TSTP Solution File: SYN036+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN036+2 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 08:58:44 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 1
% Syntax : Number of formulae : 202 ( 58 unt; 0 def)
% Number of atoms : 741 ( 0 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 796 ( 257 ~; 326 |; 84 &)
% ( 117 <=>; 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 : 53 ( 53 usr; 40 con; 0-1 aty)
% Number of variables : 415 ( 115 sgn 164 !; 112 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel34,conjecture,
( ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_p(W) ) )
<=> ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_q(W1) ) ) ) ).
fof(subgoal_0,plain,
( ( ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_p(W) ) )
& ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
& ? [U1] : big_p(U1) )
=> ! [W1] : big_q(W1) ),
inference(strip,[],[pel34]) ).
fof(subgoal_1,plain,
( ( ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_p(W) ) )
& ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
& ! [W1] : big_q(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_p(W) ) )
& ( ? [U1] : big_p(U1)
<=> ! [W1] : big_q(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_q(W1) ) )
& ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
& ? [U] : big_q(U) )
=> ! [W] : big_p(W) ),
inference(strip,[],[pel34]) ).
fof(subgoal_4,plain,
( ( ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_q(W1) ) )
& ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
& ! [W] : big_p(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_q(W1) ) )
& ( ? [U] : big_q(U)
<=> ! [W] : big_p(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_p(W) ) )
& ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
& ? [U1] : big_p(U1) )
=> ! [W1] : big_q(W1) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ( ? [U] : big_q(U)
<=> ( ? [W] : ~ big_p(W)
<=> ! [X] :
? [Y] :
( ~ big_p(X)
<=> big_p(Y) ) ) )
& ? [U1] : big_p(U1)
& ? [W1] : ~ big_q(W1)
& ? [X1] :
! [Y1] :
( ~ big_q(X1)
<=> ~ big_q(Y1) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
? [W1] : ~ big_q(W1),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ big_q(skolemFOFtoCNF_W1),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
? [X1] :
! [Y1] :
( ~ big_q(X1)
<=> ~ big_q(Y1) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_4,plain,
! [Y1] :
( ~ big_q(Y1)
<=> ~ big_q(skolemFOFtoCNF_X1) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Y1] :
( ~ big_q(Y1)
<=> ~ big_q(skolemFOFtoCNF_X1) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Y1] :
( ( ~ big_q(Y1)
| big_q(skolemFOFtoCNF_X1) )
& ( ~ big_q(skolemFOFtoCNF_X1)
| big_q(Y1) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [Y1] :
( ~ big_q(skolemFOFtoCNF_X1)
| big_q(Y1) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [Y1] :
( ~ big_q(Y1)
| big_q(skolemFOFtoCNF_X1) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_9,plain,
( ? [U] : big_q(U)
<=> ( ? [W] : ~ big_p(W)
<=> ! [X] :
? [Y] :
( ~ big_p(X)
<=> big_p(Y) ) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_10,plain,
! [U,W,X,Y] :
( ( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_W)
| ~ big_p(skolemFOFtoCNF_Y_1(X))
| big_q(skolemFOFtoCNF_U_1) )
& ( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_Y(X))
| ~ big_q(U)
| big_p(W) )
& ( ~ big_p(Y)
| ~ big_p(skolemFOFtoCNF_W)
| ~ big_q(U)
| big_p(skolemFOFtoCNF_X_1) )
& ( ~ big_p(Y)
| big_p(W)
| big_p(skolemFOFtoCNF_X)
| big_q(skolemFOFtoCNF_U) )
& ( ~ big_p(skolemFOFtoCNF_W)
| ~ big_p(skolemFOFtoCNF_X_1)
| ~ big_q(U)
| big_p(Y) )
& ( ~ big_p(skolemFOFtoCNF_W)
| big_p(X)
| big_p(skolemFOFtoCNF_Y_1(X))
| big_q(skolemFOFtoCNF_U_1) )
& ( ~ big_p(skolemFOFtoCNF_X)
| big_p(W)
| big_p(Y)
| big_q(skolemFOFtoCNF_U) )
& ( ~ big_q(U)
| big_p(W)
| big_p(X)
| big_p(skolemFOFtoCNF_Y(X)) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X] :
( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_W)
| ~ big_p(skolemFOFtoCNF_Y_1(X))
| big_q(skolemFOFtoCNF_U_1) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [W,Y] :
( ~ big_p(skolemFOFtoCNF_X)
| big_p(W)
| big_p(Y)
| big_q(skolemFOFtoCNF_U) ),
inference(conjunct,[],[normalize_0_10]) ).
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(W)
| big_p(skolemFOFtoCNF_X)
| big_q(skolemFOFtoCNF_U) ),
inference(conjunct,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
~ big_q(skolemFOFtoCNF_W1),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ big_q(skolemFOFtoCNF_X1)
| big_q(Y1) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_2,plain,
( ~ big_q(Y1)
| big_q(skolemFOFtoCNF_X1) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_3,plain,
( ~ big_q(skolemFOFtoCNF_U_1)
| big_q(skolemFOFtoCNF_X1) ),
inference(subst,[],[refute_0_2:[bind(Y1,$fot(skolemFOFtoCNF_U_1))]]) ).
cnf(refute_0_4,plain,
( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_W)
| ~ big_p(skolemFOFtoCNF_Y_1(X))
| big_q(skolemFOFtoCNF_U_1) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_5,plain,
( ~ big_q(skolemFOFtoCNF_U)
| big_q(skolemFOFtoCNF_X1) ),
inference(subst,[],[refute_0_2:[bind(Y1,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_6,plain,
( ~ big_p(skolemFOFtoCNF_X)
| big_p(W)
| big_p(Y)
| 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(W)
| big_p(skolemFOFtoCNF_X)
| big_q(skolemFOFtoCNF_U) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_9,plain,
( ~ big_p(skolemFOFtoCNF_U1)
| big_p(X_6)
| big_p(skolemFOFtoCNF_X)
| big_q(skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_8:[bind(W,$fot(X_6)),bind(Y,$fot(skolemFOFtoCNF_U1))]]) ).
cnf(refute_0_10,plain,
( big_p(X_6)
| big_p(skolemFOFtoCNF_X)
| big_q(skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_U1) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( big_p(X_8)
| big_p(skolemFOFtoCNF_X)
| big_q(skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_10:[bind(X_6,$fot(X_8))]]) ).
cnf(refute_0_12,plain,
( big_p(X_8)
| big_p(skolemFOFtoCNF_X)
| big_q(skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_U) )],[refute_0_11,refute_0_5]) ).
cnf(refute_0_13,plain,
( big_p(X_9)
| big_p(skolemFOFtoCNF_X)
| big_q(skolemFOFtoCNF_X1) ),
inference(subst,[],[refute_0_12:[bind(X_8,$fot(X_9))]]) ).
cnf(refute_0_14,plain,
( big_p(X_9)
| big_p(skolemFOFtoCNF_X)
| big_q(Y1) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_X1) )],[refute_0_13,refute_0_1]) ).
cnf(refute_0_15,plain,
( big_p(X_12)
| big_p(skolemFOFtoCNF_X)
| big_q(skolemFOFtoCNF_W1) ),
inference(subst,[],[refute_0_14:[bind(Y1,$fot(skolemFOFtoCNF_W1)),bind(X_9,$fot(X_12))]]) ).
cnf(refute_0_16,plain,
( big_p(X_12)
| big_p(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_W1) )],[refute_0_15,refute_0_0]) ).
cnf(refute_0_17,plain,
big_p(skolemFOFtoCNF_X),
inference(subst,[],[refute_0_16:[bind(X_12,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_18,plain,
( big_p(W)
| big_p(Y)
| big_q(skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X) )],[refute_0_17,refute_0_6]) ).
cnf(refute_0_19,plain,
( big_p(X_15)
| big_q(skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_18:[bind(W,$fot(X_15)),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_20,plain,
( big_p(X_15)
| big_q(skolemFOFtoCNF_X1) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_U) )],[refute_0_19,refute_0_5]) ).
cnf(refute_0_21,plain,
( big_p(X_16)
| big_q(skolemFOFtoCNF_X1) ),
inference(subst,[],[refute_0_20:[bind(X_15,$fot(X_16))]]) ).
cnf(refute_0_22,plain,
( big_p(X_16)
| big_q(Y1) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_X1) )],[refute_0_21,refute_0_1]) ).
cnf(refute_0_23,plain,
( big_p(skolemFOFtoCNF_Y_1(X))
| big_q(X_17) ),
inference(subst,[],[refute_0_22:[bind(Y1,$fot(X_17)),bind(X_16,$fot(skolemFOFtoCNF_Y_1(X)))]]) ).
cnf(refute_0_24,plain,
( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_W)
| big_q(X_17)
| big_q(skolemFOFtoCNF_U_1) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y_1(X)) )],[refute_0_23,refute_0_4]) ).
cnf(refute_0_25,plain,
( big_p(X_18)
| big_q(skolemFOFtoCNF_W1) ),
inference(subst,[],[refute_0_22:[bind(Y1,$fot(skolemFOFtoCNF_W1)),bind(X_16,$fot(X_18))]]) ).
cnf(refute_0_26,plain,
big_p(X_18),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_W1) )],[refute_0_25,refute_0_0]) ).
cnf(refute_0_27,plain,
big_p(X),
inference(subst,[],[refute_0_26:[bind(X_18,$fot(X))]]) ).
cnf(refute_0_28,plain,
( ~ big_p(skolemFOFtoCNF_W)
| big_q(X_17)
| big_q(skolemFOFtoCNF_U_1) ),
inference(resolve,[$cnf( big_p(X) )],[refute_0_27,refute_0_24]) ).
cnf(refute_0_29,plain,
big_p(skolemFOFtoCNF_W),
inference(subst,[],[refute_0_26:[bind(X_18,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_30,plain,
( big_q(X_17)
| big_q(skolemFOFtoCNF_U_1) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_W) )],[refute_0_29,refute_0_28]) ).
cnf(refute_0_31,plain,
big_q(skolemFOFtoCNF_U_1),
inference(subst,[],[refute_0_30:[bind(X_17,$fot(skolemFOFtoCNF_U_1))]]) ).
cnf(refute_0_32,plain,
big_q(skolemFOFtoCNF_X1),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_U_1) )],[refute_0_31,refute_0_3]) ).
cnf(refute_0_33,plain,
big_q(Y1),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_X1) )],[refute_0_32,refute_0_1]) ).
cnf(refute_0_34,plain,
big_q(skolemFOFtoCNF_W1),
inference(subst,[],[refute_0_33:[bind(Y1,$fot(skolemFOFtoCNF_W1))]]) ).
cnf(refute_0_35,plain,
$false,
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_W1) )],[refute_0_34,refute_0_0]) ).
fof(negate_1_0,plain,
~ ( ( ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_p(W) ) )
& ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
& ! [W1] : big_q(W1) )
=> ? [U1] : big_p(U1) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ( ? [U] : big_q(U)
<=> ( ? [W] : ~ big_p(W)
<=> ! [X] :
? [Y] :
( ~ big_p(X)
<=> big_p(Y) ) ) )
& ? [X1] :
! [Y1] :
( ~ big_q(X1)
<=> ~ big_q(Y1) )
& ! [U1] : ~ big_p(U1)
& ! [W1] : big_q(W1) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ? [U] : big_q(U)
<=> ( ? [W] : ~ big_p(W)
<=> ! [X] :
? [Y] :
( ~ big_p(X)
<=> big_p(Y) ) ) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [U,W,X,Y] :
( ( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_W_1)
| ~ big_p(skolemFOFtoCNF_Y_3(X))
| big_q(skolemFOFtoCNF_U_3) )
& ( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_Y_2(X))
| ~ big_q(U)
| big_p(W) )
& ( ~ big_p(Y)
| ~ big_p(skolemFOFtoCNF_W_1)
| ~ big_q(U)
| big_p(skolemFOFtoCNF_X_3) )
& ( ~ big_p(Y)
| big_p(W)
| big_p(skolemFOFtoCNF_X_2)
| big_q(skolemFOFtoCNF_U_2) )
& ( ~ big_p(skolemFOFtoCNF_W_1)
| ~ big_p(skolemFOFtoCNF_X_3)
| ~ big_q(U)
| big_p(Y) )
& ( ~ big_p(skolemFOFtoCNF_W_1)
| big_p(X)
| big_p(skolemFOFtoCNF_Y_3(X))
| big_q(skolemFOFtoCNF_U_3) )
& ( ~ big_p(skolemFOFtoCNF_X_2)
| big_p(W)
| big_p(Y)
| big_q(skolemFOFtoCNF_U_2) )
& ( ~ big_q(U)
| big_p(W)
| big_p(X)
| big_p(skolemFOFtoCNF_Y_2(X)) ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [U,W,X] :
( ~ big_q(U)
| big_p(W)
| big_p(X)
| big_p(skolemFOFtoCNF_Y_2(X)) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [W1] : big_q(W1),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_5,plain,
! [W1] : big_q(W1),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [U1] : ~ big_p(U1),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_7,plain,
! [U1] : ~ big_p(U1),
inference(specialize,[],[normalize_1_6]) ).
cnf(refute_1_0,plain,
( ~ big_q(U)
| big_p(W)
| big_p(X)
| big_p(skolemFOFtoCNF_Y_2(X)) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
big_q(W1),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_2,plain,
big_q(U),
inference(subst,[],[refute_1_1:[bind(W1,$fot(U))]]) ).
cnf(refute_1_3,plain,
( big_p(W)
| big_p(X)
| big_p(skolemFOFtoCNF_Y_2(X)) ),
inference(resolve,[$cnf( big_q(U) )],[refute_1_2,refute_1_0]) ).
cnf(refute_1_4,plain,
~ big_p(U1),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_5,plain,
~ big_p(W),
inference(subst,[],[refute_1_4:[bind(U1,$fot(W))]]) ).
cnf(refute_1_6,plain,
( big_p(X)
| big_p(skolemFOFtoCNF_Y_2(X)) ),
inference(resolve,[$cnf( big_p(W) )],[refute_1_3,refute_1_5]) ).
cnf(refute_1_7,plain,
~ big_p(X),
inference(subst,[],[refute_1_4:[bind(U1,$fot(X))]]) ).
cnf(refute_1_8,plain,
big_p(skolemFOFtoCNF_Y_2(X)),
inference(resolve,[$cnf( big_p(X) )],[refute_1_6,refute_1_7]) ).
cnf(refute_1_9,plain,
~ big_p(skolemFOFtoCNF_Y_2(X)),
inference(subst,[],[refute_1_4:[bind(U1,$fot(skolemFOFtoCNF_Y_2(X)))]]) ).
cnf(refute_1_10,plain,
$false,
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y_2(X)) )],[refute_1_8,refute_1_9]) ).
fof(negate_2_0,plain,
~ ( ( ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [U] : big_q(U)
<=> ! [W] : big_p(W) ) )
& ( ? [U1] : big_p(U1)
<=> ! [W1] : big_q(W1) ) )
=> ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) ) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
( ( ? [U] : big_q(U)
<=> ( ? [W] : ~ big_p(W)
<=> ! [X] :
? [Y] :
( ~ big_p(X)
<=> big_p(Y) ) ) )
& ( ? [U1] : big_p(U1)
<=> ! [W1] : big_q(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,
( ? [U1] : big_p(U1)
<=> ! [W1] : big_q(W1) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_7,plain,
! [U1,W1] :
( ( ~ big_p(U1)
| big_q(W1) )
& ( ~ big_q(skolemFOFtoCNF_W1_1)
| big_p(skolemFOFtoCNF_U1_1) ) ),
inference(clausify,[],[normalize_2_6]) ).
fof(normalize_2_8,plain,
! [U1,W1] :
( ~ big_p(U1)
| big_q(W1) ),
inference(conjunct,[],[normalize_2_7]) ).
fof(normalize_2_9,plain,
( ? [U] : big_q(U)
<=> ( ? [W] : ~ big_p(W)
<=> ! [X] :
? [Y] :
( ~ big_p(X)
<=> big_p(Y) ) ) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_10,plain,
! [U,W,X,Y] :
( ( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_W_2)
| ~ big_p(skolemFOFtoCNF_Y_5(X))
| big_q(skolemFOFtoCNF_U_5) )
& ( ~ big_p(X)
| ~ big_p(skolemFOFtoCNF_Y_4(X))
| ~ big_q(U)
| big_p(W) )
& ( ~ big_p(Y)
| ~ big_p(skolemFOFtoCNF_W_2)
| ~ big_q(U)
| big_p(skolemFOFtoCNF_X_5) )
& ( ~ big_p(Y)
| big_p(W)
| big_p(skolemFOFtoCNF_X_4)
| big_q(skolemFOFtoCNF_U_4) )
& ( ~ big_p(skolemFOFtoCNF_W_2)
| ~ big_p(skolemFOFtoCNF_X_5)
| ~ big_q(U)
| big_p(Y) )
& ( ~ big_p(skolemFOFtoCNF_W_2)
| big_p(X)
| big_p(skolemFOFtoCNF_Y_5(X))
| big_q(skolemFOFtoCNF_U_5) )
& ( ~ big_p(skolemFOFtoCNF_X_4)
| big_p(W)
| big_p(Y)
| big_q(skolemFOFtoCNF_U_4) )
& ( ~ big_q(U)
| big_p(W)
| big_p(X)
| big_p(skolemFOFtoCNF_Y_4(X)) ) ),
inference(clausify,[],[normalize_2_9]) ).
fof(normalize_2_11,plain,
! [U,W,X] :
( ~ big_q(U)
| big_p(W)
| big_p(X)
| big_p(skolemFOFtoCNF_Y_4(X)) ),
inference(conjunct,[],[normalize_2_10]) ).
fof(normalize_2_12,plain,
! [X1] :
( big_q(X1)
| big_q(skolemFOFtoCNF_Y1(X1)) ),
inference(conjunct,[],[normalize_2_4]) ).
cnf(refute_2_0,plain,
( ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_Y1(X1)) ),
inference(canonicalize,[],[normalize_2_5]) ).
cnf(refute_2_1,plain,
( ~ big_p(U1)
| big_q(W1) ),
inference(canonicalize,[],[normalize_2_8]) ).
cnf(refute_2_2,plain,
( ~ big_p(X_39)
| big_q(W1) ),
inference(subst,[],[refute_2_1:[bind(U1,$fot(X_39))]]) ).
cnf(refute_2_3,plain,
( ~ big_p(skolemFOFtoCNF_Y_4(X_37))
| big_q(W1) ),
inference(subst,[],[refute_2_1:[bind(U1,$fot(skolemFOFtoCNF_Y_4(X_37)))]]) ).
cnf(refute_2_4,plain,
( ~ big_q(U)
| big_p(W)
| big_p(X)
| big_p(skolemFOFtoCNF_Y_4(X)) ),
inference(canonicalize,[],[normalize_2_11]) ).
cnf(refute_2_5,plain,
( ~ big_q(X_35)
| big_p(W)
| big_p(X)
| big_p(skolemFOFtoCNF_Y_4(X)) ),
inference(subst,[],[refute_2_4:[bind(U,$fot(X_35))]]) ).
cnf(refute_2_6,plain,
( big_q(X1)
| big_q(skolemFOFtoCNF_Y1(X1)) ),
inference(canonicalize,[],[normalize_2_12]) ).
cnf(refute_2_7,plain,
( ~ big_q(skolemFOFtoCNF_Y1(X1))
| big_p(X_33)
| big_p(X_34)
| big_p(skolemFOFtoCNF_Y_4(X_34)) ),
inference(subst,[],[refute_2_4:[bind(U,$fot(skolemFOFtoCNF_Y1(X1))),bind(W,$fot(X_33)),bind(X,$fot(X_34))]]) ).
cnf(refute_2_8,plain,
( big_p(X_33)
| big_p(X_34)
| big_p(skolemFOFtoCNF_Y_4(X_34))
| big_q(X1) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_Y1(X1)) )],[refute_2_6,refute_2_7]) ).
cnf(refute_2_9,plain,
( big_p(X_36)
| big_p(skolemFOFtoCNF_Y_4(X_36))
| big_q(X_35) ),
inference(subst,[],[refute_2_8:[bind(X1,$fot(X_35)),bind(X_33,$fot(skolemFOFtoCNF_Y_4(X_36))),bind(X_34,$fot(X_36))]]) ).
cnf(refute_2_10,plain,
( big_p(W)
| big_p(X)
| big_p(X_36)
| big_p(skolemFOFtoCNF_Y_4(X))
| big_p(skolemFOFtoCNF_Y_4(X_36)) ),
inference(resolve,[$cnf( big_q(X_35) )],[refute_2_9,refute_2_5]) ).
cnf(refute_2_11,plain,
( big_p(X_37)
| big_p(skolemFOFtoCNF_Y_4(X_37)) ),
inference(subst,[],[refute_2_10:[bind(W,$fot(skolemFOFtoCNF_Y_4(X_37))),bind(X,$fot(X_37)),bind(X_36,$fot(X_37))]]) ).
cnf(refute_2_12,plain,
( big_p(X_37)
| big_q(W1) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y_4(X_37)) )],[refute_2_11,refute_2_3]) ).
cnf(refute_2_13,plain,
( big_p(X_39)
| big_q(X_38) ),
inference(subst,[],[refute_2_12:[bind(W1,$fot(X_38)),bind(X_37,$fot(X_39))]]) ).
cnf(refute_2_14,plain,
( big_q(W1)
| big_q(X_38) ),
inference(resolve,[$cnf( big_p(X_39) )],[refute_2_13,refute_2_2]) ).
cnf(refute_2_15,plain,
big_q(skolemFOFtoCNF_Y1(X1)),
inference(subst,[],[refute_2_14:[bind(W1,$fot(skolemFOFtoCNF_Y1(X1))),bind(X_38,$fot(skolemFOFtoCNF_Y1(X1)))]]) ).
cnf(refute_2_16,plain,
~ big_q(X1),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_Y1(X1)) )],[refute_2_15,refute_2_0]) ).
cnf(refute_2_17,plain,
big_q(X1),
inference(subst,[],[refute_2_14:[bind(W1,$fot(X1)),bind(X_38,$fot(X1))]]) ).
cnf(refute_2_18,plain,
$false,
inference(resolve,[$cnf( big_q(X1) )],[refute_2_17,refute_2_16]) ).
fof(negate_3_0,plain,
~ ( ( ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_q(W1) ) )
& ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
& ? [U] : big_q(U) )
=> ! [W] : big_p(W) ),
inference(negate,[],[subgoal_3]) ).
fof(normalize_3_0,plain,
( ( ? [U1] : big_p(U1)
<=> ( ? [W1] : ~ big_q(W1)
<=> ! [X1] :
? [Y1] :
( ~ big_q(X1)
<=> big_q(Y1) ) ) )
& ? [U] : big_q(U)
& ? [W] : ~ big_p(W)
& ? [X] :
! [Y] :
( ~ big_p(X)
<=> ~ big_p(Y) ) ),
inference(canonicalize,[],[negate_3_0]) ).
fof(normalize_3_1,plain,
? [W] : ~ big_p(W),
inference(conjunct,[],[normalize_3_0]) ).
fof(normalize_3_2,plain,
~ big_p(skolemFOFtoCNF_W_3),
inference(skolemize,[],[normalize_3_1]) ).
fof(normalize_3_3,plain,
? [X] :
! [Y] :
( ~ big_p(X)
<=> ~ big_p(Y) ),
inference(conjunct,[],[normalize_3_0]) ).
fof(normalize_3_4,plain,
! [Y] :
( ~ big_p(Y)
<=> ~ big_p(skolemFOFtoCNF_X_6) ),
inference(skolemize,[],[normalize_3_3]) ).
fof(normalize_3_5,plain,
! [Y] :
( ~ big_p(Y)
<=> ~ big_p(skolemFOFtoCNF_X_6) ),
inference(specialize,[],[normalize_3_4]) ).
fof(normalize_3_6,plain,
! [Y] :
( ( ~ big_p(Y)
| big_p(skolemFOFtoCNF_X_6) )
& ( ~ big_p(skolemFOFtoCNF_X_6)
| big_p(Y) ) ),
inference(clausify,[],[normalize_3_5]) ).
fof(normalize_3_7,plain,
! [Y] :
( ~ big_p(skolemFOFtoCNF_X_6)
| big_p(Y) ),
inference(conjunct,[],[normalize_3_6]) ).
fof(normalize_3_8,plain,
! [Y] :
( ~ big_p(Y)
| big_p(skolemFOFtoCNF_X_6) ),
inference(conjunct,[],[normalize_3_6]) ).
fof(normalize_3_9,plain,
? [U] : big_q(U),
inference(conjunct,[],[normalize_3_0]) ).
fof(normalize_3_10,plain,
big_q(skolemFOFtoCNF_U_6),
inference(skolemize,[],[normalize_3_9]) ).
fof(normalize_3_11,plain,
( ? [U1] : big_p(U1)
<=> ( ? [W1] : ~ big_q(W1)
<=> ! [X1] :
? [Y1] :
( ~ big_q(X1)
<=> big_q(Y1) ) ) ),
inference(conjunct,[],[normalize_3_0]) ).
fof(normalize_3_12,plain,
! [U1,W1,X1,Y1] :
( ( ~ big_p(U1)
| ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_Y1_1(X1))
| big_q(W1) )
& ( ~ big_p(U1)
| ~ big_q(Y1)
| ~ big_q(skolemFOFtoCNF_W1_2)
| big_q(skolemFOFtoCNF_X1_2) )
& ( ~ big_p(U1)
| ~ big_q(skolemFOFtoCNF_W1_2)
| ~ big_q(skolemFOFtoCNF_X1_2)
| big_q(Y1) )
& ( ~ big_p(U1)
| big_q(W1)
| big_q(X1)
| big_q(skolemFOFtoCNF_Y1_1(X1)) )
& ( ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_W1_3)
| ~ big_q(skolemFOFtoCNF_Y1_2(X1))
| big_p(skolemFOFtoCNF_U1_2) )
& ( ~ big_q(Y1)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(W1)
| big_q(skolemFOFtoCNF_X1_3) )
& ( ~ big_q(skolemFOFtoCNF_W1_3)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(X1)
| big_q(skolemFOFtoCNF_Y1_2(X1)) )
& ( ~ big_q(skolemFOFtoCNF_X1_3)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(W1)
| big_q(Y1) ) ),
inference(clausify,[],[normalize_3_11]) ).
fof(normalize_3_13,plain,
! [W1,Y1] :
( ~ big_q(Y1)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(W1)
| big_q(skolemFOFtoCNF_X1_3) ),
inference(conjunct,[],[normalize_3_12]) ).
fof(normalize_3_14,plain,
! [W1,Y1] :
( ~ big_q(skolemFOFtoCNF_X1_3)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(W1)
| big_q(Y1) ),
inference(conjunct,[],[normalize_3_12]) ).
fof(normalize_3_15,plain,
! [X1] :
( ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_W1_3)
| ~ big_q(skolemFOFtoCNF_Y1_2(X1))
| big_p(skolemFOFtoCNF_U1_2) ),
inference(conjunct,[],[normalize_3_12]) ).
cnf(refute_3_0,plain,
~ big_p(skolemFOFtoCNF_W_3),
inference(canonicalize,[],[normalize_3_2]) ).
cnf(refute_3_1,plain,
( ~ big_p(skolemFOFtoCNF_X_6)
| big_p(Y) ),
inference(canonicalize,[],[normalize_3_7]) ).
cnf(refute_3_2,plain,
( ~ big_p(Y)
| big_p(skolemFOFtoCNF_X_6) ),
inference(canonicalize,[],[normalize_3_8]) ).
cnf(refute_3_3,plain,
( ~ big_p(skolemFOFtoCNF_U1_2)
| big_p(skolemFOFtoCNF_X_6) ),
inference(subst,[],[refute_3_2:[bind(Y,$fot(skolemFOFtoCNF_U1_2))]]) ).
cnf(refute_3_4,plain,
big_q(skolemFOFtoCNF_U_6),
inference(canonicalize,[],[normalize_3_10]) ).
cnf(refute_3_5,plain,
( ~ big_q(Y1)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(W1)
| big_q(skolemFOFtoCNF_X1_3) ),
inference(canonicalize,[],[normalize_3_13]) ).
cnf(refute_3_6,plain,
( ~ big_q(skolemFOFtoCNF_U_6)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(X_49)
| big_q(skolemFOFtoCNF_X1_3) ),
inference(subst,[],[refute_3_5:[bind(W1,$fot(X_49)),bind(Y1,$fot(skolemFOFtoCNF_U_6))]]) ).
cnf(refute_3_7,plain,
( big_p(skolemFOFtoCNF_U1_2)
| big_q(X_49)
| big_q(skolemFOFtoCNF_X1_3) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_U_6) )],[refute_3_4,refute_3_6]) ).
cnf(refute_3_8,plain,
( big_p(skolemFOFtoCNF_U1_2)
| big_q(skolemFOFtoCNF_X1_3) ),
inference(subst,[],[refute_3_7:[bind(X_49,$fot(skolemFOFtoCNF_X1_3))]]) ).
cnf(refute_3_9,plain,
( ~ big_q(skolemFOFtoCNF_X1_3)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(W1)
| big_q(Y1) ),
inference(canonicalize,[],[normalize_3_14]) ).
cnf(refute_3_10,plain,
( ~ big_q(skolemFOFtoCNF_X1_3)
| big_p(skolemFOFtoCNF_U1_2)
| big_q(X_51)
| big_q(X_52) ),
inference(subst,[],[refute_3_9:[bind(W1,$fot(X_52)),bind(Y1,$fot(X_51))]]) ).
cnf(refute_3_11,plain,
( big_p(skolemFOFtoCNF_U1_2)
| big_q(X_51)
| big_q(X_52) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_X1_3) )],[refute_3_8,refute_3_10]) ).
cnf(refute_3_12,plain,
( big_p(skolemFOFtoCNF_U1_2)
| big_q(skolemFOFtoCNF_W1_3) ),
inference(subst,[],[refute_3_11:[bind(X_51,$fot(skolemFOFtoCNF_W1_3)),bind(X_52,$fot(skolemFOFtoCNF_W1_3))]]) ).
cnf(refute_3_13,plain,
( ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_W1_3)
| ~ big_q(skolemFOFtoCNF_Y1_2(X1))
| big_p(skolemFOFtoCNF_U1_2) ),
inference(canonicalize,[],[normalize_3_15]) ).
cnf(refute_3_14,plain,
( big_p(skolemFOFtoCNF_U1_2)
| big_q(skolemFOFtoCNF_Y1_2(X1)) ),
inference(subst,[],[refute_3_11:[bind(X_51,$fot(skolemFOFtoCNF_Y1_2(X1))),bind(X_52,$fot(skolemFOFtoCNF_Y1_2(X1)))]]) ).
cnf(refute_3_15,plain,
( ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_W1_3)
| big_p(skolemFOFtoCNF_U1_2) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_Y1_2(X1)) )],[refute_3_14,refute_3_13]) ).
cnf(refute_3_16,plain,
( ~ big_q(skolemFOFtoCNF_W1_3)
| big_p(skolemFOFtoCNF_U1_2) ),
inference(subst,[],[refute_3_15:[bind(X1,$fot(skolemFOFtoCNF_W1_3))]]) ).
cnf(refute_3_17,plain,
big_p(skolemFOFtoCNF_U1_2),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_W1_3) )],[refute_3_12,refute_3_16]) ).
cnf(refute_3_18,plain,
big_p(skolemFOFtoCNF_X_6),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_U1_2) )],[refute_3_17,refute_3_3]) ).
cnf(refute_3_19,plain,
big_p(Y),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X_6) )],[refute_3_18,refute_3_1]) ).
cnf(refute_3_20,plain,
big_p(skolemFOFtoCNF_W_3),
inference(subst,[],[refute_3_19:[bind(Y,$fot(skolemFOFtoCNF_W_3))]]) ).
cnf(refute_3_21,plain,
$false,
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_W_3) )],[refute_3_20,refute_3_0]) ).
fof(negate_4_0,plain,
~ ( ( ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_q(W1) ) )
& ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
& ! [W] : big_p(W) )
=> ? [U] : big_q(U) ),
inference(negate,[],[subgoal_4]) ).
fof(normalize_4_0,plain,
( ( ? [U1] : big_p(U1)
<=> ( ? [W1] : ~ big_q(W1)
<=> ! [X1] :
? [Y1] :
( ~ big_q(X1)
<=> big_q(Y1) ) ) )
& ? [X] :
! [Y] :
( ~ big_p(X)
<=> ~ big_p(Y) )
& ! [U] : ~ big_q(U)
& ! [W] : big_p(W) ),
inference(canonicalize,[],[negate_4_0]) ).
fof(normalize_4_1,plain,
( ? [U1] : big_p(U1)
<=> ( ? [W1] : ~ big_q(W1)
<=> ! [X1] :
? [Y1] :
( ~ big_q(X1)
<=> big_q(Y1) ) ) ),
inference(conjunct,[],[normalize_4_0]) ).
fof(normalize_4_2,plain,
! [U1,W1,X1,Y1] :
( ( ~ big_p(U1)
| ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_Y1_3(X1))
| big_q(W1) )
& ( ~ big_p(U1)
| ~ big_q(Y1)
| ~ big_q(skolemFOFtoCNF_W1_5)
| big_q(skolemFOFtoCNF_X1_4) )
& ( ~ big_p(U1)
| ~ big_q(skolemFOFtoCNF_W1_5)
| ~ big_q(skolemFOFtoCNF_X1_4)
| big_q(Y1) )
& ( ~ big_p(U1)
| big_q(W1)
| big_q(X1)
| big_q(skolemFOFtoCNF_Y1_3(X1)) )
& ( ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_W1_4)
| ~ big_q(skolemFOFtoCNF_Y1_3(X1))
| big_p(skolemFOFtoCNF_U1_3) )
& ( ~ big_q(Y1)
| big_p(skolemFOFtoCNF_U1_4)
| big_q(W1)
| big_q(skolemFOFtoCNF_X1_4) )
& ( ~ big_q(skolemFOFtoCNF_W1_4)
| big_p(skolemFOFtoCNF_U1_3)
| big_q(X1)
| big_q(skolemFOFtoCNF_Y1_3(X1)) )
& ( ~ big_q(skolemFOFtoCNF_X1_4)
| big_p(skolemFOFtoCNF_U1_4)
| big_q(W1)
| big_q(Y1) ) ),
inference(clausify,[],[normalize_4_1]) ).
fof(normalize_4_3,plain,
! [U1,W1,X1] :
( ~ big_p(U1)
| big_q(W1)
| big_q(X1)
| big_q(skolemFOFtoCNF_Y1_3(X1)) ),
inference(conjunct,[],[normalize_4_2]) ).
fof(normalize_4_4,plain,
! [W] : big_p(W),
inference(conjunct,[],[normalize_4_0]) ).
fof(normalize_4_5,plain,
! [W] : big_p(W),
inference(specialize,[],[normalize_4_4]) ).
fof(normalize_4_6,plain,
! [U] : ~ big_q(U),
inference(conjunct,[],[normalize_4_0]) ).
fof(normalize_4_7,plain,
! [U] : ~ big_q(U),
inference(specialize,[],[normalize_4_6]) ).
cnf(refute_4_0,plain,
( ~ big_p(U1)
| big_q(W1)
| big_q(X1)
| big_q(skolemFOFtoCNF_Y1_3(X1)) ),
inference(canonicalize,[],[normalize_4_3]) ).
cnf(refute_4_1,plain,
big_p(W),
inference(canonicalize,[],[normalize_4_5]) ).
cnf(refute_4_2,plain,
big_p(U1),
inference(subst,[],[refute_4_1:[bind(W,$fot(U1))]]) ).
cnf(refute_4_3,plain,
( big_q(W1)
| big_q(X1)
| big_q(skolemFOFtoCNF_Y1_3(X1)) ),
inference(resolve,[$cnf( big_p(U1) )],[refute_4_2,refute_4_0]) ).
cnf(refute_4_4,plain,
~ big_q(U),
inference(canonicalize,[],[normalize_4_7]) ).
cnf(refute_4_5,plain,
~ big_q(W1),
inference(subst,[],[refute_4_4:[bind(U,$fot(W1))]]) ).
cnf(refute_4_6,plain,
( big_q(X1)
| big_q(skolemFOFtoCNF_Y1_3(X1)) ),
inference(resolve,[$cnf( big_q(W1) )],[refute_4_3,refute_4_5]) ).
cnf(refute_4_7,plain,
~ big_q(X1),
inference(subst,[],[refute_4_4:[bind(U,$fot(X1))]]) ).
cnf(refute_4_8,plain,
big_q(skolemFOFtoCNF_Y1_3(X1)),
inference(resolve,[$cnf( big_q(X1) )],[refute_4_6,refute_4_7]) ).
cnf(refute_4_9,plain,
~ big_q(skolemFOFtoCNF_Y1_3(X1)),
inference(subst,[],[refute_4_4:[bind(U,$fot(skolemFOFtoCNF_Y1_3(X1)))]]) ).
cnf(refute_4_10,plain,
$false,
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_Y1_3(X1)) )],[refute_4_8,refute_4_9]) ).
fof(negate_5_0,plain,
~ ( ( ( ? [X1] :
! [Y1] :
( big_q(X1)
<=> big_q(Y1) )
<=> ( ? [U1] : big_p(U1)
<=> ! [W1] : big_q(W1) ) )
& ( ? [U] : big_q(U)
<=> ! [W] : big_p(W) ) )
=> ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) ) ),
inference(negate,[],[subgoal_5]) ).
fof(normalize_5_0,plain,
( ( ? [U1] : big_p(U1)
<=> ( ? [W1] : ~ big_q(W1)
<=> ! [X1] :
? [Y1] :
( ~ big_q(X1)
<=> big_q(Y1) ) ) )
& ( ? [U] : big_q(U)
<=> ! [W] : big_p(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,
( ? [U] : big_q(U)
<=> ! [W] : big_p(W) ),
inference(conjunct,[],[normalize_5_0]) ).
fof(normalize_5_7,plain,
! [U,W] :
( ( ~ big_p(skolemFOFtoCNF_W_4)
| big_q(skolemFOFtoCNF_U_7) )
& ( ~ big_q(U)
| big_p(W) ) ),
inference(clausify,[],[normalize_5_6]) ).
fof(normalize_5_8,plain,
! [U,W] :
( ~ big_q(U)
| big_p(W) ),
inference(conjunct,[],[normalize_5_7]) ).
fof(normalize_5_9,plain,
! [X] :
( big_p(X)
| big_p(skolemFOFtoCNF_Y_6(X)) ),
inference(conjunct,[],[normalize_5_4]) ).
fof(normalize_5_10,plain,
( ? [U1] : big_p(U1)
<=> ( ? [W1] : ~ big_q(W1)
<=> ! [X1] :
? [Y1] :
( ~ big_q(X1)
<=> big_q(Y1) ) ) ),
inference(conjunct,[],[normalize_5_0]) ).
fof(normalize_5_11,plain,
! [U1,W1,X1,Y1] :
( ( ~ big_p(U1)
| ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_Y1_4(X1))
| big_q(W1) )
& ( ~ big_p(U1)
| ~ big_q(Y1)
| ~ big_q(skolemFOFtoCNF_W1_6)
| big_q(skolemFOFtoCNF_X1_6) )
& ( ~ big_p(U1)
| ~ big_q(skolemFOFtoCNF_W1_6)
| ~ big_q(skolemFOFtoCNF_X1_6)
| big_q(Y1) )
& ( ~ big_p(U1)
| big_q(W1)
| big_q(X1)
| big_q(skolemFOFtoCNF_Y1_4(X1)) )
& ( ~ big_q(X1)
| ~ big_q(skolemFOFtoCNF_W1_6)
| ~ big_q(skolemFOFtoCNF_Y1_5(X1))
| big_p(skolemFOFtoCNF_U1_6) )
& ( ~ big_q(Y1)
| big_p(skolemFOFtoCNF_U1_5)
| big_q(W1)
| big_q(skolemFOFtoCNF_X1_5) )
& ( ~ big_q(skolemFOFtoCNF_W1_6)
| big_p(skolemFOFtoCNF_U1_6)
| big_q(X1)
| big_q(skolemFOFtoCNF_Y1_5(X1)) )
& ( ~ big_q(skolemFOFtoCNF_X1_5)
| big_p(skolemFOFtoCNF_U1_5)
| big_q(W1)
| big_q(Y1) ) ),
inference(clausify,[],[normalize_5_10]) ).
fof(normalize_5_12,plain,
! [U1,W1,X1] :
( ~ big_p(U1)
| big_q(W1)
| big_q(X1)
| big_q(skolemFOFtoCNF_Y1_4(X1)) ),
inference(conjunct,[],[normalize_5_11]) ).
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_q(U)
| big_p(W) ),
inference(canonicalize,[],[normalize_5_8]) ).
cnf(refute_5_2,plain,
( ~ big_q(X_71)
| big_p(W) ),
inference(subst,[],[refute_5_1:[bind(U,$fot(X_71))]]) ).
cnf(refute_5_3,plain,
( ~ big_q(skolemFOFtoCNF_Y1_4(X_69))
| big_p(W) ),
inference(subst,[],[refute_5_1:[bind(U,$fot(skolemFOFtoCNF_Y1_4(X_69)))]]) ).
cnf(refute_5_4,plain,
( big_p(X)
| big_p(skolemFOFtoCNF_Y_6(X)) ),
inference(canonicalize,[],[normalize_5_9]) ).
cnf(refute_5_5,plain,
( ~ big_p(U1)
| big_q(W1)
| big_q(X1)
| big_q(skolemFOFtoCNF_Y1_4(X1)) ),
inference(canonicalize,[],[normalize_5_12]) ).
cnf(refute_5_6,plain,
( ~ big_p(skolemFOFtoCNF_Y_6(X))
| big_q(X_66)
| big_q(X_67)
| big_q(skolemFOFtoCNF_Y1_4(X_67)) ),
inference(subst,[],[refute_5_5:[bind(U1,$fot(skolemFOFtoCNF_Y_6(X))),bind(W1,$fot(X_66)),bind(X1,$fot(X_67))]]) ).
cnf(refute_5_7,plain,
( big_p(X)
| big_q(X_66)
| big_q(X_67)
| big_q(skolemFOFtoCNF_Y1_4(X_67)) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y_6(X)) )],[refute_5_4,refute_5_6]) ).
cnf(refute_5_8,plain,
( big_p(X_68)
| big_q(X_69)
| big_q(skolemFOFtoCNF_Y1_4(X_69)) ),
inference(subst,[],[refute_5_7:[bind(X,$fot(X_68)),bind(X_66,$fot(skolemFOFtoCNF_Y1_4(X_69))),bind(X_67,$fot(X_69))]]) ).
cnf(refute_5_9,plain,
( big_p(W)
| big_p(X_68)
| big_q(X_69) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_Y1_4(X_69)) )],[refute_5_8,refute_5_3]) ).
cnf(refute_5_10,plain,
( big_p(X_70)
| big_q(X_71) ),
inference(subst,[],[refute_5_9:[bind(W,$fot(X_70)),bind(X_68,$fot(X_70)),bind(X_69,$fot(X_71))]]) ).
cnf(refute_5_11,plain,
( big_p(W)
| big_p(X_70) ),
inference(resolve,[$cnf( big_q(X_71) )],[refute_5_10,refute_5_2]) ).
cnf(refute_5_12,plain,
big_p(skolemFOFtoCNF_Y_6(X)),
inference(subst,[],[refute_5_11:[bind(W,$fot(skolemFOFtoCNF_Y_6(X))),bind(X_70,$fot(skolemFOFtoCNF_Y_6(X)))]]) ).
cnf(refute_5_13,plain,
~ big_p(X),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_Y_6(X)) )],[refute_5_12,refute_5_0]) ).
cnf(refute_5_14,plain,
big_p(X),
inference(subst,[],[refute_5_11:[bind(W,$fot(X)),bind(X_70,$fot(X))]]) ).
cnf(refute_5_15,plain,
$false,
inference(resolve,[$cnf( big_p(X) )],[refute_5_14,refute_5_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN036+2 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n013.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 20:24:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.39
%------------------------------------------------------------------------------