TSTP Solution File: SEU130+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU130+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 12:38:35 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 68 ( 38 unt; 0 def)
% Number of atoms : 103 ( 60 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 69 ( 34 ~; 28 |; 2 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 89 ( 5 sgn 46 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A ).
fof(t12_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ) ).
fof(t17_xboole_1,lemma,
! [A,B] : subset(set_intersection2(A,B),A) ).
fof(t26_xboole_1,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ) ).
fof(t28_xboole_1,conjecture,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ) ).
fof(subgoal_0,plain,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
inference(strip,[],[t28_xboole_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ subset(A,B)
| set_union2(A,B) = B ),
inference(canonicalize,[],[t12_xboole_1]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ subset(A,B)
| set_union2(A,B) = B ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [A,B] :
( set_intersection2(A,B) != A
& subset(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != skolemFOFtoCNF_A_2
& subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ subset(A,B)
| ! [C] : subset(set_intersection2(A,C),set_intersection2(B,C)) ),
inference(canonicalize,[],[t26_xboole_1]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ subset(A,B)
| ! [C] : subset(set_intersection2(A,C),set_intersection2(B,C)) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C] :
( ~ subset(A,B)
| subset(set_intersection2(A,C),set_intersection2(B,C)) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] : set_intersection2(A,A) = A,
inference(canonicalize,[],[idempotence_k3_xboole_0]) ).
fof(normalize_0_9,plain,
! [A] : set_intersection2(A,A) = A,
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[commutativity_k3_xboole_0]) ).
fof(normalize_0_11,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(canonicalize,[],[t17_xboole_1]) ).
fof(normalize_0_13,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[commutativity_k2_xboole_0]) ).
fof(normalize_0_15,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != skolemFOFtoCNF_A_2,
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
( ~ subset(A,B)
| set_union2(A,B) = B ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ subset(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))
| set_union2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) = set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_0_2,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ subset(A,B)
| subset(set_intersection2(A,C),set_intersection2(B,C)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| subset(set_intersection2(skolemFOFtoCNF_A_2,X_167),set_intersection2(skolemFOFtoCNF_B_1,X_167)) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(X_167))]]) ).
cnf(refute_0_5,plain,
subset(set_intersection2(skolemFOFtoCNF_A_2,X_167),set_intersection2(skolemFOFtoCNF_B_1,X_167)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)),
inference(subst,[],[refute_0_5:[bind(X_167,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_7,plain,
set_intersection2(A,A) = A,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) = skolemFOFtoCNF_A_2,
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_9,plain,
( set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) != skolemFOFtoCNF_A_2
| ~ subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2))
| subset(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) ),
introduced(tautology,[equality,[$cnf( subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) ),[0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_10,plain,
( ~ subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2))
| subset(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_A_2) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
subset(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)),
inference(resolve,[$cnf( subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_13,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_14,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_15,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( set_intersection2(A,B) != set_intersection2(B,A)
| set_intersection2(B,A) = set_intersection2(A,B) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(set_intersection2(A,B))),bind(Y,$fot(set_intersection2(B,A)))]]) ).
cnf(refute_0_17,plain,
set_intersection2(B,A) = set_intersection2(A,B),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(B,A)) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) = set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_17:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_19,plain,
( set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) != set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| ~ subset(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2))
| subset(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) ),
introduced(tautology,[equality,[$cnf( subset(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) ),[1],$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_20,plain,
( ~ subset(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2))
| subset(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
subset(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2)) )],[refute_0_11,refute_0_20]) ).
cnf(refute_0_22,plain,
set_union2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) = set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_21,refute_0_1]) ).
cnf(refute_0_23,plain,
subset(set_intersection2(A,B),A),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_24,plain,
subset(set_intersection2(X_62,B),X_62),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_62))]]) ).
cnf(refute_0_25,plain,
( ~ subset(set_intersection2(X_62,B),X_62)
| set_union2(set_intersection2(X_62,B),X_62) = X_62 ),
inference(subst,[],[refute_0_0:[bind(A,$fot(set_intersection2(X_62,B))),bind(B,$fot(X_62))]]) ).
cnf(refute_0_26,plain,
set_union2(set_intersection2(X_62,B),X_62) = X_62,
inference(resolve,[$cnf( subset(set_intersection2(X_62,B),X_62) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_28,plain,
( set_union2(A,B) != set_union2(B,A)
| set_union2(B,A) = set_union2(A,B) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(set_union2(A,B))),bind(Y,$fot(set_union2(B,A)))]]) ).
cnf(refute_0_29,plain,
set_union2(B,A) = set_union2(A,B),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
set_union2(set_intersection2(X_62,B),X_62) = set_union2(X_62,set_intersection2(X_62,B)),
inference(subst,[],[refute_0_29:[bind(A,$fot(X_62)),bind(B,$fot(set_intersection2(X_62,B)))]]) ).
cnf(refute_0_31,plain,
( set_union2(set_intersection2(X_62,B),X_62) != X_62
| set_union2(set_intersection2(X_62,B),X_62) != set_union2(X_62,set_intersection2(X_62,B))
| set_union2(X_62,set_intersection2(X_62,B)) = X_62 ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(set_intersection2(X_62,B),X_62),X_62) ),[0],$fot(set_union2(X_62,set_intersection2(X_62,B)))]]) ).
cnf(refute_0_32,plain,
( set_union2(set_intersection2(X_62,B),X_62) != X_62
| set_union2(X_62,set_intersection2(X_62,B)) = X_62 ),
inference(resolve,[$cnf( $equal(set_union2(set_intersection2(X_62,B),X_62),set_union2(X_62,set_intersection2(X_62,B))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
set_union2(X_62,set_intersection2(X_62,B)) = X_62,
inference(resolve,[$cnf( $equal(set_union2(set_intersection2(X_62,B),X_62),X_62) )],[refute_0_26,refute_0_32]) ).
cnf(refute_0_34,plain,
set_union2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) = skolemFOFtoCNF_A_2,
inference(subst,[],[refute_0_33:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(X_62,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_35,plain,
( set_union2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) != set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| set_union2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_A_2 = set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) ),[0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_36,plain,
( set_union2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) != set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| skolemFOFtoCNF_A_2 = set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_2) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
skolemFOFtoCNF_A_2 = set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_22,refute_0_36]) ).
cnf(refute_0_38,plain,
set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != skolemFOFtoCNF_A_2,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_39,plain,
( skolemFOFtoCNF_A_2 != set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_15:[bind(X,$fot(skolemFOFtoCNF_A_2)),bind(Y,$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_0_40,plain,
skolemFOFtoCNF_A_2 != set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2) )],[refute_0_39,refute_0_38]) ).
cnf(refute_0_41,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_37,refute_0_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU130+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n012.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 03:27:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45
% 0.20/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.46
%------------------------------------------------------------------------------