TSTP Solution File: SWV415+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV415+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 20:31:33 EDT 2022
% Result : Theorem 1.93s 2.09s
% Output : CNFRefutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 29 unt; 0 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 18 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 145 ( 25 sgn 54 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(main2_l12,lemma,
! [U,V,W,X,Y] : i(triple(U,W,X)) = i(triple(V,W,Y)) ).
fof(co2,conjecture,
! [U,V,W,X] : i(insert_cpq(triple(U,V,W),X)) = insert_pq(i(triple(U,V,W)),X) ).
fof(subgoal_0,plain,
! [U,V,W,X] : i(insert_cpq(triple(U,V,W),X)) = insert_pq(i(triple(U,V,W)),X),
inference(strip,[],[co2]) ).
fof(negate_0_0,plain,
~ ! [U,V,W,X] : i(insert_cpq(triple(U,V,W),X)) = insert_pq(i(triple(U,V,W)),X),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [U,V,W,X] : i(insert_cpq(triple(U,V,W),X)) != insert_pq(i(triple(U,V,W)),X),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
i(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1),skolemFOFtoCNF_X)) != insert_pq(i(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1)),skolemFOFtoCNF_X),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [U,V,W,X,Y] : i(triple(U,W,X)) = i(triple(V,W,Y)),
inference(canonicalize,[],[main2_l12]) ).
fof(normalize_0_3,plain,
! [U,V,W,X,Y] : i(triple(U,W,X)) = i(triple(V,W,Y)),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,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_5,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_4]) ).
fof(normalize_0_6,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_7,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_6]) ).
cnf(refute_0_0,plain,
i(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1),skolemFOFtoCNF_X)) != insert_pq(i(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1)),skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
i(triple(U,W,X)) = i(triple(V,W,Y)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
i(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1)) = i(triple(X_3047,skolemFOFtoCNF_V_2,X_3050)),
inference(subst,[],[refute_0_1:[bind(U,$fot(skolemFOFtoCNF_U)),bind(V,$fot(X_3047)),bind(W,$fot(skolemFOFtoCNF_V_2)),bind(X,$fot(skolemFOFtoCNF_W_1)),bind(Y,$fot(X_3050))]]) ).
cnf(refute_0_3,plain,
( i(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1),skolemFOFtoCNF_X)) != insert_pq(i(triple(X_3047,skolemFOFtoCNF_V_2,X_3050)),skolemFOFtoCNF_X)
| i(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1)) != i(triple(X_3047,skolemFOFtoCNF_V_2,X_3050))
| i(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1),skolemFOFtoCNF_X)) = insert_pq(i(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1)),skolemFOFtoCNF_X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(i(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1),skolemFOFtoCNF_X)),insert_pq(i(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1)),skolemFOFtoCNF_X)) ),[1,0],$fot(i(triple(X_3047,skolemFOFtoCNF_V_2,X_3050)))]]) ).
cnf(refute_0_4,plain,
( i(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1),skolemFOFtoCNF_X)) != insert_pq(i(triple(X_3047,skolemFOFtoCNF_V_2,X_3050)),skolemFOFtoCNF_X)
| i(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1),skolemFOFtoCNF_X)) = insert_pq(i(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1)),skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( $equal(i(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1)),i(triple(X_3047,skolemFOFtoCNF_V_2,X_3050))) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
i(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1),skolemFOFtoCNF_X)) != insert_pq(i(triple(X_3047,skolemFOFtoCNF_V_2,X_3050)),skolemFOFtoCNF_X),
inference(resolve,[$cnf( $equal(i(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1),skolemFOFtoCNF_X)),insert_pq(i(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1)),skolemFOFtoCNF_X)) )],[refute_0_4,refute_0_0]) ).
cnf(refute_0_6,plain,
i(triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),X_3049)) = i(triple(X_3047,insert_slb(V,pair(X,bottom)),X_3050)),
inference(subst,[],[refute_0_1:[bind(U,$fot(insert_pqp(U,X))),bind(V,$fot(X_3047)),bind(W,$fot(insert_slb(V,pair(X,bottom)))),bind(X,$fot(X_3049)),bind(Y,$fot(X_3050))]]) ).
cnf(refute_0_7,plain,
insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_8,plain,
insert_cpq(triple(U,V,X_3049),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),X_3049),
inference(subst,[],[refute_0_7:[bind(W,$fot(X_3049))]]) ).
cnf(refute_0_9,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_10,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_11,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( insert_cpq(triple(U,V,X_3049),X) != triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),X_3049)
| triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),X_3049) = insert_cpq(triple(U,V,X_3049),X) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(insert_cpq(triple(U,V,X_3049),X))),bind(Y0,$fot(triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),X_3049)))]]) ).
cnf(refute_0_13,plain,
triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),X_3049) = insert_cpq(triple(U,V,X_3049),X),
inference(resolve,[$cnf( $equal(insert_cpq(triple(U,V,X_3049),X),triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),X_3049)) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
( i(triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),X_3049)) != i(triple(X_3047,insert_slb(V,pair(X,bottom)),X_3050))
| triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),X_3049) != insert_cpq(triple(U,V,X_3049),X)
| i(insert_cpq(triple(U,V,X_3049),X)) = i(triple(X_3047,insert_slb(V,pair(X,bottom)),X_3050)) ),
introduced(tautology,[equality,[$cnf( $equal(i(triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),X_3049)),i(triple(X_3047,insert_slb(V,pair(X,bottom)),X_3050))) ),[0,0],$fot(insert_cpq(triple(U,V,X_3049),X))]]) ).
cnf(refute_0_15,plain,
( i(triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),X_3049)) != i(triple(X_3047,insert_slb(V,pair(X,bottom)),X_3050))
| i(insert_cpq(triple(U,V,X_3049),X)) = i(triple(X_3047,insert_slb(V,pair(X,bottom)),X_3050)) ),
inference(resolve,[$cnf( $equal(triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),X_3049),insert_cpq(triple(U,V,X_3049),X)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
i(insert_cpq(triple(U,V,X_3049),X)) = i(triple(X_3047,insert_slb(V,pair(X,bottom)),X_3050)),
inference(resolve,[$cnf( $equal(i(triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),X_3049)),i(triple(X_3047,insert_slb(V,pair(X,bottom)),X_3050))) )],[refute_0_6,refute_0_15]) ).
cnf(refute_0_17,plain,
i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_18,plain,
i(triple(X_3047,insert_slb(V,pair(X,bottom)),X_3050)) = insert_pq(i(triple(X_3047,V,X_3050)),X),
inference(subst,[],[refute_0_17:[bind(U,$fot(X_3047)),bind(W,$fot(X_3050)),bind(Y,$fot(bottom))]]) ).
cnf(refute_0_19,plain,
( i(insert_cpq(triple(U,V,X_3049),X)) != i(triple(X_3047,insert_slb(V,pair(X,bottom)),X_3050))
| i(triple(X_3047,insert_slb(V,pair(X,bottom)),X_3050)) != insert_pq(i(triple(X_3047,V,X_3050)),X)
| i(insert_cpq(triple(U,V,X_3049),X)) = insert_pq(i(triple(X_3047,V,X_3050)),X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(i(insert_cpq(triple(U,V,X_3049),X)),insert_pq(i(triple(X_3047,V,X_3050)),X)) ),[0],$fot(i(triple(X_3047,insert_slb(V,pair(X,bottom)),X_3050)))]]) ).
cnf(refute_0_20,plain,
( i(insert_cpq(triple(U,V,X_3049),X)) != i(triple(X_3047,insert_slb(V,pair(X,bottom)),X_3050))
| i(insert_cpq(triple(U,V,X_3049),X)) = insert_pq(i(triple(X_3047,V,X_3050)),X) ),
inference(resolve,[$cnf( $equal(i(triple(X_3047,insert_slb(V,pair(X,bottom)),X_3050)),insert_pq(i(triple(X_3047,V,X_3050)),X)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
i(insert_cpq(triple(U,V,X_3049),X)) = insert_pq(i(triple(X_3047,V,X_3050)),X),
inference(resolve,[$cnf( $equal(i(insert_cpq(triple(U,V,X_3049),X)),i(triple(X_3047,insert_slb(V,pair(X,bottom)),X_3050))) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
i(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1),skolemFOFtoCNF_X)) = insert_pq(i(triple(X_3047,skolemFOFtoCNF_V_2,X_3050)),skolemFOFtoCNF_X),
inference(subst,[],[refute_0_21:[bind(U,$fot(skolemFOFtoCNF_U)),bind(V,$fot(skolemFOFtoCNF_V_2)),bind(X,$fot(skolemFOFtoCNF_X)),bind(X_3049,$fot(skolemFOFtoCNF_W_1))]]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( $equal(i(insert_cpq(triple(skolemFOFtoCNF_U,skolemFOFtoCNF_V_2,skolemFOFtoCNF_W_1),skolemFOFtoCNF_X)),insert_pq(i(triple(X_3047,skolemFOFtoCNF_V_2,X_3050)),skolemFOFtoCNF_X)) )],[refute_0_22,refute_0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SWV415+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n023.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 : Wed Jun 15 22:24:20 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.93/2.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.93/2.09
% 1.93/2.09 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.93/2.09
%------------------------------------------------------------------------------