TSTP Solution File: KRS070+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS070+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 15 unt; 0 def)
% Number of atoms : 161 ( 18 equ)
% Maximal formula atoms : 30 ( 2 avg)
% Number of connectives : 190 ( 87 ~; 79 |; 18 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 62 ( 0 sgn 37 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y] :
( rrx3(X,Y)
& cc1(Y) ) ) ) ).
fof(axiom_3,axiom,
! [X,Y,Z] :
( ( rrx(X,Y)
& rrx(X,Z) )
=> Y = Z ) ).
fof(axiom_8,axiom,
cUnsatisfiable(i2003_11_14_17_18_32242) ).
fof(axiom_9,axiom,
! [X,Y] :
( rrx3(X,Y)
=> rrx(X,Y) ) ).
fof(axiom_16,axiom,
! [X,Y] :
( rrx4(X,Y)
=> rrx(X,Y) ) ).
fof(normalize_0_0,plain,
cUnsatisfiable(i2003_11_14_17_18_32242),
inference(canonicalize,[],[axiom_8]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ? [Y] :
( cc1(Y)
& cc2(Y)
& rrx3(X,Y) )
| ! [Y] :
( ~ cc1(Y)
| ~ rrx3(X,Y) )
| ! [Y] :
( ~ cc2(Y)
| ~ rrx4(X,Y) ) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_2,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ? [Y] :
( cc1(Y)
& cc2(Y)
& rrx3(X,Y) )
| ! [Y] :
( ~ cc1(Y)
| ~ rrx3(X,Y) )
| ! [Y] :
( ~ cc2(Y)
| ~ rrx4(X,Y) ) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y,Y0] :
( ( ~ cUnsatisfiable(X)
| cc1(skolemFOFtoCNF_Y_2(X)) )
& ( ~ cUnsatisfiable(X)
| cc2(skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| rrx3(X,skolemFOFtoCNF_Y_2(X)) )
& ( ~ cUnsatisfiable(X)
| rrx4(X,skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| ~ cc1(Y)
| ~ cc2(Y)
| ~ rrx3(X,Y) )
& ( ~ cc1(Y)
| ~ cc2(Y0)
| ~ rrx3(X,Y)
| ~ rrx4(X,Y0)
| cUnsatisfiable(X)
| cc1(skolemFOFtoCNF_Y(X)) )
& ( ~ cc1(Y)
| ~ cc2(Y0)
| ~ rrx3(X,Y)
| ~ rrx4(X,Y0)
| cUnsatisfiable(X)
| cc2(skolemFOFtoCNF_Y(X)) )
& ( ~ cc1(Y)
| ~ cc2(Y0)
| ~ rrx3(X,Y)
| ~ rrx4(X,Y0)
| cUnsatisfiable(X)
| rrx3(X,skolemFOFtoCNF_Y(X)) ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rrx3(X,skolemFOFtoCNF_Y_2(X)) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ cUnsatisfiable(X)
| ~ cc1(Y)
| ~ cc2(Y)
| ~ rrx3(X,Y) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_6,plain,
! [X] :
( ~ cUnsatisfiable(X)
| cc1(skolemFOFtoCNF_Y_2(X)) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ rrx3(X,Y)
| rrx(X,Y) ),
inference(canonicalize,[],[axiom_9]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ rrx3(X,Y)
| rrx(X,Y) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rrx4(X,skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ rrx4(X,Y)
| rrx(X,Y) ),
inference(canonicalize,[],[axiom_16]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ rrx4(X,Y)
| rrx(X,Y) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y,Z] :
( ~ rrx(X,Y)
| ~ rrx(X,Z)
| Y = Z ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ~ rrx(X,Y)
| ~ rrx(X,Z)
| Y = Z ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X] :
( ~ cUnsatisfiable(X)
| cc2(skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
cUnsatisfiable(i2003_11_14_17_18_32242),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( ~ cUnsatisfiable(X)
| rrx3(X,skolemFOFtoCNF_Y_2(X)) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| rrx3(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(i2003_11_14_17_18_32242))]]) ).
cnf(refute_0_3,plain,
rrx3(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_32242) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ cUnsatisfiable(X)
| ~ cc1(Y)
| ~ cc2(Y)
| ~ rrx3(X,Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ cc1(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(i2003_11_14_17_18_32242)),bind(Y,$fot(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)))]]) ).
cnf(refute_0_6,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ cc1(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)) ),
inference(resolve,[$cnf( rrx3(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ cc1(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)) ),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_32242) )],[refute_0_0,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ cUnsatisfiable(X)
| cc1(skolemFOFtoCNF_Y_2(X)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_9,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| cc1(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(i2003_11_14_17_18_32242))]]) ).
cnf(refute_0_10,plain,
cc1(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_32242) )],[refute_0_0,refute_0_9]) ).
cnf(refute_0_11,plain,
~ cc2(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)),
inference(resolve,[$cnf( cc1(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)) )],[refute_0_10,refute_0_7]) ).
cnf(refute_0_12,plain,
( ~ rrx3(X,Y)
| rrx(X,Y) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_13,plain,
( ~ rrx3(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(i2003_11_14_17_18_32242)),bind(Y,$fot(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)))]]) ).
cnf(refute_0_14,plain,
rrx(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)),
inference(resolve,[$cnf( rrx3(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)) )],[refute_0_3,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ cUnsatisfiable(X)
| rrx4(X,skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_16,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| rrx4(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242)) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(i2003_11_14_17_18_32242))]]) ).
cnf(refute_0_17,plain,
rrx4(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_32242) )],[refute_0_0,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ rrx4(X,Y)
| rrx(X,Y) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_19,plain,
( ~ rrx4(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242)) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(i2003_11_14_17_18_32242)),bind(Y,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242)))]]) ).
cnf(refute_0_20,plain,
rrx(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242)),
inference(resolve,[$cnf( rrx4(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242)) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ rrx(X,Y)
| ~ rrx(X,Z)
| Y = Z ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_22,plain,
( ~ rrx(i2003_11_14_17_18_32242,X_31)
| ~ rrx(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242))
| skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242) = X_31 ),
inference(subst,[],[refute_0_21:[bind(X,$fot(i2003_11_14_17_18_32242)),bind(Y,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242))),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_23,plain,
( ~ rrx(i2003_11_14_17_18_32242,X_31)
| skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242) = X_31 ),
inference(resolve,[$cnf( rrx(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242)) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ rrx(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242))
| skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242) = skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242) ),
inference(subst,[],[refute_0_23:[bind(X_31,$fot(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)))]]) ).
cnf(refute_0_25,plain,
skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242) = skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242),
inference(resolve,[$cnf( rrx(i2003_11_14_17_18_32242,skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)) )],[refute_0_14,refute_0_24]) ).
cnf(refute_0_26,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_27,plain,
( X0 != X0
| X0 != Y1
| Y1 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y1)]]) ).
cnf(refute_0_28,plain,
( X0 != Y1
| Y1 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242) != skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)
| skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242) = skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242))),bind(Y1,$fot(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)))]]) ).
cnf(refute_0_30,plain,
skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242) = skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242),skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
( skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242) != skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242)
| ~ cc2(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242))
| cc2(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)) ),
introduced(tautology,[equality,[$cnf( ~ cc2(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)) ),[0],$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242))]]) ).
cnf(refute_0_32,plain,
( ~ cc2(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242))
| cc2(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242),skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
~ cc2(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242)),
inference(resolve,[$cnf( cc2(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_32242)) )],[refute_0_32,refute_0_11]) ).
cnf(refute_0_34,plain,
( ~ cUnsatisfiable(X)
| cc2(skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_35,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| cc2(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242)) ),
inference(subst,[],[refute_0_34:[bind(X,$fot(i2003_11_14_17_18_32242))]]) ).
cnf(refute_0_36,plain,
cc2(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_32242) )],[refute_0_0,refute_0_35]) ).
cnf(refute_0_37,plain,
$false,
inference(resolve,[$cnf( cc2(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_32242)) )],[refute_0_36,refute_0_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : KRS070+1 : TPTP v8.1.0. Released v3.1.0.
% 0.08/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 7 09:51:32 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------