TSTP Solution File: SEU359+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU359+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 12:40:35 EDT 2022
% Result : Theorem 0.14s 0.43s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 12
% Syntax : Number of formulae : 269 ( 68 unt; 0 def)
% Number of atoms : 1297 ( 161 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 1737 ( 709 ~; 725 |; 227 &)
% ( 14 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 13 con; 0-3 aty)
% Number of variables : 300 ( 0 sgn 180 !; 56 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d9_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( ex_sup_of_relstr_set(A,B)
=> ( C = join_on_relstr(A,B)
<=> ( relstr_set_smaller(A,B,C)
& ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,B,D)
=> related(A,C,D) ) ) ) ) ) ) ) ).
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(t30_yellow_0,conjecture,
! [A] :
( ( antisymmetric_relstr(A)
& rel_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( ( ( B = join_on_relstr(A,C)
& ex_sup_of_relstr_set(A,C) )
=> ( relstr_set_smaller(A,C,B)
& ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) ) ) )
& ( ( relstr_set_smaller(A,C,B)
& ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) ) )
=> ( B = join_on_relstr(A,C)
& ex_sup_of_relstr_set(A,C) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [A] :
( ( antisymmetric_relstr(A)
& rel_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( ( B = join_on_relstr(A,C)
& ex_sup_of_relstr_set(A,C) )
=> relstr_set_smaller(A,C,B) ) ) ),
inference(strip,[],[t30_yellow_0]) ).
fof(subgoal_1,plain,
! [A] :
( ( antisymmetric_relstr(A)
& rel_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( ( B = join_on_relstr(A,C)
& ex_sup_of_relstr_set(A,C)
& relstr_set_smaller(A,C,B) )
=> ! [D] :
( ( element(D,the_carrier(A))
& relstr_set_smaller(A,C,D) )
=> related(A,B,D) ) ) ) ),
inference(strip,[],[t30_yellow_0]) ).
fof(subgoal_2,plain,
! [A] :
( ( antisymmetric_relstr(A)
& rel_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( ( ( ( B = join_on_relstr(A,C)
& ex_sup_of_relstr_set(A,C) )
=> ( relstr_set_smaller(A,C,B)
& ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) ) ) )
& relstr_set_smaller(A,C,B)
& ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) ) )
=> B = join_on_relstr(A,C) ) ) ),
inference(strip,[],[t30_yellow_0]) ).
fof(subgoal_3,plain,
! [A] :
( ( antisymmetric_relstr(A)
& rel_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( ( ( ( B = join_on_relstr(A,C)
& ex_sup_of_relstr_set(A,C) )
=> ( relstr_set_smaller(A,C,B)
& ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) ) ) )
& relstr_set_smaller(A,C,B)
& ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) )
& B = join_on_relstr(A,C) )
=> ex_sup_of_relstr_set(A,C) ) ) ),
inference(strip,[],[t30_yellow_0]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ( antisymmetric_relstr(A)
& rel_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( ( B = join_on_relstr(A,C)
& ex_sup_of_relstr_set(A,C) )
=> relstr_set_smaller(A,C,B) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ( C != join_on_relstr(A,B)
<=> ( ~ relstr_set_smaller(A,B,C)
| ? [D] :
( ~ related(A,C,D)
& element(D,the_carrier(A))
& relstr_set_smaller(A,B,D) ) ) ) ) ),
inference(canonicalize,[],[d9_yellow_0]) ).
fof(normalize_0_1,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ( C != join_on_relstr(A,B)
<=> ( ~ 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_0]) ).
fof(normalize_0_2,plain,
! [A,B,C,D] :
( ( C != join_on_relstr(A,B)
| ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| relstr_set_smaller(A,B,C) )
& ( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ related(A,C,skolemFOFtoCNF_D(A,B,C))
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B) )
& ( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B)
| element(skolemFOFtoCNF_D(A,B,C),the_carrier(A)) )
& ( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B)
| relstr_set_smaller(A,B,skolemFOFtoCNF_D(A,B,C)) )
& ( C != join_on_relstr(A,B)
| ~ element(C,the_carrier(A))
| ~ element(D,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,D)
| related(A,C,D) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] :
( C != join_on_relstr(A,B)
| ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| relstr_set_smaller(A,B,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A] :
( antisymmetric_relstr(A)
& rel_str(A)
& ? [B] :
( element(B,the_carrier(A))
& ? [C] :
( ~ relstr_set_smaller(A,C,B)
& B = join_on_relstr(A,C)
& ex_sup_of_relstr_set(A,C) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( antisymmetric_relstr(skolemFOFtoCNF_A_2)
& rel_str(skolemFOFtoCNF_A_2)
& ? [B] :
( element(B,the_carrier(skolemFOFtoCNF_A_2))
& ? [C] :
( ~ relstr_set_smaller(skolemFOFtoCNF_A_2,C,B)
& B = join_on_relstr(skolemFOFtoCNF_A_2,C)
& ex_sup_of_relstr_set(skolemFOFtoCNF_A_2,C) ) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [B] :
( element(B,the_carrier(skolemFOFtoCNF_A_2))
& ? [C] :
( ~ relstr_set_smaller(skolemFOFtoCNF_A_2,C,B)
& B = join_on_relstr(skolemFOFtoCNF_A_2,C)
& ex_sup_of_relstr_set(skolemFOFtoCNF_A_2,C) ) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_2))
& ? [C] :
( ~ relstr_set_smaller(skolemFOFtoCNF_A_2,C,skolemFOFtoCNF_B_1)
& skolemFOFtoCNF_B_1 = join_on_relstr(skolemFOFtoCNF_A_2,C)
& ex_sup_of_relstr_set(skolemFOFtoCNF_A_2,C) ) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [C] :
( ~ relstr_set_smaller(skolemFOFtoCNF_A_2,C,skolemFOFtoCNF_B_1)
& skolemFOFtoCNF_B_1 = join_on_relstr(skolemFOFtoCNF_A_2,C)
& ex_sup_of_relstr_set(skolemFOFtoCNF_A_2,C) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
( ~ relstr_set_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
& skolemFOFtoCNF_B_1 = join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1)
& ex_sup_of_relstr_set(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
skolemFOFtoCNF_B_1 = join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_2)),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_12,plain,
ex_sup_of_relstr_set(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_13,plain,
rel_str(skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_14,plain,
~ relstr_set_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( C != join_on_relstr(A,B)
| ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| relstr_set_smaller(A,B,C) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( join_on_relstr(A,B) != join_on_relstr(A,B)
| ~ element(join_on_relstr(A,B),the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| relstr_set_smaller(A,B,join_on_relstr(A,B)) ),
inference(subst,[],[refute_0_0:[bind(C,$fot(join_on_relstr(A,B)))]]) ).
cnf(refute_0_2,plain,
join_on_relstr(A,B) = join_on_relstr(A,B),
introduced(tautology,[refl,[$fot(join_on_relstr(A,B))]]) ).
cnf(refute_0_3,plain,
( ~ element(join_on_relstr(A,B),the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| relstr_set_smaller(A,B,join_on_relstr(A,B)) ),
inference(resolve,[$cnf( $equal(join_on_relstr(A,B),join_on_relstr(A,B)) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( ~ element(join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_2))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1)
| ~ rel_str(skolemFOFtoCNF_A_2)
| relstr_set_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1,join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1)) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_5,plain,
skolemFOFtoCNF_B_1 = join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_7,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_8,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_B_1 != join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1)
| join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1) = skolemFOFtoCNF_B_1 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_B_1)),bind(Y,$fot(join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1)))]]) ).
cnf(refute_0_10,plain,
join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1) = skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1) != skolemFOFtoCNF_B_1
| ~ element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_2))
| element(join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_2)) ),
introduced(tautology,[equality,[$cnf( ~ element(join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_2)) ),[0],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_0_12,plain,
( ~ element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_2))
| element(join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_2)) ),
inference(resolve,[$cnf( $equal(join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1),skolemFOFtoCNF_B_1) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_2))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1)
| ~ rel_str(skolemFOFtoCNF_A_2)
| relstr_set_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1,join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1)) ),
inference(resolve,[$cnf( element(join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1),the_carrier(skolemFOFtoCNF_A_2)) )],[refute_0_12,refute_0_4]) ).
cnf(refute_0_14,plain,
( join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1) != skolemFOFtoCNF_B_1
| ~ relstr_set_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1,join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1))
| relstr_set_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
introduced(tautology,[equality,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1,join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1)) ),[2],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_0_15,plain,
( ~ relstr_set_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1,join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1))
| relstr_set_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1),skolemFOFtoCNF_B_1) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_2))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1)
| ~ rel_str(skolemFOFtoCNF_A_2)
| relstr_set_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1,join_on_relstr(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1)) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_2)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_18,plain,
( ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1)
| ~ rel_str(skolemFOFtoCNF_A_2)
| relstr_set_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_2)) )],[refute_0_17,refute_0_16]) ).
cnf(refute_0_19,plain,
ex_sup_of_relstr_set(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_20,plain,
( ~ rel_str(skolemFOFtoCNF_A_2)
| relstr_set_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1) )],[refute_0_19,refute_0_18]) ).
cnf(refute_0_21,plain,
rel_str(skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_22,plain,
relstr_set_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_2) )],[refute_0_21,refute_0_20]) ).
cnf(refute_0_23,plain,
~ relstr_set_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_0_22,refute_0_23]) ).
fof(negate_1_0,plain,
~ ! [A] :
( ( antisymmetric_relstr(A)
& rel_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( ( B = join_on_relstr(A,C)
& ex_sup_of_relstr_set(A,C)
& relstr_set_smaller(A,C,B) )
=> ! [D] :
( ( element(D,the_carrier(A))
& relstr_set_smaller(A,C,D) )
=> related(A,B,D) ) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A] :
( antisymmetric_relstr(A)
& rel_str(A)
& ? [B] :
( element(B,the_carrier(A))
& ? [C] :
( B = join_on_relstr(A,C)
& ex_sup_of_relstr_set(A,C)
& relstr_set_smaller(A,C,B)
& ? [D] :
( ~ related(A,B,D)
& element(D,the_carrier(A))
& relstr_set_smaller(A,C,D) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( antisymmetric_relstr(skolemFOFtoCNF_A_3)
& rel_str(skolemFOFtoCNF_A_3)
& ? [B] :
( element(B,the_carrier(skolemFOFtoCNF_A_3))
& ? [C] :
( B = join_on_relstr(skolemFOFtoCNF_A_3,C)
& ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,C)
& relstr_set_smaller(skolemFOFtoCNF_A_3,C,B)
& ? [D] :
( ~ related(skolemFOFtoCNF_A_3,B,D)
& element(D,the_carrier(skolemFOFtoCNF_A_3))
& relstr_set_smaller(skolemFOFtoCNF_A_3,C,D) ) ) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
? [B] :
( element(B,the_carrier(skolemFOFtoCNF_A_3))
& ? [C] :
( B = join_on_relstr(skolemFOFtoCNF_A_3,C)
& ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,C)
& relstr_set_smaller(skolemFOFtoCNF_A_3,C,B)
& ? [D] :
( ~ related(skolemFOFtoCNF_A_3,B,D)
& element(D,the_carrier(skolemFOFtoCNF_A_3))
& relstr_set_smaller(skolemFOFtoCNF_A_3,C,D) ) ) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
( element(skolemFOFtoCNF_B_2,the_carrier(skolemFOFtoCNF_A_3))
& ? [C] :
( skolemFOFtoCNF_B_2 = join_on_relstr(skolemFOFtoCNF_A_3,C)
& ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,C)
& relstr_set_smaller(skolemFOFtoCNF_A_3,C,skolemFOFtoCNF_B_2)
& ? [D] :
( ~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,D)
& element(D,the_carrier(skolemFOFtoCNF_A_3))
& relstr_set_smaller(skolemFOFtoCNF_A_3,C,D) ) ) ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [C] :
( skolemFOFtoCNF_B_2 = join_on_relstr(skolemFOFtoCNF_A_3,C)
& ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,C)
& relstr_set_smaller(skolemFOFtoCNF_A_3,C,skolemFOFtoCNF_B_2)
& ? [D] :
( ~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,D)
& element(D,the_carrier(skolemFOFtoCNF_A_3))
& relstr_set_smaller(skolemFOFtoCNF_A_3,C,D) ) ),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
( skolemFOFtoCNF_B_2 = join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
& ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
& relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_2)
& ? [D] :
( ~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,D)
& element(D,the_carrier(skolemFOFtoCNF_A_3))
& relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,D) ) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
? [D] :
( ~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,D)
& element(D,the_carrier(skolemFOFtoCNF_A_3))
& relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,D) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
( ~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2)
& element(skolemFOFtoCNF_D_2,the_carrier(skolemFOFtoCNF_A_3))
& relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_2) ),
inference(skolemize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_2),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_9,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_1_10,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_1_9]) ).
fof(normalize_1_11,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_1_10]) ).
fof(normalize_1_12,plain,
! [A,B,D] :
( ~ 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(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
antisymmetric_relstr(skolemFOFtoCNF_A_3),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_14,plain,
element(skolemFOFtoCNF_D_2,the_carrier(skolemFOFtoCNF_A_3)),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_15,plain,
ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_16,plain,
rel_str(skolemFOFtoCNF_A_3),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_17,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ( C != join_on_relstr(A,B)
<=> ( ~ relstr_set_smaller(A,B,C)
| ? [D] :
( ~ related(A,C,D)
& element(D,the_carrier(A))
& relstr_set_smaller(A,B,D) ) ) ) ) ),
inference(canonicalize,[],[d9_yellow_0]) ).
fof(normalize_1_18,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ( C != join_on_relstr(A,B)
<=> ( ~ 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_1_17]) ).
fof(normalize_1_19,plain,
! [A,B,C,D] :
( ( C != join_on_relstr(A,B)
| ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| relstr_set_smaller(A,B,C) )
& ( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ related(A,C,skolemFOFtoCNF_D(A,B,C))
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B) )
& ( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B)
| element(skolemFOFtoCNF_D(A,B,C),the_carrier(A)) )
& ( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B)
| relstr_set_smaller(A,B,skolemFOFtoCNF_D(A,B,C)) )
& ( C != join_on_relstr(A,B)
| ~ element(C,the_carrier(A))
| ~ element(D,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,D)
| related(A,C,D) ) ),
inference(clausify,[],[normalize_1_18]) ).
fof(normalize_1_20,plain,
! [A,B,C] :
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ related(A,C,skolemFOFtoCNF_D(A,B,C))
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B) ),
inference(conjunct,[],[normalize_1_19]) ).
fof(normalize_1_21,plain,
! [A,B] :
( ~ antisymmetric_relstr(A)
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| relstr_set_smaller(A,B,skolemFOFtoCNF_C(A,B)) ),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_22,plain,
! [A,B,C] :
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B)
| element(skolemFOFtoCNF_D(A,B,C),the_carrier(A)) ),
inference(conjunct,[],[normalize_1_19]) ).
fof(normalize_1_23,plain,
skolemFOFtoCNF_B_2 = join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_24,plain,
! [A,B] :
( ~ antisymmetric_relstr(A)
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| element(skolemFOFtoCNF_C(A,B),the_carrier(A)) ),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_25,plain,
! [A,B,C] :
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B)
| relstr_set_smaller(A,B,skolemFOFtoCNF_D(A,B,C)) ),
inference(conjunct,[],[normalize_1_19]) ).
fof(normalize_1_26,plain,
~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2),
inference(conjunct,[],[normalize_1_7]) ).
cnf(refute_1_0,plain,
relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_2),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_1,plain,
( ~ 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(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_2,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_3)
| ~ element(skolemFOFtoCNF_D_2,the_carrier(skolemFOFtoCNF_A_3))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_2)
| related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D_2) ),
inference(subst,[],[refute_1_1:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_C_2)),bind(D,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_1_3,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_3)
| ~ element(skolemFOFtoCNF_D_2,the_carrier(skolemFOFtoCNF_A_3))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D_2) ),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_D_2) )],[refute_1_0,refute_1_2]) ).
cnf(refute_1_4,plain,
antisymmetric_relstr(skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_5,plain,
( ~ element(skolemFOFtoCNF_D_2,the_carrier(skolemFOFtoCNF_A_3))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D_2) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_3) )],[refute_1_4,refute_1_3]) ).
cnf(refute_1_6,plain,
element(skolemFOFtoCNF_D_2,the_carrier(skolemFOFtoCNF_A_3)),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_7,plain,
( ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D_2) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_D_2,the_carrier(skolemFOFtoCNF_A_3)) )],[refute_1_6,refute_1_5]) ).
cnf(refute_1_8,plain,
ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_9,plain,
( ~ rel_str(skolemFOFtoCNF_A_3)
| related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D_2) ),
inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) )],[refute_1_8,refute_1_7]) ).
cnf(refute_1_10,plain,
rel_str(skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_11,plain,
related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D_2),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_3) )],[refute_1_10,refute_1_9]) ).
cnf(refute_1_12,plain,
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ related(A,C,skolemFOFtoCNF_D(A,B,C))
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B) ),
inference(canonicalize,[],[normalize_1_20]) ).
cnf(refute_1_13,plain,
( ~ element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),the_carrier(skolemFOFtoCNF_A_3))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) ),
inference(subst,[],[refute_1_12:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_C_2)),bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)))]]) ).
cnf(refute_1_14,plain,
( ~ antisymmetric_relstr(A)
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| relstr_set_smaller(A,B,skolemFOFtoCNF_C(A,B)) ),
inference(canonicalize,[],[normalize_1_21]) ).
cnf(refute_1_15,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_3)
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)) ),
inference(subst,[],[refute_1_14:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_C_2))]]) ).
cnf(refute_1_16,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_3)
| ~ rel_str(skolemFOFtoCNF_A_3)
| relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)) ),
inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) )],[refute_1_8,refute_1_15]) ).
cnf(refute_1_17,plain,
( ~ rel_str(skolemFOFtoCNF_A_3)
| relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_3) )],[refute_1_4,refute_1_16]) ).
cnf(refute_1_18,plain,
relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_3) )],[refute_1_10,refute_1_17]) ).
cnf(refute_1_19,plain,
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B)
| element(skolemFOFtoCNF_D(A,B,C),the_carrier(A)) ),
inference(canonicalize,[],[normalize_1_22]) ).
cnf(refute_1_20,plain,
( ~ element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),the_carrier(skolemFOFtoCNF_A_3))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)),the_carrier(skolemFOFtoCNF_A_3)) ),
inference(subst,[],[refute_1_19:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_C_2)),bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)))]]) ).
cnf(refute_1_21,plain,
( ~ element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),the_carrier(skolemFOFtoCNF_A_3))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)),the_carrier(skolemFOFtoCNF_A_3)) ),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)) )],[refute_1_18,refute_1_20]) ).
cnf(refute_1_22,plain,
skolemFOFtoCNF_B_2 = join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_1_23]) ).
cnf(refute_1_23,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_24,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_25,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_23,refute_1_24]) ).
cnf(refute_1_26,plain,
( skolemFOFtoCNF_B_2 != join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2 ),
inference(subst,[],[refute_1_25:[bind(X,$fot(skolemFOFtoCNF_B_2)),bind(Y,$fot(join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)))]]) ).
cnf(refute_1_27,plain,
join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_2,join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)) )],[refute_1_22,refute_1_26]) ).
cnf(refute_1_28,plain,
( join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) != skolemFOFtoCNF_B_2
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) != join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)) ),[1],$fot(skolemFOFtoCNF_B_2)]]) ).
cnf(refute_1_29,plain,
( skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) != join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2 ),
inference(resolve,[$cnf( $equal(join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_B_2) )],[refute_1_27,refute_1_28]) ).
cnf(refute_1_30,plain,
( ~ element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),the_carrier(skolemFOFtoCNF_A_3))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2
| element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)),the_carrier(skolemFOFtoCNF_A_3)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)) )],[refute_1_21,refute_1_29]) ).
cnf(refute_1_31,plain,
( ~ antisymmetric_relstr(A)
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| element(skolemFOFtoCNF_C(A,B),the_carrier(A)) ),
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_32,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_3)
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),the_carrier(skolemFOFtoCNF_A_3)) ),
inference(subst,[],[refute_1_31:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_C_2))]]) ).
cnf(refute_1_33,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_3)
| ~ rel_str(skolemFOFtoCNF_A_3)
| element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),the_carrier(skolemFOFtoCNF_A_3)) ),
inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) )],[refute_1_8,refute_1_32]) ).
cnf(refute_1_34,plain,
( ~ rel_str(skolemFOFtoCNF_A_3)
| element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),the_carrier(skolemFOFtoCNF_A_3)) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_3) )],[refute_1_4,refute_1_33]) ).
cnf(refute_1_35,plain,
element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),the_carrier(skolemFOFtoCNF_A_3)),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_3) )],[refute_1_10,refute_1_34]) ).
cnf(refute_1_36,plain,
( ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2
| element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)),the_carrier(skolemFOFtoCNF_A_3)) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),the_carrier(skolemFOFtoCNF_A_3)) )],[refute_1_35,refute_1_30]) ).
cnf(refute_1_37,plain,
( ~ rel_str(skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2
| element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)),the_carrier(skolemFOFtoCNF_A_3)) ),
inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) )],[refute_1_8,refute_1_36]) ).
cnf(refute_1_38,plain,
( skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2
| element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)),the_carrier(skolemFOFtoCNF_A_3)) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_3) )],[refute_1_10,refute_1_37]) ).
cnf(refute_1_39,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_3)
| ~ element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)),the_carrier(skolemFOFtoCNF_A_3))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)))
| related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))) ),
inference(subst,[],[refute_1_1:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_C_2)),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))))]]) ).
cnf(refute_1_40,plain,
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B)
| relstr_set_smaller(A,B,skolemFOFtoCNF_D(A,B,C)) ),
inference(canonicalize,[],[normalize_1_25]) ).
cnf(refute_1_41,plain,
( ~ element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),the_carrier(skolemFOFtoCNF_A_3))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))) ),
inference(subst,[],[refute_1_40:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_C_2)),bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)))]]) ).
cnf(refute_1_42,plain,
( ~ element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),the_carrier(skolemFOFtoCNF_A_3))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))) ),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)) )],[refute_1_18,refute_1_41]) ).
cnf(refute_1_43,plain,
( ~ element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),the_carrier(skolemFOFtoCNF_A_3))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2
| relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)) )],[refute_1_42,refute_1_29]) ).
cnf(refute_1_44,plain,
( ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2
| relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),the_carrier(skolemFOFtoCNF_A_3)) )],[refute_1_35,refute_1_43]) ).
cnf(refute_1_45,plain,
( ~ rel_str(skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2
| relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))) ),
inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) )],[refute_1_8,refute_1_44]) ).
cnf(refute_1_46,plain,
( skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2
| relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_3) )],[refute_1_10,refute_1_45]) ).
cnf(refute_1_47,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_3)
| ~ element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)),the_carrier(skolemFOFtoCNF_A_3))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2
| related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))) ),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))) )],[refute_1_46,refute_1_39]) ).
cnf(refute_1_48,plain,
( ~ element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)),the_carrier(skolemFOFtoCNF_A_3))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2
| related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_3) )],[refute_1_4,refute_1_47]) ).
cnf(refute_1_49,plain,
( ~ element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)),the_carrier(skolemFOFtoCNF_A_3))
| ~ rel_str(skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2
| related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))) ),
inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) )],[refute_1_8,refute_1_48]) ).
cnf(refute_1_50,plain,
( ~ element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)),the_carrier(skolemFOFtoCNF_A_3))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2
| related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_3) )],[refute_1_10,refute_1_49]) ).
cnf(refute_1_51,plain,
( skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2
| related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)),the_carrier(skolemFOFtoCNF_A_3)) )],[refute_1_38,refute_1_50]) ).
cnf(refute_1_52,plain,
( ~ element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),the_carrier(skolemFOFtoCNF_A_3))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2 ),
inference(resolve,[$cnf( related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))) )],[refute_1_51,refute_1_13]) ).
cnf(refute_1_53,plain,
( ~ element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),the_carrier(skolemFOFtoCNF_A_3))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),join_on_relstr(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)) )],[refute_1_52,refute_1_29]) ).
cnf(refute_1_54,plain,
( ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)
| ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2 ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),the_carrier(skolemFOFtoCNF_A_3)) )],[refute_1_35,refute_1_53]) ).
cnf(refute_1_55,plain,
( ~ rel_str(skolemFOFtoCNF_A_3)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2 ),
inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) )],[refute_1_8,refute_1_54]) ).
cnf(refute_1_56,plain,
( ~ relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2))
| skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2 ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_3) )],[refute_1_10,refute_1_55]) ).
cnf(refute_1_57,plain,
skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) = skolemFOFtoCNF_B_2,
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2)) )],[refute_1_18,refute_1_56]) ).
cnf(refute_1_58,plain,
( skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) != skolemFOFtoCNF_B_2
| ~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D_2)
| related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2) ),
introduced(tautology,[equality,[$cnf( related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D_2) ),[1],$fot(skolemFOFtoCNF_B_2)]]) ).
cnf(refute_1_59,plain,
( ~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D_2)
| related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_B_2) )],[refute_1_57,refute_1_58]) ).
cnf(refute_1_60,plain,
related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2),
inference(resolve,[$cnf( related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2),skolemFOFtoCNF_D_2) )],[refute_1_11,refute_1_59]) ).
cnf(refute_1_61,plain,
~ related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2),
inference(canonicalize,[],[normalize_1_26]) ).
cnf(refute_1_62,plain,
$false,
inference(resolve,[$cnf( related(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_2) )],[refute_1_60,refute_1_61]) ).
fof(negate_2_0,plain,
~ ! [A] :
( ( antisymmetric_relstr(A)
& rel_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( ( ( ( B = join_on_relstr(A,C)
& ex_sup_of_relstr_set(A,C) )
=> ( relstr_set_smaller(A,C,B)
& ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) ) ) )
& relstr_set_smaller(A,C,B)
& ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) ) )
=> B = join_on_relstr(A,C) ) ) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ( C != join_on_relstr(A,B)
<=> ( ~ relstr_set_smaller(A,B,C)
| ? [D] :
( ~ related(A,C,D)
& element(D,the_carrier(A))
& relstr_set_smaller(A,B,D) ) ) ) ) ),
inference(canonicalize,[],[d9_yellow_0]) ).
fof(normalize_2_1,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ( C != join_on_relstr(A,B)
<=> ( ~ 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_2_0]) ).
fof(normalize_2_2,plain,
! [A,B,C,D] :
( ( C != join_on_relstr(A,B)
| ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| relstr_set_smaller(A,B,C) )
& ( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ related(A,C,skolemFOFtoCNF_D(A,B,C))
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B) )
& ( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B)
| element(skolemFOFtoCNF_D(A,B,C),the_carrier(A)) )
& ( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B)
| relstr_set_smaller(A,B,skolemFOFtoCNF_D(A,B,C)) )
& ( C != join_on_relstr(A,B)
| ~ element(C,the_carrier(A))
| ~ element(D,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,D)
| related(A,C,D) ) ),
inference(clausify,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
! [A,B,C] :
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ related(A,C,skolemFOFtoCNF_D(A,B,C))
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B) ),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_4,plain,
? [A] :
( antisymmetric_relstr(A)
& rel_str(A)
& ? [B] :
( element(B,the_carrier(A))
& ? [C] :
( B != join_on_relstr(A,C)
& relstr_set_smaller(A,C,B)
& ( B != join_on_relstr(A,C)
| ~ ex_sup_of_relstr_set(A,C)
| ( relstr_set_smaller(A,C,B)
& ! [D] :
( ~ element(D,the_carrier(A))
| ~ relstr_set_smaller(A,C,D)
| related(A,B,D) ) ) )
& ! [D] :
( ~ element(D,the_carrier(A))
| ~ relstr_set_smaller(A,C,D)
| related(A,B,D) ) ) ) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_5,plain,
( antisymmetric_relstr(skolemFOFtoCNF_A_4)
& rel_str(skolemFOFtoCNF_A_4)
& ? [B] :
( element(B,the_carrier(skolemFOFtoCNF_A_4))
& ? [C] :
( B != join_on_relstr(skolemFOFtoCNF_A_4,C)
& relstr_set_smaller(skolemFOFtoCNF_A_4,C,B)
& ( B != join_on_relstr(skolemFOFtoCNF_A_4,C)
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,C)
| ( relstr_set_smaller(skolemFOFtoCNF_A_4,C,B)
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_4))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,C,D)
| related(skolemFOFtoCNF_A_4,B,D) ) ) )
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_4))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,C,D)
| related(skolemFOFtoCNF_A_4,B,D) ) ) ) ),
inference(skolemize,[],[normalize_2_4]) ).
fof(normalize_2_6,plain,
? [B] :
( element(B,the_carrier(skolemFOFtoCNF_A_4))
& ? [C] :
( B != join_on_relstr(skolemFOFtoCNF_A_4,C)
& relstr_set_smaller(skolemFOFtoCNF_A_4,C,B)
& ( B != join_on_relstr(skolemFOFtoCNF_A_4,C)
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,C)
| ( relstr_set_smaller(skolemFOFtoCNF_A_4,C,B)
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_4))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,C,D)
| related(skolemFOFtoCNF_A_4,B,D) ) ) )
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_4))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,C,D)
| related(skolemFOFtoCNF_A_4,B,D) ) ) ),
inference(conjunct,[],[normalize_2_5]) ).
fof(normalize_2_7,plain,
( element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4))
& ? [C] :
( skolemFOFtoCNF_B_3 != join_on_relstr(skolemFOFtoCNF_A_4,C)
& relstr_set_smaller(skolemFOFtoCNF_A_4,C,skolemFOFtoCNF_B_3)
& ( skolemFOFtoCNF_B_3 != join_on_relstr(skolemFOFtoCNF_A_4,C)
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,C)
| ( relstr_set_smaller(skolemFOFtoCNF_A_4,C,skolemFOFtoCNF_B_3)
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_4))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,C,D)
| related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,D) ) ) )
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_4))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,C,D)
| related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,D) ) ) ),
inference(skolemize,[],[normalize_2_6]) ).
fof(normalize_2_8,plain,
? [C] :
( skolemFOFtoCNF_B_3 != join_on_relstr(skolemFOFtoCNF_A_4,C)
& relstr_set_smaller(skolemFOFtoCNF_A_4,C,skolemFOFtoCNF_B_3)
& ( skolemFOFtoCNF_B_3 != join_on_relstr(skolemFOFtoCNF_A_4,C)
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,C)
| ( relstr_set_smaller(skolemFOFtoCNF_A_4,C,skolemFOFtoCNF_B_3)
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_4))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,C,D)
| related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,D) ) ) )
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_4))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,C,D)
| related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,D) ) ),
inference(conjunct,[],[normalize_2_7]) ).
fof(normalize_2_9,plain,
( skolemFOFtoCNF_B_3 != join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
& relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
& ( skolemFOFtoCNF_B_3 != join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| ( relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_4))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,D)
| related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,D) ) ) )
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_4))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,D)
| related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,D) ) ),
inference(skolemize,[],[normalize_2_8]) ).
fof(normalize_2_10,plain,
! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_4))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,D)
| related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,D) ),
inference(conjunct,[],[normalize_2_9]) ).
fof(normalize_2_11,plain,
! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_4))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,D)
| related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,D) ),
inference(specialize,[],[normalize_2_10]) ).
fof(normalize_2_12,plain,
relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),
inference(conjunct,[],[normalize_2_9]) ).
fof(normalize_2_13,plain,
! [A,B,C] :
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B)
| relstr_set_smaller(A,B,skolemFOFtoCNF_D(A,B,C)) ),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_14,plain,
element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4)),
inference(conjunct,[],[normalize_2_7]) ).
fof(normalize_2_15,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_2_16,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_2_15]) ).
fof(normalize_2_17,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_2_16]) ).
fof(normalize_2_18,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_2_17]) ).
fof(normalize_2_19,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_2_17]) ).
fof(normalize_2_20,plain,
antisymmetric_relstr(skolemFOFtoCNF_A_4),
inference(conjunct,[],[normalize_2_5]) ).
fof(normalize_2_21,plain,
rel_str(skolemFOFtoCNF_A_4),
inference(conjunct,[],[normalize_2_5]) ).
fof(normalize_2_22,plain,
! [A,B,C] :
( ~ 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)) ),
inference(conjunct,[],[normalize_2_17]) ).
fof(normalize_2_23,plain,
skolemFOFtoCNF_B_3 != join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3),
inference(conjunct,[],[normalize_2_9]) ).
fof(normalize_2_24,plain,
! [A,B,C] :
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B)
| element(skolemFOFtoCNF_D(A,B,C),the_carrier(A)) ),
inference(conjunct,[],[normalize_2_2]) ).
cnf(refute_2_0,plain,
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ related(A,C,skolemFOFtoCNF_D(A,B,C))
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B) ),
inference(canonicalize,[],[normalize_2_3]) ).
cnf(refute_2_1,plain,
( ~ element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| ~ rel_str(skolemFOFtoCNF_A_4)
| ~ related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_B_3 = join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) ),
inference(subst,[],[refute_2_0:[bind(A,$fot(skolemFOFtoCNF_A_4)),bind(B,$fot(skolemFOFtoCNF_C_3)),bind(C,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_2_2,plain,
( ~ element(D,the_carrier(skolemFOFtoCNF_A_4))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,D)
| related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,D) ),
inference(canonicalize,[],[normalize_2_11]) ).
cnf(refute_2_3,plain,
( ~ element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),the_carrier(skolemFOFtoCNF_A_4))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3))
| related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_2_2:[bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_2_4,plain,
relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),
inference(canonicalize,[],[normalize_2_12]) ).
cnf(refute_2_5,plain,
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B)
| relstr_set_smaller(A,B,skolemFOFtoCNF_D(A,B,C)) ),
inference(canonicalize,[],[normalize_2_13]) ).
cnf(refute_2_6,plain,
( ~ element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| ~ rel_str(skolemFOFtoCNF_A_4)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_B_3 = join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_2_5:[bind(A,$fot(skolemFOFtoCNF_A_4)),bind(B,$fot(skolemFOFtoCNF_C_3)),bind(C,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_2_7,plain,
( ~ element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| ~ rel_str(skolemFOFtoCNF_A_4)
| skolemFOFtoCNF_B_3 = join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3) )],[refute_2_4,refute_2_6]) ).
cnf(refute_2_8,plain,
element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4)),
inference(canonicalize,[],[normalize_2_14]) ).
cnf(refute_2_9,plain,
( ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| ~ rel_str(skolemFOFtoCNF_A_4)
| skolemFOFtoCNF_B_3 = join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4)) )],[refute_2_8,refute_2_7]) ).
cnf(refute_2_10,plain,
( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ related(A,C,skolemFOFtoCNF_D_1(A,B,C))
| ~ relstr_set_smaller(A,B,C)
| ex_sup_of_relstr_set(A,B) ),
inference(canonicalize,[],[normalize_2_18]) ).
cnf(refute_2_11,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_4)
| ~ element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4))
| ~ rel_str(skolemFOFtoCNF_A_4)
| ~ related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) ),
inference(subst,[],[refute_2_10:[bind(A,$fot(skolemFOFtoCNF_A_4)),bind(B,$fot(skolemFOFtoCNF_C_3)),bind(C,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_2_12,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_2_19]) ).
cnf(refute_2_13,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_4)
| ~ element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4))
| ~ rel_str(skolemFOFtoCNF_A_4)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
| element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),the_carrier(skolemFOFtoCNF_A_4))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) ),
inference(subst,[],[refute_2_12:[bind(A,$fot(skolemFOFtoCNF_A_4)),bind(B,$fot(skolemFOFtoCNF_C_3)),bind(C,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_2_14,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_4)
| ~ element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4))
| ~ rel_str(skolemFOFtoCNF_A_4)
| element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),the_carrier(skolemFOFtoCNF_A_4))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3) )],[refute_2_4,refute_2_13]) ).
cnf(refute_2_15,plain,
antisymmetric_relstr(skolemFOFtoCNF_A_4),
inference(canonicalize,[],[normalize_2_20]) ).
cnf(refute_2_16,plain,
( ~ element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4))
| ~ rel_str(skolemFOFtoCNF_A_4)
| element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),the_carrier(skolemFOFtoCNF_A_4))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_4) )],[refute_2_15,refute_2_14]) ).
cnf(refute_2_17,plain,
( ~ rel_str(skolemFOFtoCNF_A_4)
| element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),the_carrier(skolemFOFtoCNF_A_4))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4)) )],[refute_2_8,refute_2_16]) ).
cnf(refute_2_18,plain,
rel_str(skolemFOFtoCNF_A_4),
inference(canonicalize,[],[normalize_2_21]) ).
cnf(refute_2_19,plain,
( element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),the_carrier(skolemFOFtoCNF_A_4))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_4) )],[refute_2_18,refute_2_17]) ).
cnf(refute_2_20,plain,
( ~ element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),the_carrier(skolemFOFtoCNF_A_4))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3))
| related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_2_2:[bind(D,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_2_21,plain,
( ~ 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)) ),
inference(canonicalize,[],[normalize_2_22]) ).
cnf(refute_2_22,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_4)
| ~ element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4))
| ~ rel_str(skolemFOFtoCNF_A_4)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_2_21:[bind(A,$fot(skolemFOFtoCNF_A_4)),bind(B,$fot(skolemFOFtoCNF_C_3)),bind(C,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_2_23,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_4)
| ~ element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4))
| ~ rel_str(skolemFOFtoCNF_A_4)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3) )],[refute_2_4,refute_2_22]) ).
cnf(refute_2_24,plain,
( ~ element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4))
| ~ rel_str(skolemFOFtoCNF_A_4)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_4) )],[refute_2_15,refute_2_23]) ).
cnf(refute_2_25,plain,
( ~ rel_str(skolemFOFtoCNF_A_4)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4)) )],[refute_2_8,refute_2_24]) ).
cnf(refute_2_26,plain,
( ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_4) )],[refute_2_18,refute_2_25]) ).
cnf(refute_2_27,plain,
( ~ element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),the_carrier(skolemFOFtoCNF_A_4))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) )],[refute_2_26,refute_2_20]) ).
cnf(refute_2_28,plain,
( ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),the_carrier(skolemFOFtoCNF_A_4)) )],[refute_2_19,refute_2_27]) ).
cnf(refute_2_29,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_4)
| ~ element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4))
| ~ rel_str(skolemFOFtoCNF_A_4)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) )],[refute_2_28,refute_2_11]) ).
cnf(refute_2_30,plain,
( ~ element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4))
| ~ rel_str(skolemFOFtoCNF_A_4)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_4) )],[refute_2_15,refute_2_29]) ).
cnf(refute_2_31,plain,
( ~ rel_str(skolemFOFtoCNF_A_4)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4)) )],[refute_2_8,refute_2_30]) ).
cnf(refute_2_32,plain,
( ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_4) )],[refute_2_18,refute_2_31]) ).
cnf(refute_2_33,plain,
ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3) )],[refute_2_4,refute_2_32]) ).
cnf(refute_2_34,plain,
( ~ rel_str(skolemFOFtoCNF_A_4)
| skolemFOFtoCNF_B_3 = join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) )],[refute_2_33,refute_2_9]) ).
cnf(refute_2_35,plain,
( skolemFOFtoCNF_B_3 = join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_4) )],[refute_2_18,refute_2_34]) ).
cnf(refute_2_36,plain,
skolemFOFtoCNF_B_3 != join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3),
inference(canonicalize,[],[normalize_2_23]) ).
cnf(refute_2_37,plain,
relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_3,join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)) )],[refute_2_35,refute_2_36]) ).
cnf(refute_2_38,plain,
( ~ element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),the_carrier(skolemFOFtoCNF_A_4))
| related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) )],[refute_2_37,refute_2_3]) ).
cnf(refute_2_39,plain,
( ~ element(C,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| C = join_on_relstr(A,B)
| element(skolemFOFtoCNF_D(A,B,C),the_carrier(A)) ),
inference(canonicalize,[],[normalize_2_24]) ).
cnf(refute_2_40,plain,
( ~ element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| ~ rel_str(skolemFOFtoCNF_A_4)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_B_3 = join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),the_carrier(skolemFOFtoCNF_A_4)) ),
inference(subst,[],[refute_2_39:[bind(A,$fot(skolemFOFtoCNF_A_4)),bind(B,$fot(skolemFOFtoCNF_C_3)),bind(C,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_2_41,plain,
( ~ element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| ~ rel_str(skolemFOFtoCNF_A_4)
| skolemFOFtoCNF_B_3 = join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),the_carrier(skolemFOFtoCNF_A_4)) ),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3) )],[refute_2_4,refute_2_40]) ).
cnf(refute_2_42,plain,
( ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| ~ rel_str(skolemFOFtoCNF_A_4)
| skolemFOFtoCNF_B_3 = join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),the_carrier(skolemFOFtoCNF_A_4)) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4)) )],[refute_2_8,refute_2_41]) ).
cnf(refute_2_43,plain,
( ~ rel_str(skolemFOFtoCNF_A_4)
| skolemFOFtoCNF_B_3 = join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),the_carrier(skolemFOFtoCNF_A_4)) ),
inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) )],[refute_2_33,refute_2_42]) ).
cnf(refute_2_44,plain,
( skolemFOFtoCNF_B_3 = join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),the_carrier(skolemFOFtoCNF_A_4)) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_4) )],[refute_2_18,refute_2_43]) ).
cnf(refute_2_45,plain,
element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),the_carrier(skolemFOFtoCNF_A_4)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_3,join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)) )],[refute_2_44,refute_2_36]) ).
cnf(refute_2_46,plain,
related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)),
inference(resolve,[$cnf( element(skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3),the_carrier(skolemFOFtoCNF_A_4)) )],[refute_2_45,refute_2_38]) ).
cnf(refute_2_47,plain,
( ~ element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4))
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| ~ rel_str(skolemFOFtoCNF_A_4)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_B_3 = join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( related(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_3,skolemFOFtoCNF_D(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)) )],[refute_2_46,refute_2_1]) ).
cnf(refute_2_48,plain,
( ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)
| ~ rel_str(skolemFOFtoCNF_A_4)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_B_3 = join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_3,the_carrier(skolemFOFtoCNF_A_4)) )],[refute_2_8,refute_2_47]) ).
cnf(refute_2_49,plain,
( ~ rel_str(skolemFOFtoCNF_A_4)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_B_3 = join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) )],[refute_2_33,refute_2_48]) ).
cnf(refute_2_50,plain,
( ~ relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3)
| skolemFOFtoCNF_B_3 = join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_4) )],[refute_2_18,refute_2_49]) ).
cnf(refute_2_51,plain,
skolemFOFtoCNF_B_3 = join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3,skolemFOFtoCNF_B_3) )],[refute_2_4,refute_2_50]) ).
cnf(refute_2_52,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_3,join_on_relstr(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3)) )],[refute_2_51,refute_2_36]) ).
fof(negate_3_0,plain,
~ ! [A] :
( ( antisymmetric_relstr(A)
& rel_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( ( ( ( B = join_on_relstr(A,C)
& ex_sup_of_relstr_set(A,C) )
=> ( relstr_set_smaller(A,C,B)
& ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) ) ) )
& relstr_set_smaller(A,C,B)
& ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) )
& B = join_on_relstr(A,C) )
=> ex_sup_of_relstr_set(A,C) ) ) ),
inference(negate,[],[subgoal_3]) ).
fof(normalize_3_0,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_3_1,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_3_0]) ).
fof(normalize_3_2,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_3_1]) ).
fof(normalize_3_3,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_3_2]) ).
fof(normalize_3_4,plain,
? [A] :
( antisymmetric_relstr(A)
& rel_str(A)
& ? [B] :
( element(B,the_carrier(A))
& ? [C] :
( ~ ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C)
& relstr_set_smaller(A,C,B)
& ( B != join_on_relstr(A,C)
| ~ ex_sup_of_relstr_set(A,C)
| ( relstr_set_smaller(A,C,B)
& ! [D] :
( ~ element(D,the_carrier(A))
| ~ relstr_set_smaller(A,C,D)
| related(A,B,D) ) ) )
& ! [D] :
( ~ element(D,the_carrier(A))
| ~ relstr_set_smaller(A,C,D)
| related(A,B,D) ) ) ) ),
inference(canonicalize,[],[negate_3_0]) ).
fof(normalize_3_5,plain,
( antisymmetric_relstr(skolemFOFtoCNF_A_5)
& rel_str(skolemFOFtoCNF_A_5)
& ? [B] :
( element(B,the_carrier(skolemFOFtoCNF_A_5))
& ? [C] :
( ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,C)
& B = join_on_relstr(skolemFOFtoCNF_A_5,C)
& relstr_set_smaller(skolemFOFtoCNF_A_5,C,B)
& ( B != join_on_relstr(skolemFOFtoCNF_A_5,C)
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,C)
| ( relstr_set_smaller(skolemFOFtoCNF_A_5,C,B)
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_5))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,C,D)
| related(skolemFOFtoCNF_A_5,B,D) ) ) )
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_5))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,C,D)
| related(skolemFOFtoCNF_A_5,B,D) ) ) ) ),
inference(skolemize,[],[normalize_3_4]) ).
fof(normalize_3_6,plain,
? [B] :
( element(B,the_carrier(skolemFOFtoCNF_A_5))
& ? [C] :
( ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,C)
& B = join_on_relstr(skolemFOFtoCNF_A_5,C)
& relstr_set_smaller(skolemFOFtoCNF_A_5,C,B)
& ( B != join_on_relstr(skolemFOFtoCNF_A_5,C)
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,C)
| ( relstr_set_smaller(skolemFOFtoCNF_A_5,C,B)
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_5))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,C,D)
| related(skolemFOFtoCNF_A_5,B,D) ) ) )
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_5))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,C,D)
| related(skolemFOFtoCNF_A_5,B,D) ) ) ),
inference(conjunct,[],[normalize_3_5]) ).
fof(normalize_3_7,plain,
( element(skolemFOFtoCNF_B_4,the_carrier(skolemFOFtoCNF_A_5))
& ? [C] :
( ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,C)
& skolemFOFtoCNF_B_4 = join_on_relstr(skolemFOFtoCNF_A_5,C)
& relstr_set_smaller(skolemFOFtoCNF_A_5,C,skolemFOFtoCNF_B_4)
& ( skolemFOFtoCNF_B_4 != join_on_relstr(skolemFOFtoCNF_A_5,C)
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,C)
| ( relstr_set_smaller(skolemFOFtoCNF_A_5,C,skolemFOFtoCNF_B_4)
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_5))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,C,D)
| related(skolemFOFtoCNF_A_5,skolemFOFtoCNF_B_4,D) ) ) )
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_5))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,C,D)
| related(skolemFOFtoCNF_A_5,skolemFOFtoCNF_B_4,D) ) ) ),
inference(skolemize,[],[normalize_3_6]) ).
fof(normalize_3_8,plain,
? [C] :
( ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,C)
& skolemFOFtoCNF_B_4 = join_on_relstr(skolemFOFtoCNF_A_5,C)
& relstr_set_smaller(skolemFOFtoCNF_A_5,C,skolemFOFtoCNF_B_4)
& ( skolemFOFtoCNF_B_4 != join_on_relstr(skolemFOFtoCNF_A_5,C)
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,C)
| ( relstr_set_smaller(skolemFOFtoCNF_A_5,C,skolemFOFtoCNF_B_4)
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_5))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,C,D)
| related(skolemFOFtoCNF_A_5,skolemFOFtoCNF_B_4,D) ) ) )
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_5))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,C,D)
| related(skolemFOFtoCNF_A_5,skolemFOFtoCNF_B_4,D) ) ),
inference(conjunct,[],[normalize_3_7]) ).
fof(normalize_3_9,plain,
( ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4)
& skolemFOFtoCNF_B_4 = join_on_relstr(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4)
& relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)
& ( skolemFOFtoCNF_B_4 != join_on_relstr(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4)
| ~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4)
| ( relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_5))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,D)
| related(skolemFOFtoCNF_A_5,skolemFOFtoCNF_B_4,D) ) ) )
& ! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_5))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,D)
| related(skolemFOFtoCNF_A_5,skolemFOFtoCNF_B_4,D) ) ),
inference(skolemize,[],[normalize_3_8]) ).
fof(normalize_3_10,plain,
! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_5))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,D)
| related(skolemFOFtoCNF_A_5,skolemFOFtoCNF_B_4,D) ),
inference(conjunct,[],[normalize_3_9]) ).
fof(normalize_3_11,plain,
! [D] :
( ~ element(D,the_carrier(skolemFOFtoCNF_A_5))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,D)
| related(skolemFOFtoCNF_A_5,skolemFOFtoCNF_B_4,D) ),
inference(specialize,[],[normalize_3_10]) ).
fof(normalize_3_12,plain,
relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4),
inference(conjunct,[],[normalize_3_9]) ).
fof(normalize_3_13,plain,
! [A,B,C] :
( ~ 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)) ),
inference(conjunct,[],[normalize_3_2]) ).
fof(normalize_3_14,plain,
antisymmetric_relstr(skolemFOFtoCNF_A_5),
inference(conjunct,[],[normalize_3_5]) ).
fof(normalize_3_15,plain,
element(skolemFOFtoCNF_B_4,the_carrier(skolemFOFtoCNF_A_5)),
inference(conjunct,[],[normalize_3_7]) ).
fof(normalize_3_16,plain,
rel_str(skolemFOFtoCNF_A_5),
inference(conjunct,[],[normalize_3_5]) ).
fof(normalize_3_17,plain,
~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4),
inference(conjunct,[],[normalize_3_9]) ).
fof(normalize_3_18,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_3_2]) ).
cnf(refute_3_0,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_3_3]) ).
cnf(refute_3_1,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_5)
| ~ element(skolemFOFtoCNF_B_4,the_carrier(skolemFOFtoCNF_A_5))
| ~ rel_str(skolemFOFtoCNF_A_5)
| ~ related(skolemFOFtoCNF_A_5,skolemFOFtoCNF_B_4,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_3_0:[bind(A,$fot(skolemFOFtoCNF_A_5)),bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_4))]]) ).
cnf(refute_3_2,plain,
( ~ element(D,the_carrier(skolemFOFtoCNF_A_5))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,D)
| related(skolemFOFtoCNF_A_5,skolemFOFtoCNF_B_4,D) ),
inference(canonicalize,[],[normalize_3_11]) ).
cnf(refute_3_3,plain,
( ~ element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4),the_carrier(skolemFOFtoCNF_A_5))
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4))
| related(skolemFOFtoCNF_A_5,skolemFOFtoCNF_B_4,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)) ),
inference(subst,[],[refute_3_2:[bind(D,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)))]]) ).
cnf(refute_3_4,plain,
relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4),
inference(canonicalize,[],[normalize_3_12]) ).
cnf(refute_3_5,plain,
( ~ antisymmetric_relstr(A)
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| ex_sup_of_relstr_set(A,B)
| relstr_set_smaller(A,B,skolemFOFtoCNF_D_1(A,B,C)) ),
inference(canonicalize,[],[normalize_3_13]) ).
cnf(refute_3_6,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_5)
| ~ element(skolemFOFtoCNF_B_4,the_carrier(skolemFOFtoCNF_A_5))
| ~ rel_str(skolemFOFtoCNF_A_5)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4)
| relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)) ),
inference(subst,[],[refute_3_5:[bind(A,$fot(skolemFOFtoCNF_A_5)),bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_4))]]) ).
cnf(refute_3_7,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_5)
| ~ element(skolemFOFtoCNF_B_4,the_carrier(skolemFOFtoCNF_A_5))
| ~ rel_str(skolemFOFtoCNF_A_5)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4)
| relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)) ),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4) )],[refute_3_4,refute_3_6]) ).
cnf(refute_3_8,plain,
antisymmetric_relstr(skolemFOFtoCNF_A_5),
inference(canonicalize,[],[normalize_3_14]) ).
cnf(refute_3_9,plain,
( ~ element(skolemFOFtoCNF_B_4,the_carrier(skolemFOFtoCNF_A_5))
| ~ rel_str(skolemFOFtoCNF_A_5)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4)
| relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_5) )],[refute_3_8,refute_3_7]) ).
cnf(refute_3_10,plain,
element(skolemFOFtoCNF_B_4,the_carrier(skolemFOFtoCNF_A_5)),
inference(canonicalize,[],[normalize_3_15]) ).
cnf(refute_3_11,plain,
( ~ rel_str(skolemFOFtoCNF_A_5)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4)
| relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_4,the_carrier(skolemFOFtoCNF_A_5)) )],[refute_3_10,refute_3_9]) ).
cnf(refute_3_12,plain,
rel_str(skolemFOFtoCNF_A_5),
inference(canonicalize,[],[normalize_3_16]) ).
cnf(refute_3_13,plain,
( ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4)
| relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_5) )],[refute_3_12,refute_3_11]) ).
cnf(refute_3_14,plain,
~ ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4),
inference(canonicalize,[],[normalize_3_17]) ).
cnf(refute_3_15,plain,
relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)),
inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4) )],[refute_3_13,refute_3_14]) ).
cnf(refute_3_16,plain,
( ~ element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4),the_carrier(skolemFOFtoCNF_A_5))
| related(skolemFOFtoCNF_A_5,skolemFOFtoCNF_B_4,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)) ),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)) )],[refute_3_15,refute_3_3]) ).
cnf(refute_3_17,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_3_18]) ).
cnf(refute_3_18,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_5)
| ~ element(skolemFOFtoCNF_B_4,the_carrier(skolemFOFtoCNF_A_5))
| ~ rel_str(skolemFOFtoCNF_A_5)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)
| element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4),the_carrier(skolemFOFtoCNF_A_5))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_3_17:[bind(A,$fot(skolemFOFtoCNF_A_5)),bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_4))]]) ).
cnf(refute_3_19,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_5)
| ~ element(skolemFOFtoCNF_B_4,the_carrier(skolemFOFtoCNF_A_5))
| ~ rel_str(skolemFOFtoCNF_A_5)
| element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4),the_carrier(skolemFOFtoCNF_A_5))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4) )],[refute_3_4,refute_3_18]) ).
cnf(refute_3_20,plain,
( ~ element(skolemFOFtoCNF_B_4,the_carrier(skolemFOFtoCNF_A_5))
| ~ rel_str(skolemFOFtoCNF_A_5)
| element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4),the_carrier(skolemFOFtoCNF_A_5))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_5) )],[refute_3_8,refute_3_19]) ).
cnf(refute_3_21,plain,
( ~ rel_str(skolemFOFtoCNF_A_5)
| element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4),the_carrier(skolemFOFtoCNF_A_5))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_4,the_carrier(skolemFOFtoCNF_A_5)) )],[refute_3_10,refute_3_20]) ).
cnf(refute_3_22,plain,
( element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4),the_carrier(skolemFOFtoCNF_A_5))
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_5) )],[refute_3_12,refute_3_21]) ).
cnf(refute_3_23,plain,
element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4),the_carrier(skolemFOFtoCNF_A_5)),
inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4) )],[refute_3_22,refute_3_14]) ).
cnf(refute_3_24,plain,
related(skolemFOFtoCNF_A_5,skolemFOFtoCNF_B_4,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)),
inference(resolve,[$cnf( element(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4),the_carrier(skolemFOFtoCNF_A_5)) )],[refute_3_23,refute_3_16]) ).
cnf(refute_3_25,plain,
( ~ antisymmetric_relstr(skolemFOFtoCNF_A_5)
| ~ element(skolemFOFtoCNF_B_4,the_carrier(skolemFOFtoCNF_A_5))
| ~ rel_str(skolemFOFtoCNF_A_5)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( related(skolemFOFtoCNF_A_5,skolemFOFtoCNF_B_4,skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)) )],[refute_3_24,refute_3_1]) ).
cnf(refute_3_26,plain,
( ~ element(skolemFOFtoCNF_B_4,the_carrier(skolemFOFtoCNF_A_5))
| ~ rel_str(skolemFOFtoCNF_A_5)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( antisymmetric_relstr(skolemFOFtoCNF_A_5) )],[refute_3_8,refute_3_25]) ).
cnf(refute_3_27,plain,
( ~ rel_str(skolemFOFtoCNF_A_5)
| ~ relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_4,the_carrier(skolemFOFtoCNF_A_5)) )],[refute_3_10,refute_3_26]) ).
cnf(refute_3_28,plain,
( ~ relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4)
| ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_5) )],[refute_3_12,refute_3_27]) ).
cnf(refute_3_29,plain,
ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4),
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_4) )],[refute_3_4,refute_3_28]) ).
cnf(refute_3_30,plain,
$false,
inference(resolve,[$cnf( ex_sup_of_relstr_set(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C_4) )],[refute_3_29,refute_3_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : SEU359+1 : TPTP v8.1.0. Released v3.3.0.
% 0.14/0.15 % Command : metis --show proof --show saturation %s
% 0.14/0.37 % Computer : n013.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 600
% 0.14/0.37 % DateTime : Sun Jun 19 09:32:29 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.14/0.38 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.43
% 0.14/0.43 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.22/0.48
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