%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV249-2 : 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 : n014.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 0.02s 0.48s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 58 ( 37 unt; 0 def)
% Number of atoms : 85 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 37 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 134 ( 12 sgn 40 !; 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_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_2,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_Orderings_Oorder__class_Oaxioms__1_0,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(VAR_1,VAR_1,VAR_0)
| ~ class_Orderings_Oorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
cnf(c_3,plain,
( c_lessequals(B,B,A)
| ~ class_Orderings_Oorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Oorder__class_Oaxioms__1_0]) ).
fof(clsarity_set_2,axiom,
! [VAR_0] : class_Orderings_Oorder(tc_set(VAR_0)),
file('theBenchmark.p',clsarity_set_2) ).
cnf(c_4,plain,
class_Orderings_Oorder(tc_set(A)),
inference(clausify,[status(thm)],[clsarity_set_2]) ).
cnf(c_5,plain,
c_lessequals(A,A,tc_set(B)),
inference(resolve,[status(thm)],[c_3,c_4]) ).
fof(cls_conjecture_1,axiom,
~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_6,plain,
~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_Message_Oanalz__analz__Un_0,axiom,
! [VAR_0,VAR_1] : c_Message_Oanalz(c_union(c_Message_Oanalz(VAR_0),VAR_1,tc_Message_Omsg)) = c_Message_Oanalz(c_union(VAR_0,VAR_1,tc_Message_Omsg)),
file('theBenchmark.p',cls_Message_Oanalz__analz__Un_0) ).
cnf(c_7,plain,
c_Message_Oanalz(c_union(c_Message_Oanalz(A),B,tc_Message_Omsg)) = c_Message_Oanalz(c_union(A,B,tc_Message_Omsg)),
inference(clausify,[status(thm)],[cls_Message_Oanalz__analz__Un_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_8,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_Oanalz__synth__Un_0,axiom,
! [VAR_0,VAR_1] : c_Message_Oanalz(c_union(c_Message_Osynth(VAR_0),VAR_1,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(VAR_0,VAR_1,tc_Message_Omsg)),c_Message_Osynth(VAR_0),tc_Message_Omsg),
file('theBenchmark.p',cls_Message_Oanalz__synth__Un_0) ).
cnf(c_9,plain,
c_Message_Oanalz(c_union(c_Message_Osynth(A),B,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(A,B,tc_Message_Omsg)),c_Message_Osynth(A),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_Message_Oanalz__synth__Un_0]) ).
cnf(c_10,plain,
c_union(c_Message_Oanalz(c_union(A,B,tc_Message_Omsg)),c_Message_Osynth(A),tc_Message_Omsg) = c_Message_Oanalz(c_union(c_Message_Osynth(A),B,tc_Message_Omsg)),
inference(copy,[status(thm)],[c_9]) ).
fof(cls_Set_OUn__insert__left_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : c_union(c_insert(VAR_0,VAR_1,VAR_2),VAR_3,VAR_2) = c_insert(VAR_0,c_union(VAR_1,VAR_3,VAR_2),VAR_2),
file('theBenchmark.p',cls_Set_OUn__insert__left_0) ).
cnf(c_13,plain,
c_union(c_insert(A,B,C),D,C) = c_insert(A,c_union(B,D,C),C),
inference(clausify,[status(thm)],[cls_Set_OUn__insert__left_0]) ).
cnf(c_14,plain,
c_insert(A,c_union(B,C,D),D) = c_union(c_insert(A,B,D),C,D),
inference(copy,[status(thm)],[c_13]) ).
fof(cls_Set_OUn__insert__right_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : c_union(VAR_0,c_insert(VAR_1,VAR_2,VAR_3),VAR_3) = c_insert(VAR_1,c_union(VAR_0,VAR_2,VAR_3),VAR_3),
file('theBenchmark.p',cls_Set_OUn__insert__right_0) ).
cnf(c_15,plain,
c_union(A,c_insert(B,C,D),D) = c_insert(B,c_union(A,C,D),D),
inference(clausify,[status(thm)],[cls_Set_OUn__insert__right_0]) ).
cnf(c_579,plain,
c_union(A,c_insert(B,C,D),D) = c_union(c_insert(B,A,D),C,D),
inference(paramod,[status(thm)],[c_14,c_15]) ).
cnf(c_16,plain,
c_union(c_insert(A,B,C),D,C) = c_union(B,c_insert(A,D,C),C),
inference(copy,[status(thm)],[c_579]) ).
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_17,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_18,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_19,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__subset_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(VAR_1,VAR_3,tc_set(VAR_2))
| ~ c_lessequals(c_insert(VAR_0,VAR_1,VAR_2),VAR_3,tc_set(VAR_2)) ),
file('theBenchmark.p',cls_Set_Oinsert__subset_1) ).
cnf(c_20,plain,
( c_lessequals(B,D,tc_set(C))
| ~ c_lessequals(c_insert(A,B,C),D,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Set_Oinsert__subset_1]) ).
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_21,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]) ).
cnf(c_22,plain,
( c_lessequals(c_insert(v_X,A,tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(A,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_25,plain,
c_union(c_Message_Oanalz(c_union(A,B,tc_Message_Omsg)),c_Message_Osynth(c_Message_Oanalz(A)),tc_Message_Omsg) = c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(A)),B,tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_7,c_10]) ).
cnf(c_43,plain,
c_lessequals(A,c_union(A,B,C),tc_set(C)),
inference(resolve,[status(thm)],[c_17,c_5]) ).
cnf(c_49,plain,
c_lessequals(A,c_union(B,A,C),tc_set(C)),
inference(resolve,[status(thm)],[c_18,c_5]) ).
cnf(c_56,plain,
c_lessequals(A,c_insert(B,A,C),tc_set(C)),
inference(resolve,[status(thm)],[c_20,c_5]) ).
cnf(c_59,plain,
c_lessequals(c_insert(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_22,c_5]) ).
cnf(c_580,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_19,c_43]) ).
cnf(c_92,plain,
c_lessequals(c_union(A,B,C),c_union(B,A,C),tc_set(C)),
inference(resolve,[status(thm)],[c_580,c_49]) ).
cnf(c_581,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_21,c_92]) ).
cnf(c_266,plain,
c_union(A,B,C) = c_union(B,A,C),
inference(resolve,[status(thm)],[c_581,c_92]) ).
cnf(c_330,plain,
c_union(c_Message_Osynth(c_Message_Oanalz(A)),c_Message_Oanalz(c_union(A,B,tc_Message_Omsg)),tc_Message_Omsg) = c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(A)),B,tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_266,c_25]) ).
cnf(c_582,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(paramod,[status(thm)],[c_330,c_6]) ).
cnf(c_371,plain,
~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(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_266,c_582]) ).
cnf(c_386,plain,
~ c_lessequals(c_insert(v_X,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(resolve,[status(thm)],[c_8,c_371]) ).
cnf(c_388,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(resolve,[status(thm)],[c_18,c_386]) ).
cnf(c_583,plain,
~ c_lessequals(c_union(c_insert(v_X,A,tc_Message_Omsg),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_16,c_388]) ).
cnf(c_395,plain,
~ c_lessequals(c_union(v_H,c_insert(v_X,A,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_266,c_583]) ).
cnf(c_584,plain,
( c_lessequals(c_union(B,A,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_19,c_43]) ).
cnf(c_447,plain,
~ c_lessequals(c_insert(v_X,A,tc_Message_Omsg),c_union(v_H,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_584,c_395]) ).
cnf(c_585,plain,
( c_insert(A,B,C) = B
| ~ c_lessequals(c_insert(A,B,C),B,tc_set(C)) ),
inference(resolve,[status(thm)],[c_21,c_56]) ).
cnf(c_575,plain,
c_insert(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg) = c_Message_Osynth(c_Message_Oanalz(v_G)),
inference(resolve,[status(thm)],[c_585,c_59]) ).
cnf(c_577,plain,
~ c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)),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_575,c_447]) ).
cnf(c_578,plain,
$false,
inference(resolve,[status(thm)],[c_577,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV249-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Sat Sep 26 13:23:01 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.36 % Process 3251336 was started by sandbox2 on n014,
% 0.02/0.36 % Sat Sep 26 13:23:01 2026
% 0.02/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.37
% 0.02/0.37 % From the command line: assign(max_seconds, 300).
% 0.02/0.48
% 0.02/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.02/0.48
% 0.02/0.48 % Proof 1 at 0.09 (+ 0.02) seconds.
% 0.02/0.48 % Length of proof is 36.
% 0.02/0.48 % Level of proof is 12.
% 0.02/0.48 % Maximum clause weight is 18.000.
% 0.02/0.48 % Given clauses 87.
% 0.02/0.48
% 0.02/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------