%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV247-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 09:07:08 AM UTC 2026
% Result : Unsatisfiable 0.98s 0.49s
% Output : CNFRefutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 17 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 25 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 50 ( 7 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Message_OCrypt__synth_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(c_Message_Omsg_OCrypt(VAR_0,VAR_1),VAR_2,tc_Message_Omsg)
| c_in(VAR_1,c_Message_Osynth(VAR_2),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(VAR_0,VAR_1),c_Message_Osynth(VAR_2),tc_Message_Omsg) ),
file('theBenchmark.p',cls_Message_OCrypt__synth_1) ).
cnf(c_1,plain,
( c_in(c_Message_Omsg_OCrypt(A,B),C,tc_Message_Omsg)
| c_in(B,c_Message_Osynth(C),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(A,B),c_Message_Osynth(C),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_Message_OCrypt__synth_1]) ).
fof(cls_Message_Oanalz_ODecrypt__dest_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(VAR_1,c_Message_Oanalz(VAR_2),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(VAR_0)),c_Message_Oanalz(VAR_2),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(VAR_0,VAR_1),c_Message_Oanalz(VAR_2),tc_Message_Omsg) ),
file('theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).
cnf(c_2,plain,
( c_in(B,c_Message_Oanalz(C),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(A)),c_Message_Oanalz(C),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(A,B),c_Message_Oanalz(C),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_Message_Oanalz_ODecrypt__dest_0]) ).
fof(cls_Message_OKey__synth_0,axiom,
! [VAR_0,VAR_1] :
( c_in(c_Message_Omsg_OKey(VAR_0),VAR_1,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(VAR_0),c_Message_Osynth(VAR_1),tc_Message_Omsg) ),
file('theBenchmark.p',cls_Message_OKey__synth_0) ).
cnf(c_3,plain,
( c_in(c_Message_Omsg_OKey(A),B,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(A),c_Message_Osynth(B),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_Message_OKey__synth_0]) ).
fof(cls_Message_Oanalz_OInj_0,axiom,
! [VAR_0,VAR_1] :
( c_in(VAR_0,c_Message_Oanalz(VAR_1),tc_Message_Omsg)
| ~ c_in(VAR_0,VAR_1,tc_Message_Omsg) ),
file('theBenchmark.p',cls_Message_Oanalz_OInj_0) ).
cnf(c_4,plain,
( c_in(A,c_Message_Oanalz(B),tc_Message_Omsg)
| ~ c_in(A,B,tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_Message_Oanalz_OInj_0]) ).
fof(cls_Set_OUnCI_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_union(VAR_3,VAR_1,VAR_2),VAR_2)
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OUnCI_0) ).
cnf(c_5,plain,
( c_in(A,c_union(D,B,C),C)
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_OUnCI_0]) ).
fof(cls_Set_OUnCI_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_union(VAR_1,VAR_3,VAR_2),VAR_2)
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OUnCI_1) ).
cnf(c_6,plain,
( c_in(A,c_union(B,D,C),C)
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_OUnCI_1]) ).
fof(cls_Set_OUnE_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,VAR_1,VAR_3)
| c_in(VAR_0,VAR_2,VAR_3)
| ~ c_in(VAR_0,c_union(VAR_1,VAR_2,VAR_3),VAR_3) ),
file('theBenchmark.p',cls_Set_OUnE_0) ).
cnf(c_7,plain,
( c_in(A,B,D)
| c_in(A,C,D)
| ~ c_in(A,c_union(B,C,D),D) ),
inference(clausify,[status(thm)],[cls_Set_OUnE_0]) ).
fof(cls_conjecture_1,axiom,
c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_union(c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),c_Message_Osynth(v_G),tc_Message_Omsg),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_8,plain,
c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_union(c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),c_Message_Osynth(v_G),tc_Message_Omsg),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_3,axiom,
c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_union(c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),c_Message_Osynth(v_G),tc_Message_Omsg),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_9,plain,
c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_union(c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),c_Message_Osynth(v_G),tc_Message_Omsg),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_4,axiom,
~ c_in(v_X,c_union(c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),c_Message_Osynth(v_G),tc_Message_Omsg),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_10,plain,
~ c_in(v_X,c_union(c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),c_Message_Osynth(v_G),tc_Message_Omsg),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
cnf(c_12,plain,
( c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Osynth(v_G),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_8,c_7]) ).
cnf(c_16,plain,
( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_Message_Osynth(v_G),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_9,c_7]) ).
cnf(c_21,plain,
~ c_in(v_X,c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_6,c_10]) ).
cnf(c_22,plain,
~ c_in(v_X,c_Message_Osynth(v_G),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_5,c_10]) ).
cnf(c_1234,plain,
( c_in(v_X,c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Osynth(v_G),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_12,c_2]) ).
cnf(c_26,plain,
( ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Osynth(v_G),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_21,c_1234]) ).
cnf(c_57,plain,
( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_Message_Osynth(v_G),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Osynth(v_G),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_26,c_16]) ).
cnf(c_61,plain,
( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),v_G,tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Osynth(v_G),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_57,c_3]) ).
cnf(c_1235,plain,
( c_in(c_Message_Omsg_OCrypt(v_K,v_X),v_G,tc_Message_Omsg)
| c_in(v_X,c_Message_Osynth(v_G),tc_Message_Omsg)
| c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),v_G,tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_61,c_1]) ).
cnf(c_65,plain,
( c_in(c_Message_Omsg_OCrypt(v_K,v_X),v_G,tc_Message_Omsg)
| c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),v_G,tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_22,c_1235]) ).
cnf(c_164,plain,
( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_union(v_G,A,tc_Message_Omsg),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,v_X),v_G,tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_65,c_6]) ).
cnf(c_352,plain,
( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_Message_Oanalz(c_union(v_G,A,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,v_X),v_G,tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_164,c_4]) ).
cnf(c_931,plain,
( c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Osynth(v_G),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,v_X),v_G,tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_352,c_26]) ).
cnf(c_1236,plain,
( c_in(c_Message_Omsg_OCrypt(v_K,v_X),v_G,tc_Message_Omsg)
| c_in(v_X,c_Message_Osynth(v_G),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,v_X),v_G,tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_931,c_1]) ).
cnf(c_1237,plain,
( c_in(v_X,c_Message_Osynth(v_G),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,v_X),v_G,tc_Message_Omsg) ),
inference(copy,[status(thm)],[c_1236]) ).
cnf(c_939,plain,
c_in(c_Message_Omsg_OCrypt(v_K,v_X),v_G,tc_Message_Omsg),
inference(resolve,[status(thm)],[c_22,c_1237]) ).
cnf(c_940,plain,
c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_union(v_G,A,tc_Message_Omsg),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_939,c_6]) ).
cnf(c_949,plain,
c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Oanalz(c_union(v_G,A,tc_Message_Omsg)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_940,c_4]) ).
cnf(c_1238,plain,
( c_in(v_X,c_Message_Oanalz(c_union(v_G,A,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_Message_Oanalz(c_union(v_G,A,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_2,c_949]) ).
cnf(c_1218,plain,
~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_1238,c_21]) ).
cnf(c_1219,plain,
c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_Message_Osynth(v_G),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_1218,c_16]) ).
cnf(c_1223,plain,
c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),v_G,tc_Message_Omsg),
inference(resolve,[status(thm)],[c_1219,c_3]) ).
cnf(c_1224,plain,
c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_union(v_G,A,tc_Message_Omsg),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_1223,c_6]) ).
cnf(c_1239,plain,
~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_4,c_1218]) ).
cnf(c_1233,plain,
$false,
inference(resolve,[status(thm)],[c_1224,c_1239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV247-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 13:22:45 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3425021 was started by sandbox on n010,
% 0.10/0.36 % Sat Sep 26 13:22:45 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.98/0.49
% 0.98/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.98/0.49
% 0.98/0.49 % Proof 1 at 0.09 (+ 0.03) seconds.
% 0.98/0.49 % Length of proof is 29.
% 0.98/0.49 % Level of proof is 16.
% 0.98/0.49 % Maximum clause weight is 34.000.
% 0.98/0.49 % Given clauses 79.
% 0.98/0.49
% 0.98/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------