%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN726+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 09:05:14 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 1
% Syntax : Number of formulae : 67 ( 17 unt; 0 def)
% Number of atoms : 177 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 164 ( 54 ~; 76 |; 20 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 158 ( 13 sgn 72 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm400,conjecture,
( ( ( ! [X,Y,Z] :
( ( p(X,Y)
& p(Y,Z) )
=> p(X,Z) )
& ! [X,Y,Z] :
( ( q(X,Y)
& q(Y,Z) )
=> q(X,Z) )
& ! [X,Y] :
( q(X,Y)
=> q(Y,X) )
& ! [X,Y] :
( p(X,Y)
| q(X,Y) ) )
=> ! [X,Y] : p(X,Y) )
| ! [X,Y] : q(X,Y) ) ).
fof(subgoal_0,plain,
( ~ ( ( ! [X,Y,Z] :
( ( p(X,Y)
& p(Y,Z) )
=> p(X,Z) )
& ! [X,Y,Z] :
( ( q(X,Y)
& q(Y,Z) )
=> q(X,Z) )
& ! [X,Y] :
( q(X,Y)
=> q(Y,X) )
& ! [X,Y] :
( p(X,Y)
| q(X,Y) ) )
=> ! [X,Y] : p(X,Y) )
=> ! [X,Y] : q(X,Y) ),
inference(strip,[],[thm400]) ).
fof(negate_0_0,plain,
~ ( ~ ( ( ! [X,Y,Z] :
( ( p(X,Y)
& p(Y,Z) )
=> p(X,Z) )
& ! [X,Y,Z] :
( ( q(X,Y)
& q(Y,Z) )
=> q(X,Z) )
& ! [X,Y] :
( q(X,Y)
=> q(Y,X) )
& ! [X,Y] :
( p(X,Y)
| q(X,Y) ) )
=> ! [X,Y] : p(X,Y) )
=> ! [X,Y] : q(X,Y) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ? [X,Y] : ~ p(X,Y)
& ? [X,Y] : ~ q(X,Y)
& ! [X,Y] :
( ~ q(X,Y)
| q(Y,X) )
& ! [X,Y] :
( p(X,Y)
| q(X,Y) )
& ! [X,Y,Z] :
( ~ p(X,Y)
| ~ p(Y,Z)
| p(X,Z) )
& ! [X,Y,Z] :
( ~ q(X,Y)
| ~ q(Y,Z)
| q(X,Z) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
? [X,Y] : ~ p(X,Y),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ p(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y,Z] :
( ~ p(X,Y)
| ~ p(Y,Z)
| p(X,Z) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_4,plain,
! [X,Y,Z] :
( ~ p(X,Y)
| ~ p(Y,Z)
| p(X,Z) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
? [X,Y] : ~ q(X,Y),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_6,plain,
~ q(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( p(X,Y)
| q(X,Y) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( p(X,Y)
| q(X,Y) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ q(X,Y)
| q(Y,X) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ q(X,Y)
| q(Y,X) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y,Z] :
( ~ q(X,Y)
| ~ q(Y,Z)
| q(X,Z) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_12,plain,
! [X,Y,Z] :
( ~ q(X,Y)
| ~ q(Y,Z)
| q(X,Z) ),
inference(specialize,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
~ p(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ p(X,Y)
| ~ p(Y,Z)
| p(X,Z) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ p(X,skolemFOFtoCNF_X_1)
| ~ p(skolemFOFtoCNF_X_1,X_40)
| p(X,X_40) ),
inference(subst,[],[refute_0_1:[bind(Y,$fot(skolemFOFtoCNF_X_1)),bind(Z,$fot(X_40))]]) ).
cnf(refute_0_3,plain,
~ q(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( p(X,Y)
| q(X,Y) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( p(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| q(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_0_6,plain,
p(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(resolve,[$cnf( q(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_0_5,refute_0_3]) ).
cnf(refute_0_7,plain,
( ~ p(X,skolemFOFtoCNF_Y_1)
| ~ p(skolemFOFtoCNF_Y_1,X_37)
| p(X,X_37) ),
inference(subst,[],[refute_0_1:[bind(Y,$fot(skolemFOFtoCNF_Y_1)),bind(Z,$fot(X_37))]]) ).
cnf(refute_0_8,plain,
( ~ q(X,Y)
| q(Y,X) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
( ~ q(X_2,X_3)
| q(X_3,X_2) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_2)),bind(Y,$fot(X_3))]]) ).
cnf(refute_0_10,plain,
( p(X_2,X_3)
| q(X_2,X_3) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_2)),bind(Y,$fot(X_3))]]) ).
cnf(refute_0_11,plain,
( p(X_2,X_3)
| q(X_3,X_2) ),
inference(resolve,[$cnf( q(X_2,X_3) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
( p(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1)
| q(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_0_11:[bind(X_2,$fot(skolemFOFtoCNF_Y_1)),bind(X_3,$fot(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_0_13,plain,
p(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1),
inference(resolve,[$cnf( q(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_0_12,refute_0_3]) ).
cnf(refute_0_14,plain,
( ~ p(skolemFOFtoCNF_X_1,X_8)
| ~ p(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1)
| p(skolemFOFtoCNF_Y_1,X_8) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_Y_1)),bind(Y,$fot(skolemFOFtoCNF_X_1)),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_15,plain,
( ~ p(skolemFOFtoCNF_X_1,X_8)
| p(skolemFOFtoCNF_Y_1,X_8) ),
inference(resolve,[$cnf( p(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ p(skolemFOFtoCNF_X_1,X_35)
| p(skolemFOFtoCNF_Y_1,X_35) ),
inference(subst,[],[refute_0_15:[bind(X_8,$fot(X_35))]]) ).
cnf(refute_0_17,plain,
( p(X_28,X_29)
| q(X_28,X_29) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_28)),bind(Y,$fot(X_29))]]) ).
cnf(refute_0_18,plain,
( p(X_14,X_13)
| q(X_13,X_14) ),
inference(subst,[],[refute_0_11:[bind(X_2,$fot(X_14)),bind(X_3,$fot(X_13))]]) ).
cnf(refute_0_19,plain,
( ~ q(X,Y)
| ~ q(Y,Z)
| q(X,Z) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_20,plain,
( ~ q(X_12,X_13)
| ~ q(X_13,X_14)
| q(X_12,X_14) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(X_12)),bind(Y,$fot(X_13)),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_21,plain,
( ~ q(X_12,X_13)
| p(X_14,X_13)
| q(X_12,X_14) ),
inference(resolve,[$cnf( q(X_13,X_14) )],[refute_0_18,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ q(X_28,X_29)
| p(X_30,X_29)
| q(X_28,X_30) ),
inference(subst,[],[refute_0_21:[bind(X_12,$fot(X_28)),bind(X_13,$fot(X_29)),bind(X_14,$fot(X_30))]]) ).
cnf(refute_0_23,plain,
( p(X_28,X_29)
| p(X_30,X_29)
| q(X_28,X_30) ),
inference(resolve,[$cnf( q(X_28,X_29) )],[refute_0_17,refute_0_22]) ).
cnf(refute_0_24,plain,
( p(X_36,X_35)
| p(skolemFOFtoCNF_X_1,X_35)
| q(skolemFOFtoCNF_X_1,X_36) ),
inference(subst,[],[refute_0_23:[bind(X_28,$fot(skolemFOFtoCNF_X_1)),bind(X_29,$fot(X_35)),bind(X_30,$fot(X_36))]]) ).
cnf(refute_0_25,plain,
( p(X_36,X_35)
| p(skolemFOFtoCNF_Y_1,X_35)
| q(skolemFOFtoCNF_X_1,X_36) ),
inference(resolve,[$cnf( p(skolemFOFtoCNF_X_1,X_35) )],[refute_0_24,refute_0_16]) ).
cnf(refute_0_26,plain,
( p(skolemFOFtoCNF_Y_1,X_35)
| q(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_0_25:[bind(X_36,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_0_27,plain,
p(skolemFOFtoCNF_Y_1,X_35),
inference(resolve,[$cnf( q(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_0_26,refute_0_3]) ).
cnf(refute_0_28,plain,
p(skolemFOFtoCNF_Y_1,X_37),
inference(subst,[],[refute_0_27:[bind(X_35,$fot(X_37))]]) ).
cnf(refute_0_29,plain,
( ~ p(X,skolemFOFtoCNF_Y_1)
| p(X,X_37) ),
inference(resolve,[$cnf( p(skolemFOFtoCNF_Y_1,X_37) )],[refute_0_28,refute_0_7]) ).
cnf(refute_0_30,plain,
( ~ p(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| p(skolemFOFtoCNF_X_1,X_39) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(X_37,$fot(X_39))]]) ).
cnf(refute_0_31,plain,
p(skolemFOFtoCNF_X_1,X_39),
inference(resolve,[$cnf( p(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_0_6,refute_0_30]) ).
cnf(refute_0_32,plain,
p(skolemFOFtoCNF_X_1,X_40),
inference(subst,[],[refute_0_31:[bind(X_39,$fot(X_40))]]) ).
cnf(refute_0_33,plain,
( ~ p(X,skolemFOFtoCNF_X_1)
| p(X,X_40) ),
inference(resolve,[$cnf( p(skolemFOFtoCNF_X_1,X_40) )],[refute_0_32,refute_0_2]) ).
cnf(refute_0_34,plain,
( ~ p(X_51,skolemFOFtoCNF_X_1)
| p(X_51,X_40) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(X_51))]]) ).
cnf(refute_0_35,plain,
( ~ p(X_6,skolemFOFtoCNF_Y_1)
| ~ p(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1)
| p(X_6,skolemFOFtoCNF_X_1) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_6)),bind(Y,$fot(skolemFOFtoCNF_Y_1)),bind(Z,$fot(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_0_36,plain,
( ~ p(X_6,skolemFOFtoCNF_Y_1)
| p(X_6,skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( p(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1) )],[refute_0_13,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ p(X_50,skolemFOFtoCNF_Y_1)
| p(X_50,skolemFOFtoCNF_X_1) ),
inference(subst,[],[refute_0_36:[bind(X_6,$fot(X_50))]]) ).
cnf(refute_0_38,plain,
( p(X_16,X_17)
| q(X_16,X_17) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_16)),bind(Y,$fot(X_17))]]) ).
cnf(refute_0_39,plain,
( p(X_13,X_12)
| q(X_12,X_13) ),
inference(subst,[],[refute_0_11:[bind(X_2,$fot(X_13)),bind(X_3,$fot(X_12))]]) ).
cnf(refute_0_40,plain,
( ~ q(X_13,X_14)
| p(X_13,X_12)
| q(X_12,X_14) ),
inference(resolve,[$cnf( q(X_12,X_13) )],[refute_0_39,refute_0_20]) ).
cnf(refute_0_41,plain,
( ~ q(X_16,X_17)
| p(X_16,X_15)
| q(X_15,X_17) ),
inference(subst,[],[refute_0_40:[bind(X_12,$fot(X_15)),bind(X_13,$fot(X_16)),bind(X_14,$fot(X_17))]]) ).
cnf(refute_0_42,plain,
( p(X_16,X_15)
| p(X_16,X_17)
| q(X_15,X_17) ),
inference(resolve,[$cnf( q(X_16,X_17) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
( p(X_48,skolemFOFtoCNF_X_1)
| p(X_48,skolemFOFtoCNF_Y_1)
| q(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_0_42:[bind(X_15,$fot(skolemFOFtoCNF_X_1)),bind(X_16,$fot(X_48)),bind(X_17,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_0_44,plain,
( p(X_48,skolemFOFtoCNF_X_1)
| p(X_48,skolemFOFtoCNF_Y_1) ),
inference(resolve,[$cnf( q(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_0_43,refute_0_3]) ).
cnf(refute_0_45,plain,
( p(X_50,skolemFOFtoCNF_X_1)
| p(X_50,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_0_44:[bind(X_48,$fot(X_50))]]) ).
cnf(refute_0_46,plain,
p(X_50,skolemFOFtoCNF_X_1),
inference(resolve,[$cnf( p(X_50,skolemFOFtoCNF_Y_1) )],[refute_0_45,refute_0_37]) ).
cnf(refute_0_47,plain,
p(X_51,skolemFOFtoCNF_X_1),
inference(subst,[],[refute_0_46:[bind(X_50,$fot(X_51))]]) ).
cnf(refute_0_48,plain,
p(X_51,X_40),
inference(resolve,[$cnf( p(X_51,skolemFOFtoCNF_X_1) )],[refute_0_47,refute_0_34]) ).
cnf(refute_0_49,plain,
p(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(subst,[],[refute_0_48:[bind(X_40,$fot(skolemFOFtoCNF_Y)),bind(X_51,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_50,plain,
$false,
inference(resolve,[$cnf( p(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_49,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN726+1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 12 03:21:38 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------