%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS127+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 : n007.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 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 12 unt; 0 def)
% Number of atoms : 131 ( 14 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 160 ( 64 ~; 60 |; 30 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 68 ( 2 sgn 41 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cdxcomp_substitution_1,axiom,
! [A,B] :
( ( cdxcomp(A)
& A = B )
=> cdxcomp(B) ),
file('theBenchmark.p',cdxcomp_substitution_1) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y0,Y1] :
( ( rr(X,Y1)
& rr(X,Y0) )
=> Y0 = Y1 )
& ? [Y] :
( cd(Y)
& rr(X,Y) )
& ? [Y] :
( cc(Y)
& rr(X,Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cc(X)
=> cdxcomp(X) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cd(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X] :
( cdxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('theBenchmark.p',axiom_5) ).
cnf(c_22,plain,
( cdxcomp(A)
| ~ cdxcomp(B)
| A != B ),
inference(clausify,[status(thm)],[cdxcomp_substitution_1]) ).
fof(nnf_15,plain,
! [X] :
( ( ? [Y0,Y1] :
( Y1 != Y0
& rr(X,Y1)
& rr(X,Y0) )
| ! [Y] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ! [X4] :
( ~ cc(X4)
| ~ rr(X,X4) )
| cUnsatisfiable(X) )
& ( ( ! [X2,X3] :
( X3 = X2
| ~ rr(X,X3)
| ~ rr(X,X2) )
& ? [X1] :
( cd(X1)
& rr(X,X1) )
& ? [X0] :
( cc(X0)
& rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ( sK4(X) != sK3(X)
& rr(X,sK4(X))
& rr(X,sK3(X)) )
| ! [Y] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ! [X4] :
( ~ cc(X4)
| ~ rr(X,X4) )
| cUnsatisfiable(X) )
& ( ( ! [X2,X3] :
( X3 = X2
| ~ rr(X,X3)
| ~ rr(X,X2) )
& cd(sK1(X))
& rr(X,sK1(X))
& cc(sK0(X))
& rr(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3,sK4]),skolemize(X0,sK0(X)),skolemize(X1,sK1(X)),skolemize(Y0,sK3(X)),skolemize(Y1,sK4(X))],[nnf_15]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( sK4(VAR_0) != sK3(VAR_0)
| ~ cd(VAR_2)
| ~ rr(VAR_0,VAR_2)
| ~ cc(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( rr(VAR_0,sK4(VAR_0))
| ~ cd(VAR_2)
| ~ rr(VAR_0,VAR_2)
| ~ cc(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( rr(VAR_0,sK3(VAR_0))
| ~ cd(VAR_2)
| ~ rr(VAR_0,VAR_2)
| ~ cc(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_1
| ~ rr(VAR_0,VAR_2)
| ~ rr(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cd(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cc(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_35,plain,
( rr(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_36,plain,
( cc(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_37,plain,
( rr(A,sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_38,plain,
( cd(sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_39,plain,
( C = B
| ~ rr(A,C)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_43,plain,
( cdxcomp(A)
| ~ cc(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_44,plain,
( ~ ra_Px1(A,B)
| ~ cd(A) ),
inference(clausify,[status(thm)],[axiom_4]) ).
fof(nnf_18,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ( ? [X4] : ra_Px1(X,X4)
| ~ cdxcomp(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_5]) ).
fof(sk_axiom_5_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ( ra_Px1(X,sK2(X))
| ~ cdxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X4,sK2(X))],[nnf_18]) ).
fof(sk_axiom_5,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px1(VAR_0,VAR_1)
| cdxcomp(VAR_0) )
& ! [VAR_0] :
( ra_Px1(VAR_0,sK2(VAR_0))
| ~ cdxcomp(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_5_sk]) ).
cnf(c_46,plain,
( ra_Px1(A,sK2(A))
| ~ cdxcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_5]) ).
fof(axiom_6,axiom,
cUnsatisfiable(i2003_11_14_17_22_27794),
file('theBenchmark.p',axiom_6) ).
cnf(c_48,plain,
cUnsatisfiable(i2003_11_14_17_22_27794),
inference(clausify,[status(thm)],[axiom_6]) ).
cnf(c_56,plain,
cd(sK1(i2003_11_14_17_22_27794)),
inference(resolve,[status(thm)],[c_48,c_38]) ).
cnf(c_57,plain,
rr(i2003_11_14_17_22_27794,sK1(i2003_11_14_17_22_27794)),
inference(resolve,[status(thm)],[c_48,c_37]) ).
cnf(c_58,plain,
cc(sK0(i2003_11_14_17_22_27794)),
inference(resolve,[status(thm)],[c_48,c_36]) ).
cnf(c_59,plain,
rr(i2003_11_14_17_22_27794,sK0(i2003_11_14_17_22_27794)),
inference(resolve,[status(thm)],[c_48,c_35]) ).
cnf(c_62,plain,
~ ra_Px1(sK1(i2003_11_14_17_22_27794),A),
inference(resolve,[status(thm)],[c_44,c_56]) ).
cnf(c_63,plain,
cdxcomp(sK0(i2003_11_14_17_22_27794)),
inference(resolve,[status(thm)],[c_58,c_43]) ).
cnf(c_69,plain,
~ cdxcomp(sK1(i2003_11_14_17_22_27794)),
inference(resolve,[status(thm)],[c_46,c_62]) ).
cnf(c_76,plain,
( cdxcomp(A)
| A != sK0(i2003_11_14_17_22_27794) ),
inference(resolve,[status(thm)],[c_22,c_63]) ).
cnf(c_71,plain,
sK1(i2003_11_14_17_22_27794) != sK0(i2003_11_14_17_22_27794),
inference(resolve,[status(thm)],[c_76,c_69]) ).
cnf(c_77,plain,
( B = A
| ~ rr(i2003_11_14_17_22_27794,B)
| ~ rr(i2003_11_14_17_22_27794,A) ),
inference(resolve,[status(thm)],[c_39,c_48]) ).
cnf(c_78,plain,
( sK1(i2003_11_14_17_22_27794) = A
| ~ rr(i2003_11_14_17_22_27794,A) ),
inference(resolve,[status(thm)],[c_77,c_57]) ).
cnf(c_79,plain,
~ rr(i2003_11_14_17_22_27794,sK0(i2003_11_14_17_22_27794)),
inference(resolve,[status(thm)],[c_78,c_71]) ).
cnf(c_75,plain,
$false,
inference(resolve,[status(thm)],[c_59,c_79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS127+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % 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 19:38:41 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 1701609 was started by sandbox2 on n007,
% 0.09/0.38 % Fri Sep 25 19:38:41 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.40 % Length of proof is 24.
% 0.09/0.40 % Level of proof is 6.
% 0.09/0.40 % Maximum clause weight is 11.000.
% 0.09/0.40 % Given clauses 42.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------