%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV242-2 : 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 : 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 09:07:07 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 13 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 18 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 30 ( 4 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
c_lessequals(v_G,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
c_lessequals(v_G,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
c_lessequals(v_H,c_Message_Oanalz(v_H_H),tc_set(tc_Message_Omsg)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2,plain,
c_lessequals(v_H,c_Message_Oanalz(v_H_H),tc_set(tc_Message_Omsg)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
( ~ c_lessequals(v_G,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(v_H,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_3,plain,
( ~ c_lessequals(v_G,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(v_H,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_Message_Oanalz__mono_0,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(c_Message_Oanalz(VAR_0),c_Message_Oanalz(VAR_1),tc_set(tc_Message_Omsg))
| ~ c_lessequals(VAR_0,VAR_1,tc_set(tc_Message_Omsg)) ),
file('theBenchmark.p',cls_Message_Oanalz__mono_0) ).
cnf(c_4,plain,
( c_lessequals(c_Message_Oanalz(A),c_Message_Oanalz(B),tc_set(tc_Message_Omsg))
| ~ c_lessequals(A,B,tc_set(tc_Message_Omsg)) ),
inference(clausify,[status(thm)],[cls_Message_Oanalz__mono_0]) ).
fof(cls_Set_OUn__upper1_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_lessequals(VAR_0,c_union(VAR_0,VAR_1,VAR_2),tc_set(VAR_2)),
file('theBenchmark.p',cls_Set_OUn__upper1_0) ).
cnf(c_5,plain,
c_lessequals(A,c_union(A,B,C),tc_set(C)),
inference(clausify,[status(thm)],[cls_Set_OUn__upper1_0]) ).
fof(cls_Set_OUn__upper2_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_lessequals(VAR_0,c_union(VAR_1,VAR_0,VAR_2),tc_set(VAR_2)),
file('theBenchmark.p',cls_Set_OUn__upper2_0) ).
cnf(c_6,plain,
c_lessequals(A,c_union(B,A,C),tc_set(C)),
inference(clausify,[status(thm)],[cls_Set_OUn__upper2_0]) ).
fof(cls_Set_Osubset__trans_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(VAR_3,VAR_1,tc_set(VAR_2))
| ~ c_lessequals(VAR_3,VAR_0,tc_set(VAR_2))
| ~ c_lessequals(VAR_0,VAR_1,tc_set(VAR_2)) ),
file('theBenchmark.p',cls_Set_Osubset__trans_0) ).
cnf(c_7,plain,
( c_lessequals(D,B,tc_set(C))
| ~ c_lessequals(D,A,tc_set(C))
| ~ c_lessequals(A,B,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Set_Osubset__trans_0]) ).
cnf(c_10,plain,
c_lessequals(c_Message_Oanalz(A),c_Message_Oanalz(c_union(A,B,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_11,plain,
c_lessequals(c_Message_Oanalz(A),c_Message_Oanalz(c_union(B,A,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_4,c_6]) ).
cnf(c_12,plain,
( ~ c_lessequals(v_H,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(v_G,A,tc_set(tc_Message_Omsg))
| ~ c_lessequals(A,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_35,plain,
( ~ c_lessequals(v_H,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(v_G_H),c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_12,c_1]) ).
cnf(c_29,plain,
~ c_lessequals(v_H,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_10,c_35]) ).
cnf(c_36,plain,
( c_lessequals(v_H,A,tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(v_H_H),A,tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_7,c_2]) ).
cnf(c_37,plain,
~ c_lessequals(c_Message_Oanalz(v_H_H),c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_36,c_29]) ).
cnf(c_34,plain,
$false,
inference(resolve,[status(thm)],[c_11,c_37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV242-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.43 % Computer : n016.cluster.edu
% 0.14/0.43 % Model : x86_64 x86_64
% 0.14/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.43 % Memory : 8046.5625MB
% 0.14/0.43 % OS : Linux 6.8.0-71-generic
% 0.14/0.43 % CPULimit : 300
% 0.14/0.43 % WCLimit : 300
% 0.14/0.43 % DateTime : Sat Sep 26 13:26:15 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.44 % Process 966416 was started by sandbox2 on n016,
% 0.14/0.44 % Sat Sep 26 13:26:15 2026
% 0.14/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.44
% 0.14/0.44 % From the command line: assign(max_seconds, 300).
% 0.14/0.46
% 0.14/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.46
% 0.14/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.46 % Length of proof is 12.
% 0.14/0.46 % Level of proof is 3.
% 0.14/0.46 % Maximum clause weight is 23.000.
% 0.14/0.46 % Given clauses 10.
% 0.14/0.46
% 0.14/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------