%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS118+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:46:04 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 21 unt; 0 def)
% Number of atoms : 189 ( 10 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 209 ( 81 ~; 76 |; 41 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 92 ( 2 sgn 56 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ccxcomp_substitution_1,axiom,
! [A,B] :
( ( ccxcomp(A)
& A = B )
=> ccxcomp(B) ),
file('theBenchmark.p',ccxcomp_substitution_1) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ccxcomp(X)
& ? [Y] :
( cd(Y)
& rinvF(X,Y) )
& ! [Y] :
( rinvR(X,Y)
=> ca_Vx3(Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cc(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( ccxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X] :
( cd(X)
<=> ( cc(X)
& ? [Y] :
( ccxcomp(Y)
& rf(X,Y) ) ) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( cd(Y)
& rinvF(X,Y) ) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_7,axiom,
! [X,Y,Z] :
( ( rf(X,Z)
& rf(X,Y) )
=> Y = Z ),
file('theBenchmark.p',axiom_7) ).
fof(axiom_8,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('theBenchmark.p',axiom_8) ).
fof(axiom_9,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('theBenchmark.p',axiom_9) ).
fof(axiom_12,axiom,
! [X,Y] :
( rf(X,Y)
=> rr(X,Y) ),
file('theBenchmark.p',axiom_12) ).
cnf(c_35,plain,
( ccxcomp(A)
| ~ ccxcomp(B)
| A != B ),
inference(clausify,[status(thm)],[ccxcomp_substitution_1]) ).
fof(nnf_22,plain,
! [X] :
( ( ~ ccxcomp(X)
| ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| ? [X2] :
( ~ ca_Vx3(X2)
& rinvR(X,X2) )
| cUnsatisfiable(X) )
& ( ( ccxcomp(X)
& ? [X1] :
( cd(X1)
& rinvF(X,X1) )
& ! [X0] :
( ca_Vx3(X0)
| ~ rinvR(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ~ ccxcomp(X)
| ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| ( ~ ca_Vx3(sK4(X))
& rinvR(X,sK4(X)) )
| cUnsatisfiable(X) )
& ( ( ccxcomp(X)
& cd(sK0(X))
& rinvF(X,sK0(X))
& ! [X0] :
( ca_Vx3(X0)
| ~ rinvR(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK4]),skolemize(X1,sK0(X)),skolemize(X2,sK4(X))],[nnf_22]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( ~ ccxcomp(VAR_0)
| ~ cd(VAR_1)
| ~ rinvF(VAR_0,VAR_1)
| ~ ca_Vx3(sK4(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ ccxcomp(VAR_0)
| ~ cd(VAR_1)
| ~ rinvF(VAR_0,VAR_1)
| rinvR(VAR_0,sK4(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ccxcomp(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cd(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rinvF(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ca_Vx3(VAR_1)
| ~ rinvR(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_55,plain,
( ca_Vx3(B)
| ~ rinvR(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_56,plain,
( rinvF(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_57,plain,
( cd(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_61,plain,
( ~ ra_Px1(A,B)
| ~ cc(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(nnf_24,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| ccxcomp(X) )
& ( ? [X2] : ra_Px1(X,X2)
| ~ ccxcomp(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(sk_axiom_4_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| ccxcomp(X) )
& ( ra_Px1(X,sK1(X))
| ~ ccxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X))],[nnf_24]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px1(VAR_0,VAR_1)
| ccxcomp(VAR_0) )
& ! [VAR_0] :
( ra_Px1(VAR_0,sK1(VAR_0))
| ~ ccxcomp(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_63,plain,
( ra_Px1(A,sK1(A))
| ~ ccxcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
fof(nnf_25,plain,
! [X] :
( ( ~ cc(X)
| ! [Y] :
( ~ ccxcomp(Y)
| ~ rf(X,Y) )
| cd(X) )
& ( ( cc(X)
& ? [X2] :
( ccxcomp(X2)
& rf(X,X2) ) )
| ~ cd(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_5]) ).
fof(sk_axiom_5_sk,plain,
! [X] :
( ( ~ cc(X)
| ! [Y] :
( ~ ccxcomp(Y)
| ~ rf(X,Y) )
| cd(X) )
& ( ( cc(X)
& ccxcomp(sK2(X))
& rf(X,sK2(X)) )
| ~ cd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X))],[nnf_25]) ).
fof(sk_axiom_5,plain,
( ! [VAR_0,VAR_1] :
( ~ cc(VAR_0)
| ~ ccxcomp(VAR_1)
| ~ rf(VAR_0,VAR_1)
| cd(VAR_0) )
& ! [VAR_0] :
( cc(VAR_0)
| ~ cd(VAR_0) )
& ! [VAR_0] :
( ccxcomp(sK2(VAR_0))
| ~ cd(VAR_0) )
& ! [VAR_0] :
( rf(VAR_0,sK2(VAR_0))
| ~ cd(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_5_sk]) ).
cnf(c_65,plain,
( rf(A,sK2(A))
| ~ cd(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_5]) ).
cnf(c_66,plain,
( ccxcomp(sK2(A))
| ~ cd(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_5]) ).
cnf(c_67,plain,
( cc(A)
| ~ cd(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_5]) ).
fof(nnf_26,plain,
! [X] :
( ( ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| ca_Vx3(X) )
& ( ? [X2] :
( cd(X2)
& rinvF(X,X2) )
| ~ ca_Vx3(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_6]) ).
fof(sk_axiom_6_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| ca_Vx3(X) )
& ( ( cd(sK3(X))
& rinvF(X,sK3(X)) )
| ~ ca_Vx3(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X))],[nnf_26]) ).
fof(sk_axiom_6,plain,
( ! [VAR_0,VAR_1] :
( ~ cd(VAR_1)
| ~ rinvF(VAR_0,VAR_1)
| ca_Vx3(VAR_0) )
& ! [VAR_0] :
( cd(sK3(VAR_0))
| ~ ca_Vx3(VAR_0) )
& ! [VAR_0] :
( rinvF(VAR_0,sK3(VAR_0))
| ~ ca_Vx3(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_6_sk]) ).
cnf(c_69,plain,
( rinvF(A,sK3(A))
| ~ ca_Vx3(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_6]) ).
cnf(c_70,plain,
( cd(sK3(A))
| ~ ca_Vx3(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_6]) ).
cnf(c_72,plain,
( C = B
| ~ rf(A,C)
| ~ rf(A,B) ),
inference(clausify,[status(thm)],[axiom_7]) ).
cnf(c_73,plain,
( rf(B,A)
| ~ rinvF(A,B) ),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_76,plain,
( ~ rr(B,A)
| rinvR(A,B) ),
inference(clausify,[status(thm)],[axiom_9]) ).
fof(axiom_11,axiom,
cUnsatisfiable(i2003_11_14_17_21_4056),
file('theBenchmark.p',axiom_11) ).
cnf(c_78,plain,
cUnsatisfiable(i2003_11_14_17_21_4056),
inference(clausify,[status(thm)],[axiom_11]) ).
cnf(c_79,plain,
( rr(A,B)
| ~ rf(A,B) ),
inference(clausify,[status(thm)],[axiom_12]) ).
cnf(c_85,plain,
cd(sK0(i2003_11_14_17_21_4056)),
inference(resolve,[status(thm)],[c_78,c_57]) ).
cnf(c_86,plain,
rinvF(i2003_11_14_17_21_4056,sK0(i2003_11_14_17_21_4056)),
inference(resolve,[status(thm)],[c_78,c_56]) ).
cnf(c_91,plain,
cc(sK0(i2003_11_14_17_21_4056)),
inference(resolve,[status(thm)],[c_85,c_67]) ).
cnf(c_96,plain,
~ ra_Px1(sK0(i2003_11_14_17_21_4056),A),
inference(resolve,[status(thm)],[c_61,c_91]) ).
cnf(c_97,plain,
rf(sK0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056),
inference(resolve,[status(thm)],[c_86,c_73]) ).
cnf(c_110,plain,
~ ccxcomp(sK0(i2003_11_14_17_21_4056)),
inference(resolve,[status(thm)],[c_63,c_96]) ).
cnf(c_118,plain,
rr(sK0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056),
inference(resolve,[status(thm)],[c_97,c_79]) ).
cnf(c_127,plain,
rinvR(i2003_11_14_17_21_4056,sK0(i2003_11_14_17_21_4056)),
inference(resolve,[status(thm)],[c_118,c_76]) ).
cnf(c_251,plain,
( ca_Vx3(sK0(i2003_11_14_17_21_4056))
| ~ cUnsatisfiable(i2003_11_14_17_21_4056) ),
inference(resolve,[status(thm)],[c_127,c_55]) ).
cnf(c_144,plain,
ca_Vx3(sK0(i2003_11_14_17_21_4056)),
inference(resolve,[status(thm)],[c_78,c_251]) ).
cnf(c_147,plain,
cd(sK3(sK0(i2003_11_14_17_21_4056))),
inference(resolve,[status(thm)],[c_144,c_70]) ).
cnf(c_148,plain,
rinvF(sK0(i2003_11_14_17_21_4056),sK3(sK0(i2003_11_14_17_21_4056))),
inference(resolve,[status(thm)],[c_144,c_69]) ).
cnf(c_182,plain,
ccxcomp(sK2(sK3(sK0(i2003_11_14_17_21_4056)))),
inference(resolve,[status(thm)],[c_147,c_66]) ).
cnf(c_183,plain,
rf(sK3(sK0(i2003_11_14_17_21_4056)),sK2(sK3(sK0(i2003_11_14_17_21_4056)))),
inference(resolve,[status(thm)],[c_147,c_65]) ).
cnf(c_195,plain,
rf(sK3(sK0(i2003_11_14_17_21_4056)),sK0(i2003_11_14_17_21_4056)),
inference(resolve,[status(thm)],[c_148,c_73]) ).
cnf(c_203,plain,
( sK0(i2003_11_14_17_21_4056) = A
| ~ rf(sK3(sK0(i2003_11_14_17_21_4056)),A) ),
inference(resolve,[status(thm)],[c_195,c_72]) ).
cnf(c_252,plain,
( ccxcomp(A)
| A != sK2(sK3(sK0(i2003_11_14_17_21_4056))) ),
inference(resolve,[status(thm)],[c_35,c_182]) ).
cnf(c_253,plain,
sK0(i2003_11_14_17_21_4056) != sK2(sK3(sK0(i2003_11_14_17_21_4056))),
inference(resolve,[status(thm)],[c_252,c_110]) ).
cnf(c_247,plain,
sK2(sK3(sK0(i2003_11_14_17_21_4056))) != sK0(i2003_11_14_17_21_4056),
inference(copy,[status(thm)],[c_253]) ).
cnf(c_254,plain,
sK0(i2003_11_14_17_21_4056) = sK2(sK3(sK0(i2003_11_14_17_21_4056))),
inference(resolve,[status(thm)],[c_183,c_203]) ).
cnf(c_255,plain,
sK2(sK3(sK0(i2003_11_14_17_21_4056))) = sK0(i2003_11_14_17_21_4056),
inference(copy,[status(thm)],[c_254]) ).
cnf(c_250,plain,
$false,
inference(resolve,[status(thm)],[c_247,c_255]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS118+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 19:39:55 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.37 % Process 3574003 was started by sandbox on n006,
% 0.14/0.37 % Fri Sep 25 19:39:55 2026
% 0.14/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.42
% 0.14/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.42
% 0.14/0.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/0.42 % Length of proof is 43.
% 0.14/0.42 % Level of proof is 10.
% 0.14/0.42 % Maximum clause weight is 28.000.
% 0.14/0.42 % Given clauses 181.
% 0.14/0.42
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------