%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS121+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 : n013.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 07:46:05 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 13 unt; 0 def)
% Number of atoms : 116 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 126 ( 51 ~; 44 |; 23 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 60 ( 2 sgn 35 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( cp1(X)
& ? [Y] :
( ca_Vx3(Y)
& rr(X,Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cp1(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cp1xcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X] :
( ca_Ax2(X)
<=> ( ! [Y] :
( rinvR(X,Y)
=> cp1xcomp(Y) )
& cp1(X) ) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( ca_Ax2(Y)
& rr(X,Y) ) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_9,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('theBenchmark.p',axiom_9) ).
fof(axiom_10,axiom,
! [X,Y,Z] :
( ( rr(Y,Z)
& rr(X,Y) )
=> rr(X,Z) ),
file('theBenchmark.p',axiom_10) ).
fof(nnf_22,plain,
! [X] :
( ( ~ cp1(X)
| ! [Y] :
( ~ ca_Vx3(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ( ( cp1(X)
& ? [X0] :
( ca_Vx3(X0)
& rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ~ cp1(X)
| ! [Y] :
( ~ ca_Vx3(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ( ( cp1(X)
& ca_Vx3(sK0(X))
& rr(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(X))],[nnf_22]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( ~ cp1(VAR_0)
| ~ ca_Vx3(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp1(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ca_Vx3(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_54,plain,
( rr(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_55,plain,
( ca_Vx3(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_56,plain,
( cp1(A)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_58,plain,
( ~ ra_Px1(A,B)
| ~ cp1(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(nnf_24,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ( ? [X0] : ra_Px1(X,X0)
| ~ cp1xcomp(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(sk_axiom_4_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ( ra_Px1(X,sK1(X))
| ~ cp1xcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1(X))],[nnf_24]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px1(VAR_0,VAR_1)
| cp1xcomp(VAR_0) )
& ! [VAR_0] :
( ra_Px1(VAR_0,sK1(VAR_0))
| ~ cp1xcomp(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_60,plain,
( ra_Px1(A,sK1(A))
| ~ cp1xcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_63,plain,
( cp1xcomp(B)
| ~ rinvR(A,B)
| ~ ca_Ax2(A) ),
inference(clausify,[status(thm)],[axiom_5]) ).
fof(nnf_26,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) )
| ca_Vx3(X) )
& ( ? [X0] :
( ca_Ax2(X0)
& rr(X,X0) )
| ~ ca_Vx3(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_6]) ).
fof(sk_axiom_6_sk,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) )
| ca_Vx3(X) )
& ( ( ca_Ax2(sK2(X))
& rr(X,sK2(X)) )
| ~ ca_Vx3(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2(X))],[nnf_26]) ).
fof(sk_axiom_6,plain,
( ! [VAR_0,VAR_1] :
( ~ ca_Ax2(VAR_1)
| ~ rr(VAR_0,VAR_1)
| ca_Vx3(VAR_0) )
& ! [VAR_0] :
( ca_Ax2(sK2(VAR_0))
| ~ ca_Vx3(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK2(VAR_0))
| ~ ca_Vx3(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_6_sk]) ).
cnf(c_66,plain,
( rr(A,sK2(A))
| ~ ca_Vx3(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_6]) ).
cnf(c_67,plain,
( ca_Ax2(sK2(A))
| ~ ca_Vx3(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_6]) ).
cnf(c_73,plain,
( ~ rr(B,A)
| rinvR(A,B) ),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_74,plain,
( rr(A,C)
| ~ rr(B,C)
| ~ rr(A,B) ),
inference(clausify,[status(thm)],[axiom_10]) ).
fof(axiom_11,axiom,
cUnsatisfiable(i2003_11_14_17_21_5199),
file('theBenchmark.p',axiom_11) ).
cnf(c_75,plain,
cUnsatisfiable(i2003_11_14_17_21_5199),
inference(clausify,[status(thm)],[axiom_11]) ).
cnf(c_80,plain,
cp1(i2003_11_14_17_21_5199),
inference(resolve,[status(thm)],[c_75,c_56]) ).
cnf(c_81,plain,
ca_Vx3(sK0(i2003_11_14_17_21_5199)),
inference(resolve,[status(thm)],[c_75,c_55]) ).
cnf(c_82,plain,
rr(i2003_11_14_17_21_5199,sK0(i2003_11_14_17_21_5199)),
inference(resolve,[status(thm)],[c_75,c_54]) ).
cnf(c_86,plain,
~ ra_Px1(i2003_11_14_17_21_5199,A),
inference(resolve,[status(thm)],[c_58,c_80]) ).
cnf(c_87,plain,
ca_Ax2(sK2(sK0(i2003_11_14_17_21_5199))),
inference(resolve,[status(thm)],[c_81,c_67]) ).
cnf(c_88,plain,
rr(sK0(i2003_11_14_17_21_5199),sK2(sK0(i2003_11_14_17_21_5199))),
inference(resolve,[status(thm)],[c_81,c_66]) ).
cnf(c_99,plain,
~ cp1xcomp(i2003_11_14_17_21_5199),
inference(resolve,[status(thm)],[c_60,c_86]) ).
cnf(c_123,plain,
( cp1xcomp(A)
| ~ rinvR(sK2(sK0(i2003_11_14_17_21_5199)),A) ),
inference(resolve,[status(thm)],[c_63,c_87]) ).
cnf(c_102,plain,
~ rinvR(sK2(sK0(i2003_11_14_17_21_5199)),i2003_11_14_17_21_5199),
inference(resolve,[status(thm)],[c_123,c_99]) ).
cnf(c_109,plain,
~ rr(i2003_11_14_17_21_5199,sK2(sK0(i2003_11_14_17_21_5199))),
inference(resolve,[status(thm)],[c_73,c_102]) ).
cnf(c_124,plain,
( rr(A,sK2(sK0(i2003_11_14_17_21_5199)))
| ~ rr(A,sK0(i2003_11_14_17_21_5199)) ),
inference(resolve,[status(thm)],[c_74,c_88]) ).
cnf(c_125,plain,
~ rr(i2003_11_14_17_21_5199,sK0(i2003_11_14_17_21_5199)),
inference(resolve,[status(thm)],[c_124,c_109]) ).
cnf(c_122,plain,
$false,
inference(resolve,[status(thm)],[c_82,c_125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS121+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 19:39:36 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 1031943 was started by sandbox on n013,
% 0.11/0.36 % Fri Sep 25 19:39:36 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.11/0.38
% 0.11/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.38
% 0.11/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/0.38 % Length of proof is 28.
% 0.11/0.38 % Level of proof is 7.
% 0.11/0.38 % Maximum clause weight is 9.000.
% 0.11/0.38 % Given clauses 66.
% 0.11/0.38
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------