TSTP Solution File: SWC411+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWC411+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 : Tue Jul 19 21:28:13 EDT 2022
% Result : Theorem 1.00s 1.18s
% Output : CNFRefutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 15 unt; 0 def)
% Number of atoms : 180 ( 40 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 210 ( 73 ~; 44 |; 78 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 65 ( 0 sgn 25 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ssList(X0)
=> ( V != X0
| U != W
| ? [Y] :
( ssItem(Y)
& ~ memberP(W,Y)
& memberP(X0,Y) )
| ! [Z] :
( ssItem(Z)
=> ( ~ memberP(V,Z)
| memberP(U,Z) ) ) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ? [Y] :
( ssItem(Y)
& ~ memberP(W,Y)
& memberP(X0,Y) ) )
=> ! [Z] :
( ( ssItem(Z)
& ~ ~ memberP(V,Z) )
=> memberP(U,Z) ) ) ) ) ),
inference(strip,[],[co1]) ).
fof(negate_0_0,plain,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ? [Y] :
( ssItem(Y)
& ~ memberP(W,Y)
& memberP(X0,Y) ) )
=> ! [Z] :
( ( ssItem(Z)
& ~ ~ memberP(V,Z) )
=> memberP(U,Z) ) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( U = W
& V = X0
& ssList(X0)
& ? [Z] :
( ~ memberP(U,Z)
& memberP(V,Z)
& ssItem(Z) )
& ! [Y] :
( ~ memberP(X0,Y)
| ~ ssItem(Y)
| memberP(W,Y) ) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ssList(skolemFOFtoCNF_U_1)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( V = X0
& skolemFOFtoCNF_U_1 = W
& ssList(X0)
& ? [Z] :
( ~ memberP(skolemFOFtoCNF_U_1,Z)
& memberP(V,Z)
& ssItem(Z) )
& ! [Y] :
( ~ memberP(X0,Y)
| ~ ssItem(Y)
| memberP(W,Y) ) ) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( V = X0
& skolemFOFtoCNF_U_1 = W
& ssList(X0)
& ? [Z] :
( ~ memberP(skolemFOFtoCNF_U_1,Z)
& memberP(V,Z)
& ssItem(Z) )
& ! [Y] :
( ~ memberP(X0,Y)
| ~ ssItem(Y)
| memberP(W,Y) ) ) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ssList(skolemFOFtoCNF_V_12)
& ? [W] :
( ssList(W)
& ? [X0] :
( skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ? [Z] :
( ~ memberP(skolemFOFtoCNF_U_1,Z)
& memberP(skolemFOFtoCNF_V_12,Z)
& ssItem(Z) )
& ! [Y] :
( ~ memberP(X0,Y)
| ~ ssItem(Y)
| memberP(W,Y) ) ) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [W] :
( ssList(W)
& ? [X0] :
( skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ? [Z] :
( ~ memberP(skolemFOFtoCNF_U_1,Z)
& memberP(skolemFOFtoCNF_V_12,Z)
& ssItem(Z) )
& ! [Y] :
( ~ memberP(X0,Y)
| ~ ssItem(Y)
| memberP(W,Y) ) ) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( ssList(skolemFOFtoCNF_W_12)
& ? [X0] :
( skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ? [Z] :
( ~ memberP(skolemFOFtoCNF_U_1,Z)
& memberP(skolemFOFtoCNF_V_12,Z)
& ssItem(Z) )
& ! [Y] :
( ~ memberP(X0,Y)
| ~ ssItem(Y)
| memberP(skolemFOFtoCNF_W_12,Y) ) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [X0] :
( skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& ssList(X0)
& ? [Z] :
( ~ memberP(skolemFOFtoCNF_U_1,Z)
& memberP(skolemFOFtoCNF_V_12,Z)
& ssItem(Z) )
& ! [Y] :
( ~ memberP(X0,Y)
| ~ ssItem(Y)
| memberP(skolemFOFtoCNF_W_12,Y) ) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9
& ssList(skolemFOFtoCNF_X_9)
& ? [Z] :
( ~ memberP(skolemFOFtoCNF_U_1,Z)
& memberP(skolemFOFtoCNF_V_12,Z)
& ssItem(Z) )
& ! [Y] :
( ~ memberP(skolemFOFtoCNF_X_9,Y)
| ~ ssItem(Y)
| memberP(skolemFOFtoCNF_W_12,Y) ) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [Z] :
( ~ memberP(skolemFOFtoCNF_U_1,Z)
& memberP(skolemFOFtoCNF_V_12,Z)
& ssItem(Z) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
( ~ memberP(skolemFOFtoCNF_U_1,skolemFOFtoCNF_Z_6)
& memberP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_Z_6)
& ssItem(skolemFOFtoCNF_Z_6) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
memberP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_Z_6),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [Y] :
( ~ memberP(skolemFOFtoCNF_X_9,Y)
| ~ ssItem(Y)
| memberP(skolemFOFtoCNF_W_12,Y) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_12,plain,
! [Y] :
( ~ memberP(skolemFOFtoCNF_X_9,Y)
| ~ ssItem(Y)
| memberP(skolemFOFtoCNF_W_12,Y) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_14,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_15,plain,
ssItem(skolemFOFtoCNF_Z_6),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_16,plain,
~ memberP(skolemFOFtoCNF_U_1,skolemFOFtoCNF_Z_6),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
memberP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_Z_6),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_1,plain,
( ~ memberP(skolemFOFtoCNF_X_9,Y)
| ~ ssItem(Y)
| memberP(skolemFOFtoCNF_W_12,Y) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_2,plain,
skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_3,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_4,plain,
( X != X
| X != Y0
| Y0 = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y0)]]) ).
cnf(refute_0_5,plain,
( X != Y0
| Y0 = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( skolemFOFtoCNF_V_12 != skolemFOFtoCNF_X_9
| skolemFOFtoCNF_X_9 = skolemFOFtoCNF_V_12 ),
inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_V_12)),bind(Y0,$fot(skolemFOFtoCNF_X_9))]]) ).
cnf(refute_0_7,plain,
skolemFOFtoCNF_X_9 = skolemFOFtoCNF_V_12,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_12,skolemFOFtoCNF_X_9) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( skolemFOFtoCNF_X_9 != skolemFOFtoCNF_V_12
| ~ memberP(skolemFOFtoCNF_V_12,Y)
| memberP(skolemFOFtoCNF_X_9,Y) ),
introduced(tautology,[equality,[$cnf( ~ memberP(skolemFOFtoCNF_X_9,Y) ),[0],$fot(skolemFOFtoCNF_V_12)]]) ).
cnf(refute_0_9,plain,
( ~ memberP(skolemFOFtoCNF_V_12,Y)
| memberP(skolemFOFtoCNF_X_9,Y) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_9,skolemFOFtoCNF_V_12) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ memberP(skolemFOFtoCNF_V_12,Y)
| ~ ssItem(Y)
| memberP(skolemFOFtoCNF_W_12,Y) ),
inference(resolve,[$cnf( memberP(skolemFOFtoCNF_X_9,Y) )],[refute_0_9,refute_0_1]) ).
cnf(refute_0_11,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_W_12
| skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1 ),
inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_U_1)),bind(Y0,$fot(skolemFOFtoCNF_W_12))]]) ).
cnf(refute_0_13,plain,
skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,skolemFOFtoCNF_W_12) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( skolemFOFtoCNF_W_12 != skolemFOFtoCNF_U_1
| ~ memberP(skolemFOFtoCNF_W_12,Y)
| memberP(skolemFOFtoCNF_U_1,Y) ),
introduced(tautology,[equality,[$cnf( memberP(skolemFOFtoCNF_W_12,Y) ),[0],$fot(skolemFOFtoCNF_U_1)]]) ).
cnf(refute_0_15,plain,
( ~ memberP(skolemFOFtoCNF_W_12,Y)
| memberP(skolemFOFtoCNF_U_1,Y) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_12,skolemFOFtoCNF_U_1) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ memberP(skolemFOFtoCNF_V_12,Y)
| ~ ssItem(Y)
| memberP(skolemFOFtoCNF_U_1,Y) ),
inference(resolve,[$cnf( memberP(skolemFOFtoCNF_W_12,Y) )],[refute_0_10,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ memberP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_Z_6)
| ~ ssItem(skolemFOFtoCNF_Z_6)
| memberP(skolemFOFtoCNF_U_1,skolemFOFtoCNF_Z_6) ),
inference(subst,[],[refute_0_16:[bind(Y,$fot(skolemFOFtoCNF_Z_6))]]) ).
cnf(refute_0_18,plain,
( ~ ssItem(skolemFOFtoCNF_Z_6)
| memberP(skolemFOFtoCNF_U_1,skolemFOFtoCNF_Z_6) ),
inference(resolve,[$cnf( memberP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_Z_6) )],[refute_0_0,refute_0_17]) ).
cnf(refute_0_19,plain,
ssItem(skolemFOFtoCNF_Z_6),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_20,plain,
memberP(skolemFOFtoCNF_U_1,skolemFOFtoCNF_Z_6),
inference(resolve,[$cnf( ssItem(skolemFOFtoCNF_Z_6) )],[refute_0_19,refute_0_18]) ).
cnf(refute_0_21,plain,
~ memberP(skolemFOFtoCNF_U_1,skolemFOFtoCNF_Z_6),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( memberP(skolemFOFtoCNF_U_1,skolemFOFtoCNF_Z_6) )],[refute_0_20,refute_0_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWC411+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n027.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 : Sun Jun 12 15:05:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.00/1.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.00/1.18
% 1.00/1.18 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.00/1.19
%------------------------------------------------------------------------------