%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS128+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 : n019.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 07:46:06 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 150 ( 60 ~; 58 |; 26 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 56 ( 1 sgn 35 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y] :
( rr(X,Y)
=> ca_Cx4(Y) )
& ! [Y] :
( rr(X,Y)
=> cd(Y) )
& ? [Y] :
( cexcomp(Y)
& rr(X,Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_8,axiom,
! [X] :
( ca_Cx4(X)
<=> ? [Y0] : ra_Px4(X,Y0) ),
file('theBenchmark.p',axiom_8) ).
fof(axiom_9,axiom,
! [X] :
( ca_Cx4xcomp(X)
<=> ~ ? [Y] : ra_Px4(X,Y) ),
file('theBenchmark.p',axiom_9) ).
fof(axiom_10,axiom,
! [X] :
( ca_Cx4xcomp(X)
<=> ( cexcomp(X)
& cd(X) ) ),
file('theBenchmark.p',axiom_10) ).
fof(nnf_3,plain,
! [X] :
( ( ? [Y] :
( ~ ca_Cx4(Y)
& rr(X,Y) )
| ? [X4] :
( ~ cd(X4)
& rr(X,X4) )
| ! [X3] :
( ~ cexcomp(X3)
| ~ rr(X,X3) )
| cUnsatisfiable(X) )
& ( ( ! [X2] :
( ca_Cx4(X2)
| ~ rr(X,X2) )
& ! [X1] :
( cd(X1)
| ~ rr(X,X1) )
& ? [X0] :
( cexcomp(X0)
& rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ( ~ ca_Cx4(sK3(X))
& rr(X,sK3(X)) )
| ( ~ cd(sK2(X))
& rr(X,sK2(X)) )
| ! [X3] :
( ~ cexcomp(X3)
| ~ rr(X,X3) )
| cUnsatisfiable(X) )
& ( ( ! [X2] :
( ca_Cx4(X2)
| ~ rr(X,X2) )
& ! [X1] :
( cd(X1)
| ~ rr(X,X1) )
& cexcomp(sK0(X))
& rr(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK3]),skolemize(X0,sK0(X)),skolemize(X4,sK2(X)),skolemize(Y,sK3(X))],[nnf_3]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( ~ ca_Cx4(sK3(VAR_0))
| ~ cd(sK2(VAR_0))
| ~ cexcomp(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( rr(VAR_0,sK3(VAR_0))
| ~ cd(sK2(VAR_0))
| ~ cexcomp(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ ca_Cx4(sK3(VAR_0))
| rr(VAR_0,sK2(VAR_0))
| ~ cexcomp(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( rr(VAR_0,sK3(VAR_0))
| rr(VAR_0,sK2(VAR_0))
| ~ cexcomp(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ca_Cx4(VAR_1)
| ~ rr(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cd(VAR_1)
| ~ rr(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cexcomp(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_14,plain,
( ca_Cx4(B)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
fof(axiom_11,axiom,
cUnsatisfiable(i2003_11_14_17_22_31584),
file('theBenchmark.p',axiom_11) ).
cnf(c_19,plain,
cUnsatisfiable(i2003_11_14_17_22_31584),
inference(clausify,[status(thm)],[axiom_11]) ).
cnf(c_20,plain,
( cd(B)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_21,plain,
( cexcomp(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_22,plain,
( rr(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_27,plain,
( ~ ra_Px4(A,B)
| ~ ca_Cx4xcomp(A) ),
inference(clausify,[status(thm)],[axiom_9]) ).
fof(nnf_9,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px4(X,Y0)
| ca_Cx4(X) )
& ( ? [X4] : ra_Px4(X,X4)
| ~ ca_Cx4(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_8]) ).
fof(sk_axiom_8_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px4(X,Y0)
| ca_Cx4(X) )
& ( ra_Px4(X,sK1(X))
| ~ ca_Cx4(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X4,sK1(X))],[nnf_9]) ).
fof(sk_axiom_8,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px4(VAR_0,VAR_1)
| ca_Cx4(VAR_0) )
& ! [VAR_0] :
( ra_Px4(VAR_0,sK1(VAR_0))
| ~ ca_Cx4(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_8_sk]) ).
cnf(c_30,plain,
( ra_Px4(A,sK1(A))
| ~ ca_Cx4(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_8]) ).
cnf(c_32,plain,
( ~ ca_Cx4xcomp(A)
| ~ ca_Cx4(A) ),
inference(resolve,[status(thm)],[c_30,c_27]) ).
cnf(c_35,plain,
( ~ cexcomp(A)
| ~ cd(A)
| ca_Cx4xcomp(A) ),
inference(clausify,[status(thm)],[axiom_10]) ).
cnf(c_36,plain,
( ~ ca_Cx4(A)
| ~ cexcomp(A)
| ~ cd(A) ),
inference(resolve,[status(thm)],[c_35,c_32]) ).
cnf(c_48,plain,
( ca_Cx4(A)
| ~ rr(i2003_11_14_17_22_31584,A) ),
inference(resolve,[status(thm)],[c_14,c_19]) ).
cnf(c_53,plain,
( cd(A)
| ~ rr(i2003_11_14_17_22_31584,A) ),
inference(resolve,[status(thm)],[c_20,c_19]) ).
cnf(c_58,plain,
cexcomp(sK0(i2003_11_14_17_22_31584)),
inference(resolve,[status(thm)],[c_21,c_19]) ).
cnf(c_63,plain,
rr(i2003_11_14_17_22_31584,sK0(i2003_11_14_17_22_31584)),
inference(resolve,[status(thm)],[c_22,c_19]) ).
cnf(c_74,plain,
cd(sK0(i2003_11_14_17_22_31584)),
inference(resolve,[status(thm)],[c_63,c_53]) ).
cnf(c_75,plain,
ca_Cx4(sK0(i2003_11_14_17_22_31584)),
inference(resolve,[status(thm)],[c_63,c_48]) ).
cnf(c_79,plain,
( ~ ca_Cx4(sK0(i2003_11_14_17_22_31584))
| ~ cexcomp(sK0(i2003_11_14_17_22_31584)) ),
inference(resolve,[status(thm)],[c_36,c_74]) ).
cnf(c_80,plain,
~ ca_Cx4(sK0(i2003_11_14_17_22_31584)),
inference(resolve,[status(thm)],[c_79,c_58]) ).
cnf(c_78,plain,
$false,
inference(resolve,[status(thm)],[c_75,c_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS128+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 : n019.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 19:40:49 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3496257 was started by sandbox2 on n019,
% 0.09/0.37 % Fri Sep 25 19:40:49 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 21.
% 0.09/0.39 % Level of proof is 4.
% 0.09/0.39 % Maximum clause weight is 6.000.
% 0.09/0.39 % Given clauses 39.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------