%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV239-2 : 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 : n014.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 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 7 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 12 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 35 ( 1 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ c_lessequals(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G),v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
~ c_lessequals(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G),v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_Message_Oanalz__analzD__dest_0,axiom,
! [VAR_0,VAR_1] :
( c_in(VAR_0,c_Message_Oanalz(VAR_1),tc_Message_Omsg)
| ~ c_in(VAR_0,c_Message_Oanalz(c_Message_Oanalz(VAR_1)),tc_Message_Omsg) ),
file('theBenchmark.p',cls_Message_Oanalz__analzD__dest_0) ).
cnf(c_2,plain,
( c_in(A,c_Message_Oanalz(B),tc_Message_Omsg)
| ~ c_in(A,c_Message_Oanalz(c_Message_Oanalz(B)),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_Message_Oanalz__analzD__dest_0]) ).
fof(cls_Message_Oanalz__subset__cong_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_Message_Oanalz(c_union(VAR_2,VAR_0,tc_Message_Omsg)),c_Message_Oanalz(c_union(VAR_3,VAR_1,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(VAR_2),c_Message_Oanalz(VAR_3),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(VAR_0),c_Message_Oanalz(VAR_1),tc_set(tc_Message_Omsg)) ),
file('theBenchmark.p',cls_Message_Oanalz__subset__cong_0) ).
cnf(c_3,plain,
( c_lessequals(c_Message_Oanalz(c_union(C,A,tc_Message_Omsg)),c_Message_Oanalz(c_union(D,B,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(C),c_Message_Oanalz(D),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(A),c_Message_Oanalz(B),tc_set(tc_Message_Omsg)) ),
inference(clausify,[status(thm)],[cls_Message_Oanalz__subset__cong_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_Set_Osubset__refl_0,axiom,
! [VAR_0,VAR_1] : c_lessequals(VAR_0,VAR_0,tc_set(VAR_1)),
file('theBenchmark.p',cls_Set_Osubset__refl_0) ).
cnf(c_6,plain,
c_lessequals(A,A,tc_set(B)),
inference(clausify,[status(thm)],[cls_Set_Osubset__refl_0]) ).
cnf(c_8,plain,
( c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(A)),B,tc_Message_Omsg),c_Message_Oanalz(A),tc_Message_Omsg)
| c_lessequals(c_Message_Oanalz(c_Message_Oanalz(A)),B,tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_15,plain,
( c_lessequals(c_Message_Oanalz(c_union(A,C,tc_Message_Omsg)),c_Message_Oanalz(c_union(B,C,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(A),c_Message_Oanalz(B),tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_3,c_6]) ).
cnf(c_12,plain,
~ c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)),c_Message_Oanalz(v_G),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_15,c_1]) ).
cnf(c_16,plain,
( c_lessequals(c_Message_Oanalz(c_Message_Oanalz(A)),c_Message_Oanalz(A),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(c_Message_Oanalz(A)),c_Message_Oanalz(A),tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_13,plain,
c_lessequals(c_Message_Oanalz(c_Message_Oanalz(A)),c_Message_Oanalz(A),tc_set(tc_Message_Omsg)),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_14,plain,
$false,
inference(resolve,[status(thm)],[c_13,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV239-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n014.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 13:21:47 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 3248819 was started by sandbox on n014,
% 0.12/0.38 % Sat Sep 26 13:21:47 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 0.12/0.40
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.40
% 0.12/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.40 % Length of proof is 10.
% 0.12/0.40 % Level of proof is 3.
% 0.12/0.40 % Maximum clause weight is 27.000.
% 0.12/0.40 % Given clauses 8.
% 0.12/0.40
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------