%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN069+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 08:59:15 EDT 2022
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 53 ( 11 unt; 0 def)
% Number of atoms : 167 ( 0 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 183 ( 69 ~; 73 |; 37 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 65 ( 10 sgn 35 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel45_1,axiom,
! [X] :
( ( big_f(X)
& ! [Y] :
( ( big_g(Y)
& big_h(X,Y) )
=> big_j(X,Y) ) )
=> ! [Y1] :
( big_g(Y1)
& big_h(X,Y1)
& big_k(Y1) ) ) ).
fof(pel45_2,axiom,
~ ? [Y] :
( big_l(Y)
& big_k(Y) ) ).
fof(pel45_3,axiom,
? [X] :
( big_f(X)
& ! [Y] :
( big_h(X,Y)
=> big_l(Y) )
& ! [Y1] :
( ( big_g(Y1)
& big_h(X,Y1) )
=> big_j(X,Y1) ) ) ).
fof(pel45,conjecture,
? [X] :
( big_f(X)
& ~ ? [Y] :
( big_g(Y)
& big_h(X,Y) ) ) ).
fof(subgoal_0,plain,
? [X] :
( big_f(X)
& ~ ? [Y] :
( big_g(Y)
& big_h(X,Y) ) ),
inference(strip,[],[pel45]) ).
fof(negate_0_0,plain,
~ ? [X] :
( big_f(X)
& ~ ? [Y] :
( big_g(Y)
& big_h(X,Y) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [Y] :
( ~ big_k(Y)
| ~ big_l(Y) ),
inference(canonicalize,[],[pel45_2]) ).
fof(normalize_0_1,plain,
! [Y] :
( ~ big_k(Y)
| ~ big_l(Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [X] :
( big_f(X)
& ! [Y] :
( ~ big_h(X,Y)
| big_l(Y) )
& ! [Y1] :
( ~ big_g(Y1)
| ~ big_h(X,Y1)
| big_j(X,Y1) ) ),
inference(canonicalize,[],[pel45_3]) ).
fof(normalize_0_3,plain,
( big_f(skolemFOFtoCNF_X)
& ! [Y] :
( ~ big_h(skolemFOFtoCNF_X,Y)
| big_l(Y) )
& ! [Y1] :
( ~ big_g(Y1)
| ~ big_h(skolemFOFtoCNF_X,Y1)
| big_j(skolemFOFtoCNF_X,Y1) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Y] :
( ~ big_h(skolemFOFtoCNF_X,Y)
| big_l(Y) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Y] :
( ~ big_h(skolemFOFtoCNF_X,Y)
| big_l(Y) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
big_f(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_7,plain,
! [X] :
( ~ big_f(X)
| ? [Y] :
( big_g(Y)
& big_h(X,Y) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_8,plain,
! [X] :
( ~ big_f(X)
| ? [Y] :
( big_g(Y)
& big_h(X,Y) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X] :
( ( ~ big_f(X)
| big_g(skolemFOFtoCNF_Y_1(X)) )
& ( ~ big_f(X)
| big_h(X,skolemFOFtoCNF_Y_1(X)) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X] :
( ~ big_f(X)
| big_h(X,skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X] :
( ~ big_f(X)
| ( ! [Y1] : big_g(Y1)
& ! [Y1] : big_h(X,Y1)
& ! [Y1] : big_k(Y1) )
| ? [Y] :
( ~ big_j(X,Y)
& big_g(Y)
& big_h(X,Y) ) ),
inference(canonicalize,[],[pel45_1]) ).
fof(normalize_0_12,plain,
! [X] :
( ~ big_f(X)
| ( ! [Y1] : big_g(Y1)
& ! [Y1] : big_h(X,Y1)
& ! [Y1] : big_k(Y1) )
| ? [Y] :
( ~ big_j(X,Y)
& big_g(Y)
& big_h(X,Y) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y1] :
( ( ~ big_f(X)
| ~ big_j(X,skolemFOFtoCNF_Y(X))
| big_g(Y1) )
& ( ~ big_f(X)
| ~ big_j(X,skolemFOFtoCNF_Y(X))
| big_h(X,Y1) )
& ( ~ big_f(X)
| ~ big_j(X,skolemFOFtoCNF_Y(X))
| big_k(Y1) )
& ( ~ big_f(X)
| big_g(Y1)
| big_g(skolemFOFtoCNF_Y(X)) )
& ( ~ big_f(X)
| big_g(Y1)
| big_h(X,skolemFOFtoCNF_Y(X)) )
& ( ~ big_f(X)
| big_g(skolemFOFtoCNF_Y(X))
| big_h(X,Y1) )
& ( ~ big_f(X)
| big_g(skolemFOFtoCNF_Y(X))
| big_k(Y1) )
& ( ~ big_f(X)
| big_h(X,Y1)
| big_h(X,skolemFOFtoCNF_Y(X)) )
& ( ~ big_f(X)
| big_h(X,skolemFOFtoCNF_Y(X))
| big_k(Y1) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y1] :
( ~ big_f(X)
| ~ big_j(X,skolemFOFtoCNF_Y(X))
| big_k(Y1) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [Y1] :
( ~ big_g(Y1)
| ~ big_h(skolemFOFtoCNF_X,Y1)
| big_j(skolemFOFtoCNF_X,Y1) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_16,plain,
! [Y1] :
( ~ big_g(Y1)
| ~ big_h(skolemFOFtoCNF_X,Y1)
| big_j(skolemFOFtoCNF_X,Y1) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X,Y1] :
( ~ big_f(X)
| big_h(X,Y1)
| big_h(X,skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_18,plain,
! [X,Y1] :
( ~ big_f(X)
| big_g(Y1)
| big_g(skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
( ~ big_k(Y)
| ~ big_l(Y) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ big_k(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X))
| ~ big_l(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_0:[bind(Y,$fot(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_2,plain,
( ~ big_h(skolemFOFtoCNF_X,Y)
| big_l(Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X))
| big_l(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_2:[bind(Y,$fot(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_4,plain,
big_f(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
( ~ big_f(X)
| big_h(X,skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
( ~ big_f(skolemFOFtoCNF_X)
| big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_7,plain,
big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
big_l(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X)) )],[refute_0_7,refute_0_3]) ).
cnf(refute_0_9,plain,
~ big_k(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( big_l(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X)) )],[refute_0_8,refute_0_1]) ).
cnf(refute_0_10,plain,
( ~ big_f(X)
| ~ big_j(X,skolemFOFtoCNF_Y(X))
| big_k(Y1) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_11,plain,
( ~ big_f(skolemFOFtoCNF_X)
| ~ big_j(skolemFOFtoCNF_X,skolemFOFtoCNF_Y(skolemFOFtoCNF_X))
| big_k(Y1) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_12,plain,
( ~ big_g(Y1)
| ~ big_h(skolemFOFtoCNF_X,Y1)
| big_j(skolemFOFtoCNF_X,Y1) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_13,plain,
( ~ big_g(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))
| ~ big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_Y(skolemFOFtoCNF_X))
| big_j(skolemFOFtoCNF_X,skolemFOFtoCNF_Y(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_12:[bind(Y1,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_14,plain,
( ~ big_f(X)
| big_h(X,Y1)
| big_h(X,skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_15,plain,
( ~ big_f(skolemFOFtoCNF_X)
| big_h(skolemFOFtoCNF_X,X_19)
| big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_Y(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y1,$fot(X_19))]]) ).
cnf(refute_0_16,plain,
( big_h(skolemFOFtoCNF_X,X_19)
| big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_Y(skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X) )],[refute_0_4,refute_0_15]) ).
cnf(refute_0_17,plain,
big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_Y(skolemFOFtoCNF_X)),
inference(subst,[],[refute_0_16:[bind(X_19,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_18,plain,
( ~ big_g(skolemFOFtoCNF_Y(skolemFOFtoCNF_X))
| big_j(skolemFOFtoCNF_X,skolemFOFtoCNF_Y(skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_Y(skolemFOFtoCNF_X)) )],[refute_0_17,refute_0_13]) ).
cnf(refute_0_19,plain,
( ~ big_f(X)
| big_g(Y1)
| big_g(skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_20,plain,
( ~ big_f(skolemFOFtoCNF_X)
| big_g(X_6)
| big_g(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y1,$fot(X_6))]]) ).
cnf(refute_0_21,plain,
( big_g(X_6)
| big_g(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X) )],[refute_0_4,refute_0_20]) ).
cnf(refute_0_22,plain,
big_g(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)),
inference(subst,[],[refute_0_21:[bind(X_6,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_23,plain,
big_j(skolemFOFtoCNF_X,skolemFOFtoCNF_Y(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( big_g(skolemFOFtoCNF_Y(skolemFOFtoCNF_X)) )],[refute_0_22,refute_0_18]) ).
cnf(refute_0_24,plain,
( ~ big_f(skolemFOFtoCNF_X)
| big_k(Y1) ),
inference(resolve,[$cnf( big_j(skolemFOFtoCNF_X,skolemFOFtoCNF_Y(skolemFOFtoCNF_X)) )],[refute_0_23,refute_0_11]) ).
cnf(refute_0_25,plain,
big_k(Y1),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X) )],[refute_0_4,refute_0_24]) ).
cnf(refute_0_26,plain,
big_k(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X)),
inference(subst,[],[refute_0_25:[bind(Y1,$fot(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_27,plain,
$false,
inference(resolve,[$cnf( big_k(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_X)) )],[refute_0_26,refute_0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN069+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n029.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 18:20:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------