TSTP Solution File: NUM390+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM390+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : Mon Jul 18 12:26:22 EDT 2022
% Result : Theorem 0.60s 0.77s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 77 ( 19 unt; 0 def)
% Number of atoms : 214 ( 23 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 224 ( 87 ~; 73 |; 42 &)
% ( 6 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 85 ( 0 sgn 55 !; 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(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( subset(A,B)
& A != B ) ) ).
fof(t1_xboole_1,axiom,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ) ).
fof(t21_ordinal1,axiom,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ( proper_subset(A,B)
=> in(A,B) ) ) ) ).
fof(t22_ordinal1,conjecture,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( ordinal(C)
=> ( ( subset(A,B)
& in(B,C) )
=> in(A,C) ) ) ) ) ).
fof(t7_ordinal1,axiom,
! [A,B] :
~ ( in(A,B)
& subset(B,A) ) ).
fof(subgoal_0,plain,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( ( ordinal(C)
& subset(A,B)
& in(B,C) )
=> in(A,C) ) ) ),
inference(strip,[],[t22_ordinal1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( ( ordinal(C)
& subset(A,B)
& in(B,C) )
=> in(A,C) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] :
( epsilon_transitive(A)
& ? [B] :
( ordinal(B)
& ? [C] :
( ~ in(A,C)
& in(B,C)
& ordinal(C)
& subset(A,B) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( epsilon_transitive(skolemFOFtoCNF_A_11)
& ? [B] :
( ordinal(B)
& ? [C] :
( ~ in(skolemFOFtoCNF_A_11,C)
& in(B,C)
& ordinal(C)
& subset(skolemFOFtoCNF_A_11,B) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [B] :
( ordinal(B)
& ? [C] :
( ~ in(skolemFOFtoCNF_A_11,C)
& in(B,C)
& ordinal(C)
& subset(skolemFOFtoCNF_A_11,B) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ordinal(skolemFOFtoCNF_B_2)
& ? [C] :
( ~ in(skolemFOFtoCNF_A_11,C)
& in(skolemFOFtoCNF_B_2,C)
& ordinal(C)
& subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [C] :
( ~ in(skolemFOFtoCNF_A_11,C)
& in(skolemFOFtoCNF_B_2,C)
& ordinal(C)
& subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( ~ in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_C)
& in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C)
& ordinal(skolemFOFtoCNF_C)
& subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ proper_subset(A,B)
<=> ( ~ subset(A,B)
| A = B ) ),
inference(canonicalize,[],[d8_xboole_0]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ proper_subset(A,B)
<=> ( ~ subset(A,B)
| A = B ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ( A != B
| ~ proper_subset(A,B) )
& ( ~ proper_subset(A,B)
| subset(A,B) )
& ( ~ subset(A,B)
| A = B
| proper_subset(A,B) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ~ subset(A,B)
| A = B
| proper_subset(A,B) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_12,plain,
! [A] :
( ~ epsilon_transitive(A)
<=> ? [B] :
( ~ subset(B,A)
& in(B,A) ) ),
inference(canonicalize,[],[d2_ordinal1]) ).
fof(normalize_0_13,plain,
! [A] :
( ~ epsilon_transitive(A)
<=> ? [B] :
( ~ subset(B,A)
& in(B,A) ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,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_13]) ).
fof(normalize_0_15,plain,
! [A,B] :
( ~ epsilon_transitive(A)
| ~ in(B,A)
| subset(B,A) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
ordinal(skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_17,plain,
! [A] :
( ~ ordinal(A)
| ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
inference(canonicalize,[],[cc1_ordinal1]) ).
fof(normalize_0_18,plain,
! [A] :
( ~ ordinal(A)
| ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A] :
( ( ~ ordinal(A)
| epsilon_connected(A) )
& ( ~ ordinal(A)
| epsilon_transitive(A) ) ),
inference(clausify,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A] :
( ~ ordinal(A)
| epsilon_transitive(A) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A,B,C] :
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
inference(canonicalize,[],[t1_xboole_1]) ).
fof(normalize_0_22,plain,
! [A,B,C] :
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A] :
( ~ epsilon_transitive(A)
| ! [B] :
( ~ ordinal(B)
| ~ proper_subset(A,B)
| in(A,B) ) ),
inference(canonicalize,[],[t21_ordinal1]) ).
fof(normalize_0_24,plain,
! [A] :
( ~ epsilon_transitive(A)
| ! [B] :
( ~ ordinal(B)
| ~ proper_subset(A,B)
| in(A,B) ) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [A,B] :
( ~ epsilon_transitive(A)
| ~ ordinal(B)
| ~ proper_subset(A,B)
| in(A,B) ),
inference(clausify,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
epsilon_transitive(skolemFOFtoCNF_A_11),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_27,plain,
~ in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_28,plain,
! [A,B] :
( ~ in(A,B)
| ~ subset(B,A) ),
inference(canonicalize,[],[t7_ordinal1]) ).
fof(normalize_0_29,plain,
! [A,B] :
( ~ in(A,B)
| ~ subset(B,A) ),
inference(specialize,[],[normalize_0_28]) ).
cnf(refute_0_0,plain,
in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_1,plain,
( ~ subset(A,B)
| A = B
| proper_subset(A,B) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_2,plain,
( ~ subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_C)
| skolemFOFtoCNF_A_11 = skolemFOFtoCNF_C
| proper_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_A_11)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_3,plain,
subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_4,plain,
( ~ epsilon_transitive(A)
| ~ in(B,A)
| subset(B,A) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_5,plain,
( ~ epsilon_transitive(skolemFOFtoCNF_C)
| ~ in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C)
| subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_0_6,plain,
( ~ epsilon_transitive(skolemFOFtoCNF_C)
| subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
ordinal(skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_8,plain,
( ~ ordinal(A)
| epsilon_transitive(A) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_9,plain,
( ~ ordinal(skolemFOFtoCNF_C)
| epsilon_transitive(skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_10,plain,
epsilon_transitive(skolemFOFtoCNF_C),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_C) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( epsilon_transitive(skolemFOFtoCNF_C) )],[refute_0_10,refute_0_6]) ).
cnf(refute_0_12,plain,
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_13,plain,
( ~ subset(X_54,skolemFOFtoCNF_B_2)
| ~ subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C)
| subset(X_54,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_54)),bind(B,$fot(skolemFOFtoCNF_B_2)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_14,plain,
( ~ subset(X_54,skolemFOFtoCNF_B_2)
| subset(X_54,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2)
| subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_14:[bind(X_54,$fot(skolemFOFtoCNF_A_11))]]) ).
cnf(refute_0_16,plain,
subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_C),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) )],[refute_0_3,refute_0_15]) ).
cnf(refute_0_17,plain,
( skolemFOFtoCNF_A_11 = skolemFOFtoCNF_C
| proper_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_C) )],[refute_0_16,refute_0_2]) ).
cnf(refute_0_18,plain,
( ~ epsilon_transitive(A)
| ~ ordinal(B)
| ~ proper_subset(A,B)
| in(A,B) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_19,plain,
( ~ epsilon_transitive(skolemFOFtoCNF_A_11)
| ~ ordinal(skolemFOFtoCNF_C)
| ~ proper_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_C)
| in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_18:[bind(A,$fot(skolemFOFtoCNF_A_11)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_20,plain,
( ~ epsilon_transitive(skolemFOFtoCNF_A_11)
| ~ ordinal(skolemFOFtoCNF_C)
| skolemFOFtoCNF_A_11 = skolemFOFtoCNF_C
| in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( proper_subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_C) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
epsilon_transitive(skolemFOFtoCNF_A_11),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_22,plain,
( ~ ordinal(skolemFOFtoCNF_C)
| skolemFOFtoCNF_A_11 = skolemFOFtoCNF_C
| in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( epsilon_transitive(skolemFOFtoCNF_A_11) )],[refute_0_21,refute_0_20]) ).
cnf(refute_0_23,plain,
( skolemFOFtoCNF_A_11 = skolemFOFtoCNF_C
| in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_C) )],[refute_0_7,refute_0_22]) ).
cnf(refute_0_24,plain,
~ in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_25,plain,
skolemFOFtoCNF_A_11 = skolemFOFtoCNF_C,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_11,skolemFOFtoCNF_C) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_27,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_28,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( skolemFOFtoCNF_A_11 != skolemFOFtoCNF_C
| skolemFOFtoCNF_C = skolemFOFtoCNF_A_11 ),
inference(subst,[],[refute_0_28:[bind(X,$fot(skolemFOFtoCNF_A_11)),bind(Y,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_30,plain,
skolemFOFtoCNF_C = skolemFOFtoCNF_A_11,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_11,skolemFOFtoCNF_C) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
( skolemFOFtoCNF_C != skolemFOFtoCNF_A_11
| ~ in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C)
| in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C) ),[1],$fot(skolemFOFtoCNF_A_11)]]) ).
cnf(refute_0_32,plain,
( ~ in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C)
| in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C,skolemFOFtoCNF_A_11) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C) )],[refute_0_0,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ in(A,B)
| ~ subset(B,A) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_35,plain,
( ~ in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11)
| ~ subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_0_34:[bind(A,$fot(skolemFOFtoCNF_B_2)),bind(B,$fot(skolemFOFtoCNF_A_11))]]) ).
cnf(refute_0_36,plain,
~ in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_11,skolemFOFtoCNF_B_2) )],[refute_0_3,refute_0_35]) ).
cnf(refute_0_37,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_11) )],[refute_0_33,refute_0_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM390+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.35 % Computer : n013.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Wed Jul 6 07:05:59 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.60/0.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.77
% 0.60/0.77 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.60/0.77
%------------------------------------------------------------------------------