TSTP Solution File: SEU126+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU126+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 12:38:33 EDT 2022
% Result : Theorem 0.94s 1.16s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 27 unt; 0 def)
% Number of atoms : 102 ( 37 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 91 ( 44 ~; 34 |; 6 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 70 ( 3 sgn 41 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(A,B)
& subset(B,A) ) ) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A) ).
fof(t12_xboole_1,conjecture,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ) ).
fof(t7_xboole_1,lemma,
! [A,B] : subset(A,set_union2(A,B)) ).
fof(t8_xboole_1,lemma,
! [A,B,C] :
( ( subset(A,B)
& subset(C,B) )
=> subset(set_union2(A,C),B) ) ).
fof(subgoal_0,plain,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
inference(strip,[],[t12_xboole_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( A != B
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(canonicalize,[],[d10_xboole_0]) ).
fof(normalize_0_1,plain,
! [A,B] :
( A != B
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ( A != B
| subset(A,B) )
& ( A != B
| subset(B,A) )
& ( ~ subset(A,B)
| ~ subset(B,A)
| A = B ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A] : subset(A,A),
inference(canonicalize,[],[reflexivity_r1_tarski]) ).
fof(normalize_0_5,plain,
! [A] : subset(A,A),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [A,B] :
( set_union2(A,B) != B
& subset(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
( set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != skolemFOFtoCNF_B_1
& subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( ~ subset(A,B)
| ~ subset(C,B)
| subset(set_union2(A,C),B) ),
inference(canonicalize,[],[t8_xboole_1]) ).
fof(normalize_0_10,plain,
! [A,B,C] :
( ~ subset(A,B)
| ~ subset(C,B)
| subset(set_union2(A,C),B) ),
inference(specialize,[],[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]) ).
fof(normalize_0_13,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(canonicalize,[],[t7_xboole_1]) ).
fof(normalize_0_14,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != skolemFOFtoCNF_B_1,
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ subset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_B_1)
| ~ subset(skolemFOFtoCNF_B_1,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))
| skolemFOFtoCNF_B_1 = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_0_2,plain,
subset(A,A),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_4,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ subset(A,B)
| ~ subset(C,B)
| subset(set_union2(A,C),B) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
( ~ subset(X_1014,skolemFOFtoCNF_B_1)
| ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| subset(set_union2(X_1014,skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_1014)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_7,plain,
( ~ subset(X_1014,skolemFOFtoCNF_B_1)
| subset(set_union2(X_1014,skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1)
| subset(set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_7:[bind(X_1014,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_9,plain,
subset(set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_12,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_13,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( set_union2(A,B) != set_union2(B,A)
| set_union2(B,A) = set_union2(A,B) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(set_union2(A,B))),bind(Y,$fot(set_union2(B,A)))]]) ).
cnf(refute_0_15,plain,
set_union2(B,A) = set_union2(A,B),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_15:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_17,plain,
( set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) != set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| ~ subset(set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)
| subset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_B_1) ),
introduced(tautology,[equality,[$cnf( subset(set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) ),[0],$fot(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_18,plain,
( ~ subset(set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1)
| subset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
subset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( subset(set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),skolemFOFtoCNF_B_1) )],[refute_0_9,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ subset(skolemFOFtoCNF_B_1,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))
| skolemFOFtoCNF_B_1 = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( subset(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_B_1) )],[refute_0_19,refute_0_1]) ).
cnf(refute_0_21,plain,
subset(A,set_union2(A,B)),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_22,plain,
( set_union2(A,B) != set_union2(B,A)
| ~ subset(A,set_union2(A,B))
| subset(A,set_union2(B,A)) ),
introduced(tautology,[equality,[$cnf( subset(A,set_union2(A,B)) ),[1],$fot(set_union2(B,A))]]) ).
cnf(refute_0_23,plain,
( ~ subset(A,set_union2(A,B))
| subset(A,set_union2(B,A)) ),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_0_10,refute_0_22]) ).
cnf(refute_0_24,plain,
subset(A,set_union2(B,A)),
inference(resolve,[$cnf( subset(A,set_union2(A,B)) )],[refute_0_21,refute_0_23]) ).
cnf(refute_0_25,plain,
subset(skolemFOFtoCNF_B_1,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),
inference(subst,[],[refute_0_24:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_26,plain,
skolemFOFtoCNF_B_1 = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_1,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_25,refute_0_20]) ).
cnf(refute_0_27,plain,
set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != skolemFOFtoCNF_B_1,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_28,plain,
( skolemFOFtoCNF_B_1 != set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = skolemFOFtoCNF_B_1 ),
inference(subst,[],[refute_0_13:[bind(X,$fot(skolemFOFtoCNF_B_1)),bind(Y,$fot(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_0_29,plain,
skolemFOFtoCNF_B_1 != set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_B_1) )],[refute_0_28,refute_0_27]) ).
cnf(refute_0_30,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_26,refute_0_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU126+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 10:32:20 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.94/1.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.94/1.16
% 0.94/1.16 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.94/1.17
%------------------------------------------------------------------------------