TSTP Solution File: SEU360+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU360+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 12:40:36 EDT 2022
% Result : Theorem 22.01s 22.26s
% Output : CNFRefutation 22.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 9
% Syntax : Number of formulae : 177 ( 36 unt; 0 def)
% Number of atoms : 705 ( 0 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 930 ( 402 ~; 407 |; 84 &)
% ( 16 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 183 ( 0 sgn 125 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ( lower_bounded_relstr(A)
<=> ? [B] :
( element(B,the_carrier(A))
& relstr_element_smaller(A,the_carrier(A),B) ) ) ) ).
fof(d8_lattice3,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( relstr_element_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,B)
=> related(A,C,D) ) ) ) ) ) ).
fof(dt_l1_orders_2,axiom,
! [A] :
( rel_str(A)
=> one_sorted_str(A) ) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ~ empty(the_carrier(A)) ) ).
fof(t15_yellow_0,axiom,
! [A] :
( ( antisymmetric_relstr(A)
& rel_str(A) )
=> ! [B] :
( ex_sup_of_relstr_set(A,B)
<=> ? [C] :
( element(C,the_carrier(A))
& relstr_set_smaller(A,B,C)
& ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,B,D)
=> related(A,C,D) ) ) ) ) ) ).
fof(t16_yellow_0,axiom,
! [A] :
( ( antisymmetric_relstr(A)
& rel_str(A) )
=> ! [B] :
( ex_inf_of_relstr_set(A,B)
<=> ? [C] :
( element(C,the_carrier(A))
& relstr_element_smaller(A,B,C)
& ! [D] :
( element(D,the_carrier(A))
=> ( relstr_element_smaller(A,B,D)
=> related(A,D,C) ) ) ) ) ) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ) ).
fof(t42_yellow_0,conjecture,
! [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(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) )
=> ex_sup_of_relstr_set(A,empty_set) ),
inference(strip,[],[t42_yellow_0]) ).
fof(subgoal_1,plain,
! [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)) ),
inference(strip,[],[t42_yellow_0]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ( ~ empty_carrier(A)
& antisymmetric_relstr(A)
& lower_bounded_relstr(A)
& rel_str(A) )
=> ex_sup_of_relstr_set(A,empty_set) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(canonicalize,[],[fc1_struct_0]) ).
fof(normalize_0_1,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] :
( ~ antisymmetric_relstr(A)
| ~ rel_str(A)
| ! [B] :
( ~ ex_sup_of_relstr_set(A,B)
<=> ! [C] :
( ~ element(C,the_carrier(A))
| ~ relstr_set_smaller(A,B,C)
| ? [D] :
( ~ related(A,C,D)
& element(D,the_carrier(A))
& relstr_set_smaller(A,B,D) ) ) ) ),
inference(canonicalize,[],[t15_yellow_0]) ).
fof(normalize_0_3,plain,
! [A] :
( ~ antisymmetric_relstr(A)
| ~ rel_str(A)
| ! [B] :
( ~ ex_sup_of_relstr_set(A,B)
<=> ! [C] :
( ~ element(C,the_carrier(A))
| ~ relstr_set_smaller(A,B,C)
| ? [D] :
( ~ related(A,C,D)
& element(D,the_carrier(A))
& relstr_set_smaller(A,B,D) ) ) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C,D] :
( ( ~ antisymmetric_relstr(A)
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| element(skolemFOFtoCNF_C(A,B),the_carrier(A)) )
& ( ~ antisymmetric_relstr(A)
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| relstr_set_smaller(A,B,skolemFOFtoCNF_C(A,B)) )
& ( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ related(A,C,skolemFOFtoCNF_D_1(A,B,C))
| ~ relstr_set_smaller(A,B,C)
| ex_sup_of_relstr_set(A,B) )
& ( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| element(skolemFOFtoCNF_D_1(A,B,C),the_carrier(A))
| ex_sup_of_relstr_set(A,B) )
& ( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| ex_sup_of_relstr_set(A,B)
| relstr_set_smaller(A,B,skolemFOFtoCNF_D_1(A,B,C)) )
& ( ~ antisymmetric_relstr(A)
| ~ element(D,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,D)
| related(A,skolemFOFtoCNF_C(A,B),D) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C] :
( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ related(A,C,skolemFOFtoCNF_D_1(A,B,C))
| ~ relstr_set_smaller(A,B,C)
| ex_sup_of_relstr_set(A,B) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(canonicalize,[],[t2_subset]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [A] :
( ~ empty_carrier(A)
& ~ ex_sup_of_relstr_set(A,empty_set)
& antisymmetric_relstr(A)
& lower_bounded_relstr(A)
& rel_str(A) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
( ~ empty_carrier(skolemFOFtoCNF_A_6)
& ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set)
& antisymmetric_relstr(skolemFOFtoCNF_A_6)
& lower_bounded_relstr(skolemFOFtoCNF_A_6)
& rel_str(skolemFOFtoCNF_A_6) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
rel_str(skolemFOFtoCNF_A_6),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A] :
( ~ rel_str(A)
| ( ~ lower_bounded_relstr(A)
<=> ! [B] :
( ~ element(B,the_carrier(A))
| ~ relstr_element_smaller(A,the_carrier(A),B) ) ) ),
inference(canonicalize,[],[d4_yellow_0]) ).
fof(normalize_0_12,plain,
! [A] :
( ~ rel_str(A)
| ( ~ lower_bounded_relstr(A)
<=> ! [B] :
( ~ element(B,the_carrier(A))
| ~ relstr_element_smaller(A,the_carrier(A),B) ) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B] :
( ( ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| element(skolemFOFtoCNF_B(A),the_carrier(A)) )
& ( ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| relstr_element_smaller(A,the_carrier(A),skolemFOFtoCNF_B(A)) )
& ( ~ element(B,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,the_carrier(A),B)
| lower_bounded_relstr(A) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A] :
( ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| element(skolemFOFtoCNF_B(A),the_carrier(A)) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
lower_bounded_relstr(skolemFOFtoCNF_A_6),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_16,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_17,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_16]) ).
fof(normalize_0_18,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_17]) ).
fof(normalize_0_19,plain,
! [A,B] :
( ~ element(B,the_carrier(A))
| ~ rel_str(A)
| relstr_set_smaller(A,empty_set,B) ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A,B,C] :
( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| element(skolemFOFtoCNF_D_1(A,B,C),the_carrier(A))
| ex_sup_of_relstr_set(A,B) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_21,plain,
antisymmetric_relstr(skolemFOFtoCNF_A_6),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_22,plain,
~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_23,plain,
! [A] :
( ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| relstr_element_smaller(A,the_carrier(A),skolemFOFtoCNF_B(A)) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_24,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ( ~ relstr_element_smaller(A,B,C)
<=> ? [D] :
( ~ related(A,C,D)
& element(D,the_carrier(A))
& in(D,B) ) ) ) ),
inference(canonicalize,[],[d8_lattice3]) ).
fof(normalize_0_25,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ( ~ relstr_element_smaller(A,B,C)
<=> ? [D] :
( ~ related(A,C,D)
& element(D,the_carrier(A))
& in(D,B) ) ) ) ),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [A,B,C,D] :
( ( ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ related(A,C,skolemFOFtoCNF_D(A,B,C))
| relstr_element_smaller(A,B,C) )
& ( ~ element(C,the_carrier(A))
| ~ rel_str(A)
| element(skolemFOFtoCNF_D(A,B,C),the_carrier(A))
| relstr_element_smaller(A,B,C) )
& ( ~ element(C,the_carrier(A))
| ~ rel_str(A)
| in(skolemFOFtoCNF_D(A,B,C),B)
| relstr_element_smaller(A,B,C) )
& ( ~ element(C,the_carrier(A))
| ~ element(D,the_carrier(A))
| ~ in(D,B)
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| related(A,C,D) ) ),
inference(clausify,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [A,B,C,D] :
( ~ element(C,the_carrier(A))
| ~ element(D,the_carrier(A))
| ~ in(D,B)
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| related(A,C,D) ),
inference(conjunct,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [A] :
( ~ rel_str(A)
| one_sorted_str(A) ),
inference(canonicalize,[],[dt_l1_orders_2]) ).
fof(normalize_0_29,plain,
! [A] :
( ~ rel_str(A)
| one_sorted_str(A) ),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
~ empty_carrier(skolemFOFtoCNF_A_6),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ empty(the_carrier(skolemFOFtoCNF_A_6))
| ~ one_sorted_str(skolemFOFtoCNF_A_6)
| empty_carrier(skolemFOFtoCNF_A_6) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_2,plain,
( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ related(A,C,skolemFOFtoCNF_D_1(A,B,C))
| ~ relstr_set_smaller(A,B,C)
| ex_sup_of_relstr_set(A,B) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_6)
| ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
| ~ rel_str(skolemFOFtoCNF_A_6)
| ~ related(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_6)),bind(B,$fot(empty_set)),bind(C,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)))]]) ).
cnf(refute_0_4,plain,
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)),the_carrier(skolemFOFtoCNF_A_6))
| empty(the_carrier(skolemFOFtoCNF_A_6))
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)),the_carrier(skolemFOFtoCNF_A_6)) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)))),bind(B,$fot(the_carrier(skolemFOFtoCNF_A_6)))]]) ).
cnf(refute_0_6,plain,
rel_str(skolemFOFtoCNF_A_6),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
( ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| element(skolemFOFtoCNF_B(A),the_carrier(A)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_8,plain,
( ~ lower_bounded_relstr(skolemFOFtoCNF_A_6)
| ~ rel_str(skolemFOFtoCNF_A_6)
| element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6)) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_9,plain,
( ~ lower_bounded_relstr(skolemFOFtoCNF_A_6)
| element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
lower_bounded_relstr(skolemFOFtoCNF_A_6),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_11,plain,
element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6)),
inference(resolve,[$cnf( lower_bounded_relstr(skolemFOFtoCNF_A_6) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
( ~ element(B,the_carrier(A))
| ~ rel_str(A)
| relstr_set_smaller(A,empty_set,B) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_13,plain,
( ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
| ~ rel_str(skolemFOFtoCNF_A_6)
| relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_A_6)),bind(B,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)))]]) ).
cnf(refute_0_14,plain,
( ~ rel_str(skolemFOFtoCNF_A_6)
| relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6)) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_0_6,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| element(skolemFOFtoCNF_D_1(A,B,C),the_carrier(A))
| ex_sup_of_relstr_set(A,B) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_17,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_6)
| ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
| ~ rel_str(skolemFOFtoCNF_A_6)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6))
| element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)),the_carrier(skolemFOFtoCNF_A_6))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_A_6)),bind(B,$fot(empty_set)),bind(C,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)))]]) ).
cnf(refute_0_18,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_6)
| ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
| ~ rel_str(skolemFOFtoCNF_A_6)
| element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)),the_carrier(skolemFOFtoCNF_A_6))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)) )],[refute_0_15,refute_0_17]) ).
cnf(refute_0_19,plain,
antisymmetric_relstr(skolemFOFtoCNF_A_6),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_20,plain,
( ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
| ~ rel_str(skolemFOFtoCNF_A_6)
| element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)),the_carrier(skolemFOFtoCNF_A_6))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_6) )],[refute_0_19,refute_0_18]) ).
cnf(refute_0_21,plain,
( ~ rel_str(skolemFOFtoCNF_A_6)
| element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)),the_carrier(skolemFOFtoCNF_A_6))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6)) )],[refute_0_11,refute_0_20]) ).
cnf(refute_0_22,plain,
( element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)),the_carrier(skolemFOFtoCNF_A_6))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_0_6,refute_0_21]) ).
cnf(refute_0_23,plain,
~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_24,plain,
element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)),the_carrier(skolemFOFtoCNF_A_6)),
inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( empty(the_carrier(skolemFOFtoCNF_A_6))
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)),the_carrier(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)),the_carrier(skolemFOFtoCNF_A_6)) )],[refute_0_24,refute_0_5]) ).
cnf(refute_0_26,plain,
( ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| relstr_element_smaller(A,the_carrier(A),skolemFOFtoCNF_B(A)) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_27,plain,
( ~ lower_bounded_relstr(skolemFOFtoCNF_A_6)
| ~ rel_str(skolemFOFtoCNF_A_6)
| relstr_element_smaller(skolemFOFtoCNF_A_6,the_carrier(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)) ),
inference(subst,[],[refute_0_26:[bind(A,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_28,plain,
( ~ lower_bounded_relstr(skolemFOFtoCNF_A_6)
| relstr_element_smaller(skolemFOFtoCNF_A_6,the_carrier(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_0_6,refute_0_27]) ).
cnf(refute_0_29,plain,
relstr_element_smaller(skolemFOFtoCNF_A_6,the_carrier(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)),
inference(resolve,[$cnf( lower_bounded_relstr(skolemFOFtoCNF_A_6) )],[refute_0_10,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ element(C,the_carrier(A))
| ~ element(D,the_carrier(A))
| ~ in(D,B)
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| related(A,C,D) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_31,plain,
( ~ element(X_515,the_carrier(skolemFOFtoCNF_A_6))
| ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
| ~ in(X_515,the_carrier(skolemFOFtoCNF_A_6))
| ~ rel_str(skolemFOFtoCNF_A_6)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_6,the_carrier(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B(skolemFOFtoCNF_A_6))
| related(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),X_515) ),
inference(subst,[],[refute_0_30:[bind(A,$fot(skolemFOFtoCNF_A_6)),bind(B,$fot(the_carrier(skolemFOFtoCNF_A_6))),bind(C,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6))),bind(D,$fot(X_515))]]) ).
cnf(refute_0_32,plain,
( ~ element(X_515,the_carrier(skolemFOFtoCNF_A_6))
| ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
| ~ in(X_515,the_carrier(skolemFOFtoCNF_A_6))
| ~ rel_str(skolemFOFtoCNF_A_6)
| related(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),X_515) ),
inference(resolve,[$cnf( relstr_element_smaller(skolemFOFtoCNF_A_6,the_carrier(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)) )],[refute_0_29,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ element(X_515,the_carrier(skolemFOFtoCNF_A_6))
| ~ in(X_515,the_carrier(skolemFOFtoCNF_A_6))
| ~ rel_str(skolemFOFtoCNF_A_6)
| related(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),X_515) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6)) )],[refute_0_11,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ element(X_515,the_carrier(skolemFOFtoCNF_A_6))
| ~ in(X_515,the_carrier(skolemFOFtoCNF_A_6))
| related(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),X_515) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_0_6,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)),the_carrier(skolemFOFtoCNF_A_6))
| ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)),the_carrier(skolemFOFtoCNF_A_6))
| related(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6))) ),
inference(subst,[],[refute_0_34:[bind(X_515,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6))))]]) ).
cnf(refute_0_36,plain,
( ~ element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)),the_carrier(skolemFOFtoCNF_A_6))
| empty(the_carrier(skolemFOFtoCNF_A_6))
| related(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6))) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)),the_carrier(skolemFOFtoCNF_A_6)) )],[refute_0_25,refute_0_35]) ).
cnf(refute_0_37,plain,
( empty(the_carrier(skolemFOFtoCNF_A_6))
| related(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6))) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)),the_carrier(skolemFOFtoCNF_A_6)) )],[refute_0_24,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_6)
| ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
| ~ rel_str(skolemFOFtoCNF_A_6)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6))
| empty(the_carrier(skolemFOFtoCNF_A_6))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
inference(resolve,[$cnf( related(skolemFOFtoCNF_A_6,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6))) )],[refute_0_37,refute_0_3]) ).
cnf(refute_0_39,plain,
( ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6))
| ~ rel_str(skolemFOFtoCNF_A_6)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6))
| empty(the_carrier(skolemFOFtoCNF_A_6))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_6) )],[refute_0_19,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ rel_str(skolemFOFtoCNF_A_6)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6))
| empty(the_carrier(skolemFOFtoCNF_A_6))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_6),the_carrier(skolemFOFtoCNF_A_6)) )],[refute_0_11,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6))
| empty(the_carrier(skolemFOFtoCNF_A_6))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_0_6,refute_0_40]) ).
cnf(refute_0_42,plain,
( empty(the_carrier(skolemFOFtoCNF_A_6))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) ),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B(skolemFOFtoCNF_A_6)) )],[refute_0_15,refute_0_41]) ).
cnf(refute_0_43,plain,
empty(the_carrier(skolemFOFtoCNF_A_6)),
inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_6,empty_set) )],[refute_0_42,refute_0_23]) ).
cnf(refute_0_44,plain,
( ~ one_sorted_str(skolemFOFtoCNF_A_6)
| empty_carrier(skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( empty(the_carrier(skolemFOFtoCNF_A_6)) )],[refute_0_43,refute_0_1]) ).
cnf(refute_0_45,plain,
( ~ rel_str(A)
| one_sorted_str(A) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_46,plain,
( ~ rel_str(skolemFOFtoCNF_A_6)
| one_sorted_str(skolemFOFtoCNF_A_6) ),
inference(subst,[],[refute_0_45:[bind(A,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_47,plain,
one_sorted_str(skolemFOFtoCNF_A_6),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_0_6,refute_0_46]) ).
cnf(refute_0_48,plain,
empty_carrier(skolemFOFtoCNF_A_6),
inference(resolve,[$cnf( one_sorted_str(skolemFOFtoCNF_A_6) )],[refute_0_47,refute_0_44]) ).
cnf(refute_0_49,plain,
~ empty_carrier(skolemFOFtoCNF_A_6),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_50,plain,
$false,
inference(resolve,[$cnf( empty_carrier(skolemFOFtoCNF_A_6) )],[refute_0_48,refute_0_49]) ).
fof(negate_1_0,plain,
~ ! [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)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(canonicalize,[],[fc1_struct_0]) ).
fof(normalize_1_1,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [A] :
( ~ antisymmetric_relstr(A)
| ~ rel_str(A)
| ! [B] :
( ~ ex_inf_of_relstr_set(A,B)
<=> ! [C] :
( ~ element(C,the_carrier(A))
| ~ relstr_element_smaller(A,B,C)
| ? [D] :
( ~ related(A,D,C)
& element(D,the_carrier(A))
& relstr_element_smaller(A,B,D) ) ) ) ),
inference(canonicalize,[],[t16_yellow_0]) ).
fof(normalize_1_3,plain,
! [A] :
( ~ antisymmetric_relstr(A)
| ~ rel_str(A)
| ! [B] :
( ~ ex_inf_of_relstr_set(A,B)
<=> ! [C] :
( ~ element(C,the_carrier(A))
| ~ relstr_element_smaller(A,B,C)
| ? [D] :
( ~ related(A,D,C)
& element(D,the_carrier(A))
& relstr_element_smaller(A,B,D) ) ) ) ),
inference(specialize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [A,B,C,D] :
( ( ~ antisymmetric_relstr(A)
| ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| element(skolemFOFtoCNF_C_1(A,B),the_carrier(A)) )
& ( ~ antisymmetric_relstr(A)
| ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| relstr_element_smaller(A,B,skolemFOFtoCNF_C_1(A,B)) )
& ( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ related(A,skolemFOFtoCNF_D_2(A,B,C),C)
| ~ relstr_element_smaller(A,B,C)
| ex_inf_of_relstr_set(A,B) )
& ( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| element(skolemFOFtoCNF_D_2(A,B,C),the_carrier(A))
| ex_inf_of_relstr_set(A,B) )
& ( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| ex_inf_of_relstr_set(A,B)
| relstr_element_smaller(A,B,skolemFOFtoCNF_D_2(A,B,C)) )
& ( ~ antisymmetric_relstr(A)
| ~ element(D,the_carrier(A))
| ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,D)
| related(A,D,skolemFOFtoCNF_C_1(A,B)) ) ),
inference(clausify,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A,B,C] :
( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ related(A,skolemFOFtoCNF_D_2(A,B,C),C)
| ~ relstr_element_smaller(A,B,C)
| ex_inf_of_relstr_set(A,B) ),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
? [A] :
( ~ empty_carrier(A)
& ~ ex_inf_of_relstr_set(A,the_carrier(A))
& antisymmetric_relstr(A)
& ex_sup_of_relstr_set(A,empty_set)
& lower_bounded_relstr(A)
& rel_str(A) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_7,plain,
( ~ empty_carrier(skolemFOFtoCNF_A_7)
& ~ ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7))
& antisymmetric_relstr(skolemFOFtoCNF_A_7)
& ex_sup_of_relstr_set(skolemFOFtoCNF_A_7,empty_set)
& lower_bounded_relstr(skolemFOFtoCNF_A_7)
& rel_str(skolemFOFtoCNF_A_7) ),
inference(skolemize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
rel_str(skolemFOFtoCNF_A_7),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A] :
( ~ rel_str(A)
| ( ~ lower_bounded_relstr(A)
<=> ! [B] :
( ~ element(B,the_carrier(A))
| ~ relstr_element_smaller(A,the_carrier(A),B) ) ) ),
inference(canonicalize,[],[d4_yellow_0]) ).
fof(normalize_1_10,plain,
! [A] :
( ~ rel_str(A)
| ( ~ lower_bounded_relstr(A)
<=> ! [B] :
( ~ element(B,the_carrier(A))
| ~ relstr_element_smaller(A,the_carrier(A),B) ) ) ),
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [A,B] :
( ( ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| element(skolemFOFtoCNF_B(A),the_carrier(A)) )
& ( ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| relstr_element_smaller(A,the_carrier(A),skolemFOFtoCNF_B(A)) )
& ( ~ element(B,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,the_carrier(A),B)
| lower_bounded_relstr(A) ) ),
inference(clausify,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [A] :
( ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| element(skolemFOFtoCNF_B(A),the_carrier(A)) ),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
lower_bounded_relstr(skolemFOFtoCNF_A_7),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_14,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(canonicalize,[],[t2_subset]) ).
fof(normalize_1_15,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(specialize,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
! [A] :
( ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| relstr_element_smaller(A,the_carrier(A),skolemFOFtoCNF_B(A)) ),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_17,plain,
! [A,B,C] :
( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| ex_inf_of_relstr_set(A,B)
| relstr_element_smaller(A,B,skolemFOFtoCNF_D_2(A,B,C)) ),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_18,plain,
antisymmetric_relstr(skolemFOFtoCNF_A_7),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_19,plain,
~ ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7)),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_20,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ( ~ relstr_element_smaller(A,B,C)
<=> ? [D] :
( ~ related(A,C,D)
& element(D,the_carrier(A))
& in(D,B) ) ) ) ),
inference(canonicalize,[],[d8_lattice3]) ).
fof(normalize_1_21,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ( ~ relstr_element_smaller(A,B,C)
<=> ? [D] :
( ~ related(A,C,D)
& element(D,the_carrier(A))
& in(D,B) ) ) ) ),
inference(specialize,[],[normalize_1_20]) ).
fof(normalize_1_22,plain,
! [A,B,C,D] :
( ( ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ related(A,C,skolemFOFtoCNF_D(A,B,C))
| relstr_element_smaller(A,B,C) )
& ( ~ element(C,the_carrier(A))
| ~ rel_str(A)
| element(skolemFOFtoCNF_D(A,B,C),the_carrier(A))
| relstr_element_smaller(A,B,C) )
& ( ~ element(C,the_carrier(A))
| ~ rel_str(A)
| in(skolemFOFtoCNF_D(A,B,C),B)
| relstr_element_smaller(A,B,C) )
& ( ~ element(C,the_carrier(A))
| ~ element(D,the_carrier(A))
| ~ in(D,B)
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| related(A,C,D) ) ),
inference(clausify,[],[normalize_1_21]) ).
fof(normalize_1_23,plain,
! [A,B,C,D] :
( ~ element(C,the_carrier(A))
| ~ element(D,the_carrier(A))
| ~ in(D,B)
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| related(A,C,D) ),
inference(conjunct,[],[normalize_1_22]) ).
fof(normalize_1_24,plain,
! [A,B,C] :
( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| element(skolemFOFtoCNF_D_2(A,B,C),the_carrier(A))
| ex_inf_of_relstr_set(A,B) ),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_25,plain,
! [A] :
( ~ rel_str(A)
| one_sorted_str(A) ),
inference(canonicalize,[],[dt_l1_orders_2]) ).
fof(normalize_1_26,plain,
! [A] :
( ~ rel_str(A)
| one_sorted_str(A) ),
inference(specialize,[],[normalize_1_25]) ).
fof(normalize_1_27,plain,
~ empty_carrier(skolemFOFtoCNF_A_7),
inference(conjunct,[],[normalize_1_7]) ).
cnf(refute_1_0,plain,
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
( ~ empty(the_carrier(skolemFOFtoCNF_A_7))
| ~ one_sorted_str(skolemFOFtoCNF_A_7)
| empty_carrier(skolemFOFtoCNF_A_7) ),
inference(subst,[],[refute_1_0:[bind(A,$fot(skolemFOFtoCNF_A_7))]]) ).
cnf(refute_1_2,plain,
( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ related(A,skolemFOFtoCNF_D_2(A,B,C),C)
| ~ relstr_element_smaller(A,B,C)
| ex_inf_of_relstr_set(A,B) ),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_3,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_7)
| ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7))
| ~ rel_str(skolemFOFtoCNF_A_7)
| ~ related(skolemFOFtoCNF_A_7,skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7))
| ~ relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7))
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7)) ),
inference(subst,[],[refute_1_2:[bind(A,$fot(skolemFOFtoCNF_A_7)),bind(B,$fot(the_carrier(skolemFOFtoCNF_A_7))),bind(C,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)))]]) ).
cnf(refute_1_4,plain,
rel_str(skolemFOFtoCNF_A_7),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_5,plain,
( ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| element(skolemFOFtoCNF_B(A),the_carrier(A)) ),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_6,plain,
( ~ lower_bounded_relstr(skolemFOFtoCNF_A_7)
| ~ rel_str(skolemFOFtoCNF_A_7)
| element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7)) ),
inference(subst,[],[refute_1_5:[bind(A,$fot(skolemFOFtoCNF_A_7))]]) ).
cnf(refute_1_7,plain,
( ~ lower_bounded_relstr(skolemFOFtoCNF_A_7)
| element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7)) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_7) )],[refute_1_4,refute_1_6]) ).
cnf(refute_1_8,plain,
lower_bounded_relstr(skolemFOFtoCNF_A_7),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_9,plain,
element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7)),
inference(resolve,[$cnf( lower_bounded_relstr(skolemFOFtoCNF_A_7) )],[refute_1_8,refute_1_7]) ).
cnf(refute_1_10,plain,
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_11,plain,
( ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7))
| empty(the_carrier(skolemFOFtoCNF_A_7))
| in(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7)) ),
inference(subst,[],[refute_1_10:[bind(A,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7))),bind(B,$fot(the_carrier(skolemFOFtoCNF_A_7)))]]) ).
cnf(refute_1_12,plain,
( empty(the_carrier(skolemFOFtoCNF_A_7))
| in(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7)) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7)) )],[refute_1_9,refute_1_11]) ).
cnf(refute_1_13,plain,
( ~ lower_bounded_relstr(A)
| ~ rel_str(A)
| relstr_element_smaller(A,the_carrier(A),skolemFOFtoCNF_B(A)) ),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_14,plain,
( ~ lower_bounded_relstr(skolemFOFtoCNF_A_7)
| ~ rel_str(skolemFOFtoCNF_A_7)
| relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)) ),
inference(subst,[],[refute_1_13:[bind(A,$fot(skolemFOFtoCNF_A_7))]]) ).
cnf(refute_1_15,plain,
( ~ lower_bounded_relstr(skolemFOFtoCNF_A_7)
| relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_7) )],[refute_1_4,refute_1_14]) ).
cnf(refute_1_16,plain,
relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),
inference(resolve,[$cnf( lower_bounded_relstr(skolemFOFtoCNF_A_7) )],[refute_1_8,refute_1_15]) ).
cnf(refute_1_17,plain,
( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| ex_inf_of_relstr_set(A,B)
| relstr_element_smaller(A,B,skolemFOFtoCNF_D_2(A,B,C)) ),
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_18,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_7)
| ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7))
| ~ rel_str(skolemFOFtoCNF_A_7)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7))
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7))
| relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7))) ),
inference(subst,[],[refute_1_17:[bind(A,$fot(skolemFOFtoCNF_A_7)),bind(B,$fot(the_carrier(skolemFOFtoCNF_A_7))),bind(C,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)))]]) ).
cnf(refute_1_19,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_7)
| ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7))
| ~ rel_str(skolemFOFtoCNF_A_7)
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7))
| relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7))) ),
inference(resolve,[$cnf( relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)) )],[refute_1_16,refute_1_18]) ).
cnf(refute_1_20,plain,
antisymmetric_relstr(skolemFOFtoCNF_A_7),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_21,plain,
( ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7))
| ~ rel_str(skolemFOFtoCNF_A_7)
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7))
| relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7))) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_7) )],[refute_1_20,refute_1_19]) ).
cnf(refute_1_22,plain,
( ~ rel_str(skolemFOFtoCNF_A_7)
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7))
| relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7))) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7)) )],[refute_1_9,refute_1_21]) ).
cnf(refute_1_23,plain,
( ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7))
| relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7))) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_7) )],[refute_1_4,refute_1_22]) ).
cnf(refute_1_24,plain,
~ ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7)),
inference(canonicalize,[],[normalize_1_19]) ).
cnf(refute_1_25,plain,
relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7))),
inference(resolve,[$cnf( ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7)) )],[refute_1_23,refute_1_24]) ).
cnf(refute_1_26,plain,
( ~ element(C,the_carrier(A))
| ~ element(D,the_carrier(A))
| ~ in(D,B)
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| related(A,C,D) ),
inference(canonicalize,[],[normalize_1_23]) ).
cnf(refute_1_27,plain,
( ~ element(X_1016,the_carrier(skolemFOFtoCNF_A_7))
| ~ element(skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),the_carrier(skolemFOFtoCNF_A_7))
| ~ in(X_1016,the_carrier(skolemFOFtoCNF_A_7))
| ~ rel_str(skolemFOFtoCNF_A_7)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)))
| related(skolemFOFtoCNF_A_7,skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),X_1016) ),
inference(subst,[],[refute_1_26:[bind(A,$fot(skolemFOFtoCNF_A_7)),bind(B,$fot(the_carrier(skolemFOFtoCNF_A_7))),bind(C,$fot(skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)))),bind(D,$fot(X_1016))]]) ).
cnf(refute_1_28,plain,
( ~ element(X_1016,the_carrier(skolemFOFtoCNF_A_7))
| ~ element(skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),the_carrier(skolemFOFtoCNF_A_7))
| ~ in(X_1016,the_carrier(skolemFOFtoCNF_A_7))
| ~ rel_str(skolemFOFtoCNF_A_7)
| related(skolemFOFtoCNF_A_7,skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),X_1016) ),
inference(resolve,[$cnf( relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7))) )],[refute_1_25,refute_1_27]) ).
cnf(refute_1_29,plain,
( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| element(skolemFOFtoCNF_D_2(A,B,C),the_carrier(A))
| ex_inf_of_relstr_set(A,B) ),
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_30,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_7)
| ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7))
| ~ rel_str(skolemFOFtoCNF_A_7)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7))
| element(skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),the_carrier(skolemFOFtoCNF_A_7))
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7)) ),
inference(subst,[],[refute_1_29:[bind(A,$fot(skolemFOFtoCNF_A_7)),bind(B,$fot(the_carrier(skolemFOFtoCNF_A_7))),bind(C,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)))]]) ).
cnf(refute_1_31,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_7)
| ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7))
| ~ rel_str(skolemFOFtoCNF_A_7)
| element(skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),the_carrier(skolemFOFtoCNF_A_7))
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7)) ),
inference(resolve,[$cnf( relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)) )],[refute_1_16,refute_1_30]) ).
cnf(refute_1_32,plain,
( ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7))
| ~ rel_str(skolemFOFtoCNF_A_7)
| element(skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),the_carrier(skolemFOFtoCNF_A_7))
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7)) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_7) )],[refute_1_20,refute_1_31]) ).
cnf(refute_1_33,plain,
( ~ rel_str(skolemFOFtoCNF_A_7)
| element(skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),the_carrier(skolemFOFtoCNF_A_7))
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7)) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7)) )],[refute_1_9,refute_1_32]) ).
cnf(refute_1_34,plain,
( element(skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),the_carrier(skolemFOFtoCNF_A_7))
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7)) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_7) )],[refute_1_4,refute_1_33]) ).
cnf(refute_1_35,plain,
element(skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),the_carrier(skolemFOFtoCNF_A_7)),
inference(resolve,[$cnf( ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7)) )],[refute_1_34,refute_1_24]) ).
cnf(refute_1_36,plain,
( ~ element(X_1016,the_carrier(skolemFOFtoCNF_A_7))
| ~ in(X_1016,the_carrier(skolemFOFtoCNF_A_7))
| ~ rel_str(skolemFOFtoCNF_A_7)
| related(skolemFOFtoCNF_A_7,skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),X_1016) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),the_carrier(skolemFOFtoCNF_A_7)) )],[refute_1_35,refute_1_28]) ).
cnf(refute_1_37,plain,
( ~ element(X_1016,the_carrier(skolemFOFtoCNF_A_7))
| ~ in(X_1016,the_carrier(skolemFOFtoCNF_A_7))
| related(skolemFOFtoCNF_A_7,skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),X_1016) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_7) )],[refute_1_4,refute_1_36]) ).
cnf(refute_1_38,plain,
( ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7))
| ~ in(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7))
| related(skolemFOFtoCNF_A_7,skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)) ),
inference(subst,[],[refute_1_37:[bind(X_1016,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)))]]) ).
cnf(refute_1_39,plain,
( ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7))
| empty(the_carrier(skolemFOFtoCNF_A_7))
| related(skolemFOFtoCNF_A_7,skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7)) )],[refute_1_12,refute_1_38]) ).
cnf(refute_1_40,plain,
( empty(the_carrier(skolemFOFtoCNF_A_7))
| related(skolemFOFtoCNF_A_7,skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7)) )],[refute_1_9,refute_1_39]) ).
cnf(refute_1_41,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_7)
| ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7))
| ~ rel_str(skolemFOFtoCNF_A_7)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7))
| empty(the_carrier(skolemFOFtoCNF_A_7))
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7)) ),
inference(resolve,[$cnf( related(skolemFOFtoCNF_A_7,skolemFOFtoCNF_D_2(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)) )],[refute_1_40,refute_1_3]) ).
cnf(refute_1_42,plain,
( ~ element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7))
| ~ rel_str(skolemFOFtoCNF_A_7)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7))
| empty(the_carrier(skolemFOFtoCNF_A_7))
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7)) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_7) )],[refute_1_20,refute_1_41]) ).
cnf(refute_1_43,plain,
( ~ rel_str(skolemFOFtoCNF_A_7)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7))
| empty(the_carrier(skolemFOFtoCNF_A_7))
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7)) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B(skolemFOFtoCNF_A_7),the_carrier(skolemFOFtoCNF_A_7)) )],[refute_1_9,refute_1_42]) ).
cnf(refute_1_44,plain,
( ~ relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7))
| empty(the_carrier(skolemFOFtoCNF_A_7))
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7)) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_7) )],[refute_1_4,refute_1_43]) ).
cnf(refute_1_45,plain,
( empty(the_carrier(skolemFOFtoCNF_A_7))
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7)) ),
inference(resolve,[$cnf( relstr_element_smaller(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7),skolemFOFtoCNF_B(skolemFOFtoCNF_A_7)) )],[refute_1_16,refute_1_44]) ).
cnf(refute_1_46,plain,
empty(the_carrier(skolemFOFtoCNF_A_7)),
inference(resolve,[$cnf( ex_inf_of_relstr_set(skolemFOFtoCNF_A_7,the_carrier(skolemFOFtoCNF_A_7)) )],[refute_1_45,refute_1_24]) ).
cnf(refute_1_47,plain,
( ~ one_sorted_str(skolemFOFtoCNF_A_7)
| empty_carrier(skolemFOFtoCNF_A_7) ),
inference(resolve,[$cnf( empty(the_carrier(skolemFOFtoCNF_A_7)) )],[refute_1_46,refute_1_1]) ).
cnf(refute_1_48,plain,
( ~ rel_str(A)
| one_sorted_str(A) ),
inference(canonicalize,[],[normalize_1_26]) ).
cnf(refute_1_49,plain,
( ~ rel_str(skolemFOFtoCNF_A_7)
| one_sorted_str(skolemFOFtoCNF_A_7) ),
inference(subst,[],[refute_1_48:[bind(A,$fot(skolemFOFtoCNF_A_7))]]) ).
cnf(refute_1_50,plain,
one_sorted_str(skolemFOFtoCNF_A_7),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_7) )],[refute_1_4,refute_1_49]) ).
cnf(refute_1_51,plain,
empty_carrier(skolemFOFtoCNF_A_7),
inference(resolve,[$cnf( one_sorted_str(skolemFOFtoCNF_A_7) )],[refute_1_50,refute_1_47]) ).
cnf(refute_1_52,plain,
~ empty_carrier(skolemFOFtoCNF_A_7),
inference(canonicalize,[],[normalize_1_27]) ).
cnf(refute_1_53,plain,
$false,
inference(resolve,[$cnf( empty_carrier(skolemFOFtoCNF_A_7) )],[refute_1_51,refute_1_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU360+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 20 13:13:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 22.01/22.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.01/22.26
% 22.01/22.26 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.09/22.27
%------------------------------------------------------------------------------