%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV258-2 : 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 : n003.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 09:07:10 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 10 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 22 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Set_Oinsert__subset_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_insert(VAR_0,VAR_3,VAR_2),VAR_1,tc_set(VAR_2))
| ~ c_lessequals(VAR_3,VAR_1,tc_set(VAR_2))
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_Oinsert__subset_2) ).
cnf(c_1,plain,
( c_lessequals(c_insert(A,D,C),B,tc_set(C))
| ~ c_lessequals(D,B,tc_set(C))
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_Oinsert__subset_2]) ).
fof(cls_conjecture_0,axiom,
c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_2,plain,
c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_3,plain,
( c_lessequals(c_insert(v_X,A,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(A,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
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_4,plain,
c_lessequals(A,A,tc_set(B)),
inference(clausify,[status(thm)],[cls_Set_Osubset__refl_0]) ).
fof(cls_Message_Oparts__subset__iff_1,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(c_Message_Oparts(VAR_0),c_Message_Oparts(VAR_1),tc_set(tc_Message_Omsg))
| ~ c_lessequals(VAR_0,c_Message_Oparts(VAR_1),tc_set(tc_Message_Omsg)) ),
file('theBenchmark.p',cls_Message_Oparts__subset__iff_1) ).
cnf(c_5,plain,
( c_lessequals(c_Message_Oparts(A),c_Message_Oparts(B),tc_set(tc_Message_Omsg))
| ~ c_lessequals(A,c_Message_Oparts(B),tc_set(tc_Message_Omsg)) ),
inference(clausify,[status(thm)],[cls_Message_Oparts__subset__iff_1]) ).
fof(cls_Message_Oparts__subset__iff_0,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(VAR_0,c_Message_Oparts(VAR_1),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(VAR_0),c_Message_Oparts(VAR_1),tc_set(tc_Message_Omsg)) ),
file('theBenchmark.p',cls_Message_Oparts__subset__iff_0) ).
cnf(c_6,plain,
( c_lessequals(A,c_Message_Oparts(B),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(A),c_Message_Oparts(B),tc_set(tc_Message_Omsg)) ),
inference(clausify,[status(thm)],[cls_Message_Oparts__subset__iff_0]) ).
fof(cls_conjecture_1,axiom,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_7,plain,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_10,plain,
c_lessequals(A,c_Message_Oparts(A),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_12,plain,
~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_15,plain,
~ c_lessequals(v_H,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_12,c_3]) ).
cnf(c_16,plain,
$false,
inference(resolve,[status(thm)],[c_15,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV258-2 : 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 : n003.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 13:25:38 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 2999967 was started by sandbox on n003,
% 0.10/0.36 % Sat Sep 26 13:25:38 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).
% 0.10/0.38
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 11.
% 0.10/0.38 % Level of proof is 3.
% 0.10/0.38 % Maximum clause weight is 15.000.
% 0.10/0.38 % Given clauses 7.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------