TSTP Solution File: KRS078+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS078+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 03:18:37 EDT 2022
% Result : Unsatisfiable 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 13 unt; 0 def)
% Number of atoms : 198 ( 23 equ)
% Maximal formula atoms : 65 ( 3 avg)
% Number of connectives : 249 ( 104 ~; 111 |; 26 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 4 avg)
% Maximal term depth : 2 ( 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 : 71 ( 0 sgn 38 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( rr(X,Y)
& ? [Z] :
( rinvR(Y,Z)
& ! [W] :
( rs(Z,W)
=> cp(W) ) )
& ! [Z0,Z1] :
( ( rinvR(Y,Z0)
& rinvR(Y,Z1) )
=> Z0 = Z1 ) )
& ? [Y] :
( rs(X,Y)
& ~ cq(Y)
& ~ cp(Y) ) ) ) ).
fof(axiom_3,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ) ).
fof(axiom_4,axiom,
cUnsatisfiable(i2003_11_14_17_19_13721) ).
fof(normalize_0_0,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ! [Y] :
( ~ rr(X,Y)
| ? [Z0,Z1] :
( Z0 != Z1
& rinvR(Y,Z0)
& rinvR(Y,Z1) )
| ! [Z] :
( ~ rinvR(Y,Z)
| ? [W] :
( ~ cp(W)
& rs(Z,W) ) ) )
| ! [Y] :
( ~ rs(X,Y)
| cp(Y)
| cq(Y) ) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ! [Y] :
( ~ rr(X,Y)
| ? [Z0,Z1] :
( Z0 != Z1
& rinvR(Y,Z0)
& rinvR(Y,Z1) )
| ! [Z] :
( ~ rinvR(Y,Z)
| ? [W] :
( ~ cp(W)
& rs(Z,W) ) ) )
| ! [Y] :
( ~ rs(X,Y)
| cp(Y)
| cq(Y) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [W,X,Y,Y0,Z,Z0,Z1] :
( ( ~ cUnsatisfiable(X)
| ~ cp(skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| ~ cq(skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| rinvR(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) )
& ( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) )
& ( ~ cUnsatisfiable(X)
| rs(X,skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| ~ rs(skolemFOFtoCNF_Z(X),W)
| cp(W) )
& ( ~ cUnsatisfiable(X)
| ~ rinvR(skolemFOFtoCNF_Y(X),Z0)
| ~ rinvR(skolemFOFtoCNF_Y(X),Z1)
| Z0 = Z1 )
& ( skolemFOFtoCNF_Z0(Y) != skolemFOFtoCNF_Z1(Y)
| ~ cp(skolemFOFtoCNF_W(Z))
| ~ rinvR(Y,Z)
| ~ rr(X,Y)
| ~ rs(X,Y0)
| cUnsatisfiable(X)
| cp(Y0)
| cq(Y0) )
& ( skolemFOFtoCNF_Z0(Y) != skolemFOFtoCNF_Z1(Y)
| ~ rinvR(Y,Z)
| ~ rr(X,Y)
| ~ rs(X,Y0)
| cUnsatisfiable(X)
| cp(Y0)
| cq(Y0)
| rs(Z,skolemFOFtoCNF_W(Z)) )
& ( ~ cp(skolemFOFtoCNF_W(Z))
| ~ rinvR(Y,Z)
| ~ rr(X,Y)
| ~ rs(X,Y0)
| cUnsatisfiable(X)
| cp(Y0)
| cq(Y0)
| rinvR(Y,skolemFOFtoCNF_Z0(Y)) )
& ( ~ cp(skolemFOFtoCNF_W(Z))
| ~ rinvR(Y,Z)
| ~ rr(X,Y)
| ~ rs(X,Y0)
| cUnsatisfiable(X)
| cp(Y0)
| cq(Y0)
| rinvR(Y,skolemFOFtoCNF_Z1(Y)) )
& ( ~ rinvR(Y,Z)
| ~ rr(X,Y)
| ~ rs(X,Y0)
| cUnsatisfiable(X)
| cp(Y0)
| cq(Y0)
| rinvR(Y,skolemFOFtoCNF_Z0(Y))
| rs(Z,skolemFOFtoCNF_W(Z)) )
& ( ~ rinvR(Y,Z)
| ~ rr(X,Y)
| ~ rs(X,Y0)
| cUnsatisfiable(X)
| cp(Y0)
| cq(Y0)
| rinvR(Y,skolemFOFtoCNF_Z1(Y))
| rs(Z,skolemFOFtoCNF_W(Z)) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X] :
( ~ cUnsatisfiable(X)
| ~ cp(skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
cUnsatisfiable(i2003_11_14_17_19_13721),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_0_5,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rs(X,skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_6,plain,
! [W,X] :
( ~ cUnsatisfiable(X)
| ~ rs(skolemFOFtoCNF_Z(X),W)
| cp(W) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_7,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rinvR(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_8,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ rinvR(X,Y)
<=> ~ rr(Y,X) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ rinvR(X,Y)
<=> ~ rr(Y,X) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ( ~ rinvR(X,Y)
| rr(Y,X) )
& ( ~ rr(Y,X)
| rinvR(X,Y) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ rr(Y,X)
| rinvR(X,Y) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Z0,Z1] :
( ~ cUnsatisfiable(X)
| ~ rinvR(skolemFOFtoCNF_Y(X),Z0)
| ~ rinvR(skolemFOFtoCNF_Y(X),Z1)
| Z0 = Z1 ),
inference(conjunct,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
( ~ cUnsatisfiable(X)
| ~ cp(skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ cp(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_13721)) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(i2003_11_14_17_19_13721))]]) ).
cnf(refute_0_2,plain,
cUnsatisfiable(i2003_11_14_17_19_13721),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ cUnsatisfiable(X)
| rs(X,skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| rs(i2003_11_14_17_19_13721,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_13721)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(i2003_11_14_17_19_13721))]]) ).
cnf(refute_0_5,plain,
rs(i2003_11_14_17_19_13721,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_13721)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_13721) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ cUnsatisfiable(X)
| ~ rs(skolemFOFtoCNF_Z(X),W)
| cp(W) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_7,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ rs(skolemFOFtoCNF_Z(i2003_11_14_17_19_13721),W)
| cp(W) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(i2003_11_14_17_19_13721))]]) ).
cnf(refute_0_8,plain,
( ~ cUnsatisfiable(X)
| rinvR(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_9,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| rinvR(skolemFOFtoCNF_Y(i2003_11_14_17_19_13721),skolemFOFtoCNF_Z(i2003_11_14_17_19_13721)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(i2003_11_14_17_19_13721))]]) ).
cnf(refute_0_10,plain,
rinvR(skolemFOFtoCNF_Y(i2003_11_14_17_19_13721),skolemFOFtoCNF_Z(i2003_11_14_17_19_13721)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_13721) )],[refute_0_2,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_12,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| rr(i2003_11_14_17_19_13721,skolemFOFtoCNF_Y(i2003_11_14_17_19_13721)) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(i2003_11_14_17_19_13721))]]) ).
cnf(refute_0_13,plain,
rr(i2003_11_14_17_19_13721,skolemFOFtoCNF_Y(i2003_11_14_17_19_13721)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_13721) )],[refute_0_2,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ rr(Y,X)
| rinvR(X,Y) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_15,plain,
( ~ rr(i2003_11_14_17_19_13721,skolemFOFtoCNF_Y(i2003_11_14_17_19_13721))
| rinvR(skolemFOFtoCNF_Y(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_19_13721))),bind(Y,$fot(i2003_11_14_17_19_13721))]]) ).
cnf(refute_0_16,plain,
rinvR(skolemFOFtoCNF_Y(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721),
inference(resolve,[$cnf( rr(i2003_11_14_17_19_13721,skolemFOFtoCNF_Y(i2003_11_14_17_19_13721)) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ cUnsatisfiable(X)
| ~ rinvR(skolemFOFtoCNF_Y(X),Z0)
| ~ rinvR(skolemFOFtoCNF_Y(X),Z1)
| Z0 = Z1 ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_18,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ rinvR(skolemFOFtoCNF_Y(i2003_11_14_17_19_13721),X_17)
| ~ rinvR(skolemFOFtoCNF_Y(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721)
| i2003_11_14_17_19_13721 = X_17 ),
inference(subst,[],[refute_0_17:[bind(X,$fot(i2003_11_14_17_19_13721)),bind(Z0,$fot(i2003_11_14_17_19_13721)),bind(Z1,$fot(X_17))]]) ).
cnf(refute_0_19,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ rinvR(skolemFOFtoCNF_Y(i2003_11_14_17_19_13721),X_17)
| i2003_11_14_17_19_13721 = X_17 ),
inference(resolve,[$cnf( rinvR(skolemFOFtoCNF_Y(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ rinvR(skolemFOFtoCNF_Y(i2003_11_14_17_19_13721),X_17)
| i2003_11_14_17_19_13721 = X_17 ),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_13721) )],[refute_0_2,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ rinvR(skolemFOFtoCNF_Y(i2003_11_14_17_19_13721),skolemFOFtoCNF_Z(i2003_11_14_17_19_13721))
| i2003_11_14_17_19_13721 = skolemFOFtoCNF_Z(i2003_11_14_17_19_13721) ),
inference(subst,[],[refute_0_20:[bind(X_17,$fot(skolemFOFtoCNF_Z(i2003_11_14_17_19_13721)))]]) ).
cnf(refute_0_22,plain,
i2003_11_14_17_19_13721 = skolemFOFtoCNF_Z(i2003_11_14_17_19_13721),
inference(resolve,[$cnf( rinvR(skolemFOFtoCNF_Y(i2003_11_14_17_19_13721),skolemFOFtoCNF_Z(i2003_11_14_17_19_13721)) )],[refute_0_10,refute_0_21]) ).
cnf(refute_0_23,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_24,plain,
( X0 != X0
| X0 != Y1
| Y1 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y1)]]) ).
cnf(refute_0_25,plain,
( X0 != Y1
| Y1 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( i2003_11_14_17_19_13721 != skolemFOFtoCNF_Z(i2003_11_14_17_19_13721)
| skolemFOFtoCNF_Z(i2003_11_14_17_19_13721) = i2003_11_14_17_19_13721 ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(i2003_11_14_17_19_13721)),bind(Y1,$fot(skolemFOFtoCNF_Z(i2003_11_14_17_19_13721)))]]) ).
cnf(refute_0_27,plain,
skolemFOFtoCNF_Z(i2003_11_14_17_19_13721) = i2003_11_14_17_19_13721,
inference(resolve,[$cnf( $equal(i2003_11_14_17_19_13721,skolemFOFtoCNF_Z(i2003_11_14_17_19_13721)) )],[refute_0_22,refute_0_26]) ).
cnf(refute_0_28,plain,
( skolemFOFtoCNF_Z(i2003_11_14_17_19_13721) != i2003_11_14_17_19_13721
| ~ rs(i2003_11_14_17_19_13721,W)
| rs(skolemFOFtoCNF_Z(i2003_11_14_17_19_13721),W) ),
introduced(tautology,[equality,[$cnf( ~ rs(skolemFOFtoCNF_Z(i2003_11_14_17_19_13721),W) ),[0],$fot(i2003_11_14_17_19_13721)]]) ).
cnf(refute_0_29,plain,
( ~ rs(i2003_11_14_17_19_13721,W)
| rs(skolemFOFtoCNF_Z(i2003_11_14_17_19_13721),W) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z(i2003_11_14_17_19_13721),i2003_11_14_17_19_13721) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_13721)
| ~ rs(i2003_11_14_17_19_13721,W)
| cp(W) ),
inference(resolve,[$cnf( rs(skolemFOFtoCNF_Z(i2003_11_14_17_19_13721),W) )],[refute_0_29,refute_0_7]) ).
cnf(refute_0_31,plain,
( ~ rs(i2003_11_14_17_19_13721,W)
| cp(W) ),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_13721) )],[refute_0_2,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ rs(i2003_11_14_17_19_13721,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_13721))
| cp(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_13721)) ),
inference(subst,[],[refute_0_31:[bind(W,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_13721)))]]) ).
cnf(refute_0_33,plain,
cp(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_13721)),
inference(resolve,[$cnf( rs(i2003_11_14_17_19_13721,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_13721)) )],[refute_0_5,refute_0_32]) ).
cnf(refute_0_34,plain,
~ cUnsatisfiable(i2003_11_14_17_19_13721),
inference(resolve,[$cnf( cp(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_13721)) )],[refute_0_33,refute_0_1]) ).
cnf(refute_0_35,plain,
$false,
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_13721) )],[refute_0_2,refute_0_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : KRS078+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 7 13:54:50 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.37
% 0.14/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.37
%------------------------------------------------------------------------------