TSTP Solution File: NUM394+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM394+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 : Mon Jul 18 12:26:23 EDT 2022
% Result : Theorem 3.24s 3.50s
% Output : CNFRefutation 3.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 21
% Syntax : Number of formulae : 130 ( 26 unt; 0 def)
% Number of atoms : 334 ( 50 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 363 ( 159 ~; 157 |; 26 &)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 121 ( 6 sgn 81 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ) ).
fof(connectedness_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
| ordinal_subset(B,A) ) ) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ) ).
fof(redefinition_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ) ).
fof(reflexivity_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ordinal_subset(A,A) ) ).
fof(t24_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(A,B)
& A != B
& ~ in(B,A) ) ) ) ).
fof(t26_ordinal1,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( ordinal_subset(A,B)
| in(B,A) ) ) ) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( in(A,B)
& element(B,powerset(C))
& empty(C) ) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ) ).
fof(subgoal_0,plain,
! [A] :
( ordinal(A)
=> ! [B] :
( ( ordinal(B)
& ~ ordinal_subset(A,B) )
=> in(B,A) ) ),
inference(strip,[],[t26_ordinal1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ( ordinal(B)
& ~ ordinal_subset(A,B) )
=> in(B,A) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] :
( ordinal(A)
& ? [B] :
( ~ in(B,A)
& ~ ordinal_subset(A,B)
& ordinal(B) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ordinal(skolemFOFtoCNF_A_11)
& ? [B] :
( ~ in(B,skolemFOFtoCNF_A_11)
& ~ ordinal_subset(skolemFOFtoCNF_A_11,B)
& ordinal(B) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [B] :
( ~ in(B,skolemFOFtoCNF_A_11)
& ~ ordinal_subset(skolemFOFtoCNF_A_11,B)
& ordinal(B) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ~ in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11)
& ~ ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2)
& ordinal(skolemFOFtoCNF_B_2) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
~ ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
ordinal(skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_6,plain,
! [A] :
( ~ ordinal(A)
| ordinal_subset(A,A)
| ! [B] : ~ ordinal(B) ),
inference(canonicalize,[],[reflexivity_r1_ordinal1]) ).
fof(normalize_0_7,plain,
! [A] :
( ~ ordinal(A)
| ordinal_subset(A,A)
| ! [B] : ~ ordinal(B) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ordinal_subset(A,A) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[t6_boole]) ).
fof(normalize_0_10,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(canonicalize,[],[t2_subset]) ).
fof(normalize_0_12,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B] :
( ~ element(A,powerset(B))
<=> ~ subset(A,B) ),
inference(canonicalize,[],[t3_subset]) ).
fof(normalize_0_14,plain,
! [A,B] :
( ~ element(A,powerset(B))
<=> ~ subset(A,B) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B] :
( ( ~ element(A,powerset(B))
| subset(A,B) )
& ( ~ subset(A,B)
| element(A,powerset(B)) ) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
ordinal(skolemFOFtoCNF_A_11),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_18,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ordinal_subset(A,B)
| ordinal_subset(B,A) ),
inference(canonicalize,[],[connectedness_r1_ordinal1]) ).
fof(normalize_0_19,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ordinal_subset(A,B)
| ordinal_subset(B,A) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ( ~ ordinal_subset(A,B)
<=> ~ subset(A,B) ) ),
inference(canonicalize,[],[redefinition_r1_ordinal1]) ).
fof(normalize_0_21,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ( ~ ordinal_subset(A,B)
<=> ~ subset(A,B) ) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [A,B] :
( ( ~ ordinal(A)
| ~ ordinal(B)
| ~ ordinal_subset(A,B)
| subset(A,B) )
& ( ~ ordinal(A)
| ~ ordinal(B)
| ~ subset(A,B)
| ordinal_subset(A,B) ) ),
inference(clausify,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| ~ ordinal_subset(A,B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [A,B,C] :
( ~ element(B,powerset(C))
| ~ in(A,B)
| element(A,C) ),
inference(canonicalize,[],[t4_subset]) ).
fof(normalize_0_25,plain,
! [A,B,C] :
( ~ element(B,powerset(C))
| ~ in(A,B)
| element(A,C) ),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [A] :
( ~ ordinal(A)
| ! [B] :
( ~ ordinal(B)
| A = B
| in(A,B)
| in(B,A) ) ),
inference(canonicalize,[],[t24_ordinal1]) ).
fof(normalize_0_27,plain,
! [A] :
( ~ ordinal(A)
| ! [B] :
( ~ ordinal(B)
| A = B
| in(A,B)
| in(B,A) ) ),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [A,B] :
( ~ ordinal(A)
| ~ ordinal(B)
| A = B
| in(A,B)
| in(B,A) ),
inference(clausify,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
~ in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_30,plain,
! [A,B] :
( ~ in(A,B)
| ~ in(B,A) ),
inference(canonicalize,[],[antisymmetry_r2_hidden]) ).
fof(normalize_0_31,plain,
! [A,B] :
( ~ in(A,B)
| ~ in(B,A) ),
inference(specialize,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [A,B,C] :
( ~ element(B,powerset(C))
| ~ empty(C)
| ~ in(A,B) ),
inference(canonicalize,[],[t5_subset]) ).
fof(normalize_0_33,plain,
! [A,B,C] :
( ~ element(B,powerset(C))
| ~ empty(C)
| ~ in(A,B) ),
inference(specialize,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
inference(canonicalize,[],[fc12_relat_1]) ).
fof(normalize_0_35,plain,
empty(empty_set),
inference(conjunct,[],[normalize_0_34]) ).
cnf(refute_0_0,plain,
~ ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
ordinal(skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ ordinal(A)
| ~ ordinal(B)
| ordinal_subset(A,A) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_3,plain,
( ~ ordinal(skolemFOFtoCNF_B_2)
| ordinal_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_B_2)),bind(B,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_0_4,plain,
ordinal_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_B_2),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_B_2) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
( ~ empty(skolemFOFtoCNF_A_11)
| skolemFOFtoCNF_A_11 = empty_set ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_A_11))]]) ).
cnf(refute_0_7,plain,
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_8,plain,
( ~ element(skolemFOFtoCNF_A_11,skolemFOFtoCNF_A_11)
| empty(skolemFOFtoCNF_A_11)
| in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_A_11) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_A_11)),bind(B,$fot(skolemFOFtoCNF_A_11))]]) ).
cnf(refute_0_9,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_10,plain,
( ~ subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11)
| element(skolemFOFtoCNF_B_2,powerset(skolemFOFtoCNF_A_11)) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(skolemFOFtoCNF_B_2)),bind(B,$fot(skolemFOFtoCNF_A_11))]]) ).
cnf(refute_0_11,plain,
ordinal(skolemFOFtoCNF_A_11),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_12,plain,
( ~ ordinal(A)
| ~ ordinal(B)
| ordinal_subset(A,B)
| ordinal_subset(B,A) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_13,plain,
( ~ ordinal(X_56)
| ~ ordinal(skolemFOFtoCNF_A_11)
| ordinal_subset(X_56,skolemFOFtoCNF_A_11)
| ordinal_subset(skolemFOFtoCNF_A_11,X_56) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_A_11)),bind(B,$fot(X_56))]]) ).
cnf(refute_0_14,plain,
( ~ ordinal(X_56)
| ordinal_subset(X_56,skolemFOFtoCNF_A_11)
| ordinal_subset(skolemFOFtoCNF_A_11,X_56) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_A_11) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ ordinal(skolemFOFtoCNF_B_2)
| ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2)
| ordinal_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11) ),
inference(subst,[],[refute_0_14:[bind(X_56,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_0_16,plain,
( ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2)
| ordinal_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_B_2) )],[refute_0_1,refute_0_15]) ).
cnf(refute_0_17,plain,
ordinal_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11),
inference(resolve,[$cnf( ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) )],[refute_0_16,refute_0_0]) ).
cnf(refute_0_18,plain,
( ~ ordinal(A)
| ~ ordinal(B)
| ~ ordinal_subset(A,B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_19,plain,
( ~ ordinal(skolemFOFtoCNF_A_11)
| ~ ordinal(skolemFOFtoCNF_B_2)
| ~ ordinal_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11)
| subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11) ),
inference(subst,[],[refute_0_18:[bind(A,$fot(skolemFOFtoCNF_B_2)),bind(B,$fot(skolemFOFtoCNF_A_11))]]) ).
cnf(refute_0_20,plain,
( ~ ordinal(skolemFOFtoCNF_A_11)
| ~ ordinal(skolemFOFtoCNF_B_2)
| subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11) ),
inference(resolve,[$cnf( ordinal_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ ordinal(skolemFOFtoCNF_B_2)
| subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_A_11) )],[refute_0_11,refute_0_20]) ).
cnf(refute_0_22,plain,
subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_B_2) )],[refute_0_1,refute_0_21]) ).
cnf(refute_0_23,plain,
element(skolemFOFtoCNF_B_2,powerset(skolemFOFtoCNF_A_11)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11) )],[refute_0_22,refute_0_10]) ).
cnf(refute_0_24,plain,
( ~ element(B,powerset(C))
| ~ in(A,B)
| element(A,C) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_25,plain,
( ~ element(skolemFOFtoCNF_B_2,powerset(skolemFOFtoCNF_A_11))
| ~ in(X_68,skolemFOFtoCNF_B_2)
| element(X_68,skolemFOFtoCNF_A_11) ),
inference(subst,[],[refute_0_24:[bind(A,$fot(X_68)),bind(B,$fot(skolemFOFtoCNF_B_2)),bind(C,$fot(skolemFOFtoCNF_A_11))]]) ).
cnf(refute_0_26,plain,
( ~ in(X_68,skolemFOFtoCNF_B_2)
| element(X_68,skolemFOFtoCNF_A_11) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_2,powerset(skolemFOFtoCNF_A_11)) )],[refute_0_23,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2)
| element(skolemFOFtoCNF_A_11,skolemFOFtoCNF_A_11) ),
inference(subst,[],[refute_0_26:[bind(X_68,$fot(skolemFOFtoCNF_A_11))]]) ).
cnf(refute_0_28,plain,
( ~ ordinal(A)
| ~ ordinal(B)
| A = B
| in(A,B)
| in(B,A) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_29,plain,
( ~ ordinal(X_110)
| ~ ordinal(skolemFOFtoCNF_A_11)
| skolemFOFtoCNF_A_11 = X_110
| in(X_110,skolemFOFtoCNF_A_11)
| in(skolemFOFtoCNF_A_11,X_110) ),
inference(subst,[],[refute_0_28:[bind(A,$fot(skolemFOFtoCNF_A_11)),bind(B,$fot(X_110))]]) ).
cnf(refute_0_30,plain,
( ~ ordinal(X_110)
| skolemFOFtoCNF_A_11 = X_110
| in(X_110,skolemFOFtoCNF_A_11)
| in(skolemFOFtoCNF_A_11,X_110) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_A_11) )],[refute_0_11,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ ordinal(skolemFOFtoCNF_B_2)
| skolemFOFtoCNF_A_11 = skolemFOFtoCNF_B_2
| in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2)
| in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11) ),
inference(subst,[],[refute_0_30:[bind(X_110,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_0_32,plain,
( skolemFOFtoCNF_A_11 = skolemFOFtoCNF_B_2
| in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2)
| in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_B_2) )],[refute_0_1,refute_0_31]) ).
cnf(refute_0_33,plain,
~ in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_34,plain,
( skolemFOFtoCNF_A_11 = skolemFOFtoCNF_B_2
| in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( skolemFOFtoCNF_A_11 = skolemFOFtoCNF_B_2
| element(skolemFOFtoCNF_A_11,skolemFOFtoCNF_A_11) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) )],[refute_0_34,refute_0_27]) ).
cnf(refute_0_36,plain,
( skolemFOFtoCNF_A_11 = skolemFOFtoCNF_B_2
| empty(skolemFOFtoCNF_A_11)
| in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_A_11) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_A_11,skolemFOFtoCNF_A_11) )],[refute_0_35,refute_0_8]) ).
cnf(refute_0_37,plain,
( ~ in(A,B)
| ~ in(B,A) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_38,plain,
~ in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_A_11),
inference(subst,[],[refute_0_37:[bind(A,$fot(skolemFOFtoCNF_A_11)),bind(B,$fot(skolemFOFtoCNF_A_11))]]) ).
cnf(refute_0_39,plain,
( skolemFOFtoCNF_A_11 = skolemFOFtoCNF_B_2
| empty(skolemFOFtoCNF_A_11) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_A_11) )],[refute_0_36,refute_0_38]) ).
cnf(refute_0_40,plain,
( skolemFOFtoCNF_A_11 = empty_set
| skolemFOFtoCNF_A_11 = skolemFOFtoCNF_B_2 ),
inference(resolve,[$cnf( empty(skolemFOFtoCNF_A_11) )],[refute_0_39,refute_0_6]) ).
cnf(refute_0_41,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_42,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_43,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( skolemFOFtoCNF_A_11 != skolemFOFtoCNF_B_2
| skolemFOFtoCNF_B_2 = skolemFOFtoCNF_A_11 ),
inference(subst,[],[refute_0_43:[bind(X,$fot(skolemFOFtoCNF_A_11)),bind(Y,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_0_45,plain,
( skolemFOFtoCNF_A_11 = empty_set
| skolemFOFtoCNF_B_2 = skolemFOFtoCNF_A_11 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) )],[refute_0_40,refute_0_44]) ).
cnf(refute_0_46,plain,
( skolemFOFtoCNF_B_2 != skolemFOFtoCNF_A_11
| ~ ordinal_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_B_2)
| ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ),
introduced(tautology,[equality,[$cnf( ordinal_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_B_2) ),[0],$fot(skolemFOFtoCNF_A_11)]]) ).
cnf(refute_0_47,plain,
( ~ ordinal_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_B_2)
| skolemFOFtoCNF_A_11 = empty_set
| ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( skolemFOFtoCNF_A_11 = empty_set
| ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( ordinal_subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_B_2) )],[refute_0_4,refute_0_47]) ).
cnf(refute_0_49,plain,
skolemFOFtoCNF_A_11 = empty_set,
inference(resolve,[$cnf( ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) )],[refute_0_48,refute_0_0]) ).
cnf(refute_0_50,plain,
( skolemFOFtoCNF_A_11 != empty_set
| ~ ordinal_subset(empty_set,skolemFOFtoCNF_B_2)
| ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ),
introduced(tautology,[equality,[$cnf( ~ ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_51,plain,
( ~ ordinal_subset(empty_set,skolemFOFtoCNF_B_2)
| ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_11,empty_set) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
~ ordinal_subset(empty_set,skolemFOFtoCNF_B_2),
inference(resolve,[$cnf( ordinal_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) )],[refute_0_51,refute_0_0]) ).
cnf(refute_0_53,plain,
( skolemFOFtoCNF_A_11 != empty_set
| skolemFOFtoCNF_A_11 != skolemFOFtoCNF_B_2
| empty_set = skolemFOFtoCNF_B_2 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_54,plain,
( skolemFOFtoCNF_A_11 != skolemFOFtoCNF_B_2
| empty_set = skolemFOFtoCNF_B_2 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_11,empty_set) )],[refute_0_49,refute_0_53]) ).
cnf(refute_0_55,plain,
( empty_set = skolemFOFtoCNF_B_2
| in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) )],[refute_0_34,refute_0_54]) ).
cnf(refute_0_56,plain,
( skolemFOFtoCNF_A_11 != empty_set
| ~ in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2)
| in(empty_set,skolemFOFtoCNF_B_2) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_57,plain,
( ~ in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2)
| in(empty_set,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_11,empty_set) )],[refute_0_49,refute_0_56]) ).
cnf(refute_0_58,plain,
( empty_set = skolemFOFtoCNF_B_2
| in(empty_set,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) )],[refute_0_55,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ element(B,powerset(C))
| ~ empty(C)
| ~ in(A,B) ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_60,plain,
( ~ element(skolemFOFtoCNF_B_2,powerset(skolemFOFtoCNF_A_11))
| ~ empty(skolemFOFtoCNF_A_11)
| ~ in(A,skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_0_59:[bind(B,$fot(skolemFOFtoCNF_B_2)),bind(C,$fot(skolemFOFtoCNF_A_11))]]) ).
cnf(refute_0_61,plain,
( ~ empty(skolemFOFtoCNF_A_11)
| ~ in(A,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_2,powerset(skolemFOFtoCNF_A_11)) )],[refute_0_23,refute_0_60]) ).
cnf(refute_0_62,plain,
( skolemFOFtoCNF_A_11 != empty_set
| ~ empty(empty_set)
| empty(skolemFOFtoCNF_A_11) ),
introduced(tautology,[equality,[$cnf( ~ empty(skolemFOFtoCNF_A_11) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_63,plain,
( ~ empty(empty_set)
| empty(skolemFOFtoCNF_A_11) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_11,empty_set) )],[refute_0_49,refute_0_62]) ).
cnf(refute_0_64,plain,
( ~ empty(empty_set)
| ~ in(A,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( empty(skolemFOFtoCNF_A_11) )],[refute_0_63,refute_0_61]) ).
cnf(refute_0_65,plain,
empty(empty_set),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_66,plain,
~ in(A,skolemFOFtoCNF_B_2),
inference(resolve,[$cnf( empty(empty_set) )],[refute_0_65,refute_0_64]) ).
cnf(refute_0_67,plain,
~ in(empty_set,skolemFOFtoCNF_B_2),
inference(subst,[],[refute_0_66:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_68,plain,
empty_set = skolemFOFtoCNF_B_2,
inference(resolve,[$cnf( in(empty_set,skolemFOFtoCNF_B_2) )],[refute_0_58,refute_0_67]) ).
cnf(refute_0_69,plain,
( empty_set != skolemFOFtoCNF_B_2
| skolemFOFtoCNF_B_2 = empty_set ),
inference(subst,[],[refute_0_43:[bind(X,$fot(empty_set)),bind(Y,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_0_70,plain,
skolemFOFtoCNF_B_2 = empty_set,
inference(resolve,[$cnf( $equal(empty_set,skolemFOFtoCNF_B_2) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( skolemFOFtoCNF_B_2 != empty_set
| ~ ordinal_subset(empty_set,empty_set)
| ordinal_subset(empty_set,skolemFOFtoCNF_B_2) ),
introduced(tautology,[equality,[$cnf( ~ ordinal_subset(empty_set,skolemFOFtoCNF_B_2) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_72,plain,
( ~ ordinal_subset(empty_set,empty_set)
| ordinal_subset(empty_set,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_2,empty_set) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
~ ordinal_subset(empty_set,empty_set),
inference(resolve,[$cnf( ordinal_subset(empty_set,skolemFOFtoCNF_B_2) )],[refute_0_72,refute_0_52]) ).
cnf(refute_0_74,plain,
( ~ ordinal(empty_set)
| ordinal_subset(empty_set,empty_set) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(empty_set)),bind(B,$fot(empty_set))]]) ).
cnf(refute_0_75,plain,
( skolemFOFtoCNF_A_11 != empty_set
| ~ ordinal(skolemFOFtoCNF_A_11)
| ordinal(empty_set) ),
introduced(tautology,[equality,[$cnf( ordinal(skolemFOFtoCNF_A_11) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_76,plain,
( ~ ordinal(skolemFOFtoCNF_A_11)
| ordinal(empty_set) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_11,empty_set) )],[refute_0_49,refute_0_75]) ).
cnf(refute_0_77,plain,
ordinal(empty_set),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_A_11) )],[refute_0_11,refute_0_76]) ).
cnf(refute_0_78,plain,
ordinal_subset(empty_set,empty_set),
inference(resolve,[$cnf( ordinal(empty_set) )],[refute_0_77,refute_0_74]) ).
cnf(refute_0_79,plain,
$false,
inference(resolve,[$cnf( ordinal_subset(empty_set,empty_set) )],[refute_0_78,refute_0_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM394+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jul 7 16:29:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.24/3.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.24/3.50
% 3.24/3.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.24/3.51
%------------------------------------------------------------------------------