TSTP Solution File: KRS087+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS087+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 03:18:39 EDT 2022
% Result : Unsatisfiable 0.19s 0.35s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 10 unt; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 23 ( 2 avg)
% Number of connectives : 143 ( 66 ~; 55 |; 14 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 52 ( 0 sgn 36 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( cp1(X)
& ? [Y] :
( rr(X,Y)
& ? [Z] :
( rr(Y,Z)
& ! [W] :
( rinvR(Z,W)
=> ~ cp1(W) )
& cp1(Z) ) ) ) ) ).
fof(axiom_5,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ) ).
fof(axiom_6,axiom,
! [X,Y,Z] :
( ( rr(X,Y)
& rr(Y,Z) )
=> rr(X,Z) ) ).
fof(axiom_7,axiom,
cUnsatisfiable(i2003_11_14_17_19_46763) ).
fof(normalize_0_0,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ~ cp1(X)
| ! [Y] :
( ~ rr(X,Y)
| ! [Z] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ? [W] :
( cp1(W)
& rinvR(Z,W) ) ) ) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ~ cp1(X)
| ! [Y] :
( ~ rr(X,Y)
| ! [Z] :
( ~ cp1(Z)
| ~ rr(Y,Z)
| ? [W] :
( cp1(W)
& rinvR(Z,W) ) ) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [W,X,Y,Z] :
( ( ~ cUnsatisfiable(X)
| cp1(X) )
& ( ~ cUnsatisfiable(X)
| cp1(skolemFOFtoCNF_Z(X)) )
& ( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) )
& ( ~ cUnsatisfiable(X)
| rr(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) )
& ( ~ cUnsatisfiable(X)
| ~ cp1(W)
| ~ rinvR(skolemFOFtoCNF_Z(X),W) )
& ( ~ cp1(X)
| ~ cp1(Z)
| ~ rr(X,Y)
| ~ rr(Y,Z)
| cUnsatisfiable(X)
| cp1(skolemFOFtoCNF_W(Z)) )
& ( ~ cp1(X)
| ~ cp1(Z)
| ~ rr(X,Y)
| ~ rr(Y,Z)
| cUnsatisfiable(X)
| rinvR(Z,skolemFOFtoCNF_W(Z)) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [W,X] :
( ~ cUnsatisfiable(X)
| ~ cp1(W)
| ~ rinvR(skolemFOFtoCNF_Z(X),W) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ rinvR(X,Y)
<=> ~ rr(Y,X) ),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ rinvR(X,Y)
<=> ~ rr(Y,X) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ( ~ rinvR(X,Y)
| rr(Y,X) )
& ( ~ rr(Y,X)
| rinvR(X,Y) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ rr(Y,X)
| rinvR(X,Y) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
cUnsatisfiable(i2003_11_14_17_19_46763),
inference(canonicalize,[],[axiom_7]) ).
fof(normalize_0_9,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_10,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rr(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_11,plain,
! [X,Y,Z] :
( ~ rr(X,Y)
| ~ rr(Y,Z)
| rr(X,Z) ),
inference(canonicalize,[],[axiom_6]) ).
fof(normalize_0_12,plain,
! [X,Y,Z] :
( ~ rr(X,Y)
| ~ rr(Y,Z)
| rr(X,Z) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X] :
( ~ cUnsatisfiable(X)
| cp1(X) ),
inference(conjunct,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
( ~ cUnsatisfiable(X)
| ~ cp1(W)
| ~ rinvR(skolemFOFtoCNF_Z(X),W) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_46763)
| ~ cp1(i2003_11_14_17_19_46763)
| ~ rinvR(skolemFOFtoCNF_Z(i2003_11_14_17_19_46763),i2003_11_14_17_19_46763) ),
inference(subst,[],[refute_0_0:[bind(W,$fot(i2003_11_14_17_19_46763)),bind(X,$fot(i2003_11_14_17_19_46763))]]) ).
cnf(refute_0_2,plain,
( ~ rr(Y,X)
| rinvR(X,Y) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ rr(i2003_11_14_17_19_46763,skolemFOFtoCNF_Z(i2003_11_14_17_19_46763))
| rinvR(skolemFOFtoCNF_Z(i2003_11_14_17_19_46763),i2003_11_14_17_19_46763) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_Z(i2003_11_14_17_19_46763))),bind(Y,$fot(i2003_11_14_17_19_46763))]]) ).
cnf(refute_0_4,plain,
cUnsatisfiable(i2003_11_14_17_19_46763),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_46763)
| rr(i2003_11_14_17_19_46763,skolemFOFtoCNF_Y(i2003_11_14_17_19_46763)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(i2003_11_14_17_19_46763))]]) ).
cnf(refute_0_7,plain,
rr(i2003_11_14_17_19_46763,skolemFOFtoCNF_Y(i2003_11_14_17_19_46763)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_46763) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ cUnsatisfiable(X)
| rr(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_46763)
| rr(skolemFOFtoCNF_Y(i2003_11_14_17_19_46763),skolemFOFtoCNF_Z(i2003_11_14_17_19_46763)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(i2003_11_14_17_19_46763))]]) ).
cnf(refute_0_10,plain,
rr(skolemFOFtoCNF_Y(i2003_11_14_17_19_46763),skolemFOFtoCNF_Z(i2003_11_14_17_19_46763)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_46763) )],[refute_0_4,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ rr(X,Y)
| ~ rr(Y,Z)
| rr(X,Z) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_12,plain,
( ~ rr(X_23,skolemFOFtoCNF_Y(i2003_11_14_17_19_46763))
| ~ rr(skolemFOFtoCNF_Y(i2003_11_14_17_19_46763),skolemFOFtoCNF_Z(i2003_11_14_17_19_46763))
| rr(X_23,skolemFOFtoCNF_Z(i2003_11_14_17_19_46763)) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_23)),bind(Y,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_19_46763))),bind(Z,$fot(skolemFOFtoCNF_Z(i2003_11_14_17_19_46763)))]]) ).
cnf(refute_0_13,plain,
( ~ rr(X_23,skolemFOFtoCNF_Y(i2003_11_14_17_19_46763))
| rr(X_23,skolemFOFtoCNF_Z(i2003_11_14_17_19_46763)) ),
inference(resolve,[$cnf( rr(skolemFOFtoCNF_Y(i2003_11_14_17_19_46763),skolemFOFtoCNF_Z(i2003_11_14_17_19_46763)) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ rr(i2003_11_14_17_19_46763,skolemFOFtoCNF_Y(i2003_11_14_17_19_46763))
| rr(i2003_11_14_17_19_46763,skolemFOFtoCNF_Z(i2003_11_14_17_19_46763)) ),
inference(subst,[],[refute_0_13:[bind(X_23,$fot(i2003_11_14_17_19_46763))]]) ).
cnf(refute_0_15,plain,
rr(i2003_11_14_17_19_46763,skolemFOFtoCNF_Z(i2003_11_14_17_19_46763)),
inference(resolve,[$cnf( rr(i2003_11_14_17_19_46763,skolemFOFtoCNF_Y(i2003_11_14_17_19_46763)) )],[refute_0_7,refute_0_14]) ).
cnf(refute_0_16,plain,
rinvR(skolemFOFtoCNF_Z(i2003_11_14_17_19_46763),i2003_11_14_17_19_46763),
inference(resolve,[$cnf( rr(i2003_11_14_17_19_46763,skolemFOFtoCNF_Z(i2003_11_14_17_19_46763)) )],[refute_0_15,refute_0_3]) ).
cnf(refute_0_17,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_46763)
| ~ cp1(i2003_11_14_17_19_46763) ),
inference(resolve,[$cnf( rinvR(skolemFOFtoCNF_Z(i2003_11_14_17_19_46763),i2003_11_14_17_19_46763) )],[refute_0_16,refute_0_1]) ).
cnf(refute_0_18,plain,
~ cp1(i2003_11_14_17_19_46763),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_46763) )],[refute_0_4,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ cUnsatisfiable(X)
| cp1(X) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_20,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_46763)
| cp1(i2003_11_14_17_19_46763) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(i2003_11_14_17_19_46763))]]) ).
cnf(refute_0_21,plain,
cp1(i2003_11_14_17_19_46763),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_46763) )],[refute_0_4,refute_0_20]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( cp1(i2003_11_14_17_19_46763) )],[refute_0_21,refute_0_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS087+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n019.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 05:30:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.35
% 0.19/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.36
%------------------------------------------------------------------------------