%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU133+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 12:38:37 EDT 2022
% Result : Theorem 5.74s 5.98s
% Output : CNFRefutation 5.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 10 unt; 0 def)
% Number of atoms : 87 ( 13 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 95 ( 39 ~; 34 |; 12 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 75 ( 3 sgn 38 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ) ).
fof(t36_xboole_1,conjecture,
! [A,B] : subset(set_difference(A,B),A) ).
fof(subgoal_0,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(strip,[],[t36_xboole_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] : subset(set_difference(A,B),A),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] : ~ subset(set_difference(A,B),A),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ subset(set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_7,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_8,plain,
! [A,B,C] :
( C != set_difference(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,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_2(A,B,C),B)
| C = set_difference(A,B)
| in(skolemFOFtoCNF_D_2(A,B,C),C) )
& ( C = set_difference(A,B)
| in(skolemFOFtoCNF_D_2(A,B,C),A)
| in(skolemFOFtoCNF_D_2(A,B,C),C) )
& ( C != set_difference(A,B)
| ~ in(D,A)
| in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D_2(A,B,C),A)
| ~ in(skolemFOFtoCNF_D_2(A,B,C),C)
| C = set_difference(A,B)
| in(skolemFOFtoCNF_D_2(A,B,C),B) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,C,D] :
( C != set_difference(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
~ subset(set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ in(skolemFOFtoCNF_C(set_difference(X_1619,X_1620),X_1619),X_1619)
| subset(set_difference(X_1619,X_1620),X_1619) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(set_difference(X_1619,X_1620))),bind(B,$fot(X_1619))]]) ).
cnf(refute_0_3,plain,
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( in(skolemFOFtoCNF_C(set_difference(X_146,X_147),B),set_difference(X_146,X_147))
| subset(set_difference(X_146,X_147),B) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(set_difference(X_146,X_147)))]]) ).
cnf(refute_0_5,plain,
( C != set_difference(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
( set_difference(A,B) != set_difference(A,B)
| ~ in(D,set_difference(A,B))
| in(D,A) ),
inference(subst,[],[refute_0_5:[bind(C,$fot(set_difference(A,B)))]]) ).
cnf(refute_0_7,plain,
set_difference(A,B) = set_difference(A,B),
introduced(tautology,[refl,[$fot(set_difference(A,B))]]) ).
cnf(refute_0_8,plain,
( ~ in(D,set_difference(A,B))
| in(D,A) ),
inference(resolve,[$cnf( $equal(set_difference(A,B),set_difference(A,B)) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( ~ in(skolemFOFtoCNF_C(set_difference(X_146,X_147),B),set_difference(X_146,X_147))
| in(skolemFOFtoCNF_C(set_difference(X_146,X_147),B),X_146) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_146)),bind(B,$fot(X_147)),bind(D,$fot(skolemFOFtoCNF_C(set_difference(X_146,X_147),B)))]]) ).
cnf(refute_0_10,plain,
( in(skolemFOFtoCNF_C(set_difference(X_146,X_147),B),X_146)
| subset(set_difference(X_146,X_147),B) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(set_difference(X_146,X_147),B),set_difference(X_146,X_147)) )],[refute_0_4,refute_0_9]) ).
cnf(refute_0_11,plain,
( in(skolemFOFtoCNF_C(set_difference(X_1619,X_1620),X_1619),X_1619)
| subset(set_difference(X_1619,X_1620),X_1619) ),
inference(subst,[],[refute_0_10:[bind(B,$fot(X_1619)),bind(X_146,$fot(X_1619)),bind(X_147,$fot(X_1620))]]) ).
cnf(refute_0_12,plain,
subset(set_difference(X_1619,X_1620),X_1619),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(set_difference(X_1619,X_1620),X_1619),X_1619) )],[refute_0_11,refute_0_2]) ).
cnf(refute_0_13,plain,
subset(set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2),
inference(subst,[],[refute_0_12:[bind(X_1619,$fot(skolemFOFtoCNF_A_2)),bind(X_1620,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( subset(set_difference(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2) )],[refute_0_13,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU133+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 19 22:29:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5.74/5.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.74/5.98
% 5.74/5.98 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.74/5.98
%------------------------------------------------------------------------------