%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS100+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 : n020.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 07:46:02 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 7 unt; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 41 ( 5 avg)
% Number of connectives : 139 ( 51 ~; 59 |; 26 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 41 ( 0 sgn 29 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( ~ ce(Y)
& rr(X,Y) )
& ! [Y] :
( rr(X,Y)
=> cd(Y) )
& ! [Y] :
( rr(X,Y)
=> ( ~ cd(Y)
| ce(Y) ) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(nnf_3,plain,
! [X] :
( ( ! [Y] :
( ce(Y)
| ~ rr(X,Y) )
| ? [X4] :
( ~ cd(X4)
& rr(X,X4) )
| ? [X3] :
( cd(X3)
& ~ ce(X3)
& rr(X,X3) )
| cUnsatisfiable(X) )
& ( ( ? [X2] :
( ~ ce(X2)
& rr(X,X2) )
& ! [X1] :
( cd(X1)
| ~ rr(X,X1) )
& ! [X0] :
( ~ cd(X0)
| ce(X0)
| ~ rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ce(Y)
| ~ rr(X,Y) )
| ( ~ cd(sK2(X))
& rr(X,sK2(X)) )
| ( cd(sK1(X))
& ~ ce(sK1(X))
& rr(X,sK1(X)) )
| cUnsatisfiable(X) )
& ( ( ~ ce(sK0(X))
& rr(X,sK0(X))
& ! [X1] :
( cd(X1)
| ~ rr(X,X1) )
& ! [X0] :
( ~ cd(X0)
| ce(X0)
| ~ rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X)),skolemize(X3,sK1(X)),skolemize(X4,sK2(X))],[nnf_3]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( ce(VAR_1)
| ~ rr(VAR_0,VAR_1)
| ~ cd(sK2(VAR_0))
| cd(sK1(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ce(VAR_1)
| ~ rr(VAR_0,VAR_1)
| rr(VAR_0,sK2(VAR_0))
| cd(sK1(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ce(VAR_1)
| ~ rr(VAR_0,VAR_1)
| ~ cd(sK2(VAR_0))
| ~ ce(sK1(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ce(VAR_1)
| ~ rr(VAR_0,VAR_1)
| rr(VAR_0,sK2(VAR_0))
| ~ ce(sK1(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ce(VAR_1)
| ~ rr(VAR_0,VAR_1)
| ~ cd(sK2(VAR_0))
| rr(VAR_0,sK1(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ce(VAR_1)
| ~ rr(VAR_0,VAR_1)
| rr(VAR_0,sK2(VAR_0))
| rr(VAR_0,sK1(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ~ ce(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cd(VAR_1)
| ~ rr(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ cd(VAR_1)
| ce(VAR_1)
| ~ rr(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_7,plain,
( ~ ce(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
fof(axiom_4,axiom,
cUnsatisfiable(i2003_11_14_17_20_32704),
file('theBenchmark.p',axiom_4) ).
cnf(c_14,plain,
cUnsatisfiable(i2003_11_14_17_20_32704),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_15,plain,
( rr(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_16,plain,
( cd(B)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_17,plain,
( ~ cd(B)
| ce(B)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_24,plain,
~ ce(sK0(i2003_11_14_17_20_32704)),
inference(resolve,[status(thm)],[c_7,c_14]) ).
cnf(c_31,plain,
rr(i2003_11_14_17_20_32704,sK0(i2003_11_14_17_20_32704)),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_38,plain,
( cd(A)
| ~ rr(i2003_11_14_17_20_32704,A) ),
inference(resolve,[status(thm)],[c_16,c_14]) ).
cnf(c_45,plain,
( ~ cd(A)
| ce(A)
| ~ rr(i2003_11_14_17_20_32704,A) ),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_74,plain,
cd(sK0(i2003_11_14_17_20_32704)),
inference(resolve,[status(thm)],[c_38,c_31]) ).
cnf(c_76,plain,
( ~ cd(sK0(i2003_11_14_17_20_32704))
| ce(sK0(i2003_11_14_17_20_32704)) ),
inference(resolve,[status(thm)],[c_45,c_31]) ).
cnf(c_77,plain,
~ cd(sK0(i2003_11_14_17_20_32704)),
inference(resolve,[status(thm)],[c_24,c_76]) ).
cnf(c_75,plain,
$false,
inference(resolve,[status(thm)],[c_74,c_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS100+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 19:40:18 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3599464 was started by sandbox on n020,
% 0.08/0.36 % Fri Sep 25 19:40:18 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.38 % Length of proof is 12.
% 0.08/0.38 % Level of proof is 4.
% 0.08/0.38 % Maximum clause weight is 7.000.
% 0.08/0.38 % Given clauses 22.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------