TSTP Solution File: SYN036+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN036+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 08:58:43 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 1
% Syntax : Number of formulae : 210 ( 53 unt; 0 def)
% Number of atoms : 708 ( 0 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 758 ( 260 ~; 305 |; 70 &)
% ( 111 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 40 ( 40 usr; 30 con; 0-1 aty)
% Number of variables : 427 ( 147 sgn 160 !; 106 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel34,conjecture,
( ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_q(W) ) )
<=> ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_p(W1) ) ) ) ).
fof(subgoal_0,plain,
( ( ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_q(W) ) )
& ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
& ? [U1] : big_p(U1) )
=> ! [W1] : big_p(W1) ),
inference(strip,[],[pel34]) ).
fof(subgoal_1,plain,
( ( ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_q(W) ) )
& ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
& ! [W1] : big_p(W1) )
=> ? [U1] : big_p(U1) ),
inference(strip,[],[pel34]) ).
fof(subgoal_2,plain,
( ( ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_q(W) ) )
& ( ? [U1] : big_p(U1)
<=> ! [W1] : big_p(W1) ) )
=> ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) ) ),
inference(strip,[],[pel34]) ).
fof(subgoal_3,plain,
( ( ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_p(W1) ) )
& ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
& ? [U] : big_q(U) )
=> ! [W] : big_q(W) ),
inference(strip,[],[pel34]) ).
fof(subgoal_4,plain,
( ( ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_p(W1) ) )
& ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
& ! [W] : big_q(W) )
=> ? [U] : big_q(U) ),
inference(strip,[],[pel34]) ).
fof(subgoal_5,plain,
( ( ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_p(W1) ) )
& ( ? [U] : big_q(U)
<=> ! [W] : big_q(W) ) )
=> ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) ) ),
inference(strip,[],[pel34]) ).
fof(negate_0_0,plain,
~ ( ( ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_q(W) ) )
& ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
& ? [U1] : big_p(U1) )
=> ! [W1] : big_p(W1) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ( ? [U] : big_q(U)
<=> ( ? [W] : ~ big_q(W)
<=> ! [X] :
? [Y] :
( ~ big_p(X)
<=> big_p(Y) ) ) )
& ? [U1] : big_p(U1)
& ? [W1] : ~ big_p(W1)
& ? [X1] :
! [Y1] :
( ~ big_q(X1)
<=> ~ big_q(Y1) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
? [W1] : ~ big_p(W1),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ big_p(skolemFOFtoCNF_W1),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ? [U] : big_q(U)
<=> ( ? [W] : ~ big_q(W)
<=> ! [X] :
? [Y] :
( ~ big_p(X)
<=> big_p(Y) ) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_4,plain,
! [U,W,X,Y] :
( ( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_Y(X))
| ~ big_q(U)
| big_q(W) )
& ( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_Y_1(X))
| ~ big_q(skolemFOFtoCNF_W)
| big_q(skolemFOFtoCNF_U_1) )
& ( ~ big_p(Y)
| ~ big_q(U)
| ~ big_q(skolemFOFtoCNF_W)
| big_p(skolemFOFtoCNF_X_1) )
& ( ~ big_p(Y)
| big_p(skolemFOFtoCNF_X)
| big_q(W)
| big_q(skolemFOFtoCNF_U) )
& ( ~ big_p(skolemFOFtoCNF_X)
| big_p(Y)
| big_q(W)
| big_q(skolemFOFtoCNF_U) )
& ( ~ big_p(skolemFOFtoCNF_X_1)
| ~ big_q(U)
| ~ big_q(skolemFOFtoCNF_W)
| big_p(Y) )
& ( ~ big_q(U)
| big_p(X)
| big_p(skolemFOFtoCNF_Y(X))
| big_q(W) )
& ( ~ big_q(skolemFOFtoCNF_W)
| big_p(X)
| big_p(skolemFOFtoCNF_Y_1(X))
| big_q(skolemFOFtoCNF_U_1) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [U,Y] :
( ~ big_p(skolemFOFtoCNF_X_1)
| ~ big_q(U)
| ~ big_q(skolemFOFtoCNF_W)
| big_p(Y) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [X1] :
! [Y1] :
( ~ big_q(X1)
<=> ~ big_q(Y1) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_7,plain,
! [Y1] :
( ~ big_q(Y1)
<=> ~ big_q(skolemFOFtoCNF_X1) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [Y1] :
( ~ big_q(Y1)
<=> ~ big_q(skolemFOFtoCNF_X1) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [Y1] :
( ( ~ big_q(Y1)
| big_q(skolemFOFtoCNF_X1) )
& ( ~ big_q(skolemFOFtoCNF_X1)
| big_q(Y1) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [Y1] :
( ~ big_q(skolemFOFtoCNF_X1)
| big_q(Y1) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [Y1] :
( ~ big_q(Y1)
| big_q(skolemFOFtoCNF_X1) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_12,plain,
! [W,Y] :
( ~ big_p(skolemFOFtoCNF_X)
| big_p(Y)
| big_q(W)
| big_q(skolemFOFtoCNF_U) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_13,plain,
? [U1] : big_p(U1),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_14,plain,
big_p(skolemFOFtoCNF_U1),
inference(skolemize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [W,Y] :
( ~ big_p(Y)
| big_p(skolemFOFtoCNF_X)
| big_q(W)
| big_q(skolemFOFtoCNF_U) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_16,plain,
! [U,Y] :
( ~ big_p(Y)
| ~ big_q(U)
| ~ big_q(skolemFOFtoCNF_W)
| big_p(skolemFOFtoCNF_X_1) ),
inference(conjunct,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
~ big_p(skolemFOFtoCNF_W1),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ big_p(skolemFOFtoCNF_X_1)
| ~ big_q(U)
| ~ big_q(skolemFOFtoCNF_W)
| big_p(Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ big_p(skolemFOFtoCNF_X_1)
| ~ big_q(skolemFOFtoCNF_W)
| big_p(Y) ),
inference(subst,[],[refute_0_1:[bind(U,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_3,plain,
( ~ big_q(skolemFOFtoCNF_X1)
| big_q(Y1) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_4,plain,
( ~ big_q(Y1)
| big_q(skolemFOFtoCNF_X1) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_5,plain,
( ~ big_q(skolemFOFtoCNF_U)
| big_q(skolemFOFtoCNF_X1) ),
inference(subst,[],[refute_0_4:[bind(Y1,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_6,plain,
( ~ big_p(skolemFOFtoCNF_X)
| big_p(Y)
| big_q(W)
| big_q(skolemFOFtoCNF_U) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_7,plain,
big_p(skolemFOFtoCNF_U1),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_8,plain,
( ~ big_p(Y)
| big_p(skolemFOFtoCNF_X)
| big_q(W)
| big_q(skolemFOFtoCNF_U) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_9,plain,
( ~ big_p(skolemFOFtoCNF_U1)
| big_p(skolemFOFtoCNF_X)
| big_q(X_8)
| big_q(skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_8:[bind(W,$fot(X_8)),bind(Y,$fot(skolemFOFtoCNF_U1))]]) ).
cnf(refute_0_10,plain,
( big_p(skolemFOFtoCNF_X)
| big_q(X_8)
| big_q(skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_U1) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( big_p(skolemFOFtoCNF_X)
| big_q(skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_10:[bind(X_8,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_12,plain,
( big_p(skolemFOFtoCNF_X)
| big_q(skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_U) )],[refute_0_11,refute_0_5]) ).
cnf(refute_0_13,plain,
( big_p(skolemFOFtoCNF_X)
| big_q(Y1) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_X1) )],[refute_0_12,refute_0_3]) ).
cnf(refute_0_14,plain,
( big_p(skolemFOFtoCNF_X)
| big_q(skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_13:[bind(Y1,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_15,plain,
( ~ big_p(skolemFOFtoCNF_X_1)
| big_p(Y)
| big_p(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_W) )],[refute_0_14,refute_0_2]) ).
cnf(refute_0_16,plain,
( ~ big_p(Y)
| ~ big_q(U)
| ~ big_q(skolemFOFtoCNF_W)
| big_p(skolemFOFtoCNF_X_1) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_17,plain,
( ~ big_p(Y)
| ~ big_q(skolemFOFtoCNF_W)
| big_p(skolemFOFtoCNF_X_1) ),
inference(subst,[],[refute_0_16:[bind(U,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_18,plain,
( ~ big_p(Y)
| big_p(skolemFOFtoCNF_X)
| big_p(skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_W) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ big_p(skolemFOFtoCNF_U1)
| big_p(skolemFOFtoCNF_X)
| big_p(skolemFOFtoCNF_X_1) ),
inference(subst,[],[refute_0_18:[bind(Y,$fot(skolemFOFtoCNF_U1))]]) ).
cnf(refute_0_20,plain,
( big_p(skolemFOFtoCNF_X)
| big_p(skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_U1) )],[refute_0_7,refute_0_19]) ).
cnf(refute_0_21,plain,
( big_p(Y)
| big_p(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X_1) )],[refute_0_20,refute_0_15]) ).
cnf(refute_0_22,plain,
big_p(skolemFOFtoCNF_X),
inference(subst,[],[refute_0_21:[bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_23,plain,
( big_p(Y)
| big_q(W)
| big_q(skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X) )],[refute_0_22,refute_0_6]) ).
cnf(refute_0_24,plain,
( big_p(X_13)
| big_q(skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_23:[bind(W,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_25,plain,
( big_p(X_13)
| big_q(skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_U) )],[refute_0_24,refute_0_5]) ).
cnf(refute_0_26,plain,
( big_p(X_14)
| big_q(skolemFOFtoCNF_X1) ),
inference(subst,[],[refute_0_25:[bind(X_13,$fot(X_14))]]) ).
cnf(refute_0_27,plain,
( big_p(X_14)
| big_q(Y1) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_X1) )],[refute_0_26,refute_0_3]) ).
cnf(refute_0_28,plain,
( big_p(X_16)
| big_q(skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_27:[bind(Y1,$fot(skolemFOFtoCNF_W)),bind(X_14,$fot(X_16))]]) ).
cnf(refute_0_29,plain,
( ~ big_p(skolemFOFtoCNF_X_1)
| big_p(Y)
| big_p(X_16) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_W) )],[refute_0_28,refute_0_2]) ).
cnf(refute_0_30,plain,
( ~ big_p(Y)
| big_p(X_16)
| big_p(skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_W) )],[refute_0_28,refute_0_17]) ).
cnf(refute_0_31,plain,
( ~ big_p(skolemFOFtoCNF_U1)
| big_p(X_21)
| big_p(skolemFOFtoCNF_X_1) ),
inference(subst,[],[refute_0_30:[bind(Y,$fot(skolemFOFtoCNF_U1)),bind(X_16,$fot(X_21))]]) ).
cnf(refute_0_32,plain,
( big_p(X_21)
| big_p(skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_U1) )],[refute_0_7,refute_0_31]) ).
cnf(refute_0_33,plain,
big_p(skolemFOFtoCNF_X_1),
inference(subst,[],[refute_0_32:[bind(X_21,$fot(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_0_34,plain,
( big_p(Y)
| big_p(X_16) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X_1) )],[refute_0_33,refute_0_29]) ).
cnf(refute_0_35,plain,
big_p(skolemFOFtoCNF_W1),
inference(subst,[],[refute_0_34:[bind(Y,$fot(skolemFOFtoCNF_W1)),bind(X_16,$fot(skolemFOFtoCNF_W1))]]) ).
cnf(refute_0_36,plain,
$false,
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_W1) )],[refute_0_35,refute_0_0]) ).
fof(negate_1_0,plain,
~ ( ( ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_q(W) ) )
& ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
& ! [W1] : big_p(W1) )
=> ? [U1] : big_p(U1) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ( ? [U] : big_q(U)
<=> ( ? [W] : ~ big_q(W)
<=> ! [X] :
? [Y] :
( ~ big_p(X)
<=> big_p(Y) ) ) )
& ? [X1] :
! [Y1] :
( ~ big_q(X1)
<=> ~ big_q(Y1) )
& ! [U1] : ~ big_p(U1)
& ! [W1] : big_p(W1) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
! [W1] : big_p(W1),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [W1] : big_p(W1),
inference(specialize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [U1] : ~ big_p(U1),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_4,plain,
! [U1] : ~ big_p(U1),
inference(specialize,[],[normalize_1_3]) ).
cnf(refute_1_0,plain,
big_p(W1),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
~ big_p(U1),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_2,plain,
~ big_p(W1),
inference(subst,[],[refute_1_1:[bind(U1,$fot(W1))]]) ).
cnf(refute_1_3,plain,
$false,
inference(resolve,[$cnf( big_p(W1) )],[refute_1_0,refute_1_2]) ).
fof(negate_2_0,plain,
~ ( ( ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_q(W) ) )
& ( ? [U1] : big_p(U1)
<=> ! [W1] : big_p(W1) ) )
=> ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) ) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
( ( ? [U] : big_q(U)
<=> ( ? [W] : ~ big_q(W)
<=> ! [X] :
? [Y] :
( ~ big_p(X)
<=> big_p(Y) ) ) )
& ( ? [U1] : big_p(U1)
<=> ! [W1] : big_p(W1) )
& ! [X1] :
? [Y1] :
( ~ big_q(X1)
<=> big_q(Y1) ) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
! [X1] :
? [Y1] :
( ~ big_q(X1)
<=> big_q(Y1) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
! [X1] :
? [Y1] :
( ~ big_q(X1)
<=> big_q(Y1) ),
inference(specialize,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
! [X1] :
( ~ big_q(X1)
<=> big_q(skolemFOFtoCNF_Y1(X1)) ),
inference(skolemize,[],[normalize_2_2]) ).
fof(normalize_2_4,plain,
! [X1] :
( ( ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_Y1(X1)) )
& ( big_q(X1)
| big_q(skolemFOFtoCNF_Y1(X1)) ) ),
inference(clausify,[],[normalize_2_3]) ).
fof(normalize_2_5,plain,
! [X1] :
( ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_Y1(X1)) ),
inference(conjunct,[],[normalize_2_4]) ).
fof(normalize_2_6,plain,
! [X1] :
( big_q(X1)
| big_q(skolemFOFtoCNF_Y1(X1)) ),
inference(conjunct,[],[normalize_2_4]) ).
fof(normalize_2_7,plain,
( ? [U] : big_q(U)
<=> ( ? [W] : ~ big_q(W)
<=> ! [X] :
? [Y] :
( ~ big_p(X)
<=> big_p(Y) ) ) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_8,plain,
! [U,W,X,Y] :
( ( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_Y_4(X))
| ~ big_q(U)
| big_q(W) )
& ( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_Y_5(X))
| ~ big_q(skolemFOFtoCNF_W_2)
| big_q(skolemFOFtoCNF_U_5) )
& ( ~ big_p(Y)
| ~ big_q(U)
| ~ big_q(skolemFOFtoCNF_W_2)
| big_p(skolemFOFtoCNF_X_5) )
& ( ~ big_p(Y)
| big_p(skolemFOFtoCNF_X_4)
| big_q(W)
| big_q(skolemFOFtoCNF_U_4) )
& ( ~ big_p(skolemFOFtoCNF_X_4)
| big_p(Y)
| big_q(W)
| big_q(skolemFOFtoCNF_U_4) )
& ( ~ big_p(skolemFOFtoCNF_X_5)
| ~ big_q(U)
| ~ big_q(skolemFOFtoCNF_W_2)
| big_p(Y) )
& ( ~ big_q(U)
| big_p(X)
| big_p(skolemFOFtoCNF_Y_4(X))
| big_q(W) )
& ( ~ big_q(skolemFOFtoCNF_W_2)
| big_p(X)
| big_p(skolemFOFtoCNF_Y_5(X))
| big_q(skolemFOFtoCNF_U_5) ) ),
inference(clausify,[],[normalize_2_7]) ).
fof(normalize_2_9,plain,
! [U,W,X] :
( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_Y_4(X))
| ~ big_q(U)
| big_q(W) ),
inference(conjunct,[],[normalize_2_8]) ).
fof(normalize_2_10,plain,
( ? [U1] : big_p(U1)
<=> ! [W1] : big_p(W1) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_11,plain,
! [U1,W1] :
( ( ~ big_p(U1)
| big_p(W1) )
& ( ~ big_p(skolemFOFtoCNF_W1_1)
| big_p(skolemFOFtoCNF_U1_1) ) ),
inference(clausify,[],[normalize_2_10]) ).
fof(normalize_2_12,plain,
! [U1,W1] :
( ~ big_p(U1)
| big_p(W1) ),
inference(conjunct,[],[normalize_2_11]) ).
fof(normalize_2_13,plain,
! [U,W,X] :
( ~ big_q(U)
| big_p(X)
| big_p(skolemFOFtoCNF_Y_4(X))
| big_q(W) ),
inference(conjunct,[],[normalize_2_8]) ).
cnf(refute_2_0,plain,
( ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_Y1(X1)) ),
inference(canonicalize,[],[normalize_2_5]) ).
cnf(refute_2_1,plain,
( big_q(X1)
| big_q(skolemFOFtoCNF_Y1(X1)) ),
inference(canonicalize,[],[normalize_2_6]) ).
cnf(refute_2_2,plain,
( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_Y_4(X))
| ~ big_q(U)
| big_q(W) ),
inference(canonicalize,[],[normalize_2_9]) ).
cnf(refute_2_3,plain,
( ~ big_p(U1)
| big_p(W1) ),
inference(canonicalize,[],[normalize_2_12]) ).
cnf(refute_2_4,plain,
( ~ big_p(skolemFOFtoCNF_Y_4(X_33))
| big_p(W1) ),
inference(subst,[],[refute_2_3:[bind(U1,$fot(skolemFOFtoCNF_Y_4(X_33)))]]) ).
cnf(refute_2_5,plain,
( ~ big_q(U)
| big_p(X)
| big_p(skolemFOFtoCNF_Y_4(X))
| big_q(W) ),
inference(canonicalize,[],[normalize_2_13]) ).
cnf(refute_2_6,plain,
( ~ big_q(skolemFOFtoCNF_Y1(X1))
| big_p(X_31)
| big_p(skolemFOFtoCNF_Y_4(X_31))
| big_q(X_30) ),
inference(subst,[],[refute_2_5:[bind(U,$fot(skolemFOFtoCNF_Y1(X1))),bind(W,$fot(X_30)),bind(X,$fot(X_31))]]) ).
cnf(refute_2_7,plain,
( big_p(X_31)
| big_p(skolemFOFtoCNF_Y_4(X_31))
| big_q(X1)
| big_q(X_30) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_Y1(X1)) )],[refute_2_1,refute_2_6]) ).
cnf(refute_2_8,plain,
( big_p(X_33)
| big_p(skolemFOFtoCNF_Y_4(X_33))
| big_q(X_32) ),
inference(subst,[],[refute_2_7:[bind(X1,$fot(X_32)),bind(X_30,$fot(X_32)),bind(X_31,$fot(X_33))]]) ).
cnf(refute_2_9,plain,
( big_p(W1)
| big_p(X_33)
| big_q(X_32) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y_4(X_33)) )],[refute_2_8,refute_2_4]) ).
cnf(refute_2_10,plain,
( big_p(X_33)
| big_q(X_36) ),
inference(subst,[],[refute_2_9:[bind(W1,$fot(X_33)),bind(X_32,$fot(X_36))]]) ).
cnf(refute_2_11,plain,
( big_p(X_35)
| big_q(skolemFOFtoCNF_Y1(X1)) ),
inference(subst,[],[refute_2_9:[bind(W1,$fot(X_35)),bind(X_32,$fot(skolemFOFtoCNF_Y1(X1))),bind(X_33,$fot(X_35))]]) ).
cnf(refute_2_12,plain,
( ~ big_q(X1)
| big_p(X_35) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_Y1(X1)) )],[refute_2_11,refute_2_0]) ).
cnf(refute_2_13,plain,
( ~ big_q(X_36)
| big_p(X_37) ),
inference(subst,[],[refute_2_12:[bind(X1,$fot(X_36)),bind(X_35,$fot(X_37))]]) ).
cnf(refute_2_14,plain,
( big_p(X_33)
| big_p(X_37) ),
inference(resolve,[$cnf( big_q(X_36) )],[refute_2_10,refute_2_13]) ).
cnf(refute_2_15,plain,
big_p(X),
inference(subst,[],[refute_2_14:[bind(X_33,$fot(X)),bind(X_37,$fot(X))]]) ).
cnf(refute_2_16,plain,
( ~ big_p(skolemFOFtoCNF_Y_4(X))
| ~ big_q(U)
| big_q(W) ),
inference(resolve,[$cnf( big_p(X) )],[refute_2_15,refute_2_2]) ).
cnf(refute_2_17,plain,
big_p(skolemFOFtoCNF_Y_4(X)),
inference(subst,[],[refute_2_14:[bind(X_33,$fot(skolemFOFtoCNF_Y_4(X))),bind(X_37,$fot(skolemFOFtoCNF_Y_4(X)))]]) ).
cnf(refute_2_18,plain,
( ~ big_q(U)
| big_q(W) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y_4(X)) )],[refute_2_17,refute_2_16]) ).
cnf(refute_2_19,plain,
( ~ big_q(skolemFOFtoCNF_Y1(X1))
| big_q(X_40) ),
inference(subst,[],[refute_2_18:[bind(U,$fot(skolemFOFtoCNF_Y1(X1))),bind(W,$fot(X_40))]]) ).
cnf(refute_2_20,plain,
( big_q(X1)
| big_q(X_40) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_Y1(X1)) )],[refute_2_1,refute_2_19]) ).
cnf(refute_2_21,plain,
big_q(skolemFOFtoCNF_Y1(X1)),
inference(subst,[],[refute_2_20:[bind(X1,$fot(skolemFOFtoCNF_Y1(X1))),bind(X_40,$fot(skolemFOFtoCNF_Y1(X1)))]]) ).
cnf(refute_2_22,plain,
~ big_q(X1),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_Y1(X1)) )],[refute_2_21,refute_2_0]) ).
cnf(refute_2_23,plain,
big_q(X1),
inference(subst,[],[refute_2_20:[bind(X_40,$fot(X1))]]) ).
cnf(refute_2_24,plain,
$false,
inference(resolve,[$cnf( big_q(X1) )],[refute_2_23,refute_2_22]) ).
fof(negate_3_0,plain,
~ ( ( ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_p(W1) ) )
& ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
& ? [U] : big_q(U) )
=> ! [W] : big_q(W) ),
inference(negate,[],[subgoal_3]) ).
fof(normalize_3_0,plain,
( ( ? [U1] : big_p(U1)
<=> ( ? [W1] : ~ big_p(W1)
<=> ! [X1] :
? [Y1] :
( ~ big_q(X1)
<=> big_q(Y1) ) ) )
& ? [U] : big_q(U)
& ? [W] : ~ big_q(W)
& ? [X] :
! [Y] :
( ~ big_p(X)
<=> ~ big_p(Y) ) ),
inference(canonicalize,[],[negate_3_0]) ).
fof(normalize_3_1,plain,
? [W] : ~ big_q(W),
inference(conjunct,[],[normalize_3_0]) ).
fof(normalize_3_2,plain,
~ big_q(skolemFOFtoCNF_W_3),
inference(skolemize,[],[normalize_3_1]) ).
fof(normalize_3_3,plain,
( ? [U1] : big_p(U1)
<=> ( ? [W1] : ~ big_p(W1)
<=> ! [X1] :
? [Y1] :
( ~ big_q(X1)
<=> big_q(Y1) ) ) ),
inference(conjunct,[],[normalize_3_0]) ).
fof(normalize_3_4,plain,
! [U1,W1,X1,Y1] :
( ( ~ big_p(U1)
| ~ big_p(skolemFOFtoCNF_W1_2)
| ~ big_q(Y1)
| big_q(skolemFOFtoCNF_X1_2) )
& ( ~ big_p(U1)
| ~ big_p(skolemFOFtoCNF_W1_2)
| ~ big_q(skolemFOFtoCNF_X1_2)
| big_q(Y1) )
& ( ~ big_p(U1)
| ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_Y1_1(X1))
| big_p(W1) )
& ( ~ big_p(U1)
| big_p(W1)
| big_q(X1)
| big_q(skolemFOFtoCNF_Y1_1(X1)) )
& ( ~ big_p(skolemFOFtoCNF_W1_3)
| ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_Y1_2(X1))
| big_p(skolemFOFtoCNF_U1_2) )
& ( ~ big_p(skolemFOFtoCNF_W1_3)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(X1)
| big_q(skolemFOFtoCNF_Y1_2(X1)) )
& ( ~ big_q(Y1)
| big_p(W1)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(skolemFOFtoCNF_X1_3) )
& ( ~ big_q(skolemFOFtoCNF_X1_3)
| big_p(W1)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(Y1) ) ),
inference(clausify,[],[normalize_3_3]) ).
fof(normalize_3_5,plain,
! [U1,Y1] :
( ~ big_p(U1)
| ~ big_p(skolemFOFtoCNF_W1_2)
| ~ big_q(skolemFOFtoCNF_X1_2)
| big_q(Y1) ),
inference(conjunct,[],[normalize_3_4]) ).
fof(normalize_3_6,plain,
? [X] :
! [Y] :
( ~ big_p(X)
<=> ~ big_p(Y) ),
inference(conjunct,[],[normalize_3_0]) ).
fof(normalize_3_7,plain,
! [Y] :
( ~ big_p(Y)
<=> ~ big_p(skolemFOFtoCNF_X_6) ),
inference(skolemize,[],[normalize_3_6]) ).
fof(normalize_3_8,plain,
! [Y] :
( ~ big_p(Y)
<=> ~ big_p(skolemFOFtoCNF_X_6) ),
inference(specialize,[],[normalize_3_7]) ).
fof(normalize_3_9,plain,
! [Y] :
( ( ~ big_p(Y)
| big_p(skolemFOFtoCNF_X_6) )
& ( ~ big_p(skolemFOFtoCNF_X_6)
| big_p(Y) ) ),
inference(clausify,[],[normalize_3_8]) ).
fof(normalize_3_10,plain,
! [Y] :
( ~ big_p(skolemFOFtoCNF_X_6)
| big_p(Y) ),
inference(conjunct,[],[normalize_3_9]) ).
fof(normalize_3_11,plain,
! [Y] :
( ~ big_p(Y)
| big_p(skolemFOFtoCNF_X_6) ),
inference(conjunct,[],[normalize_3_9]) ).
fof(normalize_3_12,plain,
! [W1,Y1] :
( ~ big_q(skolemFOFtoCNF_X1_3)
| big_p(W1)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(Y1) ),
inference(conjunct,[],[normalize_3_4]) ).
fof(normalize_3_13,plain,
? [U] : big_q(U),
inference(conjunct,[],[normalize_3_0]) ).
fof(normalize_3_14,plain,
big_q(skolemFOFtoCNF_U_6),
inference(skolemize,[],[normalize_3_13]) ).
fof(normalize_3_15,plain,
! [W1,Y1] :
( ~ big_q(Y1)
| big_p(W1)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(skolemFOFtoCNF_X1_3) ),
inference(conjunct,[],[normalize_3_4]) ).
fof(normalize_3_16,plain,
! [U1,Y1] :
( ~ big_p(U1)
| ~ big_p(skolemFOFtoCNF_W1_2)
| ~ big_q(Y1)
| big_q(skolemFOFtoCNF_X1_2) ),
inference(conjunct,[],[normalize_3_4]) ).
cnf(refute_3_0,plain,
~ big_q(skolemFOFtoCNF_W_3),
inference(canonicalize,[],[normalize_3_2]) ).
cnf(refute_3_1,plain,
( ~ big_p(U1)
| ~ big_p(skolemFOFtoCNF_W1_2)
| ~ big_q(skolemFOFtoCNF_X1_2)
| big_q(Y1) ),
inference(canonicalize,[],[normalize_3_5]) ).
cnf(refute_3_2,plain,
( ~ big_p(X_57)
| ~ big_p(skolemFOFtoCNF_W1_2)
| ~ big_q(skolemFOFtoCNF_X1_2)
| big_q(Y1) ),
inference(subst,[],[refute_3_1:[bind(U1,$fot(X_57))]]) ).
cnf(refute_3_3,plain,
( ~ big_p(skolemFOFtoCNF_X_6)
| big_p(Y) ),
inference(canonicalize,[],[normalize_3_10]) ).
cnf(refute_3_4,plain,
( ~ big_p(Y)
| big_p(skolemFOFtoCNF_X_6) ),
inference(canonicalize,[],[normalize_3_11]) ).
cnf(refute_3_5,plain,
( ~ big_p(skolemFOFtoCNF_U1_2)
| big_p(skolemFOFtoCNF_X_6) ),
inference(subst,[],[refute_3_4:[bind(Y,$fot(skolemFOFtoCNF_U1_2))]]) ).
cnf(refute_3_6,plain,
( ~ big_q(skolemFOFtoCNF_X1_3)
| big_p(W1)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(Y1) ),
inference(canonicalize,[],[normalize_3_12]) ).
cnf(refute_3_7,plain,
big_q(skolemFOFtoCNF_U_6),
inference(canonicalize,[],[normalize_3_14]) ).
cnf(refute_3_8,plain,
( ~ big_q(Y1)
| big_p(W1)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(skolemFOFtoCNF_X1_3) ),
inference(canonicalize,[],[normalize_3_15]) ).
cnf(refute_3_9,plain,
( ~ big_q(skolemFOFtoCNF_U_6)
| big_p(X_52)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(skolemFOFtoCNF_X1_3) ),
inference(subst,[],[refute_3_8:[bind(W1,$fot(X_52)),bind(Y1,$fot(skolemFOFtoCNF_U_6))]]) ).
cnf(refute_3_10,plain,
( big_p(X_52)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(skolemFOFtoCNF_X1_3) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_U_6) )],[refute_3_7,refute_3_9]) ).
cnf(refute_3_11,plain,
( big_p(X_54)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(skolemFOFtoCNF_X1_3) ),
inference(subst,[],[refute_3_10:[bind(X_52,$fot(X_54))]]) ).
cnf(refute_3_12,plain,
( big_p(W1)
| big_p(X_54)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(Y1) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_X1_3) )],[refute_3_11,refute_3_6]) ).
cnf(refute_3_13,plain,
( big_p(X_56)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(skolemFOFtoCNF_W_3) ),
inference(subst,[],[refute_3_12:[bind(W1,$fot(skolemFOFtoCNF_U1_2)),bind(Y1,$fot(skolemFOFtoCNF_W_3)),bind(X_54,$fot(X_56))]]) ).
cnf(refute_3_14,plain,
( big_p(X_56)
| big_p(skolemFOFtoCNF_U1_2) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_W_3) )],[refute_3_13,refute_3_0]) ).
cnf(refute_3_15,plain,
big_p(skolemFOFtoCNF_U1_2),
inference(subst,[],[refute_3_14:[bind(X_56,$fot(skolemFOFtoCNF_U1_2))]]) ).
cnf(refute_3_16,plain,
big_p(skolemFOFtoCNF_X_6),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_U1_2) )],[refute_3_15,refute_3_5]) ).
cnf(refute_3_17,plain,
big_p(Y),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X_6) )],[refute_3_16,refute_3_3]) ).
cnf(refute_3_18,plain,
big_p(X_57),
inference(subst,[],[refute_3_17:[bind(Y,$fot(X_57))]]) ).
cnf(refute_3_19,plain,
( ~ big_p(skolemFOFtoCNF_W1_2)
| ~ big_q(skolemFOFtoCNF_X1_2)
| big_q(Y1) ),
inference(resolve,[$cnf( big_p(X_57) )],[refute_3_18,refute_3_2]) ).
cnf(refute_3_20,plain,
big_p(skolemFOFtoCNF_W1_2),
inference(subst,[],[refute_3_17:[bind(Y,$fot(skolemFOFtoCNF_W1_2))]]) ).
cnf(refute_3_21,plain,
( ~ big_q(skolemFOFtoCNF_X1_2)
| big_q(Y1) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_W1_2) )],[refute_3_20,refute_3_19]) ).
cnf(refute_3_22,plain,
( ~ big_p(U1)
| ~ big_p(skolemFOFtoCNF_W1_2)
| ~ big_q(Y1)
| big_q(skolemFOFtoCNF_X1_2) ),
inference(canonicalize,[],[normalize_3_16]) ).
cnf(refute_3_23,plain,
( ~ big_p(X_48)
| ~ big_p(skolemFOFtoCNF_W1_2)
| ~ big_q(skolemFOFtoCNF_U_6)
| big_q(skolemFOFtoCNF_X1_2) ),
inference(subst,[],[refute_3_22:[bind(U1,$fot(X_48)),bind(Y1,$fot(skolemFOFtoCNF_U_6))]]) ).
cnf(refute_3_24,plain,
( ~ big_p(X_48)
| ~ big_p(skolemFOFtoCNF_W1_2)
| big_q(skolemFOFtoCNF_X1_2) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_U_6) )],[refute_3_7,refute_3_23]) ).
cnf(refute_3_25,plain,
( ~ big_p(skolemFOFtoCNF_W1_2)
| big_q(skolemFOFtoCNF_X1_2) ),
inference(subst,[],[refute_3_24:[bind(X_48,$fot(skolemFOFtoCNF_W1_2))]]) ).
cnf(refute_3_26,plain,
big_q(skolemFOFtoCNF_X1_2),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_W1_2) )],[refute_3_20,refute_3_25]) ).
cnf(refute_3_27,plain,
big_q(Y1),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_X1_2) )],[refute_3_26,refute_3_21]) ).
cnf(refute_3_28,plain,
big_q(skolemFOFtoCNF_W_3),
inference(subst,[],[refute_3_27:[bind(Y1,$fot(skolemFOFtoCNF_W_3))]]) ).
cnf(refute_3_29,plain,
$false,
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_W_3) )],[refute_3_28,refute_3_0]) ).
fof(negate_4_0,plain,
~ ( ( ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_p(W1) ) )
& ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
& ! [W] : big_q(W) )
=> ? [U] : big_q(U) ),
inference(negate,[],[subgoal_4]) ).
fof(normalize_4_0,plain,
( ( ? [U1] : big_p(U1)
<=> ( ? [W1] : ~ big_p(W1)
<=> ! [X1] :
? [Y1] :
( ~ big_q(X1)
<=> big_q(Y1) ) ) )
& ? [X] :
! [Y] :
( ~ big_p(X)
<=> ~ big_p(Y) )
& ! [U] : ~ big_q(U)
& ! [W] : big_q(W) ),
inference(canonicalize,[],[negate_4_0]) ).
fof(normalize_4_1,plain,
! [W] : big_q(W),
inference(conjunct,[],[normalize_4_0]) ).
fof(normalize_4_2,plain,
! [W] : big_q(W),
inference(specialize,[],[normalize_4_1]) ).
fof(normalize_4_3,plain,
! [U] : ~ big_q(U),
inference(conjunct,[],[normalize_4_0]) ).
fof(normalize_4_4,plain,
! [U] : ~ big_q(U),
inference(specialize,[],[normalize_4_3]) ).
cnf(refute_4_0,plain,
big_q(W),
inference(canonicalize,[],[normalize_4_2]) ).
cnf(refute_4_1,plain,
~ big_q(U),
inference(canonicalize,[],[normalize_4_4]) ).
cnf(refute_4_2,plain,
~ big_q(W),
inference(subst,[],[refute_4_1:[bind(U,$fot(W))]]) ).
cnf(refute_4_3,plain,
$false,
inference(resolve,[$cnf( big_q(W) )],[refute_4_0,refute_4_2]) ).
fof(negate_5_0,plain,
~ ( ( ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_p(W1) ) )
& ( ? [U] : big_q(U)
<=> ! [W] : big_q(W) ) )
=> ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) ) ),
inference(negate,[],[subgoal_5]) ).
fof(normalize_5_0,plain,
( ( ? [U1] : big_p(U1)
<=> ( ? [W1] : ~ big_p(W1)
<=> ! [X1] :
? [Y1] :
( ~ big_q(X1)
<=> big_q(Y1) ) ) )
& ( ? [U] : big_q(U)
<=> ! [W] : big_q(W) )
& ! [X] :
? [Y] :
( ~ big_p(X)
<=> big_p(Y) ) ),
inference(canonicalize,[],[negate_5_0]) ).
fof(normalize_5_1,plain,
! [X] :
? [Y] :
( ~ big_p(X)
<=> big_p(Y) ),
inference(conjunct,[],[normalize_5_0]) ).
fof(normalize_5_2,plain,
! [X] :
? [Y] :
( ~ big_p(X)
<=> big_p(Y) ),
inference(specialize,[],[normalize_5_1]) ).
fof(normalize_5_3,plain,
! [X] :
( ~ big_p(X)
<=> big_p(skolemFOFtoCNF_Y_6(X)) ),
inference(skolemize,[],[normalize_5_2]) ).
fof(normalize_5_4,plain,
! [X] :
( ( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_Y_6(X)) )
& ( big_p(X)
| big_p(skolemFOFtoCNF_Y_6(X)) ) ),
inference(clausify,[],[normalize_5_3]) ).
fof(normalize_5_5,plain,
! [X] :
( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_Y_6(X)) ),
inference(conjunct,[],[normalize_5_4]) ).
fof(normalize_5_6,plain,
! [X] :
( big_p(X)
| big_p(skolemFOFtoCNF_Y_6(X)) ),
inference(conjunct,[],[normalize_5_4]) ).
fof(normalize_5_7,plain,
( ? [U1] : big_p(U1)
<=> ( ? [W1] : ~ big_p(W1)
<=> ! [X1] :
? [Y1] :
( ~ big_q(X1)
<=> big_q(Y1) ) ) ),
inference(conjunct,[],[normalize_5_0]) ).
fof(normalize_5_8,plain,
! [U1,W1,X1,Y1] :
( ( ~ big_p(U1)
| ~ big_p(skolemFOFtoCNF_W1_6)
| ~ big_q(Y1)
| big_q(skolemFOFtoCNF_X1_6) )
& ( ~ big_p(U1)
| ~ big_p(skolemFOFtoCNF_W1_6)
| ~ big_q(skolemFOFtoCNF_X1_6)
| big_q(Y1) )
& ( ~ big_p(U1)
| ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_Y1_4(X1))
| big_p(W1) )
& ( ~ big_p(U1)
| big_p(W1)
| big_q(X1)
| big_q(skolemFOFtoCNF_Y1_4(X1)) )
& ( ~ big_p(skolemFOFtoCNF_W1_6)
| ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_Y1_5(X1))
| big_p(skolemFOFtoCNF_U1_6) )
& ( ~ big_p(skolemFOFtoCNF_W1_6)
| big_p(skolemFOFtoCNF_U1_6)
| big_q(X1)
| big_q(skolemFOFtoCNF_Y1_5(X1)) )
& ( ~ big_q(Y1)
| big_p(W1)
| big_p(skolemFOFtoCNF_U1_5)
| big_q(skolemFOFtoCNF_X1_5) )
& ( ~ big_q(skolemFOFtoCNF_X1_5)
| big_p(W1)
| big_p(skolemFOFtoCNF_U1_5)
| big_q(Y1) ) ),
inference(clausify,[],[normalize_5_7]) ).
fof(normalize_5_9,plain,
! [U1,W1,X1] :
( ~ big_p(U1)
| ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_Y1_4(X1))
| big_p(W1) ),
inference(conjunct,[],[normalize_5_8]) ).
fof(normalize_5_10,plain,
( ? [U] : big_q(U)
<=> ! [W] : big_q(W) ),
inference(conjunct,[],[normalize_5_0]) ).
fof(normalize_5_11,plain,
! [U,W] :
( ( ~ big_q(U)
| big_q(W) )
& ( ~ big_q(skolemFOFtoCNF_W_4)
| big_q(skolemFOFtoCNF_U_7) ) ),
inference(clausify,[],[normalize_5_10]) ).
fof(normalize_5_12,plain,
! [U,W] :
( ~ big_q(U)
| big_q(W) ),
inference(conjunct,[],[normalize_5_11]) ).
fof(normalize_5_13,plain,
! [U1,W1,X1] :
( ~ big_p(U1)
| big_p(W1)
| big_q(X1)
| big_q(skolemFOFtoCNF_Y1_4(X1)) ),
inference(conjunct,[],[normalize_5_8]) ).
cnf(refute_5_0,plain,
( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_Y_6(X)) ),
inference(canonicalize,[],[normalize_5_5]) ).
cnf(refute_5_1,plain,
( big_p(X)
| big_p(skolemFOFtoCNF_Y_6(X)) ),
inference(canonicalize,[],[normalize_5_6]) ).
cnf(refute_5_2,plain,
( ~ big_p(U1)
| ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_Y1_4(X1))
| big_p(W1) ),
inference(canonicalize,[],[normalize_5_9]) ).
cnf(refute_5_3,plain,
( ~ big_q(U)
| big_q(W) ),
inference(canonicalize,[],[normalize_5_12]) ).
cnf(refute_5_4,plain,
( ~ big_q(skolemFOFtoCNF_Y1_4(X_72))
| big_q(W) ),
inference(subst,[],[refute_5_3:[bind(U,$fot(skolemFOFtoCNF_Y1_4(X_72)))]]) ).
cnf(refute_5_5,plain,
( ~ big_p(U1)
| big_p(W1)
| big_q(X1)
| big_q(skolemFOFtoCNF_Y1_4(X1)) ),
inference(canonicalize,[],[normalize_5_13]) ).
cnf(refute_5_6,plain,
( ~ big_p(skolemFOFtoCNF_Y_6(X))
| big_p(X_69)
| big_q(X_70)
| big_q(skolemFOFtoCNF_Y1_4(X_70)) ),
inference(subst,[],[refute_5_5:[bind(U1,$fot(skolemFOFtoCNF_Y_6(X))),bind(W1,$fot(X_69)),bind(X1,$fot(X_70))]]) ).
cnf(refute_5_7,plain,
( big_p(X)
| big_p(X_69)
| big_q(X_70)
| big_q(skolemFOFtoCNF_Y1_4(X_70)) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y_6(X)) )],[refute_5_1,refute_5_6]) ).
cnf(refute_5_8,plain,
( big_p(X_71)
| big_q(X_72)
| big_q(skolemFOFtoCNF_Y1_4(X_72)) ),
inference(subst,[],[refute_5_7:[bind(X,$fot(X_71)),bind(X_69,$fot(X_71)),bind(X_70,$fot(X_72))]]) ).
cnf(refute_5_9,plain,
( big_p(X_71)
| big_q(W)
| big_q(X_72) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_Y1_4(X_72)) )],[refute_5_8,refute_5_4]) ).
cnf(refute_5_10,plain,
( big_p(X_75)
| big_q(X_72) ),
inference(subst,[],[refute_5_9:[bind(W,$fot(X_72)),bind(X_71,$fot(X_75))]]) ).
cnf(refute_5_11,plain,
( big_p(skolemFOFtoCNF_Y_6(X))
| big_q(X_74) ),
inference(subst,[],[refute_5_9:[bind(W,$fot(X_74)),bind(X_71,$fot(skolemFOFtoCNF_Y_6(X))),bind(X_72,$fot(X_74))]]) ).
cnf(refute_5_12,plain,
( ~ big_p(X)
| big_q(X_74) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y_6(X)) )],[refute_5_11,refute_5_0]) ).
cnf(refute_5_13,plain,
( ~ big_p(X_75)
| big_q(X_76) ),
inference(subst,[],[refute_5_12:[bind(X,$fot(X_75)),bind(X_74,$fot(X_76))]]) ).
cnf(refute_5_14,plain,
( big_q(X_72)
| big_q(X_76) ),
inference(resolve,[$cnf( big_p(X_75) )],[refute_5_10,refute_5_13]) ).
cnf(refute_5_15,plain,
big_q(skolemFOFtoCNF_Y1_4(X1)),
inference(subst,[],[refute_5_14:[bind(X_72,$fot(skolemFOFtoCNF_Y1_4(X1))),bind(X_76,$fot(skolemFOFtoCNF_Y1_4(X1)))]]) ).
cnf(refute_5_16,plain,
( ~ big_p(U1)
| ~ big_q(X1)
| big_p(W1) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_Y1_4(X1)) )],[refute_5_15,refute_5_2]) ).
cnf(refute_5_17,plain,
big_q(X1),
inference(subst,[],[refute_5_14:[bind(X_72,$fot(X1)),bind(X_76,$fot(X1))]]) ).
cnf(refute_5_18,plain,
( ~ big_p(U1)
| big_p(W1) ),
inference(resolve,[$cnf( big_q(X1) )],[refute_5_17,refute_5_16]) ).
cnf(refute_5_19,plain,
( ~ big_p(skolemFOFtoCNF_Y_6(X))
| big_p(X_79) ),
inference(subst,[],[refute_5_18:[bind(U1,$fot(skolemFOFtoCNF_Y_6(X))),bind(W1,$fot(X_79))]]) ).
cnf(refute_5_20,plain,
( big_p(X)
| big_p(X_79) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y_6(X)) )],[refute_5_1,refute_5_19]) ).
cnf(refute_5_21,plain,
big_p(skolemFOFtoCNF_Y_6(X)),
inference(subst,[],[refute_5_20:[bind(X,$fot(skolemFOFtoCNF_Y_6(X))),bind(X_79,$fot(skolemFOFtoCNF_Y_6(X)))]]) ).
cnf(refute_5_22,plain,
~ big_p(X),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y_6(X)) )],[refute_5_21,refute_5_0]) ).
cnf(refute_5_23,plain,
big_p(X),
inference(subst,[],[refute_5_20:[bind(X_79,$fot(X))]]) ).
cnf(refute_5_24,plain,
$false,
inference(resolve,[$cnf( big_p(X) )],[refute_5_23,refute_5_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN036+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n020.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 : Mon Jul 11 11:39:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.39
%------------------------------------------------------------------------------