%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV260-2 : 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 : n001.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 0.15s 0.46s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 15 unt; 0 def)
% Number of atoms : 65 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 24 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 57 ( 5 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
c_in(v_Y,c_Message_Oparts(c_insert(v_X,v_G,tc_Message_Omsg)),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
c_in(v_Y,c_Message_Oparts(c_insert(v_X,v_G,tc_Message_Omsg)),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2,plain,
c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
~ c_in(v_Y,c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_3,plain,
~ c_in(v_Y,c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_Message_Oparts_OInj_0,axiom,
! [VAR_0,VAR_1] :
( c_in(VAR_0,c_Message_Oparts(VAR_1),tc_Message_Omsg)
| ~ c_in(VAR_0,VAR_1,tc_Message_Omsg) ),
file('theBenchmark.p',cls_Message_Oparts_OInj_0) ).
cnf(c_4,plain,
( c_in(A,c_Message_Oparts(B),tc_Message_Omsg)
| ~ c_in(A,B,tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_Message_Oparts_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_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_7,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_8,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_9,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_Message_Oparts__trans_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(VAR_0,c_Message_Oparts(VAR_2),tc_Message_Omsg)
| ~ c_lessequals(VAR_1,c_Message_Oparts(VAR_2),tc_set(tc_Message_Omsg))
| ~ c_in(VAR_0,c_Message_Oparts(VAR_1),tc_Message_Omsg) ),
file('theBenchmark.p',cls_Message_Oparts__trans_0) ).
cnf(c_10,plain,
( c_in(A,c_Message_Oparts(C),tc_Message_Omsg)
| ~ c_lessequals(B,c_Message_Oparts(C),tc_set(tc_Message_Omsg))
| ~ c_in(A,c_Message_Oparts(B),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_Message_Oparts__trans_0]) ).
cnf(c_205,plain,
( c_in(v_X,c_Message_Oparts(A),tc_Message_Omsg)
| ~ c_lessequals(v_H,c_Message_Oparts(A),tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_10,c_2]) ).
cnf(c_19,plain,
( c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(A),tc_Message_Omsg),v_H,tc_Message_Omsg)
| c_in(v_X,c_Message_Oparts(A),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_205,c_8]) ).
cnf(c_206,plain,
( c_in(v_Y,c_Message_Oparts(A),tc_Message_Omsg)
| ~ c_lessequals(c_insert(v_X,v_G,tc_Message_Omsg),c_Message_Oparts(A),tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_10,c_1]) ).
cnf(c_21,plain,
~ c_lessequals(c_insert(v_X,v_G,tc_Message_Omsg),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_206,c_3]) ).
cnf(c_29,plain,
c_in(c_Main_OsubsetI__1(c_insert(v_X,v_G,tc_Message_Omsg),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_insert(v_X,v_G,tc_Message_Omsg),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_21,c_8]) ).
cnf(c_30,plain,
~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_G,tc_Message_Omsg),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_9,c_21]) ).
cnf(c_38,plain,
( c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(A),tc_Message_Omsg),c_union(B,v_H,tc_Message_Omsg),tc_Message_Omsg)
| c_in(v_X,c_Message_Oparts(A),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_19,c_5]) ).
cnf(c_59,plain,
~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_G,tc_Message_Omsg),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_4,c_30]) ).
cnf(c_60,plain,
~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_G,tc_Message_Omsg),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_G,tc_Message_Omsg),
inference(resolve,[status(thm)],[c_6,c_59]) ).
cnf(c_92,plain,
( c_in(c_Main_OsubsetI__1(v_H,c_Message_Oparts(A),tc_Message_Omsg),c_Message_Oparts(c_union(B,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(v_X,c_Message_Oparts(A),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_38,c_4]) ).
cnf(c_109,plain,
( c_lessequals(v_H,c_Message_Oparts(c_union(A,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_in(v_X,c_Message_Oparts(c_union(A,v_H,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_92,c_9]) ).
cnf(c_207,plain,
( c_in(v_X,c_Message_Oparts(A),tc_Message_Omsg)
| ~ c_lessequals(v_H,c_Message_Oparts(A),tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_10,c_2]) ).
cnf(c_208,plain,
( c_in(v_X,c_Message_Oparts(c_union(A,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(v_X,c_Message_Oparts(c_union(A,v_H,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_207,c_109]) ).
cnf(c_128,plain,
c_in(v_X,c_Message_Oparts(c_union(A,v_H,tc_Message_Omsg)),tc_Message_Omsg),
inference(copy,[status(thm)],[c_208]) ).
cnf(c_209,plain,
( c_Main_OsubsetI__1(c_insert(v_X,v_G,tc_Message_Omsg),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg) = v_X
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_G,tc_Message_Omsg),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_G,tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_29,c_7]) ).
cnf(c_197,plain,
c_Main_OsubsetI__1(c_insert(v_X,v_G,tc_Message_Omsg),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg) = v_X,
inference(resolve,[status(thm)],[c_60,c_209]) ).
cnf(c_210,plain,
~ c_in(v_X,c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),
inference(paramod,[status(thm)],[c_197,c_30]) ).
cnf(c_204,plain,
$false,
inference(resolve,[status(thm)],[c_128,c_210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV260-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n001.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 13:29:28 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 1905865 was started by sandbox2 on n001,
% 0.15/0.42 % Sat Sep 26 13:29:28 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 0.15/0.46
% 0.15/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.46
% 0.15/0.46 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.15/0.46 % Length of proof is 22.
% 0.15/0.46 % Level of proof is 6.
% 0.15/0.46 % Maximum clause weight is 38.000.
% 0.15/0.46 % Given clauses 73.
% 0.15/0.46
% 0.15/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------