%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS126+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 : n010.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 0.02s 0.38s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 7 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 13 ~; 10 |; 3 &)
% ( 2 <=>; 2 =>; 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 : 20 ( 2 sgn 11 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
=> cd1xcomp(X) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cUnsatisfiable(X)
=> cd1(X) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_7,axiom,
! [X] :
( cd1(X)
<=> ? [Y0] : ra_Px2(X,Y0) ),
file('theBenchmark.p',axiom_7) ).
fof(axiom_8,axiom,
! [X] :
( cd1xcomp(X)
<=> ~ ? [Y] : ra_Px2(X,Y) ),
file('theBenchmark.p',axiom_8) ).
cnf(c_14,plain,
( cd1(A)
| ~ cUnsatisfiable(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(axiom_11,axiom,
cUnsatisfiable(i2003_11_14_17_22_23554),
file('theBenchmark.p',axiom_11) ).
cnf(c_15,plain,
cUnsatisfiable(i2003_11_14_17_22_23554),
inference(clausify,[status(thm)],[axiom_11]) ).
cnf(c_16,plain,
( cd1xcomp(A)
| ~ cUnsatisfiable(A) ),
inference(clausify,[status(thm)],[axiom_2]) ).
cnf(c_17,plain,
( ~ ra_Px2(A,B)
| ~ cd1xcomp(A) ),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_18,plain,
cd1xcomp(i2003_11_14_17_22_23554),
inference(resolve,[status(thm)],[c_16,c_15]) ).
fof(nnf_8,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px2(X,Y0)
| cd1(X) )
& ( ? [X0] : ra_Px2(X,X0)
| ~ cd1(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_7]) ).
fof(sk_axiom_7_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px2(X,Y0)
| cd1(X) )
& ( ra_Px2(X,sK0(X))
| ~ cd1(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_Px2(VAR_0,VAR_1)
| cd1(VAR_0) )
& ! [VAR_0] :
( ra_Px2(VAR_0,sK0(VAR_0))
| ~ cd1(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_7_sk]) ).
cnf(c_20,plain,
( ra_Px2(A,sK0(A))
| ~ cd1(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_7]) ).
cnf(c_22,plain,
cd1(i2003_11_14_17_22_23554),
inference(resolve,[status(thm)],[c_14,c_15]) ).
cnf(c_33,plain,
~ ra_Px2(i2003_11_14_17_22_23554,A),
inference(resolve,[status(thm)],[c_17,c_18]) ).
cnf(c_35,plain,
ra_Px2(i2003_11_14_17_22_23554,sK0(i2003_11_14_17_22_23554)),
inference(resolve,[status(thm)],[c_22,c_20]) ).
cnf(c_36,plain,
$false,
inference(resolve,[status(thm)],[c_35,c_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS126+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.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 19:40:44 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.36 % Process 1488070 was started by sandbox on n010,
% 0.02/0.36 % Fri Sep 25 19:40:44 2026
% 0.02/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.36
% 0.02/0.36 % From the command line: assign(max_seconds, 300).
% 0.02/0.38
% 0.02/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.02/0.38
% 0.02/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.02/0.38 % Length of proof is 14.
% 0.02/0.38 % Level of proof is 4.
% 0.02/0.38 % Maximum clause weight is 4.000.
% 0.02/0.38 % Given clauses 0.
% 0.02/0.38
% 0.02/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------