TSTP Solution File: SWC044+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWC044+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 21:26:16 EDT 2022
% Result : Theorem 2.07s 2.25s
% Output : CNFRefutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 20 unt; 0 def)
% Number of atoms : 161 ( 85 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 174 ( 64 ~; 33 |; 61 &)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 39 ( 0 sgn 17 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax52,axiom,
! [U] :
( ssList(U)
=> ( rearsegP(nil,U)
<=> nil = U ) ) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ssList(X0)
=> ( nil != V
| V != X0
| U != W
| ~ rearsegP(X0,W)
| nil = U ) ) ) ) ) ).
fof(subgoal_0,plain,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X0] :
( ( ssList(X0)
& ~ ( nil != V )
& ~ ( V != X0 )
& ~ ( U != W )
& ~ ~ rearsegP(X0,W) )
=> nil = U ) ) ) ),
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 )
& ~ ~ rearsegP(X0,W) )
=> nil = U ) ) ) ),
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
& rearsegP(X0,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
& skolemFOFtoCNF_U_1 = W
& rearsegP(X0,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
& skolemFOFtoCNF_U_1 = W
& rearsegP(X0,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 = skolemFOFtoCNF_V_12
& skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& rearsegP(X0,W)
& ssList(X0) ) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [W] :
( ssList(W)
& ? [X0] :
( nil != skolemFOFtoCNF_U_1
& nil = skolemFOFtoCNF_V_12
& skolemFOFtoCNF_U_1 = W
& skolemFOFtoCNF_V_12 = X0
& rearsegP(X0,W)
& 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
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& rearsegP(X0,skolemFOFtoCNF_W_12)
& ssList(X0) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [X0] :
( nil != skolemFOFtoCNF_U_1
& nil = skolemFOFtoCNF_V_12
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = X0
& rearsegP(X0,skolemFOFtoCNF_W_12)
& ssList(X0) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( nil != skolemFOFtoCNF_U_1
& nil = skolemFOFtoCNF_V_12
& skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
& skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9
& rearsegP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_W_12)
& ssList(skolemFOFtoCNF_X_9) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
rearsegP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_W_12),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_10,plain,
nil = skolemFOFtoCNF_V_12,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_11,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_12,plain,
! [U] :
( ~ ssList(U)
| ( nil != U
<=> ~ rearsegP(nil,U) ) ),
inference(canonicalize,[],[ax52]) ).
fof(normalize_0_13,plain,
! [U] :
( ~ ssList(U)
| ( nil != U
<=> ~ rearsegP(nil,U) ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [U] :
( ( nil != U
| ~ ssList(U)
| rearsegP(nil,U) )
& ( ~ rearsegP(nil,U)
| ~ ssList(U)
| nil = U ) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [U] :
( ~ rearsegP(nil,U)
| ~ ssList(U)
| nil = U ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
ssList(skolemFOFtoCNF_U_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_17,plain,
nil != skolemFOFtoCNF_U_1,
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
rearsegP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_W_12),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_1,plain,
skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_2,plain,
nil = skolemFOFtoCNF_V_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( $equal(X,X) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( nil != skolemFOFtoCNF_V_12
| skolemFOFtoCNF_V_12 = nil ),
inference(subst,[],[refute_0_5:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_V_12))]]) ).
cnf(refute_0_7,plain,
skolemFOFtoCNF_V_12 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_V_12) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( skolemFOFtoCNF_V_12 != nil
| skolemFOFtoCNF_V_12 != skolemFOFtoCNF_X_9
| nil = skolemFOFtoCNF_X_9 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_V_12,skolemFOFtoCNF_X_9) ),[0],$fot(nil)]]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_V_12 != skolemFOFtoCNF_X_9
| nil = skolemFOFtoCNF_X_9 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_12,nil) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
nil = skolemFOFtoCNF_X_9,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_12,skolemFOFtoCNF_X_9) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
( nil != skolemFOFtoCNF_X_9
| skolemFOFtoCNF_X_9 = nil ),
inference(subst,[],[refute_0_5:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_X_9))]]) ).
cnf(refute_0_12,plain,
skolemFOFtoCNF_X_9 = nil,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_X_9) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( skolemFOFtoCNF_X_9 != nil
| ~ rearsegP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_W_12)
| rearsegP(nil,skolemFOFtoCNF_W_12) ),
introduced(tautology,[equality,[$cnf( rearsegP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_W_12) ),[0],$fot(nil)]]) ).
cnf(refute_0_14,plain,
( ~ rearsegP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_W_12)
| rearsegP(nil,skolemFOFtoCNF_W_12) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_9,nil) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_16,plain,
( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_W_12
| skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1 ),
inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_U_1)),bind(Y,$fot(skolemFOFtoCNF_W_12))]]) ).
cnf(refute_0_17,plain,
skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,skolemFOFtoCNF_W_12) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( skolemFOFtoCNF_W_12 != skolemFOFtoCNF_U_1
| ~ rearsegP(nil,skolemFOFtoCNF_W_12)
| rearsegP(nil,skolemFOFtoCNF_U_1) ),
introduced(tautology,[equality,[$cnf( rearsegP(nil,skolemFOFtoCNF_W_12) ),[1],$fot(skolemFOFtoCNF_U_1)]]) ).
cnf(refute_0_19,plain,
( ~ rearsegP(nil,skolemFOFtoCNF_W_12)
| rearsegP(nil,skolemFOFtoCNF_U_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_12,skolemFOFtoCNF_U_1) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ rearsegP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_W_12)
| rearsegP(nil,skolemFOFtoCNF_U_1) ),
inference(resolve,[$cnf( rearsegP(nil,skolemFOFtoCNF_W_12) )],[refute_0_14,refute_0_19]) ).
cnf(refute_0_21,plain,
rearsegP(nil,skolemFOFtoCNF_U_1),
inference(resolve,[$cnf( rearsegP(skolemFOFtoCNF_X_9,skolemFOFtoCNF_W_12) )],[refute_0_0,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ rearsegP(nil,U)
| ~ ssList(U)
| nil = U ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_23,plain,
( ~ rearsegP(nil,skolemFOFtoCNF_U_1)
| ~ ssList(skolemFOFtoCNF_U_1)
| nil = skolemFOFtoCNF_U_1 ),
inference(subst,[],[refute_0_22:[bind(U,$fot(skolemFOFtoCNF_U_1))]]) ).
cnf(refute_0_24,plain,
( ~ ssList(skolemFOFtoCNF_U_1)
| nil = skolemFOFtoCNF_U_1 ),
inference(resolve,[$cnf( rearsegP(nil,skolemFOFtoCNF_U_1) )],[refute_0_21,refute_0_23]) ).
cnf(refute_0_25,plain,
ssList(skolemFOFtoCNF_U_1),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_26,plain,
nil = skolemFOFtoCNF_U_1,
inference(resolve,[$cnf( ssList(skolemFOFtoCNF_U_1) )],[refute_0_25,refute_0_24]) ).
cnf(refute_0_27,plain,
nil != skolemFOFtoCNF_U_1,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_28,plain,
$false,
inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_U_1) )],[refute_0_26,refute_0_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC044+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n008.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 05:12:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.07/2.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.07/2.25
% 2.07/2.25 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.07/2.26
%------------------------------------------------------------------------------