TSTP Solution File: SET639+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET639+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 03:36:15 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 18 unt; 0 def)
% Number of atoms : 62 ( 49 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 21 ~; 15 |; 7 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 18 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_intersection,axiom,
! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B) ).
fof(prove_th121,conjecture,
! [B,C] :
( ( subset(B,C)
& intersection(C,B) = empty_set )
=> B = empty_set ) ).
fof(subgoal_0,plain,
! [B,C] :
( ( subset(B,C)
& intersection(C,B) = empty_set )
=> B = empty_set ),
inference(strip,[],[prove_th121]) ).
fof(negate_0_0,plain,
~ ! [B,C] :
( ( subset(B,C)
& intersection(C,B) = empty_set )
=> B = empty_set ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C] :
( B != empty_set
& intersection(C,B) = empty_set
& subset(B,C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( skolemFOFtoCNF_B != empty_set
& intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B) = empty_set
& subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [B,C] :
( ~ subset(B,C)
| intersection(B,C) = B ),
inference(canonicalize,[],[subset_intersection]) ).
fof(normalize_0_4,plain,
! [B,C] :
( ~ subset(B,C)
| intersection(B,C) = B ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B) = empty_set,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_6,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[commutativity_of_intersection]) ).
fof(normalize_0_7,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
skolemFOFtoCNF_B != empty_set,
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ subset(B,C)
| intersection(B,C) = B ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
| intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_1:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_3,plain,
intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = skolemFOFtoCNF_B,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B) = empty_set,
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
intersection(B,C) = intersection(C,B),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_7,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_8,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( intersection(B,C) != intersection(C,B)
| intersection(C,B) = intersection(B,C) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(intersection(B,C))),bind(Y,$fot(intersection(C,B)))]]) ).
cnf(refute_0_10,plain,
intersection(C,B) = intersection(B,C),
inference(resolve,[$cnf( $equal(intersection(B,C),intersection(C,B)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B) = intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
inference(subst,[],[refute_0_10:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_12,plain,
( intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B) != empty_set
| intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B) != intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
| intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B),empty_set) ),[0],$fot(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_13,plain,
( intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B) != empty_set
| intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = empty_set ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B),intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = empty_set,
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B),empty_set) )],[refute_0_4,refute_0_13]) ).
cnf(refute_0_15,plain,
( intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) != empty_set
| intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) != skolemFOFtoCNF_B
| empty_set = skolemFOFtoCNF_B ),
introduced(tautology,[equality,[$cnf( $equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_B) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_16,plain,
( intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) != skolemFOFtoCNF_B
| empty_set = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
empty_set = skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),skolemFOFtoCNF_B) )],[refute_0_3,refute_0_16]) ).
cnf(refute_0_18,plain,
skolemFOFtoCNF_B != empty_set,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_19,plain,
( empty_set != skolemFOFtoCNF_B
| skolemFOFtoCNF_B = empty_set ),
inference(subst,[],[refute_0_8:[bind(X,$fot(empty_set)),bind(Y,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_20,plain,
empty_set != skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,empty_set) )],[refute_0_19,refute_0_18]) ).
cnf(refute_0_21,plain,
$false,
inference(resolve,[$cnf( $equal(empty_set,skolemFOFtoCNF_B) )],[refute_0_17,refute_0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET639+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 21:03:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------