%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV251-2 : 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 : n018.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 2.85s 0.86s
% Output : CNFRefutation 2.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 42 ( 25 unt; 0 def)
% Number of atoms : 65 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 31 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 86 ( 7 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1,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_Set_OUn__Diff__cancel_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_union(VAR_0,c_minus(VAR_1,VAR_0,tc_set(VAR_2)),VAR_2) = c_union(VAR_0,VAR_1,VAR_2),
file('theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
cnf(c_3,plain,
c_union(A,c_minus(B,A,tc_set(C)),C) = c_union(A,B,C),
inference(clausify,[status(thm)],[cls_Set_OUn__Diff__cancel_0]) ).
fof(cls_Set_OUn__subset__iff_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(VAR_0,VAR_3,tc_set(VAR_2))
| ~ c_lessequals(c_union(VAR_0,VAR_1,VAR_2),VAR_3,tc_set(VAR_2)) ),
file('theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
cnf(c_4,plain,
( c_lessequals(A,D,tc_set(C))
| ~ c_lessequals(c_union(A,B,C),D,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Set_OUn__subset__iff_0]) ).
fof(cls_Set_OUn__subset__iff_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(VAR_1,VAR_3,tc_set(VAR_2))
| ~ c_lessequals(c_union(VAR_0,VAR_1,VAR_2),VAR_3,tc_set(VAR_2)) ),
file('theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
cnf(c_5,plain,
( c_lessequals(B,D,tc_set(C))
| ~ c_lessequals(c_union(A,B,C),D,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Set_OUn__subset__iff_1]) ).
fof(cls_Set_OUn__subset__iff_2,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__subset__iff_2) ).
cnf(c_6,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__subset__iff_2]) ).
fof(cls_Set_Oinsert__Diff1_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_minus(c_insert(VAR_0,VAR_3,VAR_2),VAR_1,tc_set(VAR_2)) = c_minus(VAR_3,VAR_1,tc_set(VAR_2))
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
cnf(c_7,plain,
( c_minus(c_insert(A,D,C),B,tc_set(C)) = c_minus(D,B,tc_set(C))
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_Oinsert__Diff1_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_8,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_Osubset__antisym_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = VAR_0
| ~ c_lessequals(VAR_1,VAR_0,tc_set(VAR_2))
| ~ c_lessequals(VAR_0,VAR_1,tc_set(VAR_2)) ),
file('theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(c_9,plain,
( B = A
| ~ c_lessequals(B,A,tc_set(C))
| ~ c_lessequals(A,B,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Set_Osubset__antisym_0]) ).
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_10,plain,
c_lessequals(A,A,tc_set(B)),
inference(clausify,[status(thm)],[cls_Set_Osubset__refl_0]) ).
fof(cls_conjecture_0,axiom,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_11,plain,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_12,plain,
c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
~ c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_13,plain,
~ c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_17,plain,
c_lessequals(A,c_union(B,A,C),tc_set(C)),
inference(resolve,[status(thm)],[c_5,c_10]) ).
cnf(c_18,plain,
c_lessequals(A,c_union(A,B,C),tc_set(C)),
inference(resolve,[status(thm)],[c_4,c_10]) ).
cnf(c_19,plain,
c_minus(c_insert(v_X,A,tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)) = c_minus(A,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_7,c_11]) ).
cnf(c_1640,plain,
( c_in(v_x,A,tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),A,tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_8,c_12]) ).
cnf(c_21,plain,
~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_1640,c_13]) ).
cnf(c_36,plain,
~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_1,c_21]) ).
cnf(c_37,plain,
~ c_lessequals(c_union(A,c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_5,c_36]) ).
cnf(c_1641,plain,
( c_lessequals(c_union(A,B,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_6,c_18]) ).
cnf(c_59,plain,
c_lessequals(c_union(A,B,C),c_union(B,A,C),tc_set(C)),
inference(resolve,[status(thm)],[c_1641,c_17]) ).
cnf(c_1642,plain,
( c_union(A,B,C) = c_union(B,A,C)
| ~ c_lessequals(c_union(A,B,C),c_union(B,A,C),tc_set(C)) ),
inference(resolve,[status(thm)],[c_9,c_59]) ).
cnf(c_64,plain,
c_union(A,B,C) = c_union(B,A,C),
inference(resolve,[status(thm)],[c_1642,c_59]) ).
cnf(c_76,plain,
~ c_lessequals(c_union(A,c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(v_H,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_64,c_37]) ).
cnf(c_1643,plain,
c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_minus(A,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)),tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_insert(v_X,A,tc_Message_Omsg),tc_Message_Omsg),
inference(paramod,[status(thm)],[c_19,c_3]) ).
cnf(c_1644,plain,
c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),A,tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_insert(v_X,A,tc_Message_Omsg),tc_Message_Omsg),
inference(paramod,[status(thm)],[c_3,c_1643]) ).
cnf(c_85,plain,
c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_insert(v_X,A,tc_Message_Omsg),tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),A,tc_Message_Omsg),
inference(copy,[status(thm)],[c_1644]) ).
cnf(c_1645,plain,
~ c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),c_union(v_H,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_85,c_76]) ).
cnf(c_1638,plain,
~ c_lessequals(c_union(v_H,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),c_union(v_H,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_64,c_1645]) ).
cnf(c_1639,plain,
$false,
inference(resolve,[status(thm)],[c_1638,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV251-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n018.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sat Sep 26 13:25:07 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.45 % Process 550699 was started by sandbox2 on n018,
% 0.16/0.45 % Sat Sep 26 13:25:07 2026
% 0.16/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 2.85/0.86
% 2.85/0.86 % SZS status Unsatisfiable for theBenchmark
% 2.85/0.86
% 2.85/0.86 % Proof 1 at 0.29 (+ 0.10) seconds.
% 2.85/0.86 % Length of proof is 24.
% 2.85/0.86 % Level of proof is 6.
% 2.85/0.86 % Maximum clause weight is 40.000.
% 2.85/0.86 % Given clauses 133.
% 2.85/0.86
% 2.85/0.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------