%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS122+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 : n015.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 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 15 unt; 0 def)
% Number of atoms : 118 ( 8 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 122 ( 50 ~; 43 |; 20 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 63 ( 2 sgn 36 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cp1xcomp_substitution_1,axiom,
! [A,B] :
( ( cp1xcomp(A)
& A = B )
=> cp1xcomp(B) ),
file('theBenchmark.p',cp1xcomp_substitution_1) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ? [Y] :
( ca_Ax2(Y)
& rf(X,Y) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cp1(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cp1xcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X] :
( ca_Ax2(X)
<=> ( ! [Y] :
( rinvF(X,Y)
=> ca_Vx3(Y) )
& cp1(X) ) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( cp1xcomp(Y)
& rf(X,Y) ) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_7,axiom,
! [X,Y,Z] :
( ( rf(X,Z)
& rf(X,Y) )
=> Y = Z ),
file('theBenchmark.p',axiom_7) ).
fof(axiom_8,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('theBenchmark.p',axiom_8) ).
cnf(c_37,plain,
( cp1xcomp(A)
| ~ cp1xcomp(B)
| A != B ),
inference(clausify,[status(thm)],[cp1xcomp_substitution_1]) ).
fof(nnf_22,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) )
| cUnsatisfiable(X) )
& ( ? [X0] :
( ca_Ax2(X0)
& rf(X,X0) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) )
| cUnsatisfiable(X) )
& ( ( ca_Ax2(sK0(X))
& rf(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(X))],[nnf_22]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( ~ ca_Ax2(VAR_1)
| ~ rf(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ca_Ax2(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rf(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_54,plain,
( rf(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_55,plain,
( ca_Ax2(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_57,plain,
( ~ ra_Px1(A,B)
| ~ cp1(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(nnf_24,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ( ? [X0] : ra_Px1(X,X0)
| ~ cp1xcomp(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(sk_axiom_4_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ( ra_Px1(X,sK1(X))
| ~ cp1xcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1(X))],[nnf_24]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px1(VAR_0,VAR_1)
| cp1xcomp(VAR_0) )
& ! [VAR_0] :
( ra_Px1(VAR_0,sK1(VAR_0))
| ~ cp1xcomp(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_59,plain,
( ra_Px1(A,sK1(A))
| ~ cp1xcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_61,plain,
( cp1(A)
| ~ ca_Ax2(A) ),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_62,plain,
( ca_Vx3(B)
| ~ rinvF(A,B)
| ~ ca_Ax2(A) ),
inference(clausify,[status(thm)],[axiom_5]) ).
fof(nnf_26,plain,
! [X] :
( ( ! [Y] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) )
| ca_Vx3(X) )
& ( ? [X0] :
( cp1xcomp(X0)
& rf(X,X0) )
| ~ ca_Vx3(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_6]) ).
fof(sk_axiom_6_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) )
| ca_Vx3(X) )
& ( ( cp1xcomp(sK2(X))
& rf(X,sK2(X)) )
| ~ ca_Vx3(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2(X))],[nnf_26]) ).
fof(sk_axiom_6,plain,
( ! [VAR_0,VAR_1] :
( ~ cp1xcomp(VAR_1)
| ~ rf(VAR_0,VAR_1)
| ca_Vx3(VAR_0) )
& ! [VAR_0] :
( cp1xcomp(sK2(VAR_0))
| ~ ca_Vx3(VAR_0) )
& ! [VAR_0] :
( rf(VAR_0,sK2(VAR_0))
| ~ ca_Vx3(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_6_sk]) ).
cnf(c_65,plain,
( rf(A,sK2(A))
| ~ ca_Vx3(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_6]) ).
cnf(c_66,plain,
( cp1xcomp(sK2(A))
| ~ ca_Vx3(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_6]) ).
cnf(c_68,plain,
( C = B
| ~ rf(A,C)
| ~ rf(A,B) ),
inference(clausify,[status(thm)],[axiom_7]) ).
cnf(c_70,plain,
( ~ rf(B,A)
| rinvF(A,B) ),
inference(clausify,[status(thm)],[axiom_8]) ).
fof(axiom_11,axiom,
cUnsatisfiable(i2003_11_14_17_21_55116),
file('theBenchmark.p',axiom_11) ).
cnf(c_74,plain,
cUnsatisfiable(i2003_11_14_17_21_55116),
inference(clausify,[status(thm)],[axiom_11]) ).
cnf(c_79,plain,
ca_Ax2(sK0(i2003_11_14_17_21_55116)),
inference(resolve,[status(thm)],[c_74,c_55]) ).
cnf(c_80,plain,
rf(i2003_11_14_17_21_55116,sK0(i2003_11_14_17_21_55116)),
inference(resolve,[status(thm)],[c_74,c_54]) ).
cnf(c_82,plain,
cp1(sK0(i2003_11_14_17_21_55116)),
inference(resolve,[status(thm)],[c_79,c_61]) ).
cnf(c_85,plain,
~ ra_Px1(sK0(i2003_11_14_17_21_55116),A),
inference(resolve,[status(thm)],[c_57,c_82]) ).
cnf(c_88,plain,
rinvF(sK0(i2003_11_14_17_21_55116),i2003_11_14_17_21_55116),
inference(resolve,[status(thm)],[c_80,c_70]) ).
cnf(c_93,plain,
~ cp1xcomp(sK0(i2003_11_14_17_21_55116)),
inference(resolve,[status(thm)],[c_59,c_85]) ).
cnf(c_108,plain,
( ca_Vx3(i2003_11_14_17_21_55116)
| ~ ca_Ax2(sK0(i2003_11_14_17_21_55116)) ),
inference(resolve,[status(thm)],[c_88,c_62]) ).
cnf(c_94,plain,
ca_Vx3(i2003_11_14_17_21_55116),
inference(resolve,[status(thm)],[c_79,c_108]) ).
cnf(c_97,plain,
cp1xcomp(sK2(i2003_11_14_17_21_55116)),
inference(resolve,[status(thm)],[c_94,c_66]) ).
cnf(c_98,plain,
rf(i2003_11_14_17_21_55116,sK2(i2003_11_14_17_21_55116)),
inference(resolve,[status(thm)],[c_94,c_65]) ).
cnf(c_109,plain,
( cp1xcomp(A)
| A != sK2(i2003_11_14_17_21_55116) ),
inference(resolve,[status(thm)],[c_37,c_97]) ).
cnf(c_110,plain,
sK0(i2003_11_14_17_21_55116) != sK2(i2003_11_14_17_21_55116),
inference(resolve,[status(thm)],[c_109,c_93]) ).
cnf(c_102,plain,
sK2(i2003_11_14_17_21_55116) != sK0(i2003_11_14_17_21_55116),
inference(copy,[status(thm)],[c_110]) ).
cnf(c_111,plain,
( sK2(i2003_11_14_17_21_55116) = A
| ~ rf(i2003_11_14_17_21_55116,A) ),
inference(resolve,[status(thm)],[c_68,c_98]) ).
cnf(c_112,plain,
~ rf(i2003_11_14_17_21_55116,sK0(i2003_11_14_17_21_55116)),
inference(resolve,[status(thm)],[c_111,c_102]) ).
cnf(c_107,plain,
$false,
inference(resolve,[status(thm)],[c_80,c_112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS122+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 : n015.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 19:43:42 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 2083997 was started by sandbox on n015,
% 0.11/0.37 % Fri Sep 25 19:43:42 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % 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 31.
% 0.14/0.39 % Level of proof is 7.
% 0.14/0.39 % Maximum clause weight is 9.000.
% 0.14/0.39 % Given clauses 56.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------