TSTP Solution File: NUM388+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM388+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 12:26:21 EDT 2022
% Result : Theorem 0.22s 0.46s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 64 ( 15 unt; 0 def)
% Number of atoms : 171 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 170 ( 63 ~; 47 |; 40 &)
% ( 6 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 78 ( 1 sgn 53 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ) ).
fof(d2_ordinal1,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ) ).
fof(t19_ordinal1,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( epsilon_transitive(C)
=> ( ( in(C,A)
& in(A,B) )
=> in(C,B) ) ) ) ) ).
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(t7_boole,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ) ).
fof(subgoal_0,plain,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( ( epsilon_transitive(C)
& in(C,A)
& in(A,B) )
=> in(C,B) ) ) ),
inference(strip,[],[t19_ordinal1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( ( epsilon_transitive(C)
& in(C,A)
& in(A,B) )
=> in(C,B) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(canonicalize,[],[t2_subset]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [A] :
( ordinal(A)
& ? [B] :
( ordinal(B)
& ? [C] :
( ~ in(C,B)
& epsilon_transitive(C)
& in(A,B)
& in(C,A) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( ordinal(skolemFOFtoCNF_A_11)
& ? [B] :
( ordinal(B)
& ? [C] :
( ~ in(C,B)
& epsilon_transitive(C)
& in(C,skolemFOFtoCNF_A_11)
& in(skolemFOFtoCNF_A_11,B) ) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [B] :
( ordinal(B)
& ? [C] :
( ~ in(C,B)
& epsilon_transitive(C)
& in(C,skolemFOFtoCNF_A_11)
& in(skolemFOFtoCNF_A_11,B) ) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( ordinal(skolemFOFtoCNF_B_2)
& ? [C] :
( ~ in(C,skolemFOFtoCNF_B_2)
& epsilon_transitive(C)
& in(C,skolemFOFtoCNF_A_11)
& in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [C] :
( ~ in(C,skolemFOFtoCNF_B_2)
& epsilon_transitive(C)
& in(C,skolemFOFtoCNF_A_11)
& in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( ~ in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2)
& epsilon_transitive(skolemFOFtoCNF_C)
& in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2)
& in(skolemFOFtoCNF_C,skolemFOFtoCNF_A_11) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
in(skolemFOFtoCNF_C,skolemFOFtoCNF_A_11),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ~ element(A,powerset(B))
<=> ~ subset(A,B) ),
inference(canonicalize,[],[t3_subset]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ~ element(A,powerset(B))
<=> ~ subset(A,B) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B] :
( ( ~ element(A,powerset(B))
| subset(A,B) )
& ( ~ subset(A,B)
| element(A,powerset(B)) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_14,plain,
! [A] :
( ~ epsilon_transitive(A)
<=> ? [B] :
( ~ subset(B,A)
& in(B,A) ) ),
inference(canonicalize,[],[d2_ordinal1]) ).
fof(normalize_0_15,plain,
! [A] :
( ~ epsilon_transitive(A)
<=> ? [B] :
( ~ subset(B,A)
& in(B,A) ) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B] :
( ( ~ subset(skolemFOFtoCNF_B(A),A)
| epsilon_transitive(A) )
& ( epsilon_transitive(A)
| in(skolemFOFtoCNF_B(A),A) )
& ( ~ epsilon_transitive(A)
| ~ in(B,A)
| subset(B,A) ) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,B] :
( ~ epsilon_transitive(A)
| ~ in(B,A)
| subset(B,A) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
ordinal(skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_19,plain,
! [A] :
( ~ ordinal(A)
| ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
inference(canonicalize,[],[cc1_ordinal1]) ).
fof(normalize_0_20,plain,
! [A] :
( ~ ordinal(A)
| ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A] :
( ( ~ ordinal(A)
| epsilon_connected(A) )
& ( ~ ordinal(A)
| epsilon_transitive(A) ) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [A] :
( ~ ordinal(A)
| epsilon_transitive(A) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A,B,C] :
( ~ element(B,powerset(C))
| ~ in(A,B)
| element(A,C) ),
inference(canonicalize,[],[t4_subset]) ).
fof(normalize_0_24,plain,
! [A,B,C] :
( ~ element(B,powerset(C))
| ~ in(A,B)
| element(A,C) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(canonicalize,[],[t7_boole]) ).
fof(normalize_0_26,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
~ in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ element(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2)
| empty(skolemFOFtoCNF_B_2)
| in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_0_2,plain,
in(skolemFOFtoCNF_C,skolemFOFtoCNF_A_11),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_3,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_4,plain,
( ~ subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2)
| element(skolemFOFtoCNF_A_11,powerset(skolemFOFtoCNF_B_2)) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_A_11)),bind(B,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_0_5,plain,
in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_6,plain,
( ~ epsilon_transitive(A)
| ~ in(B,A)
| subset(B,A) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_7,plain,
( ~ epsilon_transitive(skolemFOFtoCNF_B_2)
| ~ in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2)
| subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_B_2)),bind(B,$fot(skolemFOFtoCNF_A_11))]]) ).
cnf(refute_0_8,plain,
( ~ epsilon_transitive(skolemFOFtoCNF_B_2)
| subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
ordinal(skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_10,plain,
( ~ ordinal(A)
| epsilon_transitive(A) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_11,plain,
( ~ ordinal(skolemFOFtoCNF_B_2)
| epsilon_transitive(skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_0_12,plain,
epsilon_transitive(skolemFOFtoCNF_B_2),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_B_2) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2),
inference(resolve,[$cnf( epsilon_transitive(skolemFOFtoCNF_B_2) )],[refute_0_12,refute_0_8]) ).
cnf(refute_0_14,plain,
element(skolemFOFtoCNF_A_11,powerset(skolemFOFtoCNF_B_2)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) )],[refute_0_13,refute_0_4]) ).
cnf(refute_0_15,plain,
( ~ element(B,powerset(C))
| ~ in(A,B)
| element(A,C) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_16,plain,
( ~ element(skolemFOFtoCNF_A_11,powerset(skolemFOFtoCNF_B_2))
| ~ in(X_56,skolemFOFtoCNF_A_11)
| element(X_56,skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(X_56)),bind(B,$fot(skolemFOFtoCNF_A_11)),bind(C,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_0_17,plain,
( ~ in(X_56,skolemFOFtoCNF_A_11)
| element(X_56,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_A_11,powerset(skolemFOFtoCNF_B_2)) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ in(skolemFOFtoCNF_C,skolemFOFtoCNF_A_11)
| element(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_0_17:[bind(X_56,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_19,plain,
element(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C,skolemFOFtoCNF_A_11) )],[refute_0_2,refute_0_18]) ).
cnf(refute_0_20,plain,
( empty(skolemFOFtoCNF_B_2)
| in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2) )],[refute_0_19,refute_0_1]) ).
cnf(refute_0_21,plain,
( ~ empty(B)
| ~ in(A,B) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_22,plain,
( ~ empty(skolemFOFtoCNF_B_2)
| ~ in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(skolemFOFtoCNF_A_11)),bind(B,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_0_23,plain,
~ empty(skolemFOFtoCNF_B_2),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) )],[refute_0_5,refute_0_22]) ).
cnf(refute_0_24,plain,
in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2),
inference(resolve,[$cnf( empty(skolemFOFtoCNF_B_2) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
~ in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2) )],[refute_0_24,refute_0_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM388+1 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.14 % Command : metis --show proof --show saturation %s
% 0.16/0.36 % Computer : n020.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 600
% 0.16/0.36 % DateTime : Thu Jul 7 10:33:59 EDT 2022
% 0.16/0.36 % CPUTime :
% 0.16/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.22/0.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.46
% 0.22/0.46 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.22/0.47
%------------------------------------------------------------------------------