%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS068+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 : n016.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 07:45:58 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 13 ~; 11 |; 3 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 17 ( 0 sgn 10 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
=> cc(X) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cUnsatisfiable(X)
=> ~ cd(X) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cc(X)
=> ! [Y] :
( rr(X,Y)
=> cc(Y) ) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_6,axiom,
! [X] :
( ! [Y] :
( rr(X,Y)
=> cc(Y) )
=> cd(X) ),
file('theBenchmark.p',axiom_6) ).
cnf(c_9,plain,
( ~ cd(A)
| ~ cUnsatisfiable(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(axiom_5,axiom,
cUnsatisfiable(i2003_11_14_17_18_23845),
file('theBenchmark.p',axiom_5) ).
cnf(c_10,plain,
cUnsatisfiable(i2003_11_14_17_18_23845),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_11,plain,
( cc(A)
| ~ cUnsatisfiable(A) ),
inference(clausify,[status(thm)],[axiom_2]) ).
fof(nnf_6,plain,
! [X] :
( cd(X)
| ? [Y] :
( ~ cc(Y)
& rr(X,Y) ) ),
inference(fof_nnf,[status(thm)],[axiom_6]) ).
fof(sk_axiom_6_sk,plain,
! [X] :
( cd(X)
| ( ~ cc(sK0(X))
& rr(X,sK0(X)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y,sK0(X))],[nnf_6]) ).
fof(sk_axiom_6,plain,
( ! [VAR_0] :
( cd(VAR_0)
| ~ cc(sK0(VAR_0)) )
& ! [VAR_0] :
( cd(VAR_0)
| rr(VAR_0,sK0(VAR_0)) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_6_sk]) ).
cnf(c_12,plain,
( cd(A)
| rr(A,sK0(A)) ),
inference(split_conjunct,[status(thm)],[sk_axiom_6]) ).
cnf(c_13,plain,
~ cd(i2003_11_14_17_18_23845),
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_14,plain,
( cd(A)
| ~ cc(sK0(A)) ),
inference(split_conjunct,[status(thm)],[sk_axiom_6]) ).
cnf(c_15,plain,
( cc(B)
| ~ rr(A,B)
| ~ cc(A) ),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_16,plain,
rr(i2003_11_14_17_18_23845,sK0(i2003_11_14_17_18_23845)),
inference(resolve,[status(thm)],[c_12,c_13]) ).
cnf(c_17,plain,
( cc(sK0(i2003_11_14_17_18_23845))
| ~ cc(i2003_11_14_17_18_23845) ),
inference(resolve,[status(thm)],[c_15,c_16]) ).
cnf(c_18,plain,
cc(i2003_11_14_17_18_23845),
inference(resolve,[status(thm)],[c_11,c_10]) ).
cnf(c_19,plain,
~ cc(sK0(i2003_11_14_17_18_23845)),
inference(resolve,[status(thm)],[c_14,c_13]) ).
cnf(c_20,plain,
cc(sK0(i2003_11_14_17_18_23845)),
inference(resolve,[status(thm)],[c_17,c_18]) ).
cnf(c_21,plain,
$false,
inference(resolve,[status(thm)],[c_20,c_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS068+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 19:42:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3122499 was started by sandbox2 on n016,
% 0.09/0.36 % Fri Sep 25 19:42:30 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 17.
% 0.09/0.38 % Level of proof is 6.
% 0.09/0.38 % Maximum clause weight is 5.000.
% 0.09/0.38 % Given clauses 2.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------