%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV253-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 09:07:09 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 5 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 13 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 2 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
( c_Message_OinvKey(v_K) != c_Message_OinvKey(v_K_H)
| v_K != v_K_H ),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
( c_Message_OinvKey(v_K) != c_Message_OinvKey(v_K_H)
| v_K != v_K_H ),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_8,plain,
( c_Message_OinvKey(v_K) != c_Message_OinvKey(v_K_H)
| v_K_H != v_K ),
inference(copy,[status(thm)],[c_1]) ).
cnf(c_2,plain,
( c_Message_OinvKey(v_K_H) != c_Message_OinvKey(v_K)
| v_K_H != v_K ),
inference(copy,[status(thm)],[c_8]) ).
fof(cls_conjecture_1,axiom,
( v_K = v_K_H
| c_Message_OinvKey(v_K) = c_Message_OinvKey(v_K_H) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_3,plain,
( v_K = v_K_H
| c_Message_OinvKey(v_K) = c_Message_OinvKey(v_K_H) ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_9,plain,
( v_K = v_K_H
| c_Message_OinvKey(v_K_H) = c_Message_OinvKey(v_K) ),
inference(copy,[status(thm)],[c_3]) ).
cnf(c_4,plain,
( v_K_H = v_K
| c_Message_OinvKey(v_K_H) = c_Message_OinvKey(v_K) ),
inference(copy,[status(thm)],[c_9]) ).
fof(cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0,axiom,
! [VAR_0] : c_Message_OinvKey(c_Message_OinvKey(VAR_0)) = VAR_0,
file('theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
cnf(c_5,plain,
c_Message_OinvKey(c_Message_OinvKey(A)) = A,
inference(clausify,[status(thm)],[cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0]) ).
cnf(c_10,plain,
( c_Message_OinvKey(c_Message_OinvKey(v_K)) = v_K_H
| v_K_H = v_K ),
inference(paramod,[status(thm)],[c_4,c_5]) ).
cnf(c_11,plain,
( v_K = v_K_H
| v_K_H = v_K ),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_12,plain,
( v_K_H = v_K
| v_K_H = v_K ),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_6,plain,
v_K_H = v_K,
inference(copy,[status(thm)],[c_12]) ).
cnf(c_13,plain,
( c_Message_OinvKey(v_K_H) != c_Message_OinvKey(v_K)
| v_K != v_K ),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_14,plain,
( c_Message_OinvKey(v_K) != c_Message_OinvKey(v_K)
| v_K != v_K ),
inference(paramod,[status(thm)],[c_6,c_13]) ).
cnf(c_15,plain,
c_Message_OinvKey(v_K) != c_Message_OinvKey(v_K),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_7,plain,
$false,
inference(copy,[status(thm)],[c_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV253-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n019.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 13:22:49 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 1417144 was started by sandbox2 on n019,
% 0.17/0.43 % Sat Sep 26 13:22:49 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.45
% 0.17/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.45
% 0.17/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.45 % Length of proof is 7.
% 0.17/0.45 % Level of proof is 3.
% 0.17/0.45 % Maximum clause weight is 8.000.
% 0.17/0.45 % Given clauses 3.
% 0.17/0.45
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------