%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS108+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 : n009.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 07:46:03 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 16 unt; 0 def)
% Number of atoms : 150 ( 12 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 168 ( 63 ~; 62 |; 35 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 71 ( 1 sgn 45 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( cp2(X)
& ? [Y] :
( ca_Ax14(Y)
& rinvR(X,Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cp1(X)
=> ca_Cx1(X) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cp2(X)
<=> ? [Y0] : ra_Px5(X,Y0) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_6,axiom,
! [X] :
( cp2xcomp(X)
<=> ~ ? [Y] : ra_Px5(X,Y) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_15,axiom,
! [X] :
( ca_Ax14(X)
<=> ( ! [Y0,Y1] :
( ( rr(X,Y1)
& rr(X,Y0) )
=> Y0 = Y1 )
& ? [Y] :
( cp1(Y)
& rr(X,Y) ) ) ),
file('theBenchmark.p',axiom_15) ).
fof(axiom_16,axiom,
! [X] :
( ca_Cx1(X)
<=> ( cp4xcomp(X)
& cp3xcomp(X)
& cp5xcomp(X)
& cp2xcomp(X) ) ),
file('theBenchmark.p',axiom_16) ).
fof(axiom_25,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('theBenchmark.p',axiom_25) ).
fof(nnf_42,plain,
! [X] :
( ( ~ cp2(X)
| ! [Y] :
( ~ ca_Ax14(Y)
| ~ rinvR(X,Y) )
| cUnsatisfiable(X) )
& ( ( cp2(X)
& ? [X0] :
( ca_Ax14(X0)
& rinvR(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ~ cp2(X)
| ! [Y] :
( ~ ca_Ax14(Y)
| ~ rinvR(X,Y) )
| cUnsatisfiable(X) )
& ( ( cp2(X)
& ca_Ax14(sK0(X))
& rinvR(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(X))],[nnf_42]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( ~ cp2(VAR_0)
| ~ ca_Ax14(VAR_1)
| ~ rinvR(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp2(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ca_Ax14(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rinvR(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_109,plain,
( rinvR(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_110,plain,
( ca_Ax14(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_111,plain,
( cp2(A)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_113,plain,
( ca_Cx1(A)
| ~ cp1(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(nnf_44,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px5(X,Y0)
| cp2(X) )
& ( ? [X0] : ra_Px5(X,X0)
| ~ cp2(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(sk_axiom_4_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px5(X,Y0)
| cp2(X) )
& ( ra_Px5(X,sK1(X))
| ~ cp2(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1(X))],[nnf_44]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px5(VAR_0,VAR_1)
| cp2(VAR_0) )
& ! [VAR_0] :
( ra_Px5(VAR_0,sK1(VAR_0))
| ~ cp2(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_114,plain,
( ra_Px5(A,sK1(A))
| ~ cp2(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_117,plain,
( ~ ra_Px5(A,B)
| ~ cp2xcomp(A) ),
inference(clausify,[status(thm)],[axiom_6]) ).
fof(nnf_55,plain,
! [X] :
( ( ? [Y0,Y1] :
( Y1 != Y0
& rr(X,Y1)
& rr(X,Y0) )
| ! [Y] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ca_Ax14(X) )
& ( ( ! [X0,X2] :
( X2 = X0
| ~ rr(X,X2)
| ~ rr(X,X0) )
& ? [X1] :
( cp1(X1)
& rr(X,X1) ) )
| ~ ca_Ax14(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_15]) ).
fof(sk_axiom_15_sk,plain,
! [X] :
( ( ( sK5(X) != sK4(X)
& rr(X,sK5(X))
& rr(X,sK4(X)) )
| ! [Y] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ca_Ax14(X) )
& ( ( ! [X0,X2] :
( X2 = X0
| ~ rr(X,X2)
| ~ rr(X,X0) )
& cp1(sK2(X))
& rr(X,sK2(X)) )
| ~ ca_Ax14(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK4,sK5]),skolemize(X1,sK2(X)),skolemize(Y0,sK4(X)),skolemize(Y1,sK5(X))],[nnf_55]) ).
fof(sk_axiom_15,plain,
( ! [VAR_0,VAR_1] :
( sK5(VAR_0) != sK4(VAR_0)
| ~ cp1(VAR_1)
| ~ rr(VAR_0,VAR_1)
| ca_Ax14(VAR_0) )
& ! [VAR_0,VAR_1] :
( rr(VAR_0,sK5(VAR_0))
| ~ cp1(VAR_1)
| ~ rr(VAR_0,VAR_1)
| ca_Ax14(VAR_0) )
& ! [VAR_0,VAR_1] :
( rr(VAR_0,sK4(VAR_0))
| ~ cp1(VAR_1)
| ~ rr(VAR_0,VAR_1)
| ca_Ax14(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_1
| ~ rr(VAR_0,VAR_2)
| ~ rr(VAR_0,VAR_1)
| ~ ca_Ax14(VAR_0) )
& ! [VAR_0] :
( cp1(sK2(VAR_0))
| ~ ca_Ax14(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK2(VAR_0))
| ~ ca_Ax14(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_15_sk]) ).
cnf(c_133,plain,
( rr(A,sK2(A))
| ~ ca_Ax14(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_15]) ).
cnf(c_134,plain,
( cp1(sK2(A))
| ~ ca_Ax14(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_15]) ).
cnf(c_135,plain,
( C = B
| ~ rr(A,C)
| ~ rr(A,B)
| ~ ca_Ax14(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_15]) ).
cnf(c_139,plain,
( cp2xcomp(A)
| ~ ca_Cx1(A) ),
inference(clausify,[status(thm)],[axiom_16]) ).
cnf(c_163,plain,
( rr(B,A)
| ~ rinvR(A,B) ),
inference(clausify,[status(thm)],[axiom_25]) ).
fof(axiom_26,axiom,
cUnsatisfiable(i2003_11_14_17_21_04740),
file('theBenchmark.p',axiom_26) ).
cnf(c_165,plain,
cUnsatisfiable(i2003_11_14_17_21_04740),
inference(clausify,[status(thm)],[axiom_26]) ).
cnf(c_188,plain,
cp2(i2003_11_14_17_21_04740),
inference(resolve,[status(thm)],[c_165,c_111]) ).
cnf(c_189,plain,
ca_Ax14(sK0(i2003_11_14_17_21_04740)),
inference(resolve,[status(thm)],[c_165,c_110]) ).
cnf(c_190,plain,
rinvR(i2003_11_14_17_21_04740,sK0(i2003_11_14_17_21_04740)),
inference(resolve,[status(thm)],[c_165,c_109]) ).
cnf(c_193,plain,
ra_Px5(i2003_11_14_17_21_04740,sK1(i2003_11_14_17_21_04740)),
inference(resolve,[status(thm)],[c_188,c_114]) ).
cnf(c_208,plain,
cp1(sK2(sK0(i2003_11_14_17_21_04740))),
inference(resolve,[status(thm)],[c_189,c_134]) ).
cnf(c_209,plain,
rr(sK0(i2003_11_14_17_21_04740),sK2(sK0(i2003_11_14_17_21_04740))),
inference(resolve,[status(thm)],[c_189,c_133]) ).
cnf(c_222,plain,
rr(sK0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740),
inference(resolve,[status(thm)],[c_190,c_163]) ).
cnf(c_225,plain,
~ cp2xcomp(i2003_11_14_17_21_04740),
inference(resolve,[status(thm)],[c_193,c_117]) ).
cnf(c_234,plain,
ca_Cx1(sK2(sK0(i2003_11_14_17_21_04740))),
inference(resolve,[status(thm)],[c_208,c_113]) ).
cnf(c_277,plain,
( i2003_11_14_17_21_04740 = A
| ~ rr(sK0(i2003_11_14_17_21_04740),A)
| ~ ca_Ax14(sK0(i2003_11_14_17_21_04740)) ),
inference(resolve,[status(thm)],[c_222,c_135]) ).
cnf(c_239,plain,
( i2003_11_14_17_21_04740 = A
| ~ rr(sK0(i2003_11_14_17_21_04740),A) ),
inference(resolve,[status(thm)],[c_189,c_277]) ).
cnf(c_246,plain,
cp2xcomp(sK2(sK0(i2003_11_14_17_21_04740))),
inference(resolve,[status(thm)],[c_234,c_139]) ).
cnf(c_278,plain,
i2003_11_14_17_21_04740 = sK2(sK0(i2003_11_14_17_21_04740)),
inference(resolve,[status(thm)],[c_239,c_209]) ).
cnf(c_273,plain,
sK2(sK0(i2003_11_14_17_21_04740)) = i2003_11_14_17_21_04740,
inference(copy,[status(thm)],[c_278]) ).
cnf(c_279,plain,
cp2xcomp(i2003_11_14_17_21_04740),
inference(paramod,[status(thm)],[c_273,c_246]) ).
cnf(c_276,plain,
$false,
inference(resolve,[status(thm)],[c_225,c_279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS108+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n009.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 19:39:44 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 2369190 was started by sandbox on n009,
% 0.07/0.35 % Fri Sep 25 19:39:44 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.37
% 0.07/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.41
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.41
% 0.13/0.41 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.13/0.41 % Length of proof is 32.
% 0.13/0.41 % Level of proof is 6.
% 0.13/0.41 % Maximum clause weight is 11.000.
% 0.13/0.41 % Given clauses 178.
% 0.13/0.41
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------