TSTP Solution File: SYN386+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN386+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 : Thu Jul 21 09:01:59 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 1
% Syntax : Number of formulae : 48 ( 19 unt; 0 def)
% Number of atoms : 130 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 132 ( 50 ~; 38 |; 26 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 189 ( 7 sgn 101 !; 45 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2138,conjecture,
( ( ! [X] :
? [Y] : big_f(X,Y)
& ? [X] :
! [E] :
? [N] :
! [W] :
( big_s(N,W)
=> big_d(W,X,E) )
& ! [E] :
? [D] :
! [A,B] :
( big_d(A,B,D)
=> ! [Y,Z] :
( ( big_f(A,Y)
& big_f(B,Z) )
=> big_d(Y,Z,E) ) ) )
=> ? [Y] :
! [E] :
? [M] :
! [W] :
( big_s(M,W)
=> ! [Z] :
( big_f(W,Z)
=> big_d(Z,Y,E) ) ) ) ).
fof(subgoal_0,plain,
( ( ! [X] :
? [Y] : big_f(X,Y)
& ? [X] :
! [E] :
? [N] :
! [W] :
( big_s(N,W)
=> big_d(W,X,E) )
& ! [E] :
? [D] :
! [A,B] :
( big_d(A,B,D)
=> ! [Y,Z] :
( ( big_f(A,Y)
& big_f(B,Z) )
=> big_d(Y,Z,E) ) ) )
=> ? [Y] :
! [E] :
? [M] :
! [W] :
( big_s(M,W)
=> ! [Z] :
( big_f(W,Z)
=> big_d(Z,Y,E) ) ) ),
inference(strip,[],[x2138]) ).
fof(negate_0_0,plain,
~ ( ( ! [X] :
? [Y] : big_f(X,Y)
& ? [X] :
! [E] :
? [N] :
! [W] :
( big_s(N,W)
=> big_d(W,X,E) )
& ! [E] :
? [D] :
! [A,B] :
( big_d(A,B,D)
=> ! [Y,Z] :
( ( big_f(A,Y)
& big_f(B,Z) )
=> big_d(Y,Z,E) ) ) )
=> ? [Y] :
! [E] :
? [M] :
! [W] :
( big_s(M,W)
=> ! [Z] :
( big_f(W,Z)
=> big_d(Z,Y,E) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ? [X] :
! [E] :
? [N] :
! [W] :
( ~ big_s(N,W)
| big_d(W,X,E) )
& ! [E] :
? [D] :
! [A,B] :
( ~ big_d(A,B,D)
| ! [Y,Z] :
( ~ big_f(A,Y)
| ~ big_f(B,Z)
| big_d(Y,Z,E) ) )
& ! [X] :
? [Y] : big_f(X,Y)
& ! [Y] :
? [E] :
! [M] :
? [W] :
( big_s(M,W)
& ? [Z] :
( ~ big_d(Z,Y,E)
& big_f(W,Z) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [Y] :
? [E] :
! [M] :
? [W] :
( big_s(M,W)
& ? [Z] :
( ~ big_d(Z,Y,E)
& big_f(W,Z) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Y] :
? [E] :
! [M] :
? [W] :
( big_s(M,W)
& ? [Z] :
( ~ big_d(Z,Y,E)
& big_f(W,Z) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [Y,M] :
? [W] :
( big_s(M,W)
& ? [Z] :
( ~ big_d(Z,Y,skolemFOFtoCNF_E(Y))
& big_f(W,Z) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [M,Y] :
? [W] :
( big_s(M,W)
& ? [Z] :
( ~ big_d(Z,Y,skolemFOFtoCNF_E(Y))
& big_f(W,Z) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [M,Y] :
( big_s(M,skolemFOFtoCNF_W(M,Y))
& ? [Z] :
( ~ big_d(Z,Y,skolemFOFtoCNF_E(Y))
& big_f(skolemFOFtoCNF_W(M,Y),Z) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [M,Y] :
? [Z] :
( ~ big_d(Z,Y,skolemFOFtoCNF_E(Y))
& big_f(skolemFOFtoCNF_W(M,Y),Z) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [M,Y] :
( ~ big_d(skolemFOFtoCNF_Z(M,Y),Y,skolemFOFtoCNF_E(Y))
& big_f(skolemFOFtoCNF_W(M,Y),skolemFOFtoCNF_Z(M,Y)) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [M,Y] : ~ big_d(skolemFOFtoCNF_Z(M,Y),Y,skolemFOFtoCNF_E(Y)),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [M,Y] : big_f(skolemFOFtoCNF_W(M,Y),skolemFOFtoCNF_Z(M,Y)),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_10,plain,
! [M,Y] : big_s(M,skolemFOFtoCNF_W(M,Y)),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_11,plain,
? [X] :
! [E] :
? [N] :
! [W] :
( ~ big_s(N,W)
| big_d(W,X,E) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_12,plain,
! [E] :
? [N] :
! [W] :
( ~ big_s(N,W)
| big_d(W,skolemFOFtoCNF_X,E) ),
inference(skolemize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [E] :
? [N] :
! [W] :
( ~ big_s(N,W)
| big_d(W,skolemFOFtoCNF_X,E) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [E,W] :
( ~ big_s(skolemFOFtoCNF_N(E),W)
| big_d(W,skolemFOFtoCNF_X,E) ),
inference(skolemize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [E,W] :
( ~ big_s(skolemFOFtoCNF_N(E),W)
| big_d(W,skolemFOFtoCNF_X,E) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X] :
? [Y] : big_f(X,Y),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_17,plain,
! [X] :
? [Y] : big_f(X,Y),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X] : big_f(X,skolemFOFtoCNF_Y(X)),
inference(skolemize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [E] :
? [D] :
! [A,B] :
( ~ big_d(A,B,D)
| ! [Y,Z] :
( ~ big_f(A,Y)
| ~ big_f(B,Z)
| big_d(Y,Z,E) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_20,plain,
! [E] :
? [D] :
! [A,B] :
( ~ big_d(A,B,D)
| ! [Y,Z] :
( ~ big_f(A,Y)
| ~ big_f(B,Z)
| big_d(Y,Z,E) ) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [E,A,B] :
( ~ big_d(A,B,skolemFOFtoCNF_D(E))
| ! [Y,Z] :
( ~ big_f(A,Y)
| ~ big_f(B,Z)
| big_d(Y,Z,E) ) ),
inference(skolemize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [A,B,E] :
( ~ big_d(A,B,skolemFOFtoCNF_D(E))
| ! [Y,Z] :
( ~ big_f(A,Y)
| ~ big_f(B,Z)
| big_d(Y,Z,E) ) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A,B,E,Y,Z] :
( ~ big_d(A,B,skolemFOFtoCNF_D(E))
| ~ big_f(A,Y)
| ~ big_f(B,Z)
| big_d(Y,Z,E) ),
inference(clausify,[],[normalize_0_22]) ).
cnf(refute_0_0,plain,
~ big_d(skolemFOFtoCNF_Z(M,Y),Y,skolemFOFtoCNF_E(Y)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_1,plain,
~ big_d(skolemFOFtoCNF_Z(skolemFOFtoCNF_N(skolemFOFtoCNF_D(skolemFOFtoCNF_E(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))),skolemFOFtoCNF_Y(skolemFOFtoCNF_X)),skolemFOFtoCNF_Y(skolemFOFtoCNF_X),skolemFOFtoCNF_E(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))),
inference(subst,[],[refute_0_0:[bind(M,$fot(skolemFOFtoCNF_N(skolemFOFtoCNF_D(skolemFOFtoCNF_E(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))))),bind(Y,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_2,plain,
big_f(skolemFOFtoCNF_W(M,Y),skolemFOFtoCNF_Z(M,Y)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_3,plain,
big_f(skolemFOFtoCNF_W(skolemFOFtoCNF_N(skolemFOFtoCNF_D(X_51)),X_50),skolemFOFtoCNF_Z(skolemFOFtoCNF_N(skolemFOFtoCNF_D(X_51)),X_50)),
inference(subst,[],[refute_0_2:[bind(M,$fot(skolemFOFtoCNF_N(skolemFOFtoCNF_D(X_51)))),bind(Y,$fot(X_50))]]) ).
cnf(refute_0_4,plain,
big_s(M,skolemFOFtoCNF_W(M,Y)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_5,plain,
big_s(skolemFOFtoCNF_N(X_7),skolemFOFtoCNF_W(skolemFOFtoCNF_N(X_7),Y)),
inference(subst,[],[refute_0_4:[bind(M,$fot(skolemFOFtoCNF_N(X_7)))]]) ).
cnf(refute_0_6,plain,
( ~ big_s(skolemFOFtoCNF_N(E),W)
| big_d(W,skolemFOFtoCNF_X,E) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_7,plain,
( ~ big_s(skolemFOFtoCNF_N(X_7),skolemFOFtoCNF_W(skolemFOFtoCNF_N(X_7),Y))
| big_d(skolemFOFtoCNF_W(skolemFOFtoCNF_N(X_7),Y),skolemFOFtoCNF_X,X_7) ),
inference(subst,[],[refute_0_6:[bind(E,$fot(X_7)),bind(W,$fot(skolemFOFtoCNF_W(skolemFOFtoCNF_N(X_7),Y)))]]) ).
cnf(refute_0_8,plain,
big_d(skolemFOFtoCNF_W(skolemFOFtoCNF_N(X_7),Y),skolemFOFtoCNF_X,X_7),
inference(resolve,[$cnf( big_s(skolemFOFtoCNF_N(X_7),skolemFOFtoCNF_W(skolemFOFtoCNF_N(X_7),Y)) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
big_d(skolemFOFtoCNF_W(skolemFOFtoCNF_N(skolemFOFtoCNF_D(X_48)),Y),skolemFOFtoCNF_X,skolemFOFtoCNF_D(X_48)),
inference(subst,[],[refute_0_8:[bind(X_7,$fot(skolemFOFtoCNF_D(X_48)))]]) ).
cnf(refute_0_10,plain,
big_f(X,skolemFOFtoCNF_Y(X)),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_11,plain,
big_f(X_15,skolemFOFtoCNF_Y(X_15)),
inference(subst,[],[refute_0_10:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_12,plain,
( ~ big_d(A,B,skolemFOFtoCNF_D(E))
| ~ big_f(A,Y)
| ~ big_f(B,Z)
| big_d(Y,Z,E) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_13,plain,
( ~ big_d(X_14,X_15,skolemFOFtoCNF_D(X_16))
| ~ big_f(X_14,X_17)
| ~ big_f(X_15,skolemFOFtoCNF_Y(X_15))
| big_d(X_17,skolemFOFtoCNF_Y(X_15),X_16) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_14)),bind(B,$fot(X_15)),bind(E,$fot(X_16)),bind(Y,$fot(X_17)),bind(Z,$fot(skolemFOFtoCNF_Y(X_15)))]]) ).
cnf(refute_0_14,plain,
( ~ big_d(X_14,X_15,skolemFOFtoCNF_D(X_16))
| ~ big_f(X_14,X_17)
| big_d(X_17,skolemFOFtoCNF_Y(X_15),X_16) ),
inference(resolve,[$cnf( big_f(X_15,skolemFOFtoCNF_Y(X_15)) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ big_d(skolemFOFtoCNF_W(skolemFOFtoCNF_N(skolemFOFtoCNF_D(X_48)),Y),skolemFOFtoCNF_X,skolemFOFtoCNF_D(X_48))
| ~ big_f(skolemFOFtoCNF_W(skolemFOFtoCNF_N(skolemFOFtoCNF_D(X_48)),Y),X_49)
| big_d(X_49,skolemFOFtoCNF_Y(skolemFOFtoCNF_X),X_48) ),
inference(subst,[],[refute_0_14:[bind(X_14,$fot(skolemFOFtoCNF_W(skolemFOFtoCNF_N(skolemFOFtoCNF_D(X_48)),Y))),bind(X_15,$fot(skolemFOFtoCNF_X)),bind(X_16,$fot(X_48)),bind(X_17,$fot(X_49))]]) ).
cnf(refute_0_16,plain,
( ~ big_f(skolemFOFtoCNF_W(skolemFOFtoCNF_N(skolemFOFtoCNF_D(X_48)),Y),X_49)
| big_d(X_49,skolemFOFtoCNF_Y(skolemFOFtoCNF_X),X_48) ),
inference(resolve,[$cnf( big_d(skolemFOFtoCNF_W(skolemFOFtoCNF_N(skolemFOFtoCNF_D(X_48)),Y),skolemFOFtoCNF_X,skolemFOFtoCNF_D(X_48)) )],[refute_0_9,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ big_f(skolemFOFtoCNF_W(skolemFOFtoCNF_N(skolemFOFtoCNF_D(X_51)),X_50),skolemFOFtoCNF_Z(skolemFOFtoCNF_N(skolemFOFtoCNF_D(X_51)),X_50))
| big_d(skolemFOFtoCNF_Z(skolemFOFtoCNF_N(skolemFOFtoCNF_D(X_51)),X_50),skolemFOFtoCNF_Y(skolemFOFtoCNF_X),X_51) ),
inference(subst,[],[refute_0_16:[bind(Y,$fot(X_50)),bind(X_48,$fot(X_51)),bind(X_49,$fot(skolemFOFtoCNF_Z(skolemFOFtoCNF_N(skolemFOFtoCNF_D(X_51)),X_50)))]]) ).
cnf(refute_0_18,plain,
big_d(skolemFOFtoCNF_Z(skolemFOFtoCNF_N(skolemFOFtoCNF_D(X_51)),X_50),skolemFOFtoCNF_Y(skolemFOFtoCNF_X),X_51),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_W(skolemFOFtoCNF_N(skolemFOFtoCNF_D(X_51)),X_50),skolemFOFtoCNF_Z(skolemFOFtoCNF_N(skolemFOFtoCNF_D(X_51)),X_50)) )],[refute_0_3,refute_0_17]) ).
cnf(refute_0_19,plain,
big_d(skolemFOFtoCNF_Z(skolemFOFtoCNF_N(skolemFOFtoCNF_D(skolemFOFtoCNF_E(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))),skolemFOFtoCNF_Y(skolemFOFtoCNF_X)),skolemFOFtoCNF_Y(skolemFOFtoCNF_X),skolemFOFtoCNF_E(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))),
inference(subst,[],[refute_0_18:[bind(X_50,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))),bind(X_51,$fot(skolemFOFtoCNF_E(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))))]]) ).
cnf(refute_0_20,plain,
$false,
inference(resolve,[$cnf( big_d(skolemFOFtoCNF_Z(skolemFOFtoCNF_N(skolemFOFtoCNF_D(skolemFOFtoCNF_E(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))),skolemFOFtoCNF_Y(skolemFOFtoCNF_X)),skolemFOFtoCNF_Y(skolemFOFtoCNF_X),skolemFOFtoCNF_E(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))) )],[refute_0_19,refute_0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN386+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n012.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 : Mon Jul 11 13:14:58 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
% 0.20/0.36
%------------------------------------------------------------------------------