%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV241-2 : 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 : n002.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 09:07:06 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.46s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 13 unt; 0 def)
% Number of atoms : 43 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 17 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 31 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1,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_Message_Oanalz__trans_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(VAR_0,c_Message_Oanalz(VAR_2),tc_Message_Omsg)
| ~ c_lessequals(VAR_1,c_Message_Oanalz(VAR_2),tc_set(tc_Message_Omsg))
| ~ c_in(VAR_0,c_Message_Oanalz(VAR_1),tc_Message_Omsg) ),
file('theBenchmark.p',cls_Message_Oanalz__trans_0) ).
cnf(c_2,plain,
( c_in(A,c_Message_Oanalz(C),tc_Message_Omsg)
| ~ c_lessequals(B,c_Message_Oanalz(C),tc_set(tc_Message_Omsg))
| ~ c_in(A,c_Message_Oanalz(B),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_Message_Oanalz__trans_0]) ).
fof(cls_Set_OinsertE_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_0 = VAR_1
| c_in(VAR_0,VAR_2,VAR_3)
| ~ c_in(VAR_0,c_insert(VAR_1,VAR_2,VAR_3),VAR_3) ),
file('theBenchmark.p',cls_Set_OinsertE_0) ).
cnf(c_3,plain,
( A = B
| c_in(A,C,D)
| ~ c_in(A,c_insert(B,C,D),D) ),
inference(clausify,[status(thm)],[cls_Set_OinsertE_0]) ).
fof(cls_Set_OsubsetI_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_0,VAR_1,tc_set(VAR_2))
| c_in(c_Main_OsubsetI__1(VAR_0,VAR_1,VAR_2),VAR_0,VAR_2) ),
file('theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(c_4,plain,
( c_lessequals(A,B,tc_set(C))
| c_in(c_Main_OsubsetI__1(A,B,C),A,C) ),
inference(clausify,[status(thm)],[cls_Set_OsubsetI_0]) ).
fof(cls_Set_OsubsetI_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_0,VAR_1,tc_set(VAR_2))
| ~ c_in(c_Main_OsubsetI__1(VAR_0,VAR_1,VAR_2),VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OsubsetI_1) ).
cnf(c_5,plain,
( c_lessequals(A,B,tc_set(C))
| ~ c_in(c_Main_OsubsetI__1(A,B,C),B,C) ),
inference(clausify,[status(thm)],[cls_Set_OsubsetI_1]) ).
fof(cls_conjecture_0,axiom,
c_in(v_Y,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_6,plain,
c_in(v_Y,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
c_in(v_X,c_Message_Oanalz(v_H),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_7,plain,
c_in(v_X,c_Message_Oanalz(v_H),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
~ c_in(v_Y,c_Message_Oanalz(v_H),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_8,plain,
~ c_in(v_Y,c_Message_Oanalz(v_H),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_27,plain,
( c_in(v_Y,c_Message_Oanalz(A),tc_Message_Omsg)
| ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oanalz(A),tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_2,c_6]) ).
cnf(c_13,plain,
~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oanalz(v_H),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_27,c_8]) ).
cnf(c_15,plain,
c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oanalz(v_H),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_13,c_4]) ).
cnf(c_16,plain,
~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oanalz(v_H),tc_Message_Omsg),c_Message_Oanalz(v_H),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_5,c_13]) ).
cnf(c_17,plain,
~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oanalz(v_H),tc_Message_Omsg),v_H,tc_Message_Omsg),
inference(resolve,[status(thm)],[c_1,c_16]) ).
cnf(c_28,plain,
( c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oanalz(v_H),tc_Message_Omsg) = v_X
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oanalz(v_H),tc_Message_Omsg),v_H,tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_15,c_3]) ).
cnf(c_22,plain,
c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oanalz(v_H),tc_Message_Omsg) = v_X,
inference(resolve,[status(thm)],[c_17,c_28]) ).
cnf(c_29,plain,
( c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oanalz(v_H),tc_set(tc_Message_Omsg))
| ~ c_in(v_X,c_Message_Oanalz(v_H),tc_Message_Omsg) ),
inference(paramod,[status(thm)],[c_22,c_5]) ).
cnf(c_30,plain,
c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oanalz(v_H),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_7,c_29]) ).
cnf(c_26,plain,
$false,
inference(resolve,[status(thm)],[c_13,c_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV241-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n002.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 13:24:20 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 1832316 was started by sandbox on n002,
% 0.18/0.44 % Sat Sep 26 13:24:20 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.46
% 0.18/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.46
% 0.18/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/0.46 % Length of proof is 14.
% 0.18/0.46 % Level of proof is 5.
% 0.18/0.46 % Maximum clause weight is 29.000.
% 0.18/0.46 % Given clauses 18.
% 0.18/0.46
% 0.18/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------