%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU172+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 : Tue Jul 19 12:39:02 EDT 2022
% Result : Theorem 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 86 ( 20 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 96 ( 42 ~; 29 |; 15 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 52 ( 2 sgn 33 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ) ).
fof(t54_subset_1,conjecture,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,subset_complement(A,C))
& in(B,C) ) ) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( ( element(C,powerset(A))
& in(B,subset_complement(A,C)) )
=> ~ in(B,C) ),
inference(strip,[],[t54_subset_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( ( element(C,powerset(A))
& in(B,subset_complement(A,C)) )
=> ~ in(B,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C] :
( element(C,powerset(A))
& in(B,C)
& in(B,subset_complement(A,C)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( element(skolemFOFtoCNF_C,powerset(skolemFOFtoCNF_A_2))
& in(skolemFOFtoCNF_B_3,skolemFOFtoCNF_C)
& in(skolemFOFtoCNF_B_3,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
in(skolemFOFtoCNF_B_3,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
element(skolemFOFtoCNF_C,powerset(skolemFOFtoCNF_A_2)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ~ element(B,powerset(A))
| subset_complement(A,B) = set_difference(A,B) ),
inference(canonicalize,[],[d5_subset_1]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ element(B,powerset(A))
| subset_complement(A,B) = set_difference(A,B) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C] :
( C != set_difference(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
inference(canonicalize,[],[d4_xboole_0]) ).
fof(normalize_0_7,plain,
! [A,B,C] :
( C != set_difference(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C,D] :
( ( C != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,C) )
& ( C != set_difference(A,B)
| ~ in(D,C)
| in(D,A) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),B)
| C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C != set_difference(A,B)
| ~ in(D,A)
| in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),B) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C,D] :
( C != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,C) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
in(skolemFOFtoCNF_B_3,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
in(skolemFOFtoCNF_B_3,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
element(skolemFOFtoCNF_C,powerset(skolemFOFtoCNF_A_2)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ element(B,powerset(A))
| subset_complement(A,B) = set_difference(A,B) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ element(skolemFOFtoCNF_C,powerset(skolemFOFtoCNF_A_2))
| subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) = set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_4,plain,
subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) = set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( element(skolemFOFtoCNF_C,powerset(skolemFOFtoCNF_A_2)) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) != set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| ~ in(skolemFOFtoCNF_B_3,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))
| in(skolemFOFtoCNF_B_3,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_B_3,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) ),[1],$fot(set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))]]) ).
cnf(refute_0_6,plain,
( ~ in(skolemFOFtoCNF_B_3,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))
| in(skolemFOFtoCNF_B_3,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) ),
inference(resolve,[$cnf( $equal(subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
in(skolemFOFtoCNF_B_3,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_3,subset_complement(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) )],[refute_0_0,refute_0_6]) ).
cnf(refute_0_8,plain,
( C != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,C) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_9,plain,
( set_difference(A,B) != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,set_difference(A,B)) ),
inference(subst,[],[refute_0_8:[bind(C,$fot(set_difference(A,B)))]]) ).
cnf(refute_0_10,plain,
set_difference(A,B) = set_difference(A,B),
introduced(tautology,[refl,[$fot(set_difference(A,B))]]) ).
cnf(refute_0_11,plain,
( ~ in(D,B)
| ~ in(D,set_difference(A,B)) ),
inference(resolve,[$cnf( $equal(set_difference(A,B),set_difference(A,B)) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
( ~ in(skolemFOFtoCNF_B_3,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))
| ~ in(skolemFOFtoCNF_B_3,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_C)),bind(D,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_0_13,plain,
~ in(skolemFOFtoCNF_B_3,skolemFOFtoCNF_C),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_3,set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) )],[refute_0_7,refute_0_12]) ).
cnf(refute_0_14,plain,
in(skolemFOFtoCNF_B_3,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_3,skolemFOFtoCNF_C) )],[refute_0_14,refute_0_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU172+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n019.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 : Mon Jun 20 01:31:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47
% 0.20/0.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.47
%------------------------------------------------------------------------------