TSTP Solution File: KRS118+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS118+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 03:18:47 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 105 ( 22 unt; 0 def)
% Number of atoms : 257 ( 18 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 288 ( 136 ~; 105 |; 23 &)
% ( 21 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 118 ( 1 sgn 81 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y] :
( rinvR(X,Y)
=> ca_Vx3(Y) )
& ? [Y] :
( rinvF(X,Y)
& cd(Y) )
& ccxcomp(X) ) ) ).
fof(axiom_3,axiom,
! [X] :
( cc(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ) ).
fof(axiom_4,axiom,
! [X] :
( ccxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ) ).
fof(axiom_5,axiom,
! [X] :
( cd(X)
<=> ( ? [Y] :
( rf(X,Y)
& ccxcomp(Y) )
& cc(X) ) ) ).
fof(axiom_6,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( rinvF(X,Y)
& cd(Y) ) ) ).
fof(axiom_7,axiom,
! [X,Y,Z] :
( ( rf(X,Y)
& rf(X,Z) )
=> Y = Z ) ).
fof(axiom_8,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ) ).
fof(axiom_9,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ) ).
fof(axiom_11,axiom,
cUnsatisfiable(i2003_11_14_17_21_4056) ).
fof(axiom_12,axiom,
! [X,Y] :
( rf(X,Y)
=> rr(X,Y) ) ).
fof(normalize_0_0,plain,
! [X] :
( ~ cc(X)
<=> ? [Y] : ra_Px1(X,Y) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ cc(X)
<=> ? [Y] : ra_Px1(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ( ~ cc(X)
| ~ ra_Px1(X,Y) )
& ( cc(X)
| ra_Px1(X,skolemFOFtoCNF_Y_2(X)) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ cc(X)
| ~ ra_Px1(X,Y) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] :
( ~ ccxcomp(X)
<=> ! [Y0] : ~ ra_Px1(X,Y0) ),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_0_5,plain,
! [X] :
( ~ ccxcomp(X)
<=> ! [Y0] : ~ ra_Px1(X,Y0) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y0] :
( ( ~ ccxcomp(X)
| ra_Px1(X,skolemFOFtoCNF_Y0(X)) )
& ( ~ ra_Px1(X,Y0)
| ccxcomp(X) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X] :
( ~ ccxcomp(X)
| ra_Px1(X,skolemFOFtoCNF_Y0(X)) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X] :
( ~ cd(X)
<=> ( ~ cc(X)
| ! [Y] :
( ~ ccxcomp(Y)
| ~ rf(X,Y) ) ) ),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_0_9,plain,
! [X] :
( ~ cd(X)
<=> ( ~ cc(X)
| ! [Y] :
( ~ ccxcomp(Y)
| ~ rf(X,Y) ) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ( ~ cd(X)
| cc(X) )
& ( ~ cd(X)
| ccxcomp(skolemFOFtoCNF_Y_3(X)) )
& ( ~ cd(X)
| rf(X,skolemFOFtoCNF_Y_3(X)) )
& ( ~ cc(X)
| ~ ccxcomp(Y)
| ~ rf(X,Y)
| cd(X) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X] :
( ~ cd(X)
| ccxcomp(skolemFOFtoCNF_Y_3(X)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X] :
( ~ ca_Vx3(X)
<=> ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) ) ),
inference(canonicalize,[],[axiom_6]) ).
fof(normalize_0_13,plain,
! [X] :
( ~ ca_Vx3(X)
<=> ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ( ~ ca_Vx3(X)
| cd(skolemFOFtoCNF_Y_4(X)) )
& ( ~ ca_Vx3(X)
| rinvF(X,skolemFOFtoCNF_Y_4(X)) )
& ( ~ cd(Y)
| ~ rinvF(X,Y)
| ca_Vx3(X) ) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X] :
( ~ ca_Vx3(X)
| cd(skolemFOFtoCNF_Y_4(X)) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ rinvR(X,Y)
<=> ~ rr(Y,X) ),
inference(canonicalize,[],[axiom_9]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ~ rinvR(X,Y)
<=> ~ rr(Y,X) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ( ~ rinvR(X,Y)
| rr(Y,X) )
& ( ~ rr(Y,X)
| rinvR(X,Y) ) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ~ rr(Y,X)
| rinvR(X,Y) ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
cUnsatisfiable(i2003_11_14_17_21_4056),
inference(canonicalize,[],[axiom_11]) ).
fof(normalize_0_21,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ~ ccxcomp(X)
| ? [Y] :
( ~ ca_Vx3(Y)
& rinvR(X,Y) )
| ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) ) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_22,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ~ ccxcomp(X)
| ? [Y] :
( ~ ca_Vx3(Y)
& rinvR(X,Y) )
| ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) ) ) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [X,Y] :
( ( ~ cUnsatisfiable(X)
| ccxcomp(X) )
& ( ~ cUnsatisfiable(X)
| cd(skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| rinvF(X,skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| ~ rinvR(X,Y)
| ca_Vx3(Y) )
& ( ~ ca_Vx3(skolemFOFtoCNF_Y(X))
| ~ ccxcomp(X)
| ~ cd(Y)
| ~ rinvF(X,Y)
| cUnsatisfiable(X) )
& ( ~ ccxcomp(X)
| ~ cd(Y)
| ~ rinvF(X,Y)
| cUnsatisfiable(X)
| rinvR(X,skolemFOFtoCNF_Y(X)) ) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rinvF(X,skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [X,Y] :
( ~ rf(Y,X)
<=> ~ rinvF(X,Y) ),
inference(canonicalize,[],[axiom_8]) ).
fof(normalize_0_26,plain,
! [X,Y] :
( ~ rf(Y,X)
<=> ~ rinvF(X,Y) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [X,Y] :
( ( ~ rf(Y,X)
| rinvF(X,Y) )
& ( ~ rinvF(X,Y)
| rf(Y,X) ) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [X,Y] :
( ~ rinvF(X,Y)
| rf(Y,X) ),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [X,Y] :
( ~ rf(X,Y)
| rr(X,Y) ),
inference(canonicalize,[],[axiom_12]) ).
fof(normalize_0_30,plain,
! [X,Y] :
( ~ rf(X,Y)
| rr(X,Y) ),
inference(specialize,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
! [X,Y] :
( ~ cUnsatisfiable(X)
| ~ rinvR(X,Y)
| ca_Vx3(Y) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_32,plain,
! [X] :
( ~ cd(X)
| rf(X,skolemFOFtoCNF_Y_3(X)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_33,plain,
! [X] :
( ~ ca_Vx3(X)
| rinvF(X,skolemFOFtoCNF_Y_4(X)) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_34,plain,
! [X,Y,Z] :
( ~ rf(X,Y)
| ~ rf(X,Z)
| Y = Z ),
inference(canonicalize,[],[axiom_7]) ).
fof(normalize_0_35,plain,
! [X,Y,Z] :
( ~ rf(X,Y)
| ~ rf(X,Z)
| Y = Z ),
inference(specialize,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
! [X] :
( ~ cd(X)
| cc(X) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_37,plain,
! [X] :
( ~ cUnsatisfiable(X)
| cd(skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_0_23]) ).
cnf(refute_0_0,plain,
( ~ cc(X)
| ~ ra_Px1(X,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ cc(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))))
| ~ ra_Px1(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))))) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))))),bind(Y,$fot(skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))))))]]) ).
cnf(refute_0_2,plain,
( ~ ccxcomp(X)
| ra_Px1(X,skolemFOFtoCNF_Y0(X)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ ccxcomp(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))))
| ra_Px1(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))))]]) ).
cnf(refute_0_4,plain,
( ~ cd(X)
| ccxcomp(skolemFOFtoCNF_Y_3(X)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_5,plain,
( ~ cd(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))
| ccxcomp(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))))]]) ).
cnf(refute_0_6,plain,
( ~ ca_Vx3(X)
| cd(skolemFOFtoCNF_Y_4(X)) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_7,plain,
( ~ ca_Vx3(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))
| cd(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))]]) ).
cnf(refute_0_8,plain,
( ~ rr(Y,X)
| rinvR(X,Y) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_9,plain,
( ~ rr(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056)
| rinvR(i2003_11_14_17_21_4056,skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(i2003_11_14_17_21_4056)),bind(Y,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))]]) ).
cnf(refute_0_10,plain,
cUnsatisfiable(i2003_11_14_17_21_4056),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_11,plain,
( ~ cUnsatisfiable(X)
| rinvF(X,skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_12,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| rinvF(i2003_11_14_17_21_4056,skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(i2003_11_14_17_21_4056))]]) ).
cnf(refute_0_13,plain,
rinvF(i2003_11_14_17_21_4056,skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_21_4056) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ rinvF(X,Y)
| rf(Y,X) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_15,plain,
( ~ rinvF(i2003_11_14_17_21_4056,skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))
| rf(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(i2003_11_14_17_21_4056)),bind(Y,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))]]) ).
cnf(refute_0_16,plain,
rf(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056),
inference(resolve,[$cnf( rinvF(i2003_11_14_17_21_4056,skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ rf(X,Y)
| rr(X,Y) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_18,plain,
( ~ rf(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056)
| rr(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))),bind(Y,$fot(i2003_11_14_17_21_4056))]]) ).
cnf(refute_0_19,plain,
rr(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056),
inference(resolve,[$cnf( rf(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
rinvR(i2003_11_14_17_21_4056,skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)),
inference(resolve,[$cnf( rr(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) )],[refute_0_19,refute_0_9]) ).
cnf(refute_0_21,plain,
( ~ cUnsatisfiable(X)
| ~ rinvR(X,Y)
| ca_Vx3(Y) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_22,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ rinvR(i2003_11_14_17_21_4056,skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))
| ca_Vx3(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(i2003_11_14_17_21_4056)),bind(Y,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))]]) ).
cnf(refute_0_23,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ca_Vx3(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)) ),
inference(resolve,[$cnf( rinvR(i2003_11_14_17_21_4056,skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
ca_Vx3(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_21_4056) )],[refute_0_10,refute_0_23]) ).
cnf(refute_0_25,plain,
cd(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))),
inference(resolve,[$cnf( ca_Vx3(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)) )],[refute_0_24,refute_0_7]) ).
cnf(refute_0_26,plain,
ccxcomp(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))),
inference(resolve,[$cnf( cd(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))) )],[refute_0_25,refute_0_5]) ).
cnf(refute_0_27,plain,
ra_Px1(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))))),
inference(resolve,[$cnf( ccxcomp(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))) )],[refute_0_26,refute_0_3]) ).
cnf(refute_0_28,plain,
~ cc(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))),
inference(resolve,[$cnf( ra_Px1(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))),skolemFOFtoCNF_Y0(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))))) )],[refute_0_27,refute_0_1]) ).
cnf(refute_0_29,plain,
( ~ cd(X)
| rf(X,skolemFOFtoCNF_Y_3(X)) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_30,plain,
( ~ cd(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))
| rf(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)),skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))))]]) ).
cnf(refute_0_31,plain,
rf(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)),skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))),
inference(resolve,[$cnf( cd(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))) )],[refute_0_25,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ rinvF(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056),skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))
| rf(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)),skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))),bind(Y,$fot(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))))]]) ).
cnf(refute_0_33,plain,
( ~ ca_Vx3(X)
| rinvF(X,skolemFOFtoCNF_Y_4(X)) ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_34,plain,
( ~ ca_Vx3(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))
| rinvF(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056),skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))]]) ).
cnf(refute_0_35,plain,
rinvF(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056),skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))),
inference(resolve,[$cnf( ca_Vx3(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)) )],[refute_0_24,refute_0_34]) ).
cnf(refute_0_36,plain,
rf(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)),skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)),
inference(resolve,[$cnf( rinvF(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056),skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))) )],[refute_0_35,refute_0_32]) ).
cnf(refute_0_37,plain,
( ~ rf(X,Y)
| ~ rf(X,Z)
| Y = Z ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_38,plain,
( ~ rf(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)),X_38)
| ~ rf(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)),skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))
| skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056) = X_38 ),
inference(subst,[],[refute_0_37:[bind(X,$fot(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))),bind(Y,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_39,plain,
( ~ rf(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)),X_38)
| skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056) = X_38 ),
inference(resolve,[$cnf( rf(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)),skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)) )],[refute_0_36,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ rf(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)),skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))))
| skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056) = skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))) ),
inference(subst,[],[refute_0_39:[bind(X_38,$fot(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))))]]) ).
cnf(refute_0_41,plain,
skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056) = skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))),
inference(resolve,[$cnf( rf(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)),skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))) )],[refute_0_31,refute_0_40]) ).
cnf(refute_0_42,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_43,plain,
( X0 != X0
| X0 != Y1
| Y1 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y1)]]) ).
cnf(refute_0_44,plain,
( X0 != Y1
| Y1 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056) != skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))
| skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))) = skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))),bind(Y1,$fot(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))))]]) ).
cnf(refute_0_46,plain,
skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))) = skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056),skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))) )],[refute_0_41,refute_0_45]) ).
cnf(refute_0_47,plain,
( skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))) != skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)
| ~ cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))
| cc(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))) ),
introduced(tautology,[equality,[$cnf( ~ cc(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))) ),[0],$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))]]) ).
cnf(refute_0_48,plain,
( ~ cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))
| cc(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))),skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
~ cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)),
inference(resolve,[$cnf( cc(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))) )],[refute_0_48,refute_0_28]) ).
cnf(refute_0_50,plain,
( ~ cd(X)
| cc(X) ),
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_51,plain,
( ~ cd(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056))
| cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)) ),
inference(subst,[],[refute_0_50:[bind(X,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)))]]) ).
cnf(refute_0_52,plain,
( ~ cUnsatisfiable(X)
| cd(skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_53,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| cd(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)) ),
inference(subst,[],[refute_0_52:[bind(X,$fot(i2003_11_14_17_21_4056))]]) ).
cnf(refute_0_54,plain,
cd(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_21_4056) )],[refute_0_10,refute_0_53]) ).
cnf(refute_0_55,plain,
cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)),
inference(resolve,[$cnf( cd(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)) )],[refute_0_54,refute_0_51]) ).
cnf(refute_0_56,plain,
$false,
inference(resolve,[$cnf( cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_21_4056)) )],[refute_0_55,refute_0_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KRS118+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 7 06:47:48 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45
% 0.20/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.46
%------------------------------------------------------------------------------