%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV275-2 : 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 : 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 09:07:14 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 13 unt; 0 def)
% Number of atoms : 53 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 21 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 65 ( 6 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1,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_Message_Osynth__mono_0,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(c_Message_Osynth(VAR_0),c_Message_Osynth(VAR_1),tc_set(tc_Message_Omsg))
| ~ c_lessequals(VAR_0,VAR_1,tc_set(tc_Message_Omsg)) ),
file('theBenchmark.p',cls_Message_Osynth__mono_0) ).
cnf(c_2,plain,
( c_lessequals(c_Message_Osynth(A),c_Message_Osynth(B),tc_set(tc_Message_Omsg))
| ~ c_lessequals(A,B,tc_set(tc_Message_Omsg)) ),
inference(clausify,[status(thm)],[cls_Message_Osynth__mono_0]) ).
fof(cls_Set_OinsertCI_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_insert(VAR_3,VAR_1,VAR_2),VAR_2)
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OinsertCI_0) ).
cnf(c_3,plain,
( c_in(A,c_insert(D,B,C),C)
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_OinsertCI_0]) ).
fof(cls_Set_OinsertCI_1,axiom,
! [VAR_0,VAR_1,VAR_2] : c_in(VAR_0,c_insert(VAR_0,VAR_1,VAR_2),VAR_2),
file('theBenchmark.p',cls_Set_OinsertCI_1) ).
cnf(c_4,plain,
c_in(A,c_insert(A,B,C),C),
inference(clausify,[status(thm)],[cls_Set_OinsertCI_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_5,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_OsubsetD_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,VAR_3,VAR_2)
| ~ c_lessequals(VAR_1,VAR_3,tc_set(VAR_2))
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OsubsetD_0) ).
cnf(c_6,plain,
( c_in(A,D,C)
| ~ c_lessequals(B,D,tc_set(C))
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_OsubsetD_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_7,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_8,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_lessequals(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Osynth(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_9,plain,
~ c_lessequals(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Osynth(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_14,plain,
( c_in(c_Main_OsubsetI__1(A,B,C),c_insert(D,A,C),C)
| c_lessequals(A,B,tc_set(C)) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_19,plain,
c_in(c_Main_OsubsetI__1(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Osynth(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_9,c_7]) ).
cnf(c_20,plain,
~ c_in(c_Main_OsubsetI__1(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Osynth(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Osynth(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_8,c_9]) ).
cnf(c_27,plain,
~ c_in(c_Main_OsubsetI__1(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Osynth(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_1,c_20]) ).
cnf(c_88,plain,
( c_lessequals(A,c_insert(B,A,C),tc_set(C))
| c_lessequals(A,c_insert(B,A,C),tc_set(C)) ),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_53,plain,
c_lessequals(A,c_insert(B,A,C),tc_set(C)),
inference(copy,[status(thm)],[c_88]) ).
cnf(c_69,plain,
c_lessequals(c_Message_Osynth(A),c_Message_Osynth(c_insert(B,A,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_53,c_2]) ).
cnf(c_89,plain,
( c_in(A,c_Message_Osynth(c_insert(C,B,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(A,c_Message_Osynth(B),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_6,c_69]) ).
cnf(c_73,plain,
~ c_in(c_Main_OsubsetI__1(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Osynth(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Osynth(v_H),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_89,c_20]) ).
cnf(c_90,plain,
( c_Main_OsubsetI__1(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Osynth(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg) = v_X
| c_in(c_Main_OsubsetI__1(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Osynth(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Osynth(v_H),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_19,c_5]) ).
cnf(c_83,plain,
c_Main_OsubsetI__1(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Osynth(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg) = v_X,
inference(resolve,[status(thm)],[c_73,c_90]) ).
cnf(c_91,plain,
~ c_in(v_X,c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg),
inference(paramod,[status(thm)],[c_83,c_27]) ).
cnf(c_87,plain,
$false,
inference(resolve,[status(thm)],[c_4,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV275-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 13:27:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 3003670 was started by sandbox2 on n003,
% 0.11/0.38 % Sat Sep 26 13:27:55 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.41
% 0.11/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.41
% 0.11/0.41 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/0.41 % Length of proof is 18.
% 0.11/0.41 % Level of proof is 6.
% 0.11/0.41 % Maximum clause weight is 27.000.
% 0.11/0.41 % Given clauses 32.
% 0.11/0.41
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------