TSTP Solution File: KRS110+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS110+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 03:18:45 EDT 2022
% Result : Unsatisfiable 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 10 unt; 0 def)
% Number of atoms : 123 ( 0 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 146 ( 68 ~; 50 |; 15 &)
% ( 12 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 51 ( 1 sgn 35 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( rs(X,Y)
& ca_Ax2(Y) )
& ! [Y] :
( rs(X,Y)
=> cpxcomp(Y) ) ) ) ).
fof(axiom_3,axiom,
! [X] :
( cp(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ) ).
fof(axiom_4,axiom,
! [X] :
( cpxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ) ).
fof(axiom_5,axiom,
! [X] :
( ca_Ax2(X)
<=> ( cp(X)
& ? [Y] :
( rinvS(X,Y)
& cp(Y) ) ) ) ).
fof(axiom_12,axiom,
cUnsatisfiable(i2003_11_14_17_21_12565) ).
fof(normalize_0_0,plain,
! [X] :
( ~ cp(X)
<=> ? [Y] : ra_Px1(X,Y) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ cp(X)
<=> ? [Y] : ra_Px1(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ( ~ cp(X)
| ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,skolemFOFtoCNF_Y_2(X)) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ cp(X)
| ~ ra_Px1(X,Y) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] :
( ~ cpxcomp(X)
<=> ! [Y0] : ~ ra_Px1(X,Y0) ),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_0_5,plain,
! [X] :
( ~ cpxcomp(X)
<=> ! [Y0] : ~ ra_Px1(X,Y0) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y0] :
( ( ~ cpxcomp(X)
| ra_Px1(X,skolemFOFtoCNF_Y0(X)) )
& ( ~ ra_Px1(X,Y0)
| cpxcomp(X) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X] :
( ~ cpxcomp(X)
| ra_Px1(X,skolemFOFtoCNF_Y0(X)) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
cUnsatisfiable(i2003_11_14_17_21_12565),
inference(canonicalize,[],[axiom_12]) ).
fof(normalize_0_9,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ? [Y] :
( ~ cpxcomp(Y)
& rs(X,Y) )
| ! [Y] :
( ~ ca_Ax2(Y)
| ~ rs(X,Y) ) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_10,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ? [Y] :
( ~ cpxcomp(Y)
& rs(X,Y) )
| ! [Y] :
( ~ ca_Ax2(Y)
| ~ rs(X,Y) ) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ( ~ cUnsatisfiable(X)
| ca_Ax2(skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| rs(X,skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| ~ rs(X,Y)
| cpxcomp(Y) )
& ( ~ ca_Ax2(Y)
| ~ cpxcomp(skolemFOFtoCNF_Y(X))
| ~ rs(X,Y)
| cUnsatisfiable(X) )
& ( ~ ca_Ax2(Y)
| ~ rs(X,Y)
| cUnsatisfiable(X)
| rs(X,skolemFOFtoCNF_Y(X)) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rs(X,skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ cUnsatisfiable(X)
| ~ rs(X,Y)
| cpxcomp(Y) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_14,plain,
! [X] :
( ~ ca_Ax2(X)
<=> ( ~ cp(X)
| ! [Y] :
( ~ cp(Y)
| ~ rinvS(X,Y) ) ) ),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_0_15,plain,
! [X] :
( ~ ca_Ax2(X)
<=> ( ~ cp(X)
| ! [Y] :
( ~ cp(Y)
| ~ rinvS(X,Y) ) ) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ( ~ ca_Ax2(X)
| cp(X) )
& ( ~ ca_Ax2(X)
| cp(skolemFOFtoCNF_Y_3(X)) )
& ( ~ ca_Ax2(X)
| rinvS(X,skolemFOFtoCNF_Y_3(X)) )
& ( ~ cp(X)
| ~ cp(Y)
| ~ rinvS(X,Y)
| ca_Ax2(X) ) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X] :
( ~ ca_Ax2(X)
| cp(X) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X] :
( ~ cUnsatisfiable(X)
| ca_Ax2(skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
( ~ cp(X)
| ~ ra_Px1(X,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ cp(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565))
| ~ ra_Px1(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565))) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565))),bind(Y,$fot(skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565))))]]) ).
cnf(refute_0_2,plain,
( ~ cpxcomp(X)
| ra_Px1(X,skolemFOFtoCNF_Y0(X)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ cpxcomp(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565))
| ra_Px1(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565)))]]) ).
cnf(refute_0_4,plain,
cUnsatisfiable(i2003_11_14_17_21_12565),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ cUnsatisfiable(X)
| rs(X,skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_6,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| rs(i2003_11_14_17_21_12565,skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(i2003_11_14_17_21_12565))]]) ).
cnf(refute_0_7,plain,
rs(i2003_11_14_17_21_12565,skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_21_12565) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ cUnsatisfiable(X)
| ~ rs(X,Y)
| cpxcomp(Y) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_9,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ rs(i2003_11_14_17_21_12565,skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565))
| cpxcomp(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(i2003_11_14_17_21_12565)),bind(Y,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565)))]]) ).
cnf(refute_0_10,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| cpxcomp(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565)) ),
inference(resolve,[$cnf( rs(i2003_11_14_17_21_12565,skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565)) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
cpxcomp(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_21_12565) )],[refute_0_4,refute_0_10]) ).
cnf(refute_0_12,plain,
ra_Px1(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565))),
inference(resolve,[$cnf( cpxcomp(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565)) )],[refute_0_11,refute_0_3]) ).
cnf(refute_0_13,plain,
~ cp(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565)),
inference(resolve,[$cnf( ra_Px1(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565))) )],[refute_0_12,refute_0_1]) ).
cnf(refute_0_14,plain,
( ~ ca_Ax2(X)
| cp(X) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_15,plain,
( ~ ca_Ax2(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565))
| cp(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565)))]]) ).
cnf(refute_0_16,plain,
( ~ cUnsatisfiable(X)
| ca_Ax2(skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_17,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ca_Ax2(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565)) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(i2003_11_14_17_21_12565))]]) ).
cnf(refute_0_18,plain,
ca_Ax2(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_21_12565) )],[refute_0_4,refute_0_17]) ).
cnf(refute_0_19,plain,
cp(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565)),
inference(resolve,[$cnf( ca_Ax2(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565)) )],[refute_0_18,refute_0_15]) ).
cnf(refute_0_20,plain,
$false,
inference(resolve,[$cnf( cp(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_12565)) )],[refute_0_19,refute_0_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS110+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n025.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 07:01:48 EDT 2022
% 0.12/0.33 % 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
% 0.12/0.35
%------------------------------------------------------------------------------