%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV248-2 : 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 : 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 09:07:08 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 11 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 25 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 78 ( 7 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ c_lessequals(c_union(c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),c_Message_Osynth(v_G),tc_Message_Omsg),c_Message_Oanalz(c_union(c_Message_Osynth(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_union(c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),c_Message_Osynth(v_G),tc_Message_Omsg),c_Message_Oanalz(c_union(c_Message_Osynth(v_G),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
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_2,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__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_3,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_Message_Osynth_OInj_0,axiom,
! [VAR_0,VAR_1] :
( c_in(VAR_0,c_Message_Osynth(VAR_1),tc_Message_Omsg)
| ~ c_in(VAR_0,VAR_1,tc_Message_Omsg) ),
file('theBenchmark.p',cls_Message_Osynth_OInj_0) ).
cnf(c_4,plain,
( c_in(A,c_Message_Osynth(B),tc_Message_Omsg)
| ~ c_in(A,B,tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_Message_Osynth_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_OUn__least_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_union(VAR_3,VAR_0,VAR_2),VAR_1,tc_set(VAR_2))
| ~ c_lessequals(VAR_3,VAR_1,tc_set(VAR_2))
| ~ c_lessequals(VAR_0,VAR_1,tc_set(VAR_2)) ),
file('theBenchmark.p',cls_Set_OUn__least_0) ).
cnf(c_7,plain,
( c_lessequals(c_union(D,A,C),B,tc_set(C))
| ~ c_lessequals(D,B,tc_set(C))
| ~ c_lessequals(A,B,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Set_OUn__least_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]) ).
cnf(c_11,plain,
( c_in(c_Main_OsubsetI__1(A,B,C),c_union(A,D,C),C)
| c_lessequals(A,B,tc_set(C)) ),
inference(resolve,[status(thm)],[c_8,c_6]) ).
cnf(c_12,plain,
( c_in(c_Main_OsubsetI__1(A,B,C),c_union(D,A,C),C)
| c_lessequals(A,B,tc_set(C)) ),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_13,plain,
( c_in(c_Main_OsubsetI__1(A,B,tc_Message_Omsg),c_Message_Osynth(A),tc_Message_Omsg)
| c_lessequals(A,B,tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_31,plain,
( c_in(c_Main_OsubsetI__1(A,B,tc_Message_Omsg),c_Message_Oanalz(c_union(A,C,tc_Message_Omsg)),tc_Message_Omsg)
| c_lessequals(A,B,tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_11,c_2]) ).
cnf(c_858,plain,
( c_lessequals(A,c_union(B,A,C),tc_set(C))
| c_lessequals(A,c_union(B,A,C),tc_set(C)) ),
inference(resolve,[status(thm)],[c_12,c_9]) ).
cnf(c_37,plain,
c_lessequals(A,c_union(B,A,C),tc_set(C)),
inference(copy,[status(thm)],[c_858]) ).
cnf(c_859,plain,
( c_lessequals(A,c_Message_Oanalz(c_union(A,B,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_lessequals(A,c_Message_Oanalz(c_union(A,B,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_31,c_9]) ).
cnf(c_675,plain,
c_lessequals(A,c_Message_Oanalz(c_union(A,B,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(copy,[status(thm)],[c_859]) ).
cnf(c_860,plain,
( c_lessequals(c_union(A,B,tc_Message_Omsg),c_Message_Oanalz(c_union(B,C,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(A,c_Message_Oanalz(c_union(B,C,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_7,c_675]) ).
cnf(c_704,plain,
~ c_lessequals(c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(v_G),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_860,c_1]) ).
cnf(c_840,plain,
~ c_lessequals(c_union(v_G,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(v_G),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_3,c_704]) ).
cnf(c_861,plain,
( c_lessequals(c_union(A,C,D),c_union(B,C,D),tc_set(D))
| ~ c_lessequals(A,c_union(B,C,D),tc_set(D)) ),
inference(resolve,[status(thm)],[c_7,c_37]) ).
cnf(c_846,plain,
~ c_lessequals(v_G,c_union(c_Message_Osynth(v_G),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_861,c_840]) ).
cnf(c_852,plain,
c_in(c_Main_OsubsetI__1(v_G,c_union(c_Message_Osynth(v_G),v_H,tc_Message_Omsg),tc_Message_Omsg),c_Message_Osynth(v_G),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_846,c_13]) ).
cnf(c_856,plain,
~ c_in(c_Main_OsubsetI__1(v_G,c_union(c_Message_Osynth(v_G),v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(v_G),v_H,tc_Message_Omsg),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_9,c_846]) ).
cnf(c_862,plain,
~ c_in(c_Main_OsubsetI__1(v_G,c_union(c_Message_Osynth(v_G),v_H,tc_Message_Omsg),tc_Message_Omsg),c_Message_Osynth(v_G),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_6,c_856]) ).
cnf(c_857,plain,
$false,
inference(resolve,[status(thm)],[c_852,c_862]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV248-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n016.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
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 13:28:00 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 969144 was started by sandbox on n016,
% 0.12/0.38 % Sat Sep 26 13:28:00 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).
% 0.12/0.45
% 0.12/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.45
% 0.12/0.45 % Proof 1 at 0.06 (+ 0.01) seconds.
% 0.12/0.45 % Length of proof is 21.
% 0.12/0.45 % Level of proof is 8.
% 0.12/0.45 % Maximum clause weight is 38.000.
% 0.12/0.45 % Given clauses 85.
% 0.12/0.45
% 0.12/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------