TSTP Solution File: SWC036+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWC036+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 21:26:13 EDT 2022
% Result : Theorem 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 25 unt; 0 def)
% Number of atoms : 237 ( 175 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 273 ( 97 ~; 25 |; 131 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 62 ( 0 sgn 20 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ssList(X0)
=> ( nil != V
| V != X0
| U != W
| nil = U
| ( nil != W
& nil = X0 ) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( nil != V )
& ~ ( V != X0 )
& ~ ( U != W )
& nil != U )
=> nil != W ) ) ) ),
inference(strip,[],[co1]) ).
fof(subgoal_1,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( nil != V )
& ~ ( V != X0 )
& ~ ( U != W )
& nil != U
& nil != W )
=> nil = X0 ) ) ) ),
inference(strip,[],[co1]) ).
fof(negate_0_0,plain,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( nil != V )
& ~ ( V != X0 )
& ~ ( U != W )
& nil != U )
=> nil != W ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != U
& U = W
& V = X0
& nil = V
& nil = W
& ssList(X0) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ssList(skolemFOFtoCNF_U_1)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_1
& V = X0
& nil = V
& nil = W
& skolemFOFtoCNF_U_1 = W
& ssList(X0) ) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_1
& V = X0
& nil = V
& nil = W
& skolemFOFtoCNF_U_1 = W
& ssList(X0) ) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ssList(skolemFOFtoCNF_V_12)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_1
& nil = W
& nil = skolemFOFtoCNF_V_12
& skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& ssList(X0) ) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_1
& nil = W
& nil = skolemFOFtoCNF_V_12
& skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& ssList(X0) ) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( ssList(skolemFOFtoCNF_W_12)
& ? [X0] :
( nil != skolemFOFtoCNF_U_1
& nil = skolemFOFtoCNF_V_12
& nil = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& ssList(X0) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [X0] :
( nil != skolemFOFtoCNF_U_1
& nil = skolemFOFtoCNF_V_12
& nil = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& ssList(X0) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( nil != skolemFOFtoCNF_U_1
& nil = skolemFOFtoCNF_V_12
& nil = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9
& ssList(skolemFOFtoCNF_X_9) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
nil != skolemFOFtoCNF_U_1,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_10,plain,
nil = skolemFOFtoCNF_W_12,
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
nil != skolemFOFtoCNF_U_1,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_1,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_2,plain,
nil = skolemFOFtoCNF_W_12,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_3,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_4,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_5,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( nil != skolemFOFtoCNF_W_12
| skolemFOFtoCNF_W_12 = nil ),
inference(subst,[],[refute_0_5:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_W_12))]]) ).
cnf(refute_0_7,plain,
skolemFOFtoCNF_W_12 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_W_12) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_W_12
| skolemFOFtoCNF_W_12 != nil
| skolemFOFtoCNF_U_1 = nil ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_U_1,nil) ),[0],$fot(skolemFOFtoCNF_W_12)]]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_W_12
| skolemFOFtoCNF_U_1 = nil ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_12,nil) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
skolemFOFtoCNF_U_1 = nil,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,skolemFOFtoCNF_W_12) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
( nil != nil
| skolemFOFtoCNF_U_1 != nil
| nil = skolemFOFtoCNF_U_1 ),
introduced(tautology,[equality,[$cnf( ~ $equal(nil,skolemFOFtoCNF_U_1) ),[1],$fot(nil)]]) ).
cnf(refute_0_12,plain,
( nil != nil
| nil = skolemFOFtoCNF_U_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,nil) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
nil != nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_U_1) )],[refute_0_12,refute_0_0]) ).
cnf(refute_0_14,plain,
nil = nil,
introduced(tautology,[refl,[$fot(nil)]]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( $equal(nil,nil) )],[refute_0_14,refute_0_13]) ).
fof(negate_1_0,plain,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( nil != V )
& ~ ( V != X0 )
& ~ ( U != W )
& nil != U
& nil != W )
=> nil = X0 ) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != U
& nil != W
& nil != X0
& U = W
& V = X0
& nil = V
& ssList(X0) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ssList(skolemFOFtoCNF_U_2)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != W
& nil != X0
& nil != skolemFOFtoCNF_U_2
& V = X0
& nil = V
& skolemFOFtoCNF_U_2 = W
& ssList(X0) ) ) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != W
& nil != X0
& nil != skolemFOFtoCNF_U_2
& V = X0
& nil = V
& skolemFOFtoCNF_U_2 = W
& ssList(X0) ) ) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
( ssList(skolemFOFtoCNF_V_13)
& ? [W] :
( ssList(W)
& ? [X0] :
( nil != W
& nil != X0
& nil != skolemFOFtoCNF_U_2
& nil = skolemFOFtoCNF_V_13
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& ssList(X0) ) ) ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [W] :
( ssList(W)
& ? [X0] :
( nil != W
& nil != X0
& nil != skolemFOFtoCNF_U_2
& nil = skolemFOFtoCNF_V_13
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& ssList(X0) ) ),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
( ssList(skolemFOFtoCNF_W_13)
& ? [X0] :
( nil != X0
& nil != skolemFOFtoCNF_U_2
& nil != skolemFOFtoCNF_W_13
& nil = skolemFOFtoCNF_V_13
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& ssList(X0) ) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
? [X0] :
( nil != X0
& nil != skolemFOFtoCNF_U_2
& nil != skolemFOFtoCNF_W_13
& nil = skolemFOFtoCNF_V_13
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& ssList(X0) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
( nil != skolemFOFtoCNF_U_2
& nil != skolemFOFtoCNF_W_13
& nil != skolemFOFtoCNF_X_10
& nil = skolemFOFtoCNF_V_13
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10
& ssList(skolemFOFtoCNF_X_10) ),
inference(skolemize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
nil != skolemFOFtoCNF_X_10,
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10,
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_10,plain,
nil = skolemFOFtoCNF_V_13,
inference(conjunct,[],[normalize_1_7]) ).
cnf(refute_1_0,plain,
nil != skolemFOFtoCNF_X_10,
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_1,plain,
skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10,
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_2,plain,
nil = skolemFOFtoCNF_V_13,
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_3,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_4,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_5,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_3,refute_1_4]) ).
cnf(refute_1_6,plain,
( nil != skolemFOFtoCNF_V_13
| skolemFOFtoCNF_V_13 = nil ),
inference(subst,[],[refute_1_5:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_V_13))]]) ).
cnf(refute_1_7,plain,
skolemFOFtoCNF_V_13 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_V_13) )],[refute_1_2,refute_1_6]) ).
cnf(refute_1_8,plain,
( skolemFOFtoCNF_V_13 != nil
| skolemFOFtoCNF_V_13 != skolemFOFtoCNF_X_10
| nil = skolemFOFtoCNF_X_10 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_V_13,skolemFOFtoCNF_X_10) ),[0],$fot(nil)]]) ).
cnf(refute_1_9,plain,
( skolemFOFtoCNF_V_13 != skolemFOFtoCNF_X_10
| nil = skolemFOFtoCNF_X_10 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_13,nil) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
nil = skolemFOFtoCNF_X_10,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_13,skolemFOFtoCNF_X_10) )],[refute_1_1,refute_1_9]) ).
cnf(refute_1_11,plain,
( nil != skolemFOFtoCNF_X_10
| skolemFOFtoCNF_X_10 = nil ),
inference(subst,[],[refute_1_5:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_X_10))]]) ).
cnf(refute_1_12,plain,
skolemFOFtoCNF_X_10 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_X_10) )],[refute_1_10,refute_1_11]) ).
cnf(refute_1_13,plain,
( nil != nil
| skolemFOFtoCNF_X_10 != nil
| nil = skolemFOFtoCNF_X_10 ),
introduced(tautology,[equality,[$cnf( ~ $equal(nil,skolemFOFtoCNF_X_10) ),[1],$fot(nil)]]) ).
cnf(refute_1_14,plain,
( nil != nil
| nil = skolemFOFtoCNF_X_10 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_10,nil) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
nil != nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_X_10) )],[refute_1_14,refute_1_0]) ).
cnf(refute_1_16,plain,
nil = nil,
introduced(tautology,[refl,[$fot(nil)]]) ).
cnf(refute_1_17,plain,
$false,
inference(resolve,[$cnf( $equal(nil,nil) )],[refute_1_16,refute_1_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWC036+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sun Jun 12 11:48:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.17/0.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.49
% 0.17/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.17/0.49
%------------------------------------------------------------------------------