%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS074+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 : n012.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 07:45:58 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.52s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 6 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 97 ( 38 ~; 35 |; 22 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 32 ( 0 sgn 22 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y] :
( rs(X,Y)
=> ~ cp(Y) )
& ? [Y] :
( ? [Z] :
( cp(Z)
& rinvS(Y,Z) )
& cp(Y)
& rs(X,Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(nnf_21,plain,
! [X] :
( ( ? [Y] :
( cp(Y)
& rs(X,Y) )
| ! [X3] :
( ! [Z] :
( ~ cp(Z)
| ~ rinvS(X3,Z) )
| ~ cp(X3)
| ~ rs(X,X3) )
| cUnsatisfiable(X) )
& ( ( ! [X2] :
( ~ cp(X2)
| ~ rs(X,X2) )
& ? [X0] :
( ? [X1] :
( cp(X1)
& rinvS(X0,X1) )
& cp(X0)
& rs(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ( cp(sK2(X))
& rs(X,sK2(X)) )
| ! [X3] :
( ! [Z] :
( ~ cp(Z)
| ~ rinvS(X3,Z) )
| ~ cp(X3)
| ~ rs(X,X3) )
| cUnsatisfiable(X) )
& ( ( ! [X2] :
( ~ cp(X2)
| ~ rs(X,X2) )
& cp(sK1(X))
& rinvS(sK0(X),sK1(X))
& cp(sK0(X))
& rs(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0(X)),skolemize(X1,sK1(X)),skolemize(Y,sK2(X))],[nnf_21]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( cp(sK2(VAR_0))
| ~ cp(VAR_2)
| ~ rinvS(VAR_1,VAR_2)
| ~ cp(VAR_1)
| ~ rs(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( rs(VAR_0,sK2(VAR_0))
| ~ cp(VAR_2)
| ~ rinvS(VAR_1,VAR_2)
| ~ cp(VAR_1)
| ~ rs(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ cp(VAR_1)
| ~ rs(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rinvS(sK0(VAR_0),sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp(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_52,plain,
( rs(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_53,plain,
( cp(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_56,plain,
( ~ cp(B)
| ~ rs(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
fof(axiom_9,axiom,
cUnsatisfiable(i2003_11_14_17_18_59896),
file('theBenchmark.p',axiom_9) ).
cnf(c_68,plain,
cUnsatisfiable(i2003_11_14_17_18_59896),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_76,plain,
cp(sK0(i2003_11_14_17_18_59896)),
inference(resolve,[status(thm)],[c_68,c_53]) ).
cnf(c_77,plain,
rs(i2003_11_14_17_18_59896,sK0(i2003_11_14_17_18_59896)),
inference(resolve,[status(thm)],[c_68,c_52]) ).
cnf(c_83,plain,
( ~ cp(A)
| ~ rs(i2003_11_14_17_18_59896,A) ),
inference(resolve,[status(thm)],[c_56,c_68]) ).
cnf(c_84,plain,
~ rs(i2003_11_14_17_18_59896,sK0(i2003_11_14_17_18_59896)),
inference(resolve,[status(thm)],[c_83,c_76]) ).
cnf(c_82,plain,
$false,
inference(resolve,[status(thm)],[c_77,c_84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KRS074+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.51 % Computer : n012.cluster.edu
% 0.03/0.51 % Model : x86_64 x86_64
% 0.03/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.51 % Memory : 8046.5625MB
% 0.03/0.51 % OS : Linux 6.8.0-71-generic
% 0.03/0.51 % CPULimit : 300
% 0.03/0.51 % WCLimit : 300
% 0.03/0.51 % DateTime : Fri Sep 25 19:38:06 UTC 2026
% 0.03/0.51 % CPUTime :
% 0.03/0.51 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.51 % Process 2811967 was started by sandbox on n012,
% 0.03/0.51 % Fri Sep 25 19:38:06 2026
% 0.03/0.51 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.51
% 0.03/0.51 % From the command line: assign(max_seconds, 300).
% 0.07/0.52
% 0.07/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.52
% 0.07/0.52 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.07/0.52 % Length of proof is 8.
% 0.07/0.52 % Level of proof is 3.
% 0.07/0.52 % Maximum clause weight is 7.000.
% 0.07/0.52 % Given clauses 44.
% 0.07/0.52
% 0.07/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------