%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS110+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 07:46:03 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 95 ( 37 ~; 34 |; 19 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 42 ( 2 sgn 26 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y] :
( rs(X,Y)
=> cpxcomp(Y) )
& ? [Y] :
( ca_Ax2(Y)
& rs(X,Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cp(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cpxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X] :
( ca_Ax2(X)
<=> ( ? [Y] :
( cp(Y)
& rinvS(X,Y) )
& cp(X) ) ),
file('theBenchmark.p',axiom_5) ).
fof(nnf_25,plain,
! [X] :
( ( ? [Y] :
( ~ cpxcomp(Y)
& rs(X,Y) )
| ! [X2] :
( ~ ca_Ax2(X2)
| ~ rs(X,X2) )
| cUnsatisfiable(X) )
& ( ( ! [X1] :
( cpxcomp(X1)
| ~ rs(X,X1) )
& ? [X0] :
( ca_Ax2(X0)
& rs(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ( ~ cpxcomp(sK2(X))
& rs(X,sK2(X)) )
| ! [X2] :
( ~ ca_Ax2(X2)
| ~ rs(X,X2) )
| cUnsatisfiable(X) )
& ( ( ! [X1] :
( cpxcomp(X1)
| ~ rs(X,X1) )
& ca_Ax2(sK0(X))
& rs(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2]),skolemize(X0,sK0(X)),skolemize(Y,sK2(X))],[nnf_25]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( ~ cpxcomp(sK2(VAR_0))
| ~ ca_Ax2(VAR_1)
| ~ rs(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( rs(VAR_0,sK2(VAR_0))
| ~ ca_Ax2(VAR_1)
| ~ rs(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cpxcomp(VAR_1)
| ~ rs(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ca_Ax2(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rs(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_63,plain,
( rs(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_64,plain,
( ca_Ax2(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_65,plain,
( cpxcomp(B)
| ~ rs(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_68,plain,
( ~ ra_Px1(A,B)
| ~ cp(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(nnf_27,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ( ? [X2] : ra_Px1(X,X2)
| ~ cpxcomp(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(sk_axiom_4_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ( ra_Px1(X,sK1(X))
| ~ cpxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X))],[nnf_27]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px1(VAR_0,VAR_1)
| cpxcomp(VAR_0) )
& ! [VAR_0] :
( ra_Px1(VAR_0,sK1(VAR_0))
| ~ cpxcomp(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_70,plain,
( ra_Px1(A,sK1(A))
| ~ cpxcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_72,plain,
( cp(A)
| ~ ca_Ax2(A) ),
inference(clausify,[status(thm)],[axiom_5]) ).
fof(axiom_12,axiom,
cUnsatisfiable(i2003_11_14_17_21_12565),
file('theBenchmark.p',axiom_12) ).
cnf(c_85,plain,
cUnsatisfiable(i2003_11_14_17_21_12565),
inference(clausify,[status(thm)],[axiom_12]) ).
cnf(c_93,plain,
ca_Ax2(sK0(i2003_11_14_17_21_12565)),
inference(resolve,[status(thm)],[c_85,c_64]) ).
cnf(c_94,plain,
rs(i2003_11_14_17_21_12565,sK0(i2003_11_14_17_21_12565)),
inference(resolve,[status(thm)],[c_85,c_63]) ).
cnf(c_98,plain,
cp(sK0(i2003_11_14_17_21_12565)),
inference(resolve,[status(thm)],[c_93,c_72]) ).
cnf(c_101,plain,
~ ra_Px1(sK0(i2003_11_14_17_21_12565),A),
inference(resolve,[status(thm)],[c_68,c_98]) ).
cnf(c_112,plain,
( cpxcomp(sK0(i2003_11_14_17_21_12565))
| ~ cUnsatisfiable(i2003_11_14_17_21_12565) ),
inference(resolve,[status(thm)],[c_94,c_65]) ).
cnf(c_108,plain,
cpxcomp(sK0(i2003_11_14_17_21_12565)),
inference(resolve,[status(thm)],[c_85,c_112]) ).
cnf(c_113,plain,
~ cpxcomp(sK0(i2003_11_14_17_21_12565)),
inference(resolve,[status(thm)],[c_70,c_101]) ).
cnf(c_111,plain,
$false,
inference(resolve,[status(thm)],[c_108,c_113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS110+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 19:40:48 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3600993 was started by sandbox on n020,
% 0.08/0.35 % Fri Sep 25 19:40:48 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 17.
% 0.13/0.38 % Level of proof is 5.
% 0.13/0.38 % Maximum clause weight is 7.000.
% 0.13/0.38 % Given clauses 57.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------