TSTP Solution File: KRS099+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS099+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 03:18:42 EDT 2022
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 14 unt; 0 def)
% Number of atoms : 194 ( 74 equ)
% Maximal formula atoms : 73 ( 4 avg)
% Number of connectives : 244 ( 97 ~; 112 |; 29 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 50 ( 0 sgn 26 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y0,Y1,Y2] :
( rtt(X,Y0)
& rtt(X,Y1)
& rtt(X,Y2)
& Y0 != Y1
& Y0 != Y2
& Y1 != Y2 )
& ! [Y] :
( rtt(X,Y)
=> ca(Y) )
& ! [Y0,Y1] :
( ( rtt(X,Y0)
& rtt(X,Y1) )
=> Y0 = Y1 )
& ! [Y0,Y1] :
( ( rtt(X,Y0)
& rtt(X,Y1) )
=> Y0 = Y1 ) ) ) ).
fof(axiom_5,axiom,
cUnsatisfiable(i2003_11_14_17_20_29215) ).
fof(normalize_0_0,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ? [Y] :
( ~ ca(Y)
& rtt(X,Y) )
| ? [Y0,Y1] :
( Y0 != Y1
& rtt(X,Y0)
& rtt(X,Y1) )
| ! [Y0,Y1,Y2] :
( ~ rtt(X,Y0)
| ~ rtt(X,Y1)
| ~ rtt(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2 ) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ? [Y] :
( ~ ca(Y)
& rtt(X,Y) )
| ? [Y0,Y1] :
( Y0 != Y1
& rtt(X,Y0)
& rtt(X,Y1) )
| ! [Y0,Y1,Y2] :
( ~ rtt(X,Y0)
| ~ rtt(X,Y1)
| ~ rtt(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2 ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y,Y0,Y1,Y2] :
( ( skolemFOFtoCNF_Y0_1(X) != skolemFOFtoCNF_Y1_1(X)
| ~ cUnsatisfiable(X) )
& ( skolemFOFtoCNF_Y0_1(X) != skolemFOFtoCNF_Y2(X)
| ~ cUnsatisfiable(X) )
& ( skolemFOFtoCNF_Y1_1(X) != skolemFOFtoCNF_Y2(X)
| ~ cUnsatisfiable(X) )
& ( ~ cUnsatisfiable(X)
| rtt(X,skolemFOFtoCNF_Y0_1(X)) )
& ( ~ cUnsatisfiable(X)
| rtt(X,skolemFOFtoCNF_Y1_1(X)) )
& ( ~ cUnsatisfiable(X)
| rtt(X,skolemFOFtoCNF_Y2(X)) )
& ( ~ cUnsatisfiable(X)
| ~ rtt(X,Y)
| ca(Y) )
& ( ~ cUnsatisfiable(X)
| ~ rtt(X,Y0)
| ~ rtt(X,Y1)
| Y0 = Y1 )
& ( skolemFOFtoCNF_Y0(X) != skolemFOFtoCNF_Y1(X)
| ~ ca(skolemFOFtoCNF_Y(X))
| ~ rtt(X,Y0)
| ~ rtt(X,Y1)
| ~ rtt(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2
| cUnsatisfiable(X) )
& ( skolemFOFtoCNF_Y0(X) != skolemFOFtoCNF_Y1(X)
| ~ rtt(X,Y0)
| ~ rtt(X,Y1)
| ~ rtt(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2
| cUnsatisfiable(X)
| rtt(X,skolemFOFtoCNF_Y(X)) )
& ( ~ ca(skolemFOFtoCNF_Y(X))
| ~ rtt(X,Y0)
| ~ rtt(X,Y1)
| ~ rtt(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2
| cUnsatisfiable(X)
| rtt(X,skolemFOFtoCNF_Y0(X)) )
& ( ~ ca(skolemFOFtoCNF_Y(X))
| ~ rtt(X,Y0)
| ~ rtt(X,Y1)
| ~ rtt(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2
| cUnsatisfiable(X)
| rtt(X,skolemFOFtoCNF_Y1(X)) )
& ( ~ rtt(X,Y0)
| ~ rtt(X,Y1)
| ~ rtt(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2
| cUnsatisfiable(X)
| rtt(X,skolemFOFtoCNF_Y(X))
| rtt(X,skolemFOFtoCNF_Y0(X)) )
& ( ~ rtt(X,Y0)
| ~ rtt(X,Y1)
| ~ rtt(X,Y2)
| Y0 = Y1
| Y0 = Y2
| Y1 = Y2
| cUnsatisfiable(X)
| rtt(X,skolemFOFtoCNF_Y(X))
| rtt(X,skolemFOFtoCNF_Y1(X)) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X] :
( skolemFOFtoCNF_Y1_1(X) != skolemFOFtoCNF_Y2(X)
| ~ cUnsatisfiable(X) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
cUnsatisfiable(i2003_11_14_17_20_29215),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_0_5,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rtt(X,skolemFOFtoCNF_Y2(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_6,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rtt(X,skolemFOFtoCNF_Y0_1(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_7,plain,
! [X,Y0,Y1] :
( ~ cUnsatisfiable(X)
| ~ rtt(X,Y0)
| ~ rtt(X,Y1)
| Y0 = Y1 ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_8,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rtt(X,skolemFOFtoCNF_Y1_1(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
( skolemFOFtoCNF_Y1_1(X) != skolemFOFtoCNF_Y2(X)
| ~ cUnsatisfiable(X) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215) != skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215)
| ~ cUnsatisfiable(i2003_11_14_17_20_29215) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(i2003_11_14_17_20_29215))]]) ).
cnf(refute_0_2,plain,
cUnsatisfiable(i2003_11_14_17_20_29215),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ cUnsatisfiable(X)
| rtt(X,skolemFOFtoCNF_Y2(X)) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_29215)
| rtt(i2003_11_14_17_20_29215,skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(i2003_11_14_17_20_29215))]]) ).
cnf(refute_0_5,plain,
rtt(i2003_11_14_17_20_29215,skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_29215) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ cUnsatisfiable(X)
| rtt(X,skolemFOFtoCNF_Y0_1(X)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_7,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_29215)
| rtt(i2003_11_14_17_20_29215,skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(i2003_11_14_17_20_29215))]]) ).
cnf(refute_0_8,plain,
rtt(i2003_11_14_17_20_29215,skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_29215) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ cUnsatisfiable(X)
| ~ rtt(X,Y0)
| ~ rtt(X,Y1)
| Y0 = Y1 ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_10,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_29215)
| ~ rtt(i2003_11_14_17_20_29215,X_16)
| ~ rtt(i2003_11_14_17_20_29215,skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215))
| skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215) = X_16 ),
inference(subst,[],[refute_0_9:[bind(X,$fot(i2003_11_14_17_20_29215)),bind(Y0,$fot(skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215))),bind(Y1,$fot(X_16))]]) ).
cnf(refute_0_11,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_29215)
| ~ rtt(i2003_11_14_17_20_29215,X_16)
| skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215) = X_16 ),
inference(resolve,[$cnf( rtt(i2003_11_14_17_20_29215,skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215)) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ rtt(i2003_11_14_17_20_29215,X_16)
| skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215) = X_16 ),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_29215) )],[refute_0_2,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ rtt(i2003_11_14_17_20_29215,skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215))
| skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215) = skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215) ),
inference(subst,[],[refute_0_12:[bind(X_16,$fot(skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215)))]]) ).
cnf(refute_0_14,plain,
skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215) = skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215),
inference(resolve,[$cnf( rtt(i2003_11_14_17_20_29215,skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215)) )],[refute_0_5,refute_0_13]) ).
cnf(refute_0_15,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_16,plain,
( X0 != X0
| X0 != Y3
| Y3 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y3)]]) ).
cnf(refute_0_17,plain,
( X0 != Y3
| Y3 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215) != skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215)
| skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215) = skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215))),bind(Y3,$fot(skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215)))]]) ).
cnf(refute_0_19,plain,
skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215) = skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215),skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215)) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
( skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215) != skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215)
| skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215) != skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215)
| skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215) = skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215),skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215)) ),[1],$fot(skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215))]]) ).
cnf(refute_0_21,plain,
( skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215) != skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215)
| skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215) = skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215),skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215) != skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215)
| ~ cUnsatisfiable(i2003_11_14_17_20_29215) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215),skolemFOFtoCNF_Y2(i2003_11_14_17_20_29215)) )],[refute_0_21,refute_0_1]) ).
cnf(refute_0_23,plain,
( ~ cUnsatisfiable(X)
| rtt(X,skolemFOFtoCNF_Y1_1(X)) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_24,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_29215)
| rtt(i2003_11_14_17_20_29215,skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(i2003_11_14_17_20_29215))]]) ).
cnf(refute_0_25,plain,
rtt(i2003_11_14_17_20_29215,skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_29215) )],[refute_0_2,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ rtt(i2003_11_14_17_20_29215,skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215))
| skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215) = skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215) ),
inference(subst,[],[refute_0_12:[bind(X_16,$fot(skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215)))]]) ).
cnf(refute_0_27,plain,
skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215) = skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215),
inference(resolve,[$cnf( rtt(i2003_11_14_17_20_29215,skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215) != skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215)
| skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215) = skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215))),bind(Y3,$fot(skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215)))]]) ).
cnf(refute_0_29,plain,
skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215) = skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215),skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215) != skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215)
| skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215) != skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215)
| skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215) = skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215),skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215)) ),[1],$fot(skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215))]]) ).
cnf(refute_0_31,plain,
( skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215) != skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215)
| skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215) = skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215),skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215) != skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215)
| ~ cUnsatisfiable(i2003_11_14_17_20_29215) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y1_1(i2003_11_14_17_20_29215),skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215)) )],[refute_0_31,refute_0_22]) ).
cnf(refute_0_33,plain,
skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215) = skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215))]]) ).
cnf(refute_0_34,plain,
~ cUnsatisfiable(i2003_11_14_17_20_29215),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215),skolemFOFtoCNF_Y0_1(i2003_11_14_17_20_29215)) )],[refute_0_33,refute_0_32]) ).
cnf(refute_0_35,plain,
$false,
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_29215) )],[refute_0_2,refute_0_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KRS099+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n028.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 09:11:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------