%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS105+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 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 84 ( 34 ~; 32 |; 9 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 46 ( 5 sgn 24 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
=> cdxcomp(X) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cUnsatisfiable(X)
=> cc(X) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cc(X)
=> ! [Y] :
( rr(X,Y)
=> cc(Y) ) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X] :
( cd(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X] :
( cdxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_7,axiom,
! [X] :
( ca_Ax2(X)
<=> ! [Y] :
( rr(X,Y)
=> cc(Y) ) ),
file('theBenchmark.p',axiom_7) ).
fof(axiom_8,axiom,
! [X] :
( ca_Ax2(X)
=> cd(X) ),
file('theBenchmark.p',axiom_8) ).
cnf(c_12,plain,
( cc(A)
| ~ cUnsatisfiable(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(axiom_9,axiom,
cUnsatisfiable(i2003_11_14_17_20_53634),
file('theBenchmark.p',axiom_9) ).
cnf(c_13,plain,
cUnsatisfiable(i2003_11_14_17_20_53634),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_14,plain,
( cdxcomp(A)
| ~ cUnsatisfiable(A) ),
inference(clausify,[status(thm)],[axiom_2]) ).
fof(nnf_7,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ( ? [X0] : ra_Px1(X,X0)
| ~ cdxcomp(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_6]) ).
fof(sk_axiom_6_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(X0,sK0(X))],[nnf_7]) ).
fof(sk_axiom_6,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_6_sk]) ).
cnf(c_15,plain,
( ra_Px1(A,sK0(A))
| ~ cdxcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_6]) ).
cnf(c_16,plain,
cdxcomp(i2003_11_14_17_20_53634),
inference(resolve,[status(thm)],[c_14,c_13]) ).
fof(nnf_8,plain,
! [X] :
( ( ? [Y] :
( ~ cc(Y)
& rr(X,Y) )
| ca_Ax2(X) )
& ( ! [X0] :
( cc(X0)
| ~ rr(X,X0) )
| ~ ca_Ax2(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_7]) ).
fof(sk_axiom_7_sk,plain,
! [X] :
( ( ( ~ cc(sK1(X))
& rr(X,sK1(X)) )
| ca_Ax2(X) )
& ( ! [X0] :
( cc(X0)
| ~ rr(X,X0) )
| ~ ca_Ax2(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(Y,sK1(X))],[nnf_8]) ).
fof(sk_axiom_7,plain,
( ! [VAR_0] :
( ~ cc(sK1(VAR_0))
| ca_Ax2(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK1(VAR_0))
| ca_Ax2(VAR_0) )
& ! [VAR_0,VAR_1] :
( cc(VAR_1)
| ~ rr(VAR_0,VAR_1)
| ~ ca_Ax2(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_7_sk]) ).
cnf(c_19,plain,
( rr(A,sK1(A))
| ca_Ax2(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_7]) ).
cnf(c_20,plain,
( cc(B)
| ~ rr(A,B)
| ~ cc(A) ),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_22,plain,
( ~ ra_Px1(A,B)
| ~ cd(A) ),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_23,plain,
( cd(A)
| ~ ca_Ax2(A) ),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_24,plain,
( ~ cc(sK1(A))
| ca_Ax2(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_7]) ).
cnf(c_25,plain,
( ~ ra_Px1(A,B)
| ~ ca_Ax2(A) ),
inference(resolve,[status(thm)],[c_23,c_22]) ).
cnf(c_26,plain,
( ca_Ax2(A)
| cc(sK1(A))
| ~ cc(A) ),
inference(resolve,[status(thm)],[c_20,c_19]) ).
cnf(c_27,plain,
( ~ ra_Px1(A,B)
| cc(sK1(A))
| ~ cc(A) ),
inference(resolve,[status(thm)],[c_26,c_25]) ).
cnf(c_28,plain,
( ~ ra_Px1(A,B)
| ~ cc(sK1(A)) ),
inference(resolve,[status(thm)],[c_24,c_25]) ).
cnf(c_29,plain,
cc(i2003_11_14_17_20_53634),
inference(resolve,[status(thm)],[c_12,c_13]) ).
cnf(c_30,plain,
ra_Px1(i2003_11_14_17_20_53634,sK0(i2003_11_14_17_20_53634)),
inference(resolve,[status(thm)],[c_15,c_16]) ).
cnf(c_34,plain,
~ cc(sK1(i2003_11_14_17_20_53634)),
inference(resolve,[status(thm)],[c_30,c_28]) ).
cnf(c_36,plain,
( ~ ra_Px1(i2003_11_14_17_20_53634,A)
| cc(sK1(i2003_11_14_17_20_53634)) ),
inference(resolve,[status(thm)],[c_27,c_29]) ).
cnf(c_37,plain,
cc(sK1(i2003_11_14_17_20_53634)),
inference(resolve,[status(thm)],[c_36,c_30]) ).
cnf(c_35,plain,
$false,
inference(resolve,[status(thm)],[c_34,c_37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS105+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n020.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 19:40:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3600216 was started by sandbox on n020,
% 0.11/0.37 % Fri Sep 25 19:40:33 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 25.
% 0.14/0.39 % Level of proof is 5.
% 0.14/0.39 % Maximum clause weight is 8.000.
% 0.14/0.39 % Given clauses 4.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------