TSTP Solution File: KRS072+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS072+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 03:18:36 EDT 2022
% Result : Unsatisfiable 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 14 unt; 0 def)
% Number of atoms : 168 ( 22 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 212 ( 99 ~; 79 |; 26 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 60 ( 0 sgn 36 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( rinvR(X,Y)
& ! [Z0,Z1] :
( ( rr(Y,Z0)
& rr(Y,Z1) )
=> Z0 = Z1 )
& ? [Z] :
( rr(Y,Z)
& cp1(Z) ) )
& cp2(X) ) ) ).
fof(axiom_3,axiom,
! [X] :
( cp1(X)
=> ~ ( cp3(X)
| cp2(X)
| cp4(X)
| cp5(X) ) ) ).
fof(axiom_7,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ) ).
fof(axiom_8,axiom,
cUnsatisfiable(i2003_11_14_17_18_50190) ).
fof(normalize_0_0,plain,
cUnsatisfiable(i2003_11_14_17_18_50190),
inference(canonicalize,[],[axiom_8]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ~ cp2(X)
| ! [Y] :
( ~ rinvR(X,Y)
| ? [Z0,Z1] :
( Z0 != Z1
& rr(Y,Z0)
& rr(Y,Z1) )
| ! [Z] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_2,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ~ cp2(X)
| ! [Y] :
( ~ rinvR(X,Y)
| ? [Z0,Z1] :
( Z0 != Z1
& rr(Y,Z0)
& rr(Y,Z1) )
| ! [Z] :
( ~ cp1(Z)
| ~ rr(Y,Z) ) ) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y,Z,Z0,Z1] :
( ( ~ cUnsatisfiable(X)
| cp1(skolemFOFtoCNF_Z(X)) )
& ( ~ cUnsatisfiable(X)
| cp2(X) )
& ( ~ cUnsatisfiable(X)
| rinvR(X,skolemFOFtoCNF_Y(X)) )
& ( ~ cUnsatisfiable(X)
| rr(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) )
& ( ~ cUnsatisfiable(X)
| ~ rr(skolemFOFtoCNF_Y(X),Z0)
| ~ rr(skolemFOFtoCNF_Y(X),Z1)
| Z0 = Z1 )
& ( skolemFOFtoCNF_Z0(Y) != skolemFOFtoCNF_Z1(Y)
| ~ cp1(Z)
| ~ cp2(X)
| ~ rinvR(X,Y)
| ~ rr(Y,Z)
| cUnsatisfiable(X) )
& ( ~ cp1(Z)
| ~ cp2(X)
| ~ rinvR(X,Y)
| ~ rr(Y,Z)
| cUnsatisfiable(X)
| rr(Y,skolemFOFtoCNF_Z0(Y)) )
& ( ~ cp1(Z)
| ~ cp2(X)
| ~ rinvR(X,Y)
| ~ rr(Y,Z)
| cUnsatisfiable(X)
| rr(Y,skolemFOFtoCNF_Z1(Y)) ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] :
( ~ cUnsatisfiable(X)
| cp1(skolemFOFtoCNF_Z(X)) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rr(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_6,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rinvR(X,skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ rinvR(X,Y)
<=> ~ rr(Y,X) ),
inference(canonicalize,[],[axiom_7]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ rinvR(X,Y)
<=> ~ rr(Y,X) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ( ~ rinvR(X,Y)
| rr(Y,X) )
& ( ~ rr(Y,X)
| rinvR(X,Y) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ rinvR(X,Y)
| rr(Y,X) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Z0,Z1] :
( ~ cUnsatisfiable(X)
| ~ rr(skolemFOFtoCNF_Y(X),Z0)
| ~ rr(skolemFOFtoCNF_Y(X),Z1)
| Z0 = Z1 ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_12,plain,
! [X] :
( ~ cUnsatisfiable(X)
| cp2(X) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_13,plain,
! [X] :
( ~ cp1(X)
| ( ~ cp2(X)
& ~ cp3(X)
& ~ cp4(X)
& ~ cp5(X) ) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_0_14,plain,
! [X] :
( ~ cp1(X)
| ( ~ cp2(X)
& ~ cp3(X)
& ~ cp4(X)
& ~ cp5(X) ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X] :
( ( ~ cp1(X)
| ~ cp2(X) )
& ( ~ cp1(X)
| ~ cp3(X) )
& ( ~ cp1(X)
| ~ cp4(X) )
& ( ~ cp1(X)
| ~ cp5(X) ) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X] :
( ~ cp1(X)
| ~ cp2(X) ),
inference(conjunct,[],[normalize_0_15]) ).
cnf(refute_0_0,plain,
cUnsatisfiable(i2003_11_14_17_18_50190),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( ~ cUnsatisfiable(X)
| cp1(skolemFOFtoCNF_Z(X)) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
| cp1(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(i2003_11_14_17_18_50190))]]) ).
cnf(refute_0_3,plain,
cp1(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_50190) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ cUnsatisfiable(X)
| rr(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
| rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(i2003_11_14_17_18_50190))]]) ).
cnf(refute_0_6,plain,
rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_50190) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ cUnsatisfiable(X)
| rinvR(X,skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_8,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
| rinvR(i2003_11_14_17_18_50190,skolemFOFtoCNF_Y(i2003_11_14_17_18_50190)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(i2003_11_14_17_18_50190))]]) ).
cnf(refute_0_9,plain,
rinvR(i2003_11_14_17_18_50190,skolemFOFtoCNF_Y(i2003_11_14_17_18_50190)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_50190) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ rinvR(X,Y)
| rr(Y,X) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_11,plain,
( ~ rinvR(i2003_11_14_17_18_50190,skolemFOFtoCNF_Y(i2003_11_14_17_18_50190))
| rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(i2003_11_14_17_18_50190)),bind(Y,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190)))]]) ).
cnf(refute_0_12,plain,
rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190),
inference(resolve,[$cnf( rinvR(i2003_11_14_17_18_50190,skolemFOFtoCNF_Y(i2003_11_14_17_18_50190)) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ cUnsatisfiable(X)
| ~ rr(skolemFOFtoCNF_Y(X),Z0)
| ~ rr(skolemFOFtoCNF_Y(X),Z1)
| Z0 = Z1 ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_14,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
| ~ rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),X_24)
| ~ rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190)
| i2003_11_14_17_18_50190 = X_24 ),
inference(subst,[],[refute_0_13:[bind(X,$fot(i2003_11_14_17_18_50190)),bind(Z0,$fot(i2003_11_14_17_18_50190)),bind(Z1,$fot(X_24))]]) ).
cnf(refute_0_15,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
| ~ rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),X_24)
| i2003_11_14_17_18_50190 = X_24 ),
inference(resolve,[$cnf( rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),X_24)
| i2003_11_14_17_18_50190 = X_24 ),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_50190) )],[refute_0_0,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),skolemFOFtoCNF_Z(i2003_11_14_17_18_50190))
| i2003_11_14_17_18_50190 = skolemFOFtoCNF_Z(i2003_11_14_17_18_50190) ),
inference(subst,[],[refute_0_16:[bind(X_24,$fot(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)))]]) ).
cnf(refute_0_18,plain,
i2003_11_14_17_18_50190 = skolemFOFtoCNF_Z(i2003_11_14_17_18_50190),
inference(resolve,[$cnf( rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)) )],[refute_0_6,refute_0_17]) ).
cnf(refute_0_19,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_20,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_21,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( i2003_11_14_17_18_50190 != skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)
| skolemFOFtoCNF_Z(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190 ),
inference(subst,[],[refute_0_21:[bind(X0,$fot(i2003_11_14_17_18_50190)),bind(Y0,$fot(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)))]]) ).
cnf(refute_0_23,plain,
skolemFOFtoCNF_Z(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190,
inference(resolve,[$cnf( $equal(i2003_11_14_17_18_50190,skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
( skolemFOFtoCNF_Z(i2003_11_14_17_18_50190) != i2003_11_14_17_18_50190
| ~ cp1(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190))
| cp1(i2003_11_14_17_18_50190) ),
introduced(tautology,[equality,[$cnf( cp1(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)) ),[0],$fot(i2003_11_14_17_18_50190)]]) ).
cnf(refute_0_25,plain,
( ~ cp1(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190))
| cp1(i2003_11_14_17_18_50190) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
cp1(i2003_11_14_17_18_50190),
inference(resolve,[$cnf( cp1(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)) )],[refute_0_3,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ cUnsatisfiable(X)
| cp2(X) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_28,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
| cp2(i2003_11_14_17_18_50190) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(i2003_11_14_17_18_50190))]]) ).
cnf(refute_0_29,plain,
cp2(i2003_11_14_17_18_50190),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_50190) )],[refute_0_0,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ cp1(X)
| ~ cp2(X) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_31,plain,
( ~ cp1(i2003_11_14_17_18_50190)
| ~ cp2(i2003_11_14_17_18_50190) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(i2003_11_14_17_18_50190))]]) ).
cnf(refute_0_32,plain,
~ cp1(i2003_11_14_17_18_50190),
inference(resolve,[$cnf( cp2(i2003_11_14_17_18_50190) )],[refute_0_29,refute_0_31]) ).
cnf(refute_0_33,plain,
$false,
inference(resolve,[$cnf( cp1(i2003_11_14_17_18_50190) )],[refute_0_26,refute_0_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS072+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 7 20:24:51 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------