TSTP Solution File: KRS077+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS077+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 0.12s 0.34s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 12 unt; 0 def)
% Number of atoms : 178 ( 14 equ)
% Maximal formula atoms : 57 ( 3 avg)
% Number of connectives : 224 ( 95 ~; 96 |; 24 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 63 ( 0 sgn 40 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y1,Y2] :
( ( rr(X,Y1)
& rr(X,Y2) )
=> Y1 = Y2 )
& ? [Y] :
( rr(X,Y)
& ! [Z] :
( rinvS(Y,Z)
=> cp(Z) ) )
& ~ cp(X)
& ? [Y] :
( rs(X,Y)
& cp(Y) ) ) ) ).
fof(axiom_3,axiom,
! [X,Y] :
( rinvS(X,Y)
<=> rs(Y,X) ) ).
fof(axiom_4,axiom,
cUnsatisfiable(i2003_11_14_17_19_09372) ).
fof(axiom_5,axiom,
! [X,Y] :
( rs(X,Y)
=> rr(X,Y) ) ).
fof(normalize_0_0,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( cp(X)
| ? [Y1,Y2] :
( Y1 != Y2
& rr(X,Y1)
& rr(X,Y2) )
| ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [Y] :
( ~ rr(X,Y)
| ? [Z] :
( ~ cp(Z)
& rinvS(Y,Z) ) ) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( cp(X)
| ? [Y1,Y2] :
( Y1 != Y2
& rr(X,Y1)
& rr(X,Y2) )
| ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [Y] :
( ~ rr(X,Y)
| ? [Z] :
( ~ cp(Z)
& rinvS(Y,Z) ) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y,Y0,Y1,Y2,Z] :
( ( ~ cUnsatisfiable(X)
| ~ cp(X) )
& ( ~ cUnsatisfiable(X)
| cp(skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) )
& ( ~ cUnsatisfiable(X)
| rs(X,skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| ~ rinvS(skolemFOFtoCNF_Y(X),Z)
| cp(Z) )
& ( ~ cUnsatisfiable(X)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| Y1 = Y2 )
& ( skolemFOFtoCNF_Y0(X) != skolemFOFtoCNF_Y1(X)
| ~ cp(Y)
| ~ cp(skolemFOFtoCNF_Z(Y0))
| ~ rr(X,Y0)
| ~ rs(X,Y)
| cUnsatisfiable(X)
| cp(X) )
& ( skolemFOFtoCNF_Y0(X) != skolemFOFtoCNF_Y1(X)
| ~ cp(Y)
| ~ rr(X,Y0)
| ~ rs(X,Y)
| cUnsatisfiable(X)
| cp(X)
| rinvS(Y0,skolemFOFtoCNF_Z(Y0)) )
& ( ~ cp(Y)
| ~ cp(skolemFOFtoCNF_Z(Y0))
| ~ rr(X,Y0)
| ~ rs(X,Y)
| cUnsatisfiable(X)
| cp(X)
| rr(X,skolemFOFtoCNF_Y0(X)) )
& ( ~ cp(Y)
| ~ cp(skolemFOFtoCNF_Z(Y0))
| ~ rr(X,Y0)
| ~ rs(X,Y)
| cUnsatisfiable(X)
| cp(X)
| rr(X,skolemFOFtoCNF_Y1(X)) )
& ( ~ cp(Y)
| ~ rr(X,Y0)
| ~ rs(X,Y)
| cUnsatisfiable(X)
| cp(X)
| rinvS(Y0,skolemFOFtoCNF_Z(Y0))
| rr(X,skolemFOFtoCNF_Y0(X)) )
& ( ~ cp(Y)
| ~ rr(X,Y0)
| ~ rs(X,Y)
| cUnsatisfiable(X)
| cp(X)
| rinvS(Y0,skolemFOFtoCNF_Z(Y0))
| rr(X,skolemFOFtoCNF_Y1(X)) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X] :
( ~ cUnsatisfiable(X)
| ~ cp(X) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Z] :
( ~ cUnsatisfiable(X)
| ~ rinvS(skolemFOFtoCNF_Y(X),Z)
| cp(Z) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
cUnsatisfiable(i2003_11_14_17_19_09372),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_0_6,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rs(X,skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ rinvS(X,Y)
<=> ~ rs(Y,X) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ rinvS(X,Y)
<=> ~ rs(Y,X) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ( ~ rinvS(X,Y)
| rs(Y,X) )
& ( ~ rs(Y,X)
| rinvS(X,Y) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ rs(Y,X)
| rinvS(X,Y) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ rs(X,Y)
| rr(X,Y) ),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ rs(X,Y)
| rr(X,Y) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y1,Y2] :
( ~ cUnsatisfiable(X)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| Y1 = Y2 ),
inference(conjunct,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
( ~ cUnsatisfiable(X)
| ~ cp(X) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ cp(i2003_11_14_17_19_09372) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(i2003_11_14_17_19_09372))]]) ).
cnf(refute_0_2,plain,
( ~ cUnsatisfiable(X)
| ~ rinvS(skolemFOFtoCNF_Y(X),Z)
| cp(Z) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ rinvS(skolemFOFtoCNF_Y(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| cp(i2003_11_14_17_19_09372) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(i2003_11_14_17_19_09372)),bind(Z,$fot(i2003_11_14_17_19_09372))]]) ).
cnf(refute_0_4,plain,
cUnsatisfiable(i2003_11_14_17_19_09372),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
( ~ cUnsatisfiable(X)
| rs(X,skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_6,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| rs(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(i2003_11_14_17_19_09372))]]) ).
cnf(refute_0_7,plain,
rs(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_09372) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ rs(Y,X)
| rinvS(X,Y) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
( ~ rs(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372))
| rinvS(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372))),bind(Y,$fot(i2003_11_14_17_19_09372))]]) ).
cnf(refute_0_10,plain,
rinvS(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372),
inference(resolve,[$cnf( rs(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372)) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_12,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| rr(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y(i2003_11_14_17_19_09372)) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(i2003_11_14_17_19_09372))]]) ).
cnf(refute_0_13,plain,
rr(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y(i2003_11_14_17_19_09372)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_09372) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ rs(X,Y)
| rr(X,Y) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_15,plain,
( ~ rs(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372))
| rr(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(i2003_11_14_17_19_09372)),bind(Y,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372)))]]) ).
cnf(refute_0_16,plain,
rr(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372)),
inference(resolve,[$cnf( rs(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372)) )],[refute_0_7,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ cUnsatisfiable(X)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| Y1 = Y2 ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_18,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,X_18)
| ~ rr(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372))
| skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372) = X_18 ),
inference(subst,[],[refute_0_17:[bind(X,$fot(i2003_11_14_17_19_09372)),bind(Y1,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372))),bind(Y2,$fot(X_18))]]) ).
cnf(refute_0_19,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,X_18)
| skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372) = X_18 ),
inference(resolve,[$cnf( rr(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372)) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ rr(i2003_11_14_17_19_09372,X_18)
| skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372) = X_18 ),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_09372) )],[refute_0_4,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ rr(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y(i2003_11_14_17_19_09372))
| skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372) = skolemFOFtoCNF_Y(i2003_11_14_17_19_09372) ),
inference(subst,[],[refute_0_20:[bind(X_18,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_19_09372)))]]) ).
cnf(refute_0_22,plain,
skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372) = skolemFOFtoCNF_Y(i2003_11_14_17_19_09372),
inference(resolve,[$cnf( rr(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y(i2003_11_14_17_19_09372)) )],[refute_0_13,refute_0_21]) ).
cnf(refute_0_23,plain,
( skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372) != skolemFOFtoCNF_Y(i2003_11_14_17_19_09372)
| ~ rinvS(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| rinvS(skolemFOFtoCNF_Y(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ),
introduced(tautology,[equality,[$cnf( rinvS(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ),[0],$fot(skolemFOFtoCNF_Y(i2003_11_14_17_19_09372))]]) ).
cnf(refute_0_24,plain,
( ~ rinvS(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| rinvS(skolemFOFtoCNF_Y(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372),skolemFOFtoCNF_Y(i2003_11_14_17_19_09372)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
rinvS(skolemFOFtoCNF_Y(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372),
inference(resolve,[$cnf( rinvS(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) )],[refute_0_10,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| cp(i2003_11_14_17_19_09372) ),
inference(resolve,[$cnf( rinvS(skolemFOFtoCNF_Y(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) )],[refute_0_25,refute_0_3]) ).
cnf(refute_0_27,plain,
cp(i2003_11_14_17_19_09372),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_09372) )],[refute_0_4,refute_0_26]) ).
cnf(refute_0_28,plain,
~ cUnsatisfiable(i2003_11_14_17_19_09372),
inference(resolve,[$cnf( cp(i2003_11_14_17_19_09372) )],[refute_0_27,refute_0_1]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_09372) )],[refute_0_4,refute_0_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KRS077+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.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 : Tue Jun 7 13:27:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.35
%------------------------------------------------------------------------------