ex_sup_of_relstr_set(A,empty_set) ) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A] :
( ( ~ antisymmetric_relstr(A)
| ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| empty_carrier(A)
| ex_inf_of_relstr_set(A,the_carrier(A)) )
& ( ~ antisymmetric_relstr(A)
| ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| empty_carrier(A)
| ex_sup_of_relstr_set(A,empty_set) ) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [A] :
( ~ antisymmetric_relstr(A)
| ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| empty_carrier(A)
| ex_sup_of_relstr_set(A,empty_set) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
lower_bounded_relstr(skolemFOFtoCNF_A_6),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_24,plain,
~ empty_carrier(skolemFOFtoCNF_A_6),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_25,plain,
~ related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_6)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( ~ element(B,the_carrier(A))
| ~ rel_str(A)
| relstr_set_smaller(A,empty_set,B) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_2,plain,
( ~ element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_6))
| ~ rel_str(skolemFOFtoCNF_A_6)
| relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_A_6)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_3,plain,
( ~ rel_str(skolemFOFtoCNF_A_6)
| relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_6)) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
rel_str(skolemFOFtoCNF_A_6),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( B != join_on_relstr(A,C)
| ~ antisymmetric_relstr(A)
| ~ element(B,the_carrier(A))
| ~ element(D,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,C)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,C,D)
| related(A,B,D) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_7,plain,
( join_on_relstr(A,C) != join_on_relstr(A,C)
| ~ antisymmetric_relstr(A)
| ~ element(D,the_carrier(A))
| ~ element(join_on_relstr(A,C),the_carrier(A))
| ~ ex_sup_of_relstr_set(A,C)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,C,D)
| related(A,join_on_relstr(A,C),D) ),
inference(subst,[],[refute_0_6:[bind(B,$fot(join_on_relstr(A,C)))]]) ).
cnf(refute_0_8,plain,
join_on_relstr(A,C) = join_on_relstr(A,C),
introduced(tautology,[refl,[$fot(join_on_relstr(A,C))]]) ).
cnf(refute_0_9,plain,
( ~ antisymmetric_relstr(A)
| ~ element(D,the_carrier(A))
| ~ element(join_on_relstr(A,C),the_carrier(A))
| ~ ex_sup_of_relstr_set(A,C)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,C,D)
| related(A,join_on_relstr(A,C),D) ),
inference(resolve,[$cnf( $equal(join_on_relstr(A,C),join_on_relstr(A,C)) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_6)
| ~ element(X_81,the_carrier(skolemFOFtoCNF_A_6))
| ~ element(join_on_relstr(skolemFOFtoCNF_A_6,empty_set),the_carrier(skolemFOFtoCNF_A_6))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set)
| ~ rel_str(skolemFOFtoCNF_A_6)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,X_81)
| related(skolemFOFtoCNF_A_6,join_on_relstr(skolemFOFtoCNF_A_6,empty_set),X_81) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(skolemFOFtoCNF_A_6)),bind(C,$fot(empty_set)),bind(D,$fot(X_81))]]) ).
cnf(refute_0_11,plain,
( ~ rel_str(A)
| bottom_of_relstr(A) = join_on_relstr(A,empty_set) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_12,plain,
( ~ rel_str(skolemFOFtoCNF_A_6)
| bottom_of_relstr(skolemFOFtoCNF_A_6) = join_on_relstr(skolemFOFtoCNF_A_6,empty_set) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_13,plain,
bottom_of_relstr(skolemFOFtoCNF_A_6) = join_on_relstr(skolemFOFtoCNF_A_6,empty_set),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_15,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_16,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( bottom_of_relstr(skolemFOFtoCNF_A_6) != join_on_relstr(skolemFOFtoCNF_A_6,empty_set)
| join_on_relstr(skolemFOFtoCNF_A_6,empty_set) = bottom_of_relstr(skolemFOFtoCNF_A_6) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(bottom_of_relstr(skolemFOFtoCNF_A_6))),bind(Y,$fot(join_on_relstr(skolemFOFtoCNF_A_6,empty_set)))]]) ).
cnf(refute_0_18,plain,
join_on_relstr(skolemFOFtoCNF_A_6,empty_set) = bottom_of_relstr(skolemFOFtoCNF_A_6),
inference(resolve,[$cnf( $equal(bottom_of_relstr(skolemFOFtoCNF_A_6),join_on_relstr(skolemFOFtoCNF_A_6,empty_set)) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
( join_on_relstr(skolemFOFtoCNF_A_6,empty_set) != bottom_of_relstr(skolemFOFtoCNF_A_6)
| ~ element(bottom_of_relstr(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
| element(join_on_relstr(skolemFOFtoCNF_A_6,empty_set),the_carrier(skolemFOFtoCNF_A_6)) ),
introduced(tautology,[equality,[$cnf( ~ element(join_on_relstr(skolemFOFtoCNF_A_6,empty_set),the_carrier(skolemFOFtoCNF_A_6)) ),[0],$fot(bottom_of_relstr(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_20,plain,
( ~ element(bottom_of_relstr(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
| element(join_on_relstr(skolemFOFtoCNF_A_6,empty_set),the_carrier(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( $equal(join_on_relstr(skolemFOFtoCNF_A_6,empty_set),bottom_of_relstr(skolemFOFtoCNF_A_6)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_6)
| ~ element(X_81,the_carrier(skolemFOFtoCNF_A_6))
| ~ element(bottom_of_relstr(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set)
| ~ rel_str(skolemFOFtoCNF_A_6)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,X_81)
| related(skolemFOFtoCNF_A_6,join_on_relstr(skolemFOFtoCNF_A_6,empty_set),X_81) ),
inference(resolve,[$cnf( element(join_on_relstr(skolemFOFtoCNF_A_6,empty_set),the_carrier(skolemFOFtoCNF_A_6)) )],[refute_0_20,refute_0_10]) ).
cnf(refute_0_22,plain,
( join_on_relstr(skolemFOFtoCNF_A_6,empty_set) != bottom_of_relstr(skolemFOFtoCNF_A_6)
| ~ related(skolemFOFtoCNF_A_6,join_on_relstr(skolemFOFtoCNF_A_6,empty_set),X_81)
| related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),X_81) ),
introduced(tautology,[equality,[$cnf( related(skolemFOFtoCNF_A_6,join_on_relstr(skolemFOFtoCNF_A_6,empty_set),X_81) ),[1],$fot(bottom_of_relstr(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_23,plain,
( ~ related(skolemFOFtoCNF_A_6,join_on_relstr(skolemFOFtoCNF_A_6,empty_set),X_81)
| related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),X_81) ),
inference(resolve,[$cnf( $equal(join_on_relstr(skolemFOFtoCNF_A_6,empty_set),bottom_of_relstr(skolemFOFtoCNF_A_6)) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_6)
| ~ element(X_81,the_carrier(skolemFOFtoCNF_A_6))
| ~ element(bottom_of_relstr(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set)
| ~ rel_str(skolemFOFtoCNF_A_6)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,X_81)
| related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),X_81) ),
inference(resolve,[$cnf( related(skolemFOFtoCNF_A_6,join_on_relstr(skolemFOFtoCNF_A_6,empty_set),X_81) )],[refute_0_21,refute_0_23]) ).
cnf(refute_0_25,plain,
antisymmetric_relstr(skolemFOFtoCNF_A_6),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_26,plain,
( ~ element(X_81,the_carrier(skolemFOFtoCNF_A_6))
| ~ element(bottom_of_relstr(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set)
| ~ rel_str(skolemFOFtoCNF_A_6)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,X_81)
| related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),X_81) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_6) )],[refute_0_25,refute_0_24]) ).
cnf(refute_0_27,plain,
( ~ rel_str(A)
| element(bottom_of_relstr(A),the_carrier(A)) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_28,plain,
( ~ rel_str(skolemFOFtoCNF_A_6)
| element(bottom_of_relstr(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6)) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_29,plain,
element(bottom_of_relstr(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6)),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_0_4,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ element(X_81,the_carrier(skolemFOFtoCNF_A_6))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set)
| ~ rel_str(skolemFOFtoCNF_A_6)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,X_81)
| related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),X_81) ),
inference(resolve,[$cnf( element(bottom_of_relstr(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6)) )],[refute_0_29,refute_0_26]) ).
cnf(refute_0_31,plain,
( ~ antisymmetric_relstr(A)
| ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| empty_carrier(A)
| ex_sup_of_relstr_set(A,empty_set) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_32,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_6)
| ~ lower_bounded_relstr(skolemFOFtoCNF_A_6)
| ~ rel_str(skolemFOFtoCNF_A_6)
| empty_carrier(skolemFOFtoCNF_A_6)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
inference(subst,[],[refute_0_31:[bind(A,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_33,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_6)
| ~ lower_bounded_relstr(skolemFOFtoCNF_A_6)
| empty_carrier(skolemFOFtoCNF_A_6)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_0_4,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ lower_bounded_relstr(skolemFOFtoCNF_A_6)
| empty_carrier(skolemFOFtoCNF_A_6)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_6) )],[refute_0_25,refute_0_33]) ).
cnf(refute_0_35,plain,
lower_bounded_relstr(skolemFOFtoCNF_A_6),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_36,plain,
( empty_carrier(skolemFOFtoCNF_A_6)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
inference(resolve,[$cnf( lower_bounded_relstr(skolemFOFtoCNF_A_6) )],[refute_0_35,refute_0_34]) ).
cnf(refute_0_37,plain,
~ empty_carrier(skolemFOFtoCNF_A_6),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_38,plain,
ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set),
inference(resolve,[$cnf( empty_carrier(skolemFOFtoCNF_A_6) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ element(X_81,the_carrier(skolemFOFtoCNF_A_6))
| ~ rel_str(skolemFOFtoCNF_A_6)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,X_81)
| related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),X_81) ),
inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) )],[refute_0_38,refute_0_30]) ).
cnf(refute_0_40,plain,
( ~ element(X_81,the_carrier(skolemFOFtoCNF_A_6))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,X_81)
| related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),X_81) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_0_4,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_6))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B_1)
| related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_40:[bind(X_81,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_42,plain,
( ~ element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_6))
| related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B_1) )],[refute_0_5,refute_0_41]) ).
cnf(refute_0_43,plain,
related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_6)) )],[refute_0_0,refute_0_42]) ).
cnf(refute_0_44,plain,
~ related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_45,plain,
$false,
inference(resolve,[$cnf( related(skolemFOFtoCNF_A_6,bottom_of_relstr(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_1) )],[refute_0_43,refute_0_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU361+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jun 19 22:44:22 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.38
% 0.18/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.39
%------------------------------------------------------------------------------