%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS123+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 0.20s 0.46s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 8 unt; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 14 ~; 11 |; 4 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 21 ( 2 sgn 11 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( cd(X)
& cc(X) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cc(X)
=> cdxcomp(X) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_6,axiom,
! [X] :
( cd(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_7,axiom,
! [X] :
( cdxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('theBenchmark.p',axiom_7) ).
cnf(c_15,plain,
( cd(A)
| ~ cUnsatisfiable(A) ),
inference(clausify,[status(thm)],[axiom_2]) ).
fof(axiom_12,axiom,
cUnsatisfiable(i2003_11_14_17_22_02803),
file('theBenchmark.p',axiom_12) ).
cnf(c_17,plain,
cUnsatisfiable(i2003_11_14_17_22_02803),
inference(clausify,[status(thm)],[axiom_12]) ).
cnf(c_18,plain,
( cc(A)
| ~ cUnsatisfiable(A) ),
inference(clausify,[status(thm)],[axiom_2]) ).
cnf(c_19,plain,
( cdxcomp(A)
| ~ cc(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_20,plain,
cc(i2003_11_14_17_22_02803),
inference(resolve,[status(thm)],[c_18,c_17]) ).
cnf(c_22,plain,
( ~ ra_Px1(A,B)
| ~ cd(A) ),
inference(clausify,[status(thm)],[axiom_6]) ).
cnf(c_25,plain,
cd(i2003_11_14_17_22_02803),
inference(resolve,[status(thm)],[c_15,c_17]) ).
fof(nnf_8,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ( ? [X0] : ra_Px1(X,X0)
| ~ cdxcomp(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_7]) ).
fof(sk_axiom_7_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ( ra_Px1(X,sK0(X))
| ~ cdxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(X))],[nnf_8]) ).
fof(sk_axiom_7,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px1(VAR_0,VAR_1)
| cdxcomp(VAR_0) )
& ! [VAR_0] :
( ra_Px1(VAR_0,sK0(VAR_0))
| ~ cdxcomp(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_7_sk]) ).
cnf(c_27,plain,
( ra_Px1(A,sK0(A))
| ~ cdxcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_7]) ).
cnf(c_28,plain,
cdxcomp(i2003_11_14_17_22_02803),
inference(resolve,[status(thm)],[c_19,c_20]) ).
cnf(c_35,plain,
~ ra_Px1(i2003_11_14_17_22_02803,A),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_38,plain,
ra_Px1(i2003_11_14_17_22_02803,sK0(i2003_11_14_17_22_02803)),
inference(resolve,[status(thm)],[c_28,c_27]) ).
cnf(c_39,plain,
$false,
inference(resolve,[status(thm)],[c_38,c_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KRS123+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.43 % Computer : n018.cluster.edu
% 0.20/0.43 % Model : x86_64 x86_64
% 0.20/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.43 % Memory : 8046.5625MB
% 0.20/0.43 % OS : Linux 6.8.0-71-generic
% 0.20/0.43 % CPULimit : 300
% 0.20/0.43 % WCLimit : 300
% 0.20/0.43 % DateTime : Fri Sep 25 19:42:35 UTC 2026
% 0.20/0.44 % CPUTime :
% 0.20/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.44 % Process 2679658 was started by sandbox2 on n018,
% 0.20/0.44 % Fri Sep 25 19:42:35 2026
% 0.20/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.45
% 0.20/0.45 % From the command line: assign(max_seconds, 300).
% 0.20/0.46
% 0.20/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.46
% 0.20/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.20/0.46 % Length of proof is 16.
% 0.20/0.46 % Level of proof is 5.
% 0.20/0.46 % Maximum clause weight is 4.000.
% 0.20/0.46 % Given clauses 0.
% 0.20/0.46
% 0.20/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------