TSTP Solution File: SEU357+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU357+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 12:40:34 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of formulae : 133 ( 34 unt; 1 def)
% Number of atoms : 640 ( 43 equ)
% Maximal formula atoms : 53 ( 4 avg)
% Number of connectives : 870 ( 363 ~; 356 |; 110 &)
% ( 11 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 212 ( 6 sgn 123 !; 43 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d8_yellow_0,axiom,
! [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) ) )
& ! [D] :
( element(D,the_carrier(A))
=> ( ( relstr_element_smaller(A,B,D)
& ! [E] :
( element(E,the_carrier(A))
=> ( relstr_element_smaller(A,B,E)
=> related(A,E,D) ) ) )
=> D = C ) ) ) ) ) ).
fof(t16_yellow_0,conjecture,
! [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(t25_orders_2,axiom,
! [A] :
( ( antisymmetric_relstr(A)
& rel_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( related(A,B,C)
& related(A,C,B) )
=> B = C ) ) ) ) ).
fof(definition_0,definition,
! [A,B,C,D] :
( definitionFOFtoCNF_0(A,B,C,D)
<=> ( ~ element(D,the_carrier(A))
| ~ relstr_element_smaller(A,B,D)
| related(A,D,C) ) ) ).
fof(subgoal_0,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] :
( element(D,the_carrier(A))
=> ( relstr_element_smaller(A,B,D)
=> related(A,D,C) ) ) ) ) ),
inference(strip,[],[t16_yellow_0]) ).
fof(subgoal_1,plain,
! [A] :
( ( antisymmetric_relstr(A)
& rel_str(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) ) ) )
=> ex_inf_of_relstr_set(A,B) ) ),
inference(strip,[],[t16_yellow_0]) ).
fof(negate_0_0,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] :
( element(D,the_carrier(A))
=> ( relstr_element_smaller(A,B,D)
=> related(A,D,C) ) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,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,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [A,B,C,D] :
( ~ definitionFOFtoCNF_0(A,B,C,D)
<=> ( ~ related(A,D,C)
& element(D,the_carrier(A))
& relstr_element_smaller(A,B,D) ) ),
inference(canonicalize,[],[definition_0]) ).
fof(normalize_0_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] : ~ definitionFOFtoCNF_0(A,B,C,D) ) ) ),
inference(simplify,[],[normalize_0_0,normalize_0_1]) ).
fof(normalize_0_3,plain,
( antisymmetric_relstr(skolemFOFtoCNF_A_2)
& rel_str(skolemFOFtoCNF_A_2)
& ? [B] :
( ex_inf_of_relstr_set(skolemFOFtoCNF_A_2,B)
& ! [C] :
( ~ element(C,the_carrier(skolemFOFtoCNF_A_2))
| ~ relstr_element_smaller(skolemFOFtoCNF_A_2,B,C)
| ? [D] : ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_2,B,C,D) ) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [B] :
( ex_inf_of_relstr_set(skolemFOFtoCNF_A_2,B)
& ! [C] :
( ~ element(C,the_carrier(skolemFOFtoCNF_A_2))
| ~ relstr_element_smaller(skolemFOFtoCNF_A_2,B,C)
| ? [D] : ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_2,B,C,D) ) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( ex_inf_of_relstr_set(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
& ! [C] :
( ~ element(C,the_carrier(skolemFOFtoCNF_A_2))
| ~ relstr_element_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,C)
| ? [D] : ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,C,D) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [C] :
( ~ element(C,the_carrier(skolemFOFtoCNF_A_2))
| ~ relstr_element_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,C)
| ? [D] : ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,C,D) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [C] :
( ~ element(C,the_carrier(skolemFOFtoCNF_A_2))
| ~ relstr_element_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,C)
| ? [D] : ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,C,D) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [C] :
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,C,skolemFOFtoCNF_D_2(C))
| ~ element(C,the_carrier(skolemFOFtoCNF_A_2))
| ~ relstr_element_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,C) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
ex_inf_of_relstr_set(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_10,plain,
! [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) )
| ? [D] :
( D != C
& element(D,the_carrier(A))
& relstr_element_smaller(A,B,D)
& ! [E] :
( ~ element(E,the_carrier(A))
| ~ relstr_element_smaller(A,B,E)
| related(A,E,D) ) ) ) ) ),
inference(canonicalize,[],[d8_yellow_0]) ).
fof(normalize_0_11,plain,
! [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) )
| ? [D] :
( D != C
& element(D,the_carrier(A))
& relstr_element_smaller(A,B,D)
& ! [E] :
( ~ element(E,the_carrier(A))
| ~ relstr_element_smaller(A,B,E)
| related(A,E,D) ) ) ) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [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] : ~ definitionFOFtoCNF_0(A,B,C,D)
| ? [D] :
( D != C
& element(D,the_carrier(A))
& relstr_element_smaller(A,B,D)
& ! [E] :
( ~ element(E,the_carrier(A))
| ~ relstr_element_smaller(A,B,E)
| related(A,E,D) ) ) ) ) ),
inference(simplify,[],[normalize_0_11,normalize_0_1]) ).
fof(normalize_0_13,plain,
! [A,B,C,D,E] :
( ( ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| definitionFOFtoCNF_0(A,B,skolemFOFtoCNF_C(A,B),D) )
& ( ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| element(skolemFOFtoCNF_C(A,B),the_carrier(A)) )
& ( ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| relstr_element_smaller(A,B,skolemFOFtoCNF_C(A,B)) )
& ( skolemFOFtoCNF_D_1(A,B,C) != C
| ~ definitionFOFtoCNF_0(A,B,C,skolemFOFtoCNF_D(A,B,C))
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| ex_inf_of_relstr_set(A,B) )
& ( ~ definitionFOFtoCNF_0(A,B,C,skolemFOFtoCNF_D(A,B,C))
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| element(skolemFOFtoCNF_D_1(A,B,C),the_carrier(A))
| ex_inf_of_relstr_set(A,B) )
& ( ~ definitionFOFtoCNF_0(A,B,C,skolemFOFtoCNF_D(A,B,C))
| ~ 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_1(A,B,C)) )
& ( ~ element(D,the_carrier(A))
| ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ related(A,skolemFOFtoCNF_E(A,B,D),D)
| ~ relstr_element_smaller(A,B,D)
| D = skolemFOFtoCNF_C(A,B) )
& ( ~ element(D,the_carrier(A))
| ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,D)
| D = skolemFOFtoCNF_C(A,B)
| element(skolemFOFtoCNF_E(A,B,D),the_carrier(A)) )
& ( ~ element(D,the_carrier(A))
| ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,D)
| D = skolemFOFtoCNF_C(A,B)
| relstr_element_smaller(A,B,skolemFOFtoCNF_E(A,B,D)) )
& ( ~ definitionFOFtoCNF_0(A,B,C,skolemFOFtoCNF_D(A,B,C))
| ~ element(C,the_carrier(A))
| ~ element(E,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| ~ relstr_element_smaller(A,B,E)
| ex_inf_of_relstr_set(A,B)
| related(A,E,skolemFOFtoCNF_D_1(A,B,C)) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,D] :
( ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| definitionFOFtoCNF_0(A,B,skolemFOFtoCNF_C(A,B),D) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
rel_str(skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_16,plain,
! [A,B] :
( ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| element(skolemFOFtoCNF_C(A,B),the_carrier(A)) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_17,plain,
! [A,B] :
( ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| relstr_element_smaller(A,B,skolemFOFtoCNF_C(A,B)) ),
inference(conjunct,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,C,skolemFOFtoCNF_D_2(C))
| ~ element(C,the_carrier(skolemFOFtoCNF_A_2))
| ~ relstr_element_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,C) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_1,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_D_2(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)))
| ~ element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),the_carrier(skolemFOFtoCNF_A_2))
| ~ relstr_element_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) ),
inference(subst,[],[refute_0_0:[bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_0_2,plain,
ex_inf_of_relstr_set(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_3,plain,
( ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| definitionFOFtoCNF_0(A,B,skolemFOFtoCNF_C(A,B),D) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_4,plain,
( ~ ex_inf_of_relstr_set(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| ~ rel_str(skolemFOFtoCNF_A_2)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),X_23) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(X_23))]]) ).
cnf(refute_0_5,plain,
( ~ rel_str(skolemFOFtoCNF_A_2)
| definitionFOFtoCNF_0(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),X_23) ),
inference(resolve,[$cnf( ex_inf_of_relstr_set(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
rel_str(skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_7,plain,
definitionFOFtoCNF_0(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),X_23),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_2) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
definitionFOFtoCNF_0(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_D_2(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))),
inference(subst,[],[refute_0_7:[bind(X_23,$fot(skolemFOFtoCNF_D_2(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))))]]) ).
cnf(refute_0_9,plain,
( ~ element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),the_carrier(skolemFOFtoCNF_A_2))
| ~ relstr_element_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_D_2(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))) )],[refute_0_8,refute_0_1]) ).
cnf(refute_0_10,plain,
( ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| element(skolemFOFtoCNF_C(A,B),the_carrier(A)) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_11,plain,
( ~ ex_inf_of_relstr_set(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| ~ rel_str(skolemFOFtoCNF_A_2)
| element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),the_carrier(skolemFOFtoCNF_A_2)) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_12,plain,
( ~ rel_str(skolemFOFtoCNF_A_2)
| element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),the_carrier(skolemFOFtoCNF_A_2)) ),
inference(resolve,[$cnf( ex_inf_of_relstr_set(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) )],[refute_0_2,refute_0_11]) ).
cnf(refute_0_13,plain,
element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),the_carrier(skolemFOFtoCNF_A_2)),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_2) )],[refute_0_6,refute_0_12]) ).
cnf(refute_0_14,plain,
~ relstr_element_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),
inference(resolve,[$cnf( element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),the_carrier(skolemFOFtoCNF_A_2)) )],[refute_0_13,refute_0_9]) ).
cnf(refute_0_15,plain,
( ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| relstr_element_smaller(A,B,skolemFOFtoCNF_C(A,B)) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_16,plain,
( ~ ex_inf_of_relstr_set(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| ~ rel_str(skolemFOFtoCNF_A_2)
| relstr_element_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_17,plain,
( ~ rel_str(skolemFOFtoCNF_A_2)
| relstr_element_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) ),
inference(resolve,[$cnf( ex_inf_of_relstr_set(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) )],[refute_0_2,refute_0_16]) ).
cnf(refute_0_18,plain,
relstr_element_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_2) )],[refute_0_6,refute_0_17]) ).
cnf(refute_0_19,plain,
$false,
inference(resolve,[$cnf( relstr_element_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1,skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_18,refute_0_14]) ).
fof(negate_1_0,plain,
~ ! [A] :
( ( antisymmetric_relstr(A)
& rel_str(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) ) ) )
=> ex_inf_of_relstr_set(A,B) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,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] :
( ~ element(D,the_carrier(A))
| ~ relstr_element_smaller(A,B,D)
| related(A,D,C) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
! [A,B,C,D] :
( ~ definitionFOFtoCNF_0(A,B,C,D)
<=> ( ~ related(A,D,C)
& element(D,the_carrier(A))
& relstr_element_smaller(A,B,D) ) ),
inference(canonicalize,[],[definition_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] : definitionFOFtoCNF_0(A,B,C,D) ) ) ),
inference(simplify,[],[normalize_1_0,normalize_1_1]) ).
fof(normalize_1_3,plain,
( antisymmetric_relstr(skolemFOFtoCNF_A_3)
& rel_str(skolemFOFtoCNF_A_3)
& ? [B] :
( ~ ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,B)
& ? [C] :
( element(C,the_carrier(skolemFOFtoCNF_A_3))
& relstr_element_smaller(skolemFOFtoCNF_A_3,B,C)
& ! [D] : definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,B,C,D) ) ) ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [B] :
( ~ ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,B)
& ? [C] :
( element(C,the_carrier(skolemFOFtoCNF_A_3))
& relstr_element_smaller(skolemFOFtoCNF_A_3,B,C)
& ! [D] : definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,B,C,D) ) ),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
( ~ ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
& ? [C] :
( element(C,the_carrier(skolemFOFtoCNF_A_3))
& relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,C)
& ! [D] : definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,C,D) ) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
? [C] :
( element(C,the_carrier(skolemFOFtoCNF_A_3))
& relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,C)
& ! [D] : definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,C,D) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
( element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3))
& relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
& ! [D] : definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1,D) ),
inference(skolemize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [D] : definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1,D),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_10,plain,
! [D] : definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1,D),
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [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) )
| ? [D] :
( D != C
& element(D,the_carrier(A))
& relstr_element_smaller(A,B,D)
& ! [E] :
( ~ element(E,the_carrier(A))
| ~ relstr_element_smaller(A,B,E)
| related(A,E,D) ) ) ) ) ),
inference(canonicalize,[],[d8_yellow_0]) ).
fof(normalize_1_12,plain,
! [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) )
| ? [D] :
( D != C
& element(D,the_carrier(A))
& relstr_element_smaller(A,B,D)
& ! [E] :
( ~ element(E,the_carrier(A))
| ~ relstr_element_smaller(A,B,E)
| related(A,E,D) ) ) ) ) ),
inference(specialize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [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] : ~ definitionFOFtoCNF_0(A,B,C,D)
| ? [D] :
( D != C
& element(D,the_carrier(A))
& relstr_element_smaller(A,B,D)
& ! [E] :
( ~ element(E,the_carrier(A))
| ~ relstr_element_smaller(A,B,E)
| related(A,E,D) ) ) ) ) ),
inference(simplify,[],[normalize_1_12,normalize_1_1]) ).
fof(normalize_1_14,plain,
! [A,B,C,D,E] :
( ( ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| definitionFOFtoCNF_0(A,B,skolemFOFtoCNF_C(A,B),D) )
& ( ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| element(skolemFOFtoCNF_C(A,B),the_carrier(A)) )
& ( ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| relstr_element_smaller(A,B,skolemFOFtoCNF_C(A,B)) )
& ( skolemFOFtoCNF_D_1(A,B,C) != C
| ~ definitionFOFtoCNF_0(A,B,C,skolemFOFtoCNF_D(A,B,C))
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| ex_inf_of_relstr_set(A,B) )
& ( ~ definitionFOFtoCNF_0(A,B,C,skolemFOFtoCNF_D(A,B,C))
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| element(skolemFOFtoCNF_D_1(A,B,C),the_carrier(A))
| ex_inf_of_relstr_set(A,B) )
& ( ~ definitionFOFtoCNF_0(A,B,C,skolemFOFtoCNF_D(A,B,C))
| ~ 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_1(A,B,C)) )
& ( ~ element(D,the_carrier(A))
| ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ related(A,skolemFOFtoCNF_E(A,B,D),D)
| ~ relstr_element_smaller(A,B,D)
| D = skolemFOFtoCNF_C(A,B) )
& ( ~ element(D,the_carrier(A))
| ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,D)
| D = skolemFOFtoCNF_C(A,B)
| element(skolemFOFtoCNF_E(A,B,D),the_carrier(A)) )
& ( ~ element(D,the_carrier(A))
| ~ ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,D)
| D = skolemFOFtoCNF_C(A,B)
| relstr_element_smaller(A,B,skolemFOFtoCNF_E(A,B,D)) )
& ( ~ definitionFOFtoCNF_0(A,B,C,skolemFOFtoCNF_D(A,B,C))
| ~ element(C,the_carrier(A))
| ~ element(E,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| ~ relstr_element_smaller(A,B,E)
| ex_inf_of_relstr_set(A,B)
| related(A,E,skolemFOFtoCNF_D_1(A,B,C)) ) ),
inference(clausify,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [A,B,C,E] :
( ~ definitionFOFtoCNF_0(A,B,C,skolemFOFtoCNF_D(A,B,C))
| ~ element(C,the_carrier(A))
| ~ element(E,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| ~ relstr_element_smaller(A,B,E)
| ex_inf_of_relstr_set(A,B)
| related(A,E,skolemFOFtoCNF_D_1(A,B,C)) ),
inference(conjunct,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3)),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_17,plain,
rel_str(skolemFOFtoCNF_A_3),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_18,plain,
~ ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_19,plain,
! [A] :
( ~ antisymmetric_relstr(A)
| ~ rel_str(A)
| ! [B] :
( ~ element(B,the_carrier(A))
| ! [C] :
( ~ element(C,the_carrier(A))
| ~ related(A,B,C)
| ~ related(A,C,B)
| B = C ) ) ),
inference(canonicalize,[],[t25_orders_2]) ).
fof(normalize_1_20,plain,
! [A] :
( ~ antisymmetric_relstr(A)
| ~ rel_str(A)
| ! [B] :
( ~ element(B,the_carrier(A))
| ! [C] :
( ~ element(C,the_carrier(A))
| ~ related(A,B,C)
| ~ related(A,C,B)
| B = C ) ) ),
inference(specialize,[],[normalize_1_19]) ).
fof(normalize_1_21,plain,
! [A,B,C] :
( ~ antisymmetric_relstr(A)
| ~ element(B,the_carrier(A))
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ related(A,B,C)
| ~ related(A,C,B)
| B = C ),
inference(clausify,[],[normalize_1_20]) ).
fof(normalize_1_22,plain,
! [A,B,C,D] :
( ( ~ related(A,D,C)
| definitionFOFtoCNF_0(A,B,C,D) )
& ( definitionFOFtoCNF_0(A,B,C,D)
| element(D,the_carrier(A)) )
& ( definitionFOFtoCNF_0(A,B,C,D)
| relstr_element_smaller(A,B,D) )
& ( ~ definitionFOFtoCNF_0(A,B,C,D)
| ~ element(D,the_carrier(A))
| ~ relstr_element_smaller(A,B,D)
| related(A,D,C) ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_23,plain,
! [A,B,C,D] :
( ~ definitionFOFtoCNF_0(A,B,C,D)
| ~ element(D,the_carrier(A))
| ~ relstr_element_smaller(A,B,D)
| related(A,D,C) ),
inference(conjunct,[],[normalize_1_22]) ).
fof(normalize_1_24,plain,
! [A,B,C] :
( ~ definitionFOFtoCNF_0(A,B,C,skolemFOFtoCNF_D(A,B,C))
| ~ 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_1(A,B,C)) ),
inference(conjunct,[],[normalize_1_14]) ).
fof(normalize_1_25,plain,
! [A,B,C] :
( ~ definitionFOFtoCNF_0(A,B,C,skolemFOFtoCNF_D(A,B,C))
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| element(skolemFOFtoCNF_D_1(A,B,C),the_carrier(A))
| ex_inf_of_relstr_set(A,B) ),
inference(conjunct,[],[normalize_1_14]) ).
fof(normalize_1_26,plain,
antisymmetric_relstr(skolemFOFtoCNF_A_3),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_27,plain,
! [A,B,C] :
( skolemFOFtoCNF_D_1(A,B,C) != C
| ~ definitionFOFtoCNF_0(A,B,C,skolemFOFtoCNF_D(A,B,C))
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| ex_inf_of_relstr_set(A,B) ),
inference(conjunct,[],[normalize_1_14]) ).
cnf(refute_1_0,plain,
relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_1,plain,
definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1,D),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_2,plain,
definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)),
inference(subst,[],[refute_1_1:[bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)))]]) ).
cnf(refute_1_3,plain,
( ~ definitionFOFtoCNF_0(A,B,C,skolemFOFtoCNF_D(A,B,C))
| ~ element(C,the_carrier(A))
| ~ element(E,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| ~ relstr_element_smaller(A,B,E)
| ex_inf_of_relstr_set(A,B)
| related(A,E,skolemFOFtoCNF_D_1(A,B,C)) ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_4,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1))
| ~ element(X_98,the_carrier(skolemFOFtoCNF_A_3))
| ~ element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3))
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,X_98)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
| related(skolemFOFtoCNF_A_3,X_98,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) ),
inference(subst,[],[refute_1_3:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_2)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(E,$fot(X_98))]]) ).
cnf(refute_1_5,plain,
( ~ element(X_98,the_carrier(skolemFOFtoCNF_A_3))
| ~ element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3))
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,X_98)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
| related(skolemFOFtoCNF_A_3,X_98,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) )],[refute_1_2,refute_1_4]) ).
cnf(refute_1_6,plain,
element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3)),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_7,plain,
( ~ element(X_98,the_carrier(skolemFOFtoCNF_A_3))
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,X_98)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
| related(skolemFOFtoCNF_A_3,X_98,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3)) )],[refute_1_6,refute_1_5]) ).
cnf(refute_1_8,plain,
rel_str(skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_9,plain,
( ~ element(X_98,the_carrier(skolemFOFtoCNF_A_3))
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,X_98)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
| related(skolemFOFtoCNF_A_3,X_98,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_3) )],[refute_1_8,refute_1_7]) ).
cnf(refute_1_10,plain,
( ~ element(X_98,the_carrier(skolemFOFtoCNF_A_3))
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,X_98)
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
| related(skolemFOFtoCNF_A_3,X_98,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) ),
inference(resolve,[$cnf( relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) )],[refute_1_0,refute_1_9]) ).
cnf(refute_1_11,plain,
~ ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_12,plain,
( ~ element(X_98,the_carrier(skolemFOFtoCNF_A_3))
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,X_98)
| related(skolemFOFtoCNF_A_3,X_98,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) ),
inference(resolve,[$cnf( ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) )],[refute_1_10,refute_1_11]) ).
cnf(refute_1_13,plain,
( ~ element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3))
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) ),
inference(subst,[],[refute_1_12:[bind(X_98,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_1_14,plain,
( ~ element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3))
| related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) ),
inference(resolve,[$cnf( relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) )],[refute_1_0,refute_1_13]) ).
cnf(refute_1_15,plain,
related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)),
inference(resolve,[$cnf( element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3)) )],[refute_1_6,refute_1_14]) ).
cnf(refute_1_16,plain,
( ~ antisymmetric_relstr(A)
| ~ element(B,the_carrier(A))
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ related(A,B,C)
| ~ related(A,C,B)
| B = C ),
inference(canonicalize,[],[normalize_1_21]) ).
cnf(refute_1_17,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_3)
| ~ element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3))
| ~ element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_3))
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1))
| ~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1)
| skolemFOFtoCNF_C_1 = skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_1_16:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)))]]) ).
cnf(refute_1_18,plain,
definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1,X_50),
inference(subst,[],[refute_1_1:[bind(D,$fot(X_50))]]) ).
cnf(refute_1_19,plain,
( ~ definitionFOFtoCNF_0(A,B,C,D)
| ~ element(D,the_carrier(A))
| ~ relstr_element_smaller(A,B,D)
| related(A,D,C) ),
inference(canonicalize,[],[normalize_1_23]) ).
cnf(refute_1_20,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1,X_50)
| ~ element(X_50,the_carrier(skolemFOFtoCNF_A_3))
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,X_50)
| related(skolemFOFtoCNF_A_3,X_50,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_1_19:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_2)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(X_50))]]) ).
cnf(refute_1_21,plain,
( ~ element(X_50,the_carrier(skolemFOFtoCNF_A_3))
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,X_50)
| related(skolemFOFtoCNF_A_3,X_50,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1,X_50) )],[refute_1_18,refute_1_20]) ).
cnf(refute_1_22,plain,
( ~ element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_3))
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1))
| related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_1_21:[bind(X_50,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)))]]) ).
cnf(refute_1_23,plain,
( ~ definitionFOFtoCNF_0(A,B,C,skolemFOFtoCNF_D(A,B,C))
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| ex_inf_of_relstr_set(A,B)
| relstr_element_smaller(A,B,skolemFOFtoCNF_D_1(A,B,C)) ),
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_24,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1))
| ~ element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3))
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
| relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) ),
inference(subst,[],[refute_1_23:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_2)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_1_25,plain,
( ~ element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3))
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
| relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) )],[refute_1_2,refute_1_24]) ).
cnf(refute_1_26,plain,
( ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
| relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3)) )],[refute_1_6,refute_1_25]) ).
cnf(refute_1_27,plain,
( ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
| relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_3) )],[refute_1_8,refute_1_26]) ).
cnf(refute_1_28,plain,
( ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
| relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) ),
inference(resolve,[$cnf( relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) )],[refute_1_0,refute_1_27]) ).
cnf(refute_1_29,plain,
relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)),
inference(resolve,[$cnf( ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) )],[refute_1_28,refute_1_11]) ).
cnf(refute_1_30,plain,
( ~ element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_3))
| related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) )],[refute_1_29,refute_1_22]) ).
cnf(refute_1_31,plain,
( ~ definitionFOFtoCNF_0(A,B,C,skolemFOFtoCNF_D(A,B,C))
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| element(skolemFOFtoCNF_D_1(A,B,C),the_carrier(A))
| ex_inf_of_relstr_set(A,B) ),
inference(canonicalize,[],[normalize_1_25]) ).
cnf(refute_1_32,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1))
| ~ element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3))
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_3))
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_1_31:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_2)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_1_33,plain,
( ~ element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3))
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_3))
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) )],[refute_1_2,refute_1_32]) ).
cnf(refute_1_34,plain,
( ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_3))
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3)) )],[refute_1_6,refute_1_33]) ).
cnf(refute_1_35,plain,
( ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_3))
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_3) )],[refute_1_8,refute_1_34]) ).
cnf(refute_1_36,plain,
( element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_3))
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) )],[refute_1_0,refute_1_35]) ).
cnf(refute_1_37,plain,
element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_3)),
inference(resolve,[$cnf( ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) )],[refute_1_36,refute_1_11]) ).
cnf(refute_1_38,plain,
related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_3)) )],[refute_1_37,refute_1_30]) ).
cnf(refute_1_39,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_3)
| ~ element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3))
| ~ element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_3))
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1))
| skolemFOFtoCNF_C_1 = skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) )],[refute_1_38,refute_1_17]) ).
cnf(refute_1_40,plain,
antisymmetric_relstr(skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_1_26]) ).
cnf(refute_1_41,plain,
( ~ element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3))
| ~ element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_3))
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1))
| skolemFOFtoCNF_C_1 = skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_3) )],[refute_1_40,refute_1_39]) ).
cnf(refute_1_42,plain,
( ~ element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_3))
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1))
| skolemFOFtoCNF_C_1 = skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3)) )],[refute_1_6,refute_1_41]) ).
cnf(refute_1_43,plain,
( ~ rel_str(skolemFOFtoCNF_A_3)
| ~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1))
| skolemFOFtoCNF_C_1 = skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_3)) )],[refute_1_37,refute_1_42]) ).
cnf(refute_1_44,plain,
( ~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1))
| skolemFOFtoCNF_C_1 = skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_3) )],[refute_1_8,refute_1_43]) ).
cnf(refute_1_45,plain,
( skolemFOFtoCNF_D_1(A,B,C) != C
| ~ definitionFOFtoCNF_0(A,B,C,skolemFOFtoCNF_D(A,B,C))
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| ex_inf_of_relstr_set(A,B) ),
inference(canonicalize,[],[normalize_1_27]) ).
cnf(refute_1_46,plain,
( skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) != skolemFOFtoCNF_C_1
| ~ definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1))
| ~ element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3))
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_1_45:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_2)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_1_47,plain,
( skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) != skolemFOFtoCNF_C_1
| ~ element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3))
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) )],[refute_1_2,refute_1_46]) ).
cnf(refute_1_48,plain,
( skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) != skolemFOFtoCNF_C_1
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_C_1,the_carrier(skolemFOFtoCNF_A_3)) )],[refute_1_6,refute_1_47]) ).
cnf(refute_1_49,plain,
( skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) != skolemFOFtoCNF_C_1
| ~ relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_3) )],[refute_1_8,refute_1_48]) ).
cnf(refute_1_50,plain,
( skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) != skolemFOFtoCNF_C_1
| ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( relstr_element_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) )],[refute_1_0,refute_1_49]) ).
cnf(refute_1_51,plain,
skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) != skolemFOFtoCNF_C_1,
inference(resolve,[$cnf( ex_inf_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) )],[refute_1_50,refute_1_11]) ).
cnf(refute_1_52,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_53,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_54,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_52,refute_1_53]) ).
cnf(refute_1_55,plain,
( skolemFOFtoCNF_C_1 != skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)
| skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) = skolemFOFtoCNF_C_1 ),
inference(subst,[],[refute_1_54:[bind(X,$fot(skolemFOFtoCNF_C_1)),bind(Y,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)))]]) ).
cnf(refute_1_56,plain,
skolemFOFtoCNF_C_1 != skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) )],[refute_1_55,refute_1_51]) ).
cnf(refute_1_57,plain,
~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) )],[refute_1_44,refute_1_56]) ).
cnf(refute_1_58,plain,
$false,
inference(resolve,[$cnf( related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1)) )],[refute_1_15,refute_1_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU357+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.12 % 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 11:29:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44
% 0.19/0.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.46
%------------------------------------------------------------------------------