TSTP Solution File: KRS096+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS096+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 03:18:42 EDT 2022
% Result : Unsatisfiable 0.13s 0.34s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 11 unt; 0 def)
% Number of atoms : 123 ( 13 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 153 ( 70 ~; 62 |; 16 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 41 ( 0 sgn 24 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( rr(X,Y)
& cc(Y) )
& ? [Y] :
( rr(X,Y)
& cd(Y) )
& ! [Y1,Y2] :
( ( rr(X,Y1)
& rr(X,Y2) )
=> Y1 = Y2 ) ) ) ).
fof(axiom_3,axiom,
! [X] :
( cc(X)
=> ~ cd(X) ) ).
fof(axiom_4,axiom,
cUnsatisfiable(i2003_11_14_17_20_18265) ).
fof(normalize_0_0,plain,
cUnsatisfiable(i2003_11_14_17_20_18265),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ? [Y1,Y2] :
( Y1 != Y2
& rr(X,Y1)
& rr(X,Y2) )
| ! [Y] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cd(Y)
| ~ rr(X,Y) ) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_2,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ? [Y1,Y2] :
( Y1 != Y2
& rr(X,Y1)
& rr(X,Y2) )
| ! [Y] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cd(Y)
| ~ rr(X,Y) ) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y,Y0,Y1,Y2] :
( ( ~ cUnsatisfiable(X)
| cc(skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| cd(skolemFOFtoCNF_Y(X)) )
& ( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) )
& ( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| Y1 = Y2 )
& ( skolemFOFtoCNF_Y0(X) != skolemFOFtoCNF_Y1(X)
| ~ cc(Y)
| ~ cd(Y0)
| ~ rr(X,Y)
| ~ rr(X,Y0)
| cUnsatisfiable(X) )
& ( ~ cc(Y)
| ~ cd(Y0)
| ~ rr(X,Y)
| ~ rr(X,Y0)
| cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y0(X)) )
& ( ~ cc(Y)
| ~ cd(Y0)
| ~ rr(X,Y)
| ~ rr(X,Y0)
| cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y1(X)) ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] :
( ~ cUnsatisfiable(X)
| cc(skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_6,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_7,plain,
! [X,Y1,Y2] :
( ~ cUnsatisfiable(X)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| Y1 = Y2 ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_8,plain,
! [X] :
( ~ cc(X)
| ~ cd(X) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_0_9,plain,
! [X] :
( ~ cc(X)
| ~ cd(X) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X] :
( ~ cUnsatisfiable(X)
| cd(skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
cUnsatisfiable(i2003_11_14_17_20_18265),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( ~ cUnsatisfiable(X)
| cc(skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265)) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(i2003_11_14_17_20_18265))]]) ).
cnf(refute_0_3,plain,
cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_18265) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| rr(i2003_11_14_17_20_18265,skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(i2003_11_14_17_20_18265))]]) ).
cnf(refute_0_6,plain,
rr(i2003_11_14_17_20_18265,skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_18265) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_8,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| rr(i2003_11_14_17_20_18265,skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(i2003_11_14_17_20_18265))]]) ).
cnf(refute_0_9,plain,
rr(i2003_11_14_17_20_18265,skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_18265) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ cUnsatisfiable(X)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| Y1 = Y2 ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_11,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ rr(i2003_11_14_17_20_18265,X_11)
| ~ rr(i2003_11_14_17_20_18265,skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265))
| skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265) = X_11 ),
inference(subst,[],[refute_0_10:[bind(X,$fot(i2003_11_14_17_20_18265)),bind(Y1,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265))),bind(Y2,$fot(X_11))]]) ).
cnf(refute_0_12,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ rr(i2003_11_14_17_20_18265,X_11)
| skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265) = X_11 ),
inference(resolve,[$cnf( rr(i2003_11_14_17_20_18265,skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265)) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ rr(i2003_11_14_17_20_18265,X_11)
| skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265) = X_11 ),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_18265) )],[refute_0_0,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ rr(i2003_11_14_17_20_18265,skolemFOFtoCNF_Y(i2003_11_14_17_20_18265))
| skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265) = skolemFOFtoCNF_Y(i2003_11_14_17_20_18265) ),
inference(subst,[],[refute_0_13:[bind(X_11,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)))]]) ).
cnf(refute_0_15,plain,
skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265) = skolemFOFtoCNF_Y(i2003_11_14_17_20_18265),
inference(resolve,[$cnf( rr(i2003_11_14_17_20_18265,skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) )],[refute_0_6,refute_0_14]) ).
cnf(refute_0_16,plain,
( skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265) != skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)
| ~ cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265))
| cc(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) ),
introduced(tautology,[equality,[$cnf( cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265)) ),[0],$fot(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265))]]) ).
cnf(refute_0_17,plain,
( ~ cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265))
| cc(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265),skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
cc(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)),
inference(resolve,[$cnf( cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265)) )],[refute_0_3,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ cc(X)
| ~ cd(X) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_20,plain,
( ~ cc(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265))
| ~ cd(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)))]]) ).
cnf(refute_0_21,plain,
( ~ cUnsatisfiable(X)
| cd(skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_22,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| cd(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(i2003_11_14_17_20_18265))]]) ).
cnf(refute_0_23,plain,
cd(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_18265) )],[refute_0_0,refute_0_22]) ).
cnf(refute_0_24,plain,
~ cc(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)),
inference(resolve,[$cnf( cd(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) )],[refute_0_23,refute_0_20]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( cc(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) )],[refute_0_18,refute_0_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS096+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 7 15:52:21 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34
% 0.13/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35
%------------------------------------------------------------------------------