TSTP Solution File: SWV366+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV366+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 20:31:23 EDT 2022
% Result : Theorem 0.60s 0.84s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 18 unt; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 19 ~; 10 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 100 ( 11 sgn 64 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax55,axiom,
! [U,V,W,X,Y] : i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X) ).
fof(l2_co,conjecture,
! [U] :
( ! [V,W,X,Y] : i(triple(V,U,X)) = i(triple(W,U,Y))
=> ! [Z,X1,X2,X3,X4,X5] : i(triple(Z,insert_slb(U,pair(X4,X5)),X2)) = i(triple(X1,insert_slb(U,pair(X4,X5)),X3)) ) ).
fof(subgoal_0,plain,
! [U] :
( ! [V,W,X,Y] : i(triple(V,U,X)) = i(triple(W,U,Y))
=> ! [Z,X1,X2,X3,X4,X5] : i(triple(Z,insert_slb(U,pair(X4,X5)),X2)) = i(triple(X1,insert_slb(U,pair(X4,X5)),X3)) ),
inference(strip,[],[l2_co]) ).
fof(negate_0_0,plain,
~ ! [U] :
( ! [V,W,X,Y] : i(triple(V,U,X)) = i(triple(W,U,Y))
=> ! [Z,X1,X2,X3,X4,X5] : i(triple(Z,insert_slb(U,pair(X4,X5)),X2)) = i(triple(X1,insert_slb(U,pair(X4,X5)),X3)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [U] :
( ? [X1,X2,X3,X4,X5,Z] : i(triple(Z,insert_slb(U,pair(X4,X5)),X2)) != i(triple(X1,insert_slb(U,pair(X4,X5)),X3))
& ! [V,W,X,Y] : i(triple(V,U,X)) = i(triple(W,U,Y)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ? [X1,X2,X3,X4,X5,Z] : i(triple(Z,insert_slb(skolemFOFtoCNF_U,pair(X4,X5)),X2)) != i(triple(X1,insert_slb(skolemFOFtoCNF_U,pair(X4,X5)),X3))
& ! [V,W,X,Y] : i(triple(V,skolemFOFtoCNF_U,X)) = i(triple(W,skolemFOFtoCNF_U,Y)) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [X1,X2,X3,X4,X5,Z] : i(triple(Z,insert_slb(skolemFOFtoCNF_U,pair(X4,X5)),X2)) != i(triple(X1,insert_slb(skolemFOFtoCNF_U,pair(X4,X5)),X3)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)) != i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [U,V,W,X,Y] : i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X),
inference(canonicalize,[],[ax55]) ).
fof(normalize_0_5,plain,
! [U,V,W,X,Y] : i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [V,W,X,Y] : i(triple(V,skolemFOFtoCNF_U,X)) = i(triple(W,skolemFOFtoCNF_U,Y)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_7,plain,
! [V,W,X,Y] : i(triple(V,skolemFOFtoCNF_U,X)) = i(triple(W,skolemFOFtoCNF_U,Y)),
inference(specialize,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)) != i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)) = insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4),
inference(subst,[],[refute_0_1:[bind(U,$fot(skolemFOFtoCNF_Z)),bind(V,$fot(skolemFOFtoCNF_U)),bind(W,$fot(skolemFOFtoCNF_X2)),bind(X,$fot(skolemFOFtoCNF_X4)),bind(Y,$fot(skolemFOFtoCNF_X5))]]) ).
cnf(refute_0_3,plain,
( i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)) != insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4)
| insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3))
| i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)) = i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)),i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3))) ),[0],$fot(insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4))]]) ).
cnf(refute_0_4,plain,
( insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3))
| i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)) = i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)) ),
inference(resolve,[$cnf( $equal(i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)),insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)) = insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4),
inference(subst,[],[refute_0_1:[bind(U,$fot(skolemFOFtoCNF_X1)),bind(V,$fot(skolemFOFtoCNF_U)),bind(W,$fot(skolemFOFtoCNF_X3)),bind(X,$fot(skolemFOFtoCNF_X4)),bind(Y,$fot(skolemFOFtoCNF_X5))]]) ).
cnf(refute_0_6,plain,
( i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)) != insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4)
| insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4)
| insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) = i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4),i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3))) ),[1],$fot(insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4))]]) ).
cnf(refute_0_7,plain,
( insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4)
| insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) = i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)) ),
inference(resolve,[$cnf( $equal(i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)),insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4)
| i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)) = i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3)) ),
inference(resolve,[$cnf( $equal(insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4),i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3))) )],[refute_0_7,refute_0_4]) ).
cnf(refute_0_9,plain,
insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4),
inference(resolve,[$cnf( $equal(i(triple(skolemFOFtoCNF_Z,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X2)),i(triple(skolemFOFtoCNF_X1,insert_slb(skolemFOFtoCNF_U,pair(skolemFOFtoCNF_X4,skolemFOFtoCNF_X5)),skolemFOFtoCNF_X3))) )],[refute_0_8,refute_0_0]) ).
cnf(refute_0_10,plain,
i(triple(V,skolemFOFtoCNF_U,X)) = i(triple(W,skolemFOFtoCNF_U,Y)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_11,plain,
i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)) = i(triple(X_665,skolemFOFtoCNF_U,X_667)),
inference(subst,[],[refute_0_10:[bind(V,$fot(skolemFOFtoCNF_X1)),bind(W,$fot(X_665)),bind(X,$fot(skolemFOFtoCNF_X3)),bind(Y,$fot(X_667))]]) ).
cnf(refute_0_12,plain,
( i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)) != i(triple(X_665,skolemFOFtoCNF_U,X_667))
| insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != insert_pq(i(triple(X_665,skolemFOFtoCNF_U,X_667)),skolemFOFtoCNF_X4)
| insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) = insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4) ),
introduced(tautology,[equality,[$cnf( ~ $equal(insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4),insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4)) ),[1,0],$fot(i(triple(X_665,skolemFOFtoCNF_U,X_667)))]]) ).
cnf(refute_0_13,plain,
( insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != insert_pq(i(triple(X_665,skolemFOFtoCNF_U,X_667)),skolemFOFtoCNF_X4)
| insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) = insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4) ),
inference(resolve,[$cnf( $equal(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),i(triple(X_665,skolemFOFtoCNF_U,X_667))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != insert_pq(i(triple(X_665,skolemFOFtoCNF_U,X_667)),skolemFOFtoCNF_X4),
inference(resolve,[$cnf( $equal(insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4),insert_pq(i(triple(skolemFOFtoCNF_X1,skolemFOFtoCNF_U,skolemFOFtoCNF_X3)),skolemFOFtoCNF_X4)) )],[refute_0_13,refute_0_9]) ).
cnf(refute_0_15,plain,
insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) != insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4),
inference(subst,[],[refute_0_14:[bind(X_665,$fot(skolemFOFtoCNF_Z)),bind(X_667,$fot(skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_16,plain,
insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4) = insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4),
introduced(tautology,[refl,[$fot(insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4))]]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( $equal(insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4),insert_pq(i(triple(skolemFOFtoCNF_Z,skolemFOFtoCNF_U,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X4)) )],[refute_0_16,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV366+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 15 04:50:39 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.60/0.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.84
% 0.60/0.84 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.60/0.85
%------------------------------------------------------------------------------