TSTP Solution File: SWC255+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWC255+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 21:27:22 EDT 2022
% Result : Theorem 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 20 unt; 0 def)
% Number of atoms : 231 ( 66 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 270 ( 90 ~; 39 |; 121 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 3 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)
=> ( V != X0
| U != W
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X0,nil) ) ) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ~ neq(V,nil)
& ~ ~ singletonP(W) )
=> singletonP(U) ) ) ) ),
inference(strip,[],[co1]) ).
fof(subgoal_1,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ~ ~ neq(V,nil) )
=> neq(X0,nil) ) ) ) ),
inference(strip,[],[co1]) ).
fof(negate_0_0,plain,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ~ neq(V,nil)
& ~ ~ singletonP(W) )
=> singletonP(U) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ singletonP(U)
& U = W
& V = X0
& neq(V,nil)
& singletonP(W)
& ssList(X0) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ssList(skolemFOFtoCNF_U_1)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_1)
& V = X0
& skolemFOFtoCNF_U_1 = W
& neq(V,nil)
& singletonP(W)
& ssList(X0) ) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_1)
& V = X0
& skolemFOFtoCNF_U_1 = W
& neq(V,nil)
& singletonP(W)
& ssList(X0) ) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ssList(skolemFOFtoCNF_V_12)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& neq(skolemFOFtoCNF_V_12,nil)
& singletonP(W)
& ssList(X0) ) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [W] :
( ssList(W)
& ? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& neq(skolemFOFtoCNF_V_12,nil)
& singletonP(W)
& ssList(X0) ) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( ssList(skolemFOFtoCNF_W_12)
& ? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& neq(skolemFOFtoCNF_V_12,nil)
& singletonP(skolemFOFtoCNF_W_12)
& ssList(X0) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [X0] :
( ~ singletonP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& neq(skolemFOFtoCNF_V_12,nil)
& singletonP(skolemFOFtoCNF_W_12)
& ssList(X0) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( ~ singletonP(skolemFOFtoCNF_U_1)
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9
& neq(skolemFOFtoCNF_V_12,nil)
& singletonP(skolemFOFtoCNF_W_12)
& ssList(skolemFOFtoCNF_X_9) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
singletonP(skolemFOFtoCNF_W_12),
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,
~ singletonP(skolemFOFtoCNF_U_1),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
singletonP(skolemFOFtoCNF_W_12),
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,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_W_12
| skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_U_1)),bind(Y,$fot(skolemFOFtoCNF_W_12))]]) ).
cnf(refute_0_6,plain,
skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,skolemFOFtoCNF_W_12) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( skolemFOFtoCNF_W_12 != skolemFOFtoCNF_U_1
| ~ singletonP(skolemFOFtoCNF_W_12)
| singletonP(skolemFOFtoCNF_U_1) ),
introduced(tautology,[equality,[$cnf( singletonP(skolemFOFtoCNF_W_12) ),[0],$fot(skolemFOFtoCNF_U_1)]]) ).
cnf(refute_0_8,plain,
( ~ singletonP(skolemFOFtoCNF_W_12)
| singletonP(skolemFOFtoCNF_U_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_12,skolemFOFtoCNF_U_1) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
singletonP(skolemFOFtoCNF_U_1),
inference(resolve,[$cnf( singletonP(skolemFOFtoCNF_W_12) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
~ singletonP(skolemFOFtoCNF_U_1),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( singletonP(skolemFOFtoCNF_U_1) )],[refute_0_9,refute_0_10]) ).
fof(negate_1_0,plain,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( V != X0 )
& ~ ( U != W )
& ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ~ ~ neq(V,nil) )
=> neq(X0,nil) ) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ neq(X0,nil)
& U = W
& V = X0
& neq(V,nil)
& ssList(X0)
& ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) ) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ssList(skolemFOFtoCNF_U_2)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ neq(X0,nil)
& V = X0
& skolemFOFtoCNF_U_2 = W
& neq(V,nil)
& ssList(X0)
& ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(skolemFOFtoCNF_U_2) ) ) ) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ neq(X0,nil)
& V = X0
& skolemFOFtoCNF_U_2 = W
& neq(V,nil)
& ssList(X0)
& ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(skolemFOFtoCNF_U_2) ) ) ) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
( ssList(skolemFOFtoCNF_V_13)
& ? [W] :
( ssList(W)
& ? [X0] :
( ~ neq(X0,nil)
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(X0)
& ( ~ neq(skolemFOFtoCNF_V_13,nil)
| ~ singletonP(W)
| singletonP(skolemFOFtoCNF_U_2) ) ) ) ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [W] :
( ssList(W)
& ? [X0] :
( ~ neq(X0,nil)
& skolemFOFtoCNF_U_2 = W
& skolemFOFtoCNF_V_13 = X0
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(X0)
& ( ~ neq(skolemFOFtoCNF_V_13,nil)
| ~ singletonP(W)
| singletonP(skolemFOFtoCNF_U_2) ) ) ),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
( ssList(skolemFOFtoCNF_W_13)
& ? [X0] :
( ~ neq(X0,nil)
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(X0)
& ( ~ neq(skolemFOFtoCNF_V_13,nil)
| ~ singletonP(skolemFOFtoCNF_W_13)
| singletonP(skolemFOFtoCNF_U_2) ) ) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
? [X0] :
( ~ neq(X0,nil)
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = X0
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(X0)
& ( ~ neq(skolemFOFtoCNF_V_13,nil)
| ~ singletonP(skolemFOFtoCNF_W_13)
| singletonP(skolemFOFtoCNF_U_2) ) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
( ~ neq(skolemFOFtoCNF_X_10,nil)
& skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
& skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10
& neq(skolemFOFtoCNF_V_13,nil)
& ssList(skolemFOFtoCNF_X_10)
& ( ~ neq(skolemFOFtoCNF_V_13,nil)
| ~ singletonP(skolemFOFtoCNF_W_13)
| singletonP(skolemFOFtoCNF_U_2) ) ),
inference(skolemize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
neq(skolemFOFtoCNF_V_13,nil),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
~ neq(skolemFOFtoCNF_X_10,nil),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_10,plain,
skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10,
inference(conjunct,[],[normalize_1_7]) ).
cnf(refute_1_0,plain,
neq(skolemFOFtoCNF_V_13,nil),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_1,plain,
~ neq(skolemFOFtoCNF_X_10,nil),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_2,plain,
skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10,
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( $equal(X,X) )],[refute_1_3,refute_1_4]) ).
cnf(refute_1_6,plain,
( skolemFOFtoCNF_V_13 != skolemFOFtoCNF_X_10
| skolemFOFtoCNF_X_10 = skolemFOFtoCNF_V_13 ),
inference(subst,[],[refute_1_5:[bind(X,$fot(skolemFOFtoCNF_V_13)),bind(Y,$fot(skolemFOFtoCNF_X_10))]]) ).
cnf(refute_1_7,plain,
skolemFOFtoCNF_X_10 = skolemFOFtoCNF_V_13,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_13,skolemFOFtoCNF_X_10) )],[refute_1_2,refute_1_6]) ).
cnf(refute_1_8,plain,
( skolemFOFtoCNF_X_10 != skolemFOFtoCNF_V_13
| ~ neq(skolemFOFtoCNF_V_13,nil)
| neq(skolemFOFtoCNF_X_10,nil) ),
introduced(tautology,[equality,[$cnf( ~ neq(skolemFOFtoCNF_X_10,nil) ),[0],$fot(skolemFOFtoCNF_V_13)]]) ).
cnf(refute_1_9,plain,
( ~ neq(skolemFOFtoCNF_V_13,nil)
| neq(skolemFOFtoCNF_X_10,nil) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_10,skolemFOFtoCNF_V_13) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
~ neq(skolemFOFtoCNF_V_13,nil),
inference(resolve,[$cnf( neq(skolemFOFtoCNF_X_10,nil) )],[refute_1_9,refute_1_1]) ).
cnf(refute_1_11,plain,
$false,
inference(resolve,[$cnf( neq(skolemFOFtoCNF_V_13,nil) )],[refute_1_0,refute_1_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWC255+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 : n023.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 03:31:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48
% 0.18/0.48 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.49
%------------------------------------------------------------------------------