TSTP Solution File: NUM383+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM383+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 12:26:20 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 10 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 106 ( 53 ~; 38 |; 7 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 64 ( 3 sgn 46 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(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(t7_ordinal1,conjecture,
! [A,B] :
~ ( in(A,B)
& subset(B,A) ) ).
fof(subgoal_0,plain,
! [A,B] :
( in(A,B)
=> ~ subset(B,A) ),
inference(strip,[],[t7_ordinal1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( in(A,B)
=> ~ subset(B,A) ),
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,B] :
( in(A,B)
& subset(B,A) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( in(skolemFOFtoCNF_A_10,skolemFOFtoCNF_B_1)
& subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_10) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
in(skolemFOFtoCNF_A_10,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_10),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ element(A,powerset(B))
<=> ~ subset(A,B) ),
inference(canonicalize,[],[t3_subset]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ element(A,powerset(B))
<=> ~ subset(A,B) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ( ~ element(A,powerset(B))
| subset(A,B) )
& ( ~ subset(A,B)
| element(A,powerset(B)) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,C] :
( ~ element(B,powerset(C))
| ~ in(A,B)
| element(A,C) ),
inference(canonicalize,[],[t4_subset]) ).
fof(normalize_0_11,plain,
! [A,B,C] :
( ~ element(B,powerset(C))
| ~ in(A,B)
| element(A,C) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B,C] :
( ~ element(B,powerset(C))
| ~ empty(C)
| ~ in(A,B) ),
inference(canonicalize,[],[t5_subset]) ).
fof(normalize_0_13,plain,
! [A,B,C] :
( ~ element(B,powerset(C))
| ~ empty(C)
| ~ in(A,B) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B] :
( ~ in(A,B)
| ~ in(B,A) ),
inference(canonicalize,[],[antisymmetry_r2_hidden]) ).
fof(normalize_0_15,plain,
! [A,B] :
( ~ in(A,B)
| ~ in(B,A) ),
inference(specialize,[],[normalize_0_14]) ).
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_A_10,skolemFOFtoCNF_A_10)
| empty(skolemFOFtoCNF_A_10)
| in(skolemFOFtoCNF_A_10,skolemFOFtoCNF_A_10) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_10)),bind(B,$fot(skolemFOFtoCNF_A_10))]]) ).
cnf(refute_0_2,plain,
in(skolemFOFtoCNF_A_10,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_10),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
( ~ subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_10)
| element(skolemFOFtoCNF_B_1,powerset(skolemFOFtoCNF_A_10)) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A_10))]]) ).
cnf(refute_0_6,plain,
element(skolemFOFtoCNF_B_1,powerset(skolemFOFtoCNF_A_10)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_10) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ element(B,powerset(C))
| ~ in(A,B)
| element(A,C) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( ~ element(skolemFOFtoCNF_B_1,powerset(skolemFOFtoCNF_A_10))
| ~ in(X_36,skolemFOFtoCNF_B_1)
| element(X_36,skolemFOFtoCNF_A_10) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_36)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A_10))]]) ).
cnf(refute_0_9,plain,
( ~ in(X_36,skolemFOFtoCNF_B_1)
| element(X_36,skolemFOFtoCNF_A_10) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_1,powerset(skolemFOFtoCNF_A_10)) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ in(skolemFOFtoCNF_A_10,skolemFOFtoCNF_B_1)
| element(skolemFOFtoCNF_A_10,skolemFOFtoCNF_A_10) ),
inference(subst,[],[refute_0_9:[bind(X_36,$fot(skolemFOFtoCNF_A_10))]]) ).
cnf(refute_0_11,plain,
element(skolemFOFtoCNF_A_10,skolemFOFtoCNF_A_10),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_10,skolemFOFtoCNF_B_1) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
( empty(skolemFOFtoCNF_A_10)
| in(skolemFOFtoCNF_A_10,skolemFOFtoCNF_A_10) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_A_10,skolemFOFtoCNF_A_10) )],[refute_0_11,refute_0_1]) ).
cnf(refute_0_13,plain,
( ~ element(B,powerset(C))
| ~ empty(C)
| ~ in(A,B) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_14,plain,
( ~ element(skolemFOFtoCNF_B_1,powerset(skolemFOFtoCNF_A_10))
| ~ empty(skolemFOFtoCNF_A_10)
| ~ in(X_26,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_13:[bind(A,$fot(X_26)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A_10))]]) ).
cnf(refute_0_15,plain,
( ~ empty(skolemFOFtoCNF_A_10)
| ~ in(X_26,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_1,powerset(skolemFOFtoCNF_A_10)) )],[refute_0_6,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ empty(skolemFOFtoCNF_A_10)
| ~ in(skolemFOFtoCNF_A_10,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_15:[bind(X_26,$fot(skolemFOFtoCNF_A_10))]]) ).
cnf(refute_0_17,plain,
~ empty(skolemFOFtoCNF_A_10),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_10,skolemFOFtoCNF_B_1) )],[refute_0_2,refute_0_16]) ).
cnf(refute_0_18,plain,
in(skolemFOFtoCNF_A_10,skolemFOFtoCNF_A_10),
inference(resolve,[$cnf( empty(skolemFOFtoCNF_A_10) )],[refute_0_12,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ in(A,B)
| ~ in(B,A) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_20,plain,
~ in(skolemFOFtoCNF_A_10,skolemFOFtoCNF_A_10),
inference(subst,[],[refute_0_19:[bind(A,$fot(skolemFOFtoCNF_A_10)),bind(B,$fot(skolemFOFtoCNF_A_10))]]) ).
cnf(refute_0_21,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_10,skolemFOFtoCNF_A_10) )],[refute_0_18,refute_0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM383+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jul 7 00:51:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------