TSTP Solution File: KRS127+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS127+1 : TPTP v8.1.0. Released v3.1.0.
% 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 : Sun Jul 17 03:18:49 EDT 2022
% Result : Unsatisfiable 0.15s 0.38s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 15 unt; 0 def)
% Number of atoms : 166 ( 22 equ)
% Maximal formula atoms : 30 ( 2 avg)
% Number of connectives : 195 ( 90 ~; 76 |; 18 &)
% ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 68 ( 1 sgn 39 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( rr(X,Y)
& cc(Y) )
& ? [Y] :
( rr(X,Y)
& cd(Y) )
& ! [Y1,Y2] :
( ( rr(X,Y1)
& rr(X,Y2) )
=> Y1 = Y2 ) ) ) ).
fof(axiom_3,axiom,
! [X] :
( cc(X)
=> cdxcomp(X) ) ).
fof(axiom_4,axiom,
! [X] :
( cd(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ) ).
fof(axiom_5,axiom,
! [X] :
( cdxcomp(X)
<=> ? [Y1] : ra_Px1(X,Y1) ) ).
fof(axiom_6,axiom,
cUnsatisfiable(i2003_11_14_17_22_27794) ).
fof(normalize_0_0,plain,
! [X] :
( ~ cc(X)
| cdxcomp(X) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ cc(X)
| cdxcomp(X) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
cUnsatisfiable(i2003_11_14_17_22_27794),
inference(canonicalize,[],[axiom_6]) ).
fof(normalize_0_3,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ? [Y1,Y2] :
( Y1 != Y2
& rr(X,Y1)
& rr(X,Y2) )
| ! [Y] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cd(Y)
| ~ rr(X,Y) ) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_4,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ? [Y1,Y2] :
( Y1 != Y2
& rr(X,Y1)
& rr(X,Y2) )
| ! [Y] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cd(Y)
| ~ rr(X,Y) ) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Y,Y0,Y1,Y2] :
( ( ~ cUnsatisfiable(X)
| cc(skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| cd(skolemFOFtoCNF_Y(X)) )
& ( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) )
& ( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| Y1 = Y2 )
& ( skolemFOFtoCNF_Y0(X) != skolemFOFtoCNF_Y1(X)
| ~ cc(Y)
| ~ cd(Y0)
| ~ rr(X,Y)
| ~ rr(X,Y0)
| cUnsatisfiable(X) )
& ( ~ cc(Y)
| ~ cd(Y0)
| ~ rr(X,Y)
| ~ rr(X,Y0)
| cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y0(X)) )
& ( ~ cc(Y)
| ~ cd(Y0)
| ~ rr(X,Y)
| ~ rr(X,Y0)
| cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y1(X)) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X] :
( ~ cUnsatisfiable(X)
| cc(skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X] :
( ~ cdxcomp(X)
<=> ! [Y1] : ~ ra_Px1(X,Y1) ),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_0_8,plain,
! [X] :
( ~ cdxcomp(X)
<=> ! [Y1] : ~ ra_Px1(X,Y1) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y1] :
( ( ~ cdxcomp(X)
| ra_Px1(X,skolemFOFtoCNF_Y0_1(X)) )
& ( ~ ra_Px1(X,Y1)
| cdxcomp(X) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X] :
( ~ cdxcomp(X)
| ra_Px1(X,skolemFOFtoCNF_Y0_1(X)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X] :
( ~ cd(X)
<=> ? [Y] : ra_Px1(X,Y) ),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_0_12,plain,
! [X] :
( ~ cd(X)
<=> ? [Y] : ra_Px1(X,Y) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ( ~ cd(X)
| ~ ra_Px1(X,Y) )
& ( cd(X)
| ra_Px1(X,skolemFOFtoCNF_Y_2(X)) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ cd(X)
| ~ ra_Px1(X,Y) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_16,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_17,plain,
! [X,Y1,Y2] :
( ~ cUnsatisfiable(X)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| Y1 = Y2 ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_18,plain,
! [X] :
( ~ cUnsatisfiable(X)
| cd(skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( ~ cc(X)
| cdxcomp(X) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794))
| cdxcomp(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)))]]) ).
cnf(refute_0_2,plain,
cUnsatisfiable(i2003_11_14_17_22_27794),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_3,plain,
( ~ cUnsatisfiable(X)
| cc(skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(i2003_11_14_17_22_27794))]]) ).
cnf(refute_0_5,plain,
cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_22_27794) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
cdxcomp(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)),
inference(resolve,[$cnf( cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)) )],[refute_0_5,refute_0_1]) ).
cnf(refute_0_7,plain,
( ~ cdxcomp(X)
| ra_Px1(X,skolemFOFtoCNF_Y0_1(X)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( ~ cdxcomp(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794))
| ra_Px1(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794),skolemFOFtoCNF_Y0_1(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)))]]) ).
cnf(refute_0_9,plain,
ra_Px1(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794),skolemFOFtoCNF_Y0_1(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794))),
inference(resolve,[$cnf( cdxcomp(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ cd(X)
| ~ ra_Px1(X,Y) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_11,plain,
( ~ cd(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794))
| ~ ra_Px1(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794),skolemFOFtoCNF_Y0_1(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794))) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794))),bind(Y,$fot(skolemFOFtoCNF_Y0_1(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794))))]]) ).
cnf(refute_0_12,plain,
~ cd(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)),
inference(resolve,[$cnf( ra_Px1(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794),skolemFOFtoCNF_Y0_1(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794))) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_14,plain,
( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| rr(i2003_11_14_17_22_27794,skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(i2003_11_14_17_22_27794))]]) ).
cnf(refute_0_15,plain,
rr(i2003_11_14_17_22_27794,skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_22_27794) )],[refute_0_2,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_17,plain,
( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| rr(i2003_11_14_17_22_27794,skolemFOFtoCNF_Y(i2003_11_14_17_22_27794)) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(i2003_11_14_17_22_27794))]]) ).
cnf(refute_0_18,plain,
rr(i2003_11_14_17_22_27794,skolemFOFtoCNF_Y(i2003_11_14_17_22_27794)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_22_27794) )],[refute_0_2,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ cUnsatisfiable(X)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| Y1 = Y2 ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_20,plain,
( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ rr(i2003_11_14_17_22_27794,X_19)
| ~ rr(i2003_11_14_17_22_27794,skolemFOFtoCNF_Y(i2003_11_14_17_22_27794))
| skolemFOFtoCNF_Y(i2003_11_14_17_22_27794) = X_19 ),
inference(subst,[],[refute_0_19:[bind(X,$fot(i2003_11_14_17_22_27794)),bind(Y1,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_22_27794))),bind(Y2,$fot(X_19))]]) ).
cnf(refute_0_21,plain,
( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ rr(i2003_11_14_17_22_27794,X_19)
| skolemFOFtoCNF_Y(i2003_11_14_17_22_27794) = X_19 ),
inference(resolve,[$cnf( rr(i2003_11_14_17_22_27794,skolemFOFtoCNF_Y(i2003_11_14_17_22_27794)) )],[refute_0_18,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ rr(i2003_11_14_17_22_27794,X_19)
| skolemFOFtoCNF_Y(i2003_11_14_17_22_27794) = X_19 ),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_22_27794) )],[refute_0_2,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ rr(i2003_11_14_17_22_27794,skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794))
| skolemFOFtoCNF_Y(i2003_11_14_17_22_27794) = skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794) ),
inference(subst,[],[refute_0_22:[bind(X_19,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)))]]) ).
cnf(refute_0_24,plain,
skolemFOFtoCNF_Y(i2003_11_14_17_22_27794) = skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794),
inference(resolve,[$cnf( rr(i2003_11_14_17_22_27794,skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)) )],[refute_0_15,refute_0_23]) ).
cnf(refute_0_25,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_26,plain,
( X0 != X0
| X0 != Y3
| Y3 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y3)]]) ).
cnf(refute_0_27,plain,
( X0 != Y3
| Y3 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( skolemFOFtoCNF_Y(i2003_11_14_17_22_27794) != skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)
| skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794) = skolemFOFtoCNF_Y(i2003_11_14_17_22_27794) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_22_27794))),bind(Y3,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)))]]) ).
cnf(refute_0_29,plain,
skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794) = skolemFOFtoCNF_Y(i2003_11_14_17_22_27794),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(i2003_11_14_17_22_27794),skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)) )],[refute_0_24,refute_0_28]) ).
cnf(refute_0_30,plain,
( skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794) != skolemFOFtoCNF_Y(i2003_11_14_17_22_27794)
| ~ cd(skolemFOFtoCNF_Y(i2003_11_14_17_22_27794))
| cd(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)) ),
introduced(tautology,[equality,[$cnf( ~ cd(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)) ),[0],$fot(skolemFOFtoCNF_Y(i2003_11_14_17_22_27794))]]) ).
cnf(refute_0_31,plain,
( ~ cd(skolemFOFtoCNF_Y(i2003_11_14_17_22_27794))
| cd(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794),skolemFOFtoCNF_Y(i2003_11_14_17_22_27794)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
~ cd(skolemFOFtoCNF_Y(i2003_11_14_17_22_27794)),
inference(resolve,[$cnf( cd(skolemFOFtoCNF_Y_1(i2003_11_14_17_22_27794)) )],[refute_0_31,refute_0_12]) ).
cnf(refute_0_33,plain,
( ~ cUnsatisfiable(X)
| cd(skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_34,plain,
( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| cd(skolemFOFtoCNF_Y(i2003_11_14_17_22_27794)) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(i2003_11_14_17_22_27794))]]) ).
cnf(refute_0_35,plain,
cd(skolemFOFtoCNF_Y(i2003_11_14_17_22_27794)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_22_27794) )],[refute_0_2,refute_0_34]) ).
cnf(refute_0_36,plain,
$false,
inference(resolve,[$cnf( cd(skolemFOFtoCNF_Y(i2003_11_14_17_22_27794)) )],[refute_0_35,refute_0_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KRS127+1 : TPTP v8.1.0. Released v3.1.0.
% 0.08/0.15 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Tue Jun 7 09:16:40 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.15/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.38
% 0.15/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.15/0.38
%------------------------------------------------------------------------------