TSTP Solution File: SEU140+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU140+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 12:38:40 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 14 unt; 0 def)
% Number of atoms : 85 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 73 ( 33 ~; 24 |; 8 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ) ).
fof(t26_xboole_1,axiom,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ) ).
fof(t3_xboole_1,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ) ).
fof(t63_xboole_1,conjecture,
! [A,B,C] :
( ( subset(A,B)
& disjoint(B,C) )
=> disjoint(A,C) ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( ( subset(A,B)
& disjoint(B,C) )
=> disjoint(A,C) ),
inference(strip,[],[t63_xboole_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( ( subset(A,B)
& disjoint(B,C) )
=> disjoint(A,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
<=> ~ disjoint(A,B) ),
inference(canonicalize,[],[d7_xboole_0]) ).
fof(normalize_0_1,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
<=> ~ disjoint(A,B) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
| disjoint(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A] :
( ~ subset(A,empty_set)
| A = empty_set ),
inference(canonicalize,[],[t3_xboole_1]) ).
fof(normalize_0_5,plain,
! [A] :
( ~ subset(A,empty_set)
| A = empty_set ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [A,B,C] :
( ~ disjoint(A,C)
& disjoint(B,C)
& subset(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
( ~ disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
& disjoint(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
& subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ~ subset(A,B)
| ! [C] : subset(set_intersection2(A,C),set_intersection2(B,C)) ),
inference(canonicalize,[],[t26_xboole_1]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ~ subset(A,B)
| ! [C] : subset(set_intersection2(A,C),set_intersection2(B,C)) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C] :
( ~ subset(A,B)
| subset(set_intersection2(A,C),set_intersection2(B,C)) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
disjoint(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_13,plain,
! [A,B] :
( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_14,plain,
~ disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
( set_intersection2(A,B) != empty_set
| disjoint(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) != empty_set
| disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_2,plain,
( ~ subset(A,empty_set)
| A = empty_set ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),empty_set)
| set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) = empty_set ),
inference(subst,[],[refute_0_2:[bind(A,$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_4,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ subset(A,B)
| subset(set_intersection2(A,C),set_intersection2(B,C)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_6,plain,
( ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| subset(set_intersection2(skolemFOFtoCNF_A_2,X_27),set_intersection2(skolemFOFtoCNF_B,X_27)) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(X_27))]]) ).
cnf(refute_0_7,plain,
subset(set_intersection2(skolemFOFtoCNF_A_2,X_27),set_intersection2(skolemFOFtoCNF_B,X_27)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
inference(subst,[],[refute_0_7:[bind(X_27,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_9,plain,
disjoint(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_11,plain,
( ~ disjoint(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = empty_set ),
inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_12,plain,
set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = empty_set,
inference(resolve,[$cnf( disjoint(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != empty_set
| ~ subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
| subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),empty_set) ),
introduced(tautology,[equality,[$cnf( subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_14,plain,
( ~ subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
| subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),empty_set) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),empty_set) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),empty_set),
inference(resolve,[$cnf( subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_8,refute_0_14]) ).
cnf(refute_0_16,plain,
set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) = empty_set,
inference(resolve,[$cnf( subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),empty_set) )],[refute_0_15,refute_0_3]) ).
cnf(refute_0_17,plain,
( empty_set != empty_set
| set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) != empty_set
| set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_18,plain,
( empty_set != empty_set
| set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) = empty_set ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),empty_set) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( empty_set != empty_set
| disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),empty_set) )],[refute_0_18,refute_0_1]) ).
cnf(refute_0_20,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_21,plain,
disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_20,refute_0_19]) ).
cnf(refute_0_22,plain,
~ disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) )],[refute_0_21,refute_0_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU140+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 05:15:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------