TSTP Solution File: SWV377+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV377+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 : Wed Jul 20 20:31:25 EDT 2022
% Result : Theorem 0.48s 0.68s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 25 unt; 0 def)
% Number of atoms : 74 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 61 ( 34 ~; 20 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 80 ( 9 sgn 39 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax40,axiom,
! [U,V] :
( ok(triple(U,V,bad))
<=> $false ) ).
fof(ax41,axiom,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> W = bad ) ).
fof(ax42,axiom,
! [U,V,W,X] : insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W) ).
fof(l13_co,conjecture,
! [U,V,W,X] :
( ~ ok(triple(U,V,W))
=> ~ ok(insert_cpq(triple(U,V,W),X)) ) ).
fof(subgoal_0,plain,
! [U,V,W,X] :
( ~ ok(triple(U,V,W))
=> ~ ok(insert_cpq(triple(U,V,W),X)) ),
inference(strip,[],[l13_co]) ).
fof(negate_0_0,plain,
~ ! [U,V,W,X] :
( ~ ok(triple(U,V,W))
=> ~ ok(insert_cpq(triple(U,V,W),X)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [U,V,W] :
( ~ ok(triple(U,V,W))
& ? [X] : ok(insert_cpq(triple(U,V,W),X)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ ok(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W))
& ? [X] : ok(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),X)) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [X] : ok(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),X)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
ok(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X)),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
~ ok(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_5,plain,
! [U,V,W] :
( W = bad
| ok(triple(U,V,W)) ),
inference(canonicalize,[],[ax41]) ).
fof(normalize_0_6,plain,
! [U,V,W] :
( W = bad
| ok(triple(U,V,W)) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [U,V] : ~ ok(triple(U,V,bad)),
inference(canonicalize,[],[ax40]) ).
fof(normalize_0_8,plain,
! [U,V] : ~ ok(triple(U,V,bad)),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [U,V,W,X] : insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W),
inference(canonicalize,[],[ax42]) ).
fof(normalize_0_10,plain,
! [U,V,W,X] : insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W),
inference(specialize,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
ok(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
~ ok(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( W = bad
| ok(triple(U,V,W)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( skolemFOFtoCNF_W = bad
| ok(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W)) ),
inference(subst,[],[refute_0_2:[bind(U,$fot(skolemFOFtoCNF_U)),bind(V,$fot(skolemFOFtoCNF_V)),bind(W,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_4,plain,
skolemFOFtoCNF_W = bad,
inference(resolve,[$cnf( ok(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W)) )],[refute_0_3,refute_0_1]) ).
cnf(refute_0_5,plain,
triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W) = triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),
introduced(tautology,[refl,[$fot(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W))]]) ).
cnf(refute_0_6,plain,
( skolemFOFtoCNF_W != bad
| triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W) != triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W)
| triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W) = triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad) ),
introduced(tautology,[equality,[$cnf( $equal(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W)) ),[1,2],$fot(bad)]]) ).
cnf(refute_0_7,plain,
( skolemFOFtoCNF_W != bad
| triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W) = triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad) ),
inference(resolve,[$cnf( $equal(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W) = triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W,bad) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X) = insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X),
introduced(tautology,[refl,[$fot(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X))]]) ).
cnf(refute_0_10,plain,
( insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X) != insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X)
| triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W) != triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad)
| insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X) = insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad),skolemFOFtoCNF_X) ),
introduced(tautology,[equality,[$cnf( $equal(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X),insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X)) ),[1,0],$fot(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad))]]) ).
cnf(refute_0_11,plain,
( triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W) != triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad)
| insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X) = insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad),skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( $equal(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X),insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X) = insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad),skolemFOFtoCNF_X),
inference(resolve,[$cnf( $equal(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad)) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
( insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X) != insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad),skolemFOFtoCNF_X)
| ~ ok(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X))
| ok(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad),skolemFOFtoCNF_X)) ),
introduced(tautology,[equality,[$cnf( ok(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X)) ),[0],$fot(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad),skolemFOFtoCNF_X))]]) ).
cnf(refute_0_14,plain,
( ~ ok(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X))
| ok(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad),skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( $equal(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X),insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad),skolemFOFtoCNF_X)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
ok(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad),skolemFOFtoCNF_X)),
inference(resolve,[$cnf( ok(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),skolemFOFtoCNF_X)) )],[refute_0_0,refute_0_14]) ).
cnf(refute_0_16,plain,
~ ok(triple(U,V,bad)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_17,plain,
~ ok(triple(insert_pqp(X_224,X_227),insert_slb(X_225,pair(X_227,bottom)),bad)),
inference(subst,[],[refute_0_16:[bind(U,$fot(insert_pqp(X_224,X_227))),bind(V,$fot(insert_slb(X_225,pair(X_227,bottom))))]]) ).
cnf(refute_0_18,plain,
insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_19,plain,
insert_cpq(triple(X_224,X_225,bad),X_227) = triple(insert_pqp(X_224,X_227),insert_slb(X_225,pair(X_227,bottom)),bad),
inference(subst,[],[refute_0_18:[bind(U,$fot(X_224)),bind(V,$fot(X_225)),bind(W,$fot(bad)),bind(X,$fot(X_227))]]) ).
cnf(refute_0_20,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_21,plain,
( X0 != X0
| X0 != Y
| Y = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y)]]) ).
cnf(refute_0_22,plain,
( X0 != Y
| Y = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( insert_cpq(triple(X_224,X_225,bad),X_227) != triple(insert_pqp(X_224,X_227),insert_slb(X_225,pair(X_227,bottom)),bad)
| triple(insert_pqp(X_224,X_227),insert_slb(X_225,pair(X_227,bottom)),bad) = insert_cpq(triple(X_224,X_225,bad),X_227) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(insert_cpq(triple(X_224,X_225,bad),X_227))),bind(Y,$fot(triple(insert_pqp(X_224,X_227),insert_slb(X_225,pair(X_227,bottom)),bad)))]]) ).
cnf(refute_0_24,plain,
triple(insert_pqp(X_224,X_227),insert_slb(X_225,pair(X_227,bottom)),bad) = insert_cpq(triple(X_224,X_225,bad),X_227),
inference(resolve,[$cnf( $equal(insert_cpq(triple(X_224,X_225,bad),X_227),triple(insert_pqp(X_224,X_227),insert_slb(X_225,pair(X_227,bottom)),bad)) )],[refute_0_19,refute_0_23]) ).
cnf(refute_0_25,plain,
( triple(insert_pqp(X_224,X_227),insert_slb(X_225,pair(X_227,bottom)),bad) != insert_cpq(triple(X_224,X_225,bad),X_227)
| ~ ok(insert_cpq(triple(X_224,X_225,bad),X_227))
| ok(triple(insert_pqp(X_224,X_227),insert_slb(X_225,pair(X_227,bottom)),bad)) ),
introduced(tautology,[equality,[$cnf( ~ ok(triple(insert_pqp(X_224,X_227),insert_slb(X_225,pair(X_227,bottom)),bad)) ),[0],$fot(insert_cpq(triple(X_224,X_225,bad),X_227))]]) ).
cnf(refute_0_26,plain,
( ~ ok(insert_cpq(triple(X_224,X_225,bad),X_227))
| ok(triple(insert_pqp(X_224,X_227),insert_slb(X_225,pair(X_227,bottom)),bad)) ),
inference(resolve,[$cnf( $equal(triple(insert_pqp(X_224,X_227),insert_slb(X_225,pair(X_227,bottom)),bad),insert_cpq(triple(X_224,X_225,bad),X_227)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
~ ok(insert_cpq(triple(X_224,X_225,bad),X_227)),
inference(resolve,[$cnf( ok(triple(insert_pqp(X_224,X_227),insert_slb(X_225,pair(X_227,bottom)),bad)) )],[refute_0_26,refute_0_17]) ).
cnf(refute_0_28,plain,
~ ok(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad),skolemFOFtoCNF_X)),
inference(subst,[],[refute_0_27:[bind(X_224,$fot(skolemFOFtoCNF_U)),bind(X_225,$fot(skolemFOFtoCNF_V)),bind(X_227,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( ok(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V,bad),skolemFOFtoCNF_X)) )],[refute_0_15,refute_0_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV377+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Tue Jun 14 14:47:03 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.48/0.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.68
% 0.48/0.68 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.48/0.68
%------------------------------------------------------------------------------