TSTP Solution File: NUM405+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM405+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 12:26:26 EDT 2022
% Result : Theorem 0.20s 0.38s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 8 unt; 0 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 95 ( 48 ~; 31 |; 4 &)
% ( 9 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 55 ( 5 sgn 33 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_xboole_0__e2_43__ordinal1,axiom,
! [A] :
? [B] :
! [C] :
( in(C,B)
<=> ( in(C,A)
& ordinal(C) ) ) ).
fof(t37_ordinal1,axiom,
! [A] :
~ ! [B] :
( in(B,A)
<=> ordinal(B) ) ).
fof(t38_ordinal1,conjecture,
! [A] :
~ ! [B] :
( ordinal(B)
=> in(B,A) ) ).
fof(subgoal_0,plain,
! [A] :
~ ! [B] :
( ordinal(B)
=> in(B,A) ),
inference(strip,[],[t38_ordinal1]) ).
fof(negate_0_0,plain,
~ ! [A] :
~ ! [B] :
( ordinal(B)
=> in(B,A) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A] :
? [B] :
( ~ in(B,A)
<=> ordinal(B) ),
inference(canonicalize,[],[t37_ordinal1]) ).
fof(normalize_0_1,plain,
! [A] :
? [B] :
( ~ in(B,A)
<=> ordinal(B) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] :
( ~ in(skolemFOFtoCNF_B_2(A),A)
<=> ordinal(skolemFOFtoCNF_B_2(A)) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A] :
( ( ~ in(skolemFOFtoCNF_B_2(A),A)
| ~ ordinal(skolemFOFtoCNF_B_2(A)) )
& ( in(skolemFOFtoCNF_B_2(A),A)
| ordinal(skolemFOFtoCNF_B_2(A)) ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A] :
( ~ in(skolemFOFtoCNF_B_2(A),A)
| ~ ordinal(skolemFOFtoCNF_B_2(A)) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
? [A] :
! [B] :
( ~ ordinal(B)
| in(B,A) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_6,plain,
! [B] :
( ~ ordinal(B)
| in(B,skolemFOFtoCNF_A_13) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B] :
( ~ ordinal(B)
| in(B,skolemFOFtoCNF_A_13) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] :
( in(skolemFOFtoCNF_B_2(A),A)
| ordinal(skolemFOFtoCNF_B_2(A)) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_9,plain,
! [A] :
? [B] :
! [C] :
( ~ in(C,B)
<=> ( ~ in(C,A)
| ~ ordinal(C) ) ),
inference(canonicalize,[],[s1_xboole_0__e2_43__ordinal1]) ).
fof(normalize_0_10,plain,
! [A] :
? [B] :
! [C] :
( ~ in(C,B)
<=> ( ~ in(C,A)
| ~ ordinal(C) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,C] :
( ~ in(C,skolemFOFtoCNF_B_1(A))
<=> ( ~ in(C,A)
| ~ ordinal(C) ) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,C] :
( ~ in(C,skolemFOFtoCNF_B_1(A))
<=> ( ~ in(C,A)
| ~ ordinal(C) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,C] :
( ( ~ in(C,skolemFOFtoCNF_B_1(A))
| in(C,A) )
& ( ~ in(C,skolemFOFtoCNF_B_1(A))
| ordinal(C) )
& ( ~ in(C,A)
| ~ ordinal(C)
| in(C,skolemFOFtoCNF_B_1(A)) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,C] :
( ~ in(C,skolemFOFtoCNF_B_1(A))
| ordinal(C) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,C] :
( ~ in(C,A)
| ~ ordinal(C)
| in(C,skolemFOFtoCNF_B_1(A)) ),
inference(conjunct,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
( ~ in(skolemFOFtoCNF_B_2(A),A)
| ~ ordinal(skolemFOFtoCNF_B_2(A)) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( ~ in(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_13)),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_13))
| ~ ordinal(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_13))) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_13)))]]) ).
cnf(refute_0_2,plain,
( ~ ordinal(B)
| in(B,skolemFOFtoCNF_A_13) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ ordinal(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_22)))
| in(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_22)),skolemFOFtoCNF_A_13) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_22))))]]) ).
cnf(refute_0_4,plain,
( in(skolemFOFtoCNF_B_2(A),A)
| ordinal(skolemFOFtoCNF_B_2(A)) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( in(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_20)),skolemFOFtoCNF_B_1(X_20))
| ordinal(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_20))) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_B_1(X_20)))]]) ).
cnf(refute_0_6,plain,
( ~ in(C,skolemFOFtoCNF_B_1(A))
| ordinal(C) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_7,plain,
( ~ in(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_20)),skolemFOFtoCNF_B_1(X_20))
| ordinal(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_20))) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_20)),bind(C,$fot(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_20))))]]) ).
cnf(refute_0_8,plain,
ordinal(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_20))),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_20)),skolemFOFtoCNF_B_1(X_20)) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
ordinal(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_22))),
inference(subst,[],[refute_0_8:[bind(X_20,$fot(X_22))]]) ).
cnf(refute_0_10,plain,
in(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_22)),skolemFOFtoCNF_A_13),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_22))) )],[refute_0_9,refute_0_3]) ).
cnf(refute_0_11,plain,
( ~ in(C,A)
| ~ ordinal(C)
| in(C,skolemFOFtoCNF_B_1(A)) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_12,plain,
( ~ in(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_22)),skolemFOFtoCNF_A_13)
| ~ ordinal(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_22)))
| in(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_22)),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_13)) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(skolemFOFtoCNF_A_13)),bind(C,$fot(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_22))))]]) ).
cnf(refute_0_13,plain,
( ~ ordinal(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_22)))
| in(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_22)),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_13)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_22)),skolemFOFtoCNF_A_13) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
in(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_22)),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_13)),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(X_22))) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
in(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_13)),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_13)),
inference(subst,[],[refute_0_14:[bind(X_22,$fot(skolemFOFtoCNF_A_13))]]) ).
cnf(refute_0_16,plain,
~ ordinal(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_13))),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_13)),skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_13)) )],[refute_0_15,refute_0_1]) ).
cnf(refute_0_17,plain,
ordinal(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_13))),
inference(subst,[],[refute_0_8:[bind(X_20,$fot(skolemFOFtoCNF_A_13))]]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_B_2(skolemFOFtoCNF_B_1(skolemFOFtoCNF_A_13))) )],[refute_0_17,refute_0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM405+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 12:33:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.38
% 0.20/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.39
%------------------------------------------------------------------------------