%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU124+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 12:38:32 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 19 unt; 0 def)
% Number of atoms : 108 ( 28 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 106 ( 43 ~; 44 |; 9 &)
% ( 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 : 101 ( 7 sgn 44 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(t7_xboole_1,conjecture,
! [A,B] : subset(A,set_union2(A,B)) ).
fof(subgoal_0,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(strip,[],[t7_xboole_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] : subset(A,set_union2(A,B)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] : ~ subset(A,set_union2(A,B)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ subset(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),
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_union2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(canonicalize,[],[d2_xboole_0]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( C != set_union2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C,D] :
( ( C != set_union2(A,B)
| ~ in(D,A)
| in(D,C) )
& ( C != set_union2(A,B)
| ~ in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_union2(A,B) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),B)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_union2(A,B) )
& ( C != set_union2(A,B)
| ~ in(D,C)
| in(D,A)
| in(D,B) )
& ( C = set_union2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),B)
| in(skolemFOFtoCNF_D(A,B,C),C) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,C,D] :
( C != set_union2(A,B)
| ~ in(D,B)
| in(D,C) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[commutativity_k2_xboole_0]) ).
fof(normalize_0_12,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(specialize,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
~ subset(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),
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(X_133,set_union2(X_132,X_133)),set_union2(X_132,X_133))
| subset(X_133,set_union2(X_132,X_133)) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_133)),bind(B,$fot(set_union2(X_132,X_133)))]]) ).
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(X_56,B),X_56)
| subset(X_56,B) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_56))]]) ).
cnf(refute_0_5,plain,
( C != set_union2(A,B)
| ~ in(D,B)
| in(D,C) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
( set_union2(A,B) != set_union2(A,B)
| ~ in(D,B)
| in(D,set_union2(A,B)) ),
inference(subst,[],[refute_0_5:[bind(C,$fot(set_union2(A,B)))]]) ).
cnf(refute_0_7,plain,
set_union2(A,B) = set_union2(A,B),
introduced(tautology,[refl,[$fot(set_union2(A,B))]]) ).
cnf(refute_0_8,plain,
( ~ in(D,B)
| in(D,set_union2(A,B)) ),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(A,B)) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( ~ in(skolemFOFtoCNF_C(X_56,B),X_56)
| in(skolemFOFtoCNF_C(X_56,B),set_union2(X_55,X_56)) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_55)),bind(B,$fot(X_56)),bind(D,$fot(skolemFOFtoCNF_C(X_56,B)))]]) ).
cnf(refute_0_10,plain,
( in(skolemFOFtoCNF_C(X_56,B),set_union2(X_55,X_56))
| subset(X_56,B) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(X_56,B),X_56) )],[refute_0_4,refute_0_9]) ).
cnf(refute_0_11,plain,
( in(skolemFOFtoCNF_C(X_133,set_union2(X_132,X_133)),set_union2(X_132,X_133))
| subset(X_133,set_union2(X_132,X_133)) ),
inference(subst,[],[refute_0_10:[bind(B,$fot(set_union2(X_132,X_133))),bind(X_55,$fot(X_132)),bind(X_56,$fot(X_133))]]) ).
cnf(refute_0_12,plain,
subset(X_133,set_union2(X_132,X_133)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(X_133,set_union2(X_132,X_133)),set_union2(X_132,X_133)) )],[refute_0_11,refute_0_2]) ).
cnf(refute_0_13,plain,
subset(X_135,set_union2(X_134,X_135)),
inference(subst,[],[refute_0_12:[bind(X_132,$fot(X_134)),bind(X_133,$fot(X_135))]]) ).
cnf(refute_0_14,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_15,plain,
set_union2(X_135,X_134) = set_union2(X_134,X_135),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_135)),bind(B,$fot(X_134))]]) ).
cnf(refute_0_16,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_17,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_18,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( set_union2(X_135,X_134) != set_union2(X_134,X_135)
| set_union2(X_134,X_135) = set_union2(X_135,X_134) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(set_union2(X_135,X_134))),bind(Y,$fot(set_union2(X_134,X_135)))]]) ).
cnf(refute_0_20,plain,
set_union2(X_134,X_135) = set_union2(X_135,X_134),
inference(resolve,[$cnf( $equal(set_union2(X_135,X_134),set_union2(X_134,X_135)) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
( set_union2(X_134,X_135) != set_union2(X_135,X_134)
| ~ subset(X_135,set_union2(X_134,X_135))
| subset(X_135,set_union2(X_135,X_134)) ),
introduced(tautology,[equality,[$cnf( subset(X_135,set_union2(X_134,X_135)) ),[1],$fot(set_union2(X_135,X_134))]]) ).
cnf(refute_0_22,plain,
( ~ subset(X_135,set_union2(X_134,X_135))
| subset(X_135,set_union2(X_135,X_134)) ),
inference(resolve,[$cnf( $equal(set_union2(X_134,X_135),set_union2(X_135,X_134)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
subset(X_135,set_union2(X_135,X_134)),
inference(resolve,[$cnf( subset(X_135,set_union2(X_134,X_135)) )],[refute_0_13,refute_0_22]) ).
cnf(refute_0_24,plain,
subset(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),
inference(subst,[],[refute_0_23:[bind(X_134,$fot(skolemFOFtoCNF_B_1)),bind(X_135,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_24,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU124+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n003.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 : Mon Jun 20 10:01:44 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.42
% 0.20/0.42 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.43
%------------------------------------------------------------------------------