%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS124+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 : n002.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 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 6 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 120 ( 50 ~; 46 |; 18 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 56 ( 4 sgn 27 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y] :
( rr(X,Y)
=> ca_Ax3(Y) )
& ? [Y] :
( cowlThing(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_6,axiom,
! [X] :
( cd(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_7,axiom,
! [X] :
( cdxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('theBenchmark.p',axiom_7) ).
fof(axiom_12,axiom,
! [X] :
( ca_Ax3(X)
<=> ( cc(X)
& cd(X) ) ),
file('theBenchmark.p',axiom_12) ).
cnf(c_23,plain,
( cc(A)
| ~ ca_Ax3(A) ),
inference(clausify,[status(thm)],[axiom_12]) ).
cnf(c_24,plain,
( cd(A)
| ~ ca_Ax3(A) ),
inference(clausify,[status(thm)],[axiom_12]) ).
fof(nnf_3,plain,
! [X] :
( ( ? [Y] :
( ~ ca_Ax3(Y)
& rr(X,Y) )
| ! [X2] :
( ~ cowlThing(X2)
| ~ rr(X,X2) )
| cUnsatisfiable(X) )
& ( ( ! [X1] :
( ca_Ax3(X1)
| ~ rr(X,X1) )
& ? [X0] :
( cowlThing(X0)
& rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ( ~ ca_Ax3(sK2(X))
& rr(X,sK2(X)) )
| ! [X2] :
( ~ cowlThing(X2)
| ~ rr(X,X2) )
| cUnsatisfiable(X) )
& ( ( ! [X1] :
( ca_Ax3(X1)
| ~ rr(X,X1) )
& cowlThing(sK1(X))
& rr(X,sK1(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1(X)),skolemize(Y,sK2(X))],[nnf_3]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( ~ ca_Ax3(sK2(VAR_0))
| ~ cowlThing(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( rr(VAR_0,sK2(VAR_0))
| ~ cowlThing(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ca_Ax3(VAR_1)
| ~ rr(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cowlThing(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_25,plain,
( ca_Ax3(B)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_27,plain,
( cc(B)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(resolve,[status(thm)],[c_25,c_23]) ).
cnf(c_29,plain,
( cdxcomp(A)
| ~ cc(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(nnf_8,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ( ? [X2] : ra_Px1(X,X2)
| ~ cdxcomp(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_7]) ).
fof(sk_axiom_7_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ( ra_Px1(X,sK0(X))
| ~ cdxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X))],[nnf_8]) ).
fof(sk_axiom_7,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px1(VAR_0,VAR_1)
| cdxcomp(VAR_0) )
& ! [VAR_0] :
( ra_Px1(VAR_0,sK0(VAR_0))
| ~ cdxcomp(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_7_sk]) ).
cnf(c_31,plain,
( ra_Px1(A,sK0(A))
| ~ cdxcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_7]) ).
cnf(c_33,plain,
( ~ rr(B,A)
| ~ cUnsatisfiable(B)
| cdxcomp(A) ),
inference(resolve,[status(thm)],[c_29,c_27]) ).
cnf(c_44,plain,
( ~ ra_Px1(A,B)
| ~ cd(A) ),
inference(clausify,[status(thm)],[axiom_6]) ).
cnf(c_45,plain,
( cd(B)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(resolve,[status(thm)],[c_25,c_24]) ).
cnf(c_46,plain,
( ~ ra_Px1(B,C)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(resolve,[status(thm)],[c_45,c_44]) ).
cnf(c_49,plain,
( ~ rr(B,A)
| ~ cUnsatisfiable(B)
| ra_Px1(A,sK0(A)) ),
inference(resolve,[status(thm)],[c_31,c_33]) ).
cnf(c_52,plain,
( rr(A,sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
fof(axiom_13,axiom,
cUnsatisfiable(i2003_11_14_17_22_10903),
file('theBenchmark.p',axiom_13) ).
cnf(c_53,plain,
cUnsatisfiable(i2003_11_14_17_22_10903),
inference(clausify,[status(thm)],[axiom_13]) ).
cnf(c_57,plain,
rr(i2003_11_14_17_22_10903,sK1(i2003_11_14_17_22_10903)),
inference(resolve,[status(thm)],[c_53,c_52]) ).
cnf(c_61,plain,
( ~ cUnsatisfiable(i2003_11_14_17_22_10903)
| ra_Px1(sK1(i2003_11_14_17_22_10903),sK0(sK1(i2003_11_14_17_22_10903))) ),
inference(resolve,[status(thm)],[c_57,c_49]) ).
cnf(c_58,plain,
ra_Px1(sK1(i2003_11_14_17_22_10903),sK0(sK1(i2003_11_14_17_22_10903))),
inference(resolve,[status(thm)],[c_53,c_61]) ).
cnf(c_62,plain,
( ~ ra_Px1(A,B)
| ~ rr(i2003_11_14_17_22_10903,A) ),
inference(resolve,[status(thm)],[c_46,c_53]) ).
cnf(c_59,plain,
~ ra_Px1(sK1(i2003_11_14_17_22_10903),A),
inference(resolve,[status(thm)],[c_62,c_57]) ).
cnf(c_60,plain,
$false,
inference(resolve,[status(thm)],[c_59,c_58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS124+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 : n002.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 19:43:04 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 3972582 was started by sandbox on n002,
% 0.12/0.36 % Fri Sep 25 19:43:04 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.12/0.38
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.38
% 0.12/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.38 % Length of proof is 22.
% 0.12/0.38 % Level of proof is 6.
% 0.12/0.38 % Maximum clause weight is 9.000.
% 0.12/0.38 % Given clauses 11.
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------