%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS095+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 : n016.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 07:46:01 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.61s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 7 unt; 0 def)
% Number of atoms : 82 ( 21 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 106 ( 41 ~; 41 |; 22 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 43 ( 0 sgn 28 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y0,Y1] :
( ( rr(X,Y1)
& rr(X,Y0) )
=> Y0 = Y1 )
& ? [Y0,Y1] :
( Y0 != Y1
& rr(X,Y1)
& rr(X,Y0) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(nnf_12,plain,
! [X] :
( ( ? [Y0,Y1] :
( Y1 != Y0
& rr(X,Y1)
& rr(X,Y0) )
| ! [X4,X5] :
( X5 = X4
| ~ rr(X,X5)
| ~ rr(X,X4) )
| cUnsatisfiable(X) )
& ( ( ! [X2,X3] :
( X3 = X2
| ~ rr(X,X3)
| ~ rr(X,X2) )
& ? [X0,X1] :
( X1 != X0
& rr(X,X1)
& rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ( sK3(X) != sK2(X)
& rr(X,sK3(X))
& rr(X,sK2(X)) )
| ! [X4,X5] :
( X5 = X4
| ~ rr(X,X5)
| ~ rr(X,X4) )
| cUnsatisfiable(X) )
& ( ( ! [X2,X3] :
( X3 = X2
| ~ rr(X,X3)
| ~ rr(X,X2) )
& sK1(X) != sK0(X)
& rr(X,sK1(X))
& rr(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0(X)),skolemize(X1,sK1(X)),skolemize(Y0,sK2(X)),skolemize(Y1,sK3(X))],[nnf_12]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( sK3(VAR_0) != sK2(VAR_0)
| VAR_2 = VAR_1
| ~ rr(VAR_0,VAR_2)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( rr(VAR_0,sK3(VAR_0))
| VAR_2 = VAR_1
| ~ rr(VAR_0,VAR_2)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( rr(VAR_0,sK2(VAR_0))
| VAR_2 = VAR_1
| ~ rr(VAR_0,VAR_2)
| ~ 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] :
( sK1(VAR_0) != sK0(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK1(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_27,plain,
( rr(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_28,plain,
( rr(A,sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_29,plain,
( sK1(A) != sK0(A)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_30,plain,
( C = B
| ~ rr(A,C)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
fof(axiom_4,axiom,
cUnsatisfiable(i2003_11_14_17_20_14253),
file('theBenchmark.p',axiom_4) ).
cnf(c_35,plain,
cUnsatisfiable(i2003_11_14_17_20_14253),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_37,plain,
sK1(i2003_11_14_17_20_14253) != sK0(i2003_11_14_17_20_14253),
inference(resolve,[status(thm)],[c_35,c_29]) ).
cnf(c_38,plain,
rr(i2003_11_14_17_20_14253,sK1(i2003_11_14_17_20_14253)),
inference(resolve,[status(thm)],[c_35,c_28]) ).
cnf(c_39,plain,
rr(i2003_11_14_17_20_14253,sK0(i2003_11_14_17_20_14253)),
inference(resolve,[status(thm)],[c_35,c_27]) ).
cnf(c_45,plain,
( B = A
| ~ rr(i2003_11_14_17_20_14253,B)
| ~ rr(i2003_11_14_17_20_14253,A) ),
inference(resolve,[status(thm)],[c_30,c_35]) ).
cnf(c_46,plain,
( sK1(i2003_11_14_17_20_14253) = A
| ~ rr(i2003_11_14_17_20_14253,A) ),
inference(resolve,[status(thm)],[c_45,c_38]) ).
cnf(c_47,plain,
~ rr(i2003_11_14_17_20_14253,sK0(i2003_11_14_17_20_14253)),
inference(resolve,[status(thm)],[c_46,c_37]) ).
cnf(c_44,plain,
$false,
inference(resolve,[status(thm)],[c_39,c_47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS095+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.58 % Computer : n016.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Fri Sep 25 19:44:00 UTC 2026
% 0.11/0.59 % CPUTime :
% 0.11/0.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.59 % Process 3125920 was started by sandbox on n016,
% 0.11/0.59 % Fri Sep 25 19:44:00 2026
% 0.11/0.59 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.59
% 0.11/0.59 % From the command line: assign(max_seconds, 300).
% 0.11/0.61
% 0.11/0.61 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.61
% 0.11/0.61 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.61 % Length of proof is 10.
% 0.11/0.61 % Level of proof is 3.
% 0.11/0.61 % Maximum clause weight is 11.000.
% 0.11/0.61 % Given clauses 23.
% 0.11/0.61
% 0.11/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------