%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV252-2 : 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 : n011.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 09:07:09 AM UTC 2026
% Result : Unsatisfiable 3.35s 1.03s
% Output : CNFRefutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 65 ( 34 unt; 0 def)
% Number of atoms : 103 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 85 ( 47 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 130 ( 13 sgn 39 !; 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_Set_Oinsert__subset_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,VAR_3,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_0) ).
cnf(c_2,plain,
( c_in(A,D,C)
| ~ c_lessequals(c_insert(A,B,C),D,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Set_Oinsert__subset_0]) ).
fof(cls_conjecture_0,axiom,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_H)),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_3,plain,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_H)),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_4,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_5,plain,
class_Orderings_Oorder(tc_set(A)),
inference(clausify,[status(thm)],[clsarity_set_2]) ).
cnf(c_6,plain,
c_lessequals(A,A,tc_set(B)),
inference(resolve,[status(thm)],[c_4,c_5]) ).
fof(cls_conjecture_1,axiom,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Osynth(c_Message_Oanalz(v_H)),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_7,plain,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Osynth(c_Message_Oanalz(v_H)),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_Message_Oanalz__parts_0,axiom,
! [VAR_0] : c_Message_Oanalz(c_Message_Oparts(VAR_0)) = c_Message_Oparts(VAR_0),
file('theBenchmark.p',cls_Message_Oanalz__parts_0) ).
cnf(c_8,plain,
c_Message_Oanalz(c_Message_Oparts(A)) = c_Message_Oparts(A),
inference(clausify,[status(thm)],[cls_Message_Oanalz__parts_0]) ).
fof(cls_Message_Oanalz__subset__iff_0,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(VAR_0,c_Message_Oanalz(VAR_1),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(VAR_0),c_Message_Oanalz(VAR_1),tc_set(tc_Message_Omsg)) ),
file('theBenchmark.p',cls_Message_Oanalz__subset__iff_0) ).
cnf(c_9,plain,
( c_lessequals(A,c_Message_Oanalz(B),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(A),c_Message_Oanalz(B),tc_set(tc_Message_Omsg)) ),
inference(clausify,[status(thm)],[cls_Message_Oanalz__subset__iff_0]) ).
fof(cls_Message_Oparts__analz_0,axiom,
! [VAR_0] : c_Message_Oparts(c_Message_Oanalz(VAR_0)) = c_Message_Oparts(VAR_0),
file('theBenchmark.p',cls_Message_Oparts__analz_0) ).
cnf(c_10,plain,
c_Message_Oparts(c_Message_Oanalz(A)) = c_Message_Oparts(A),
inference(clausify,[status(thm)],[cls_Message_Oparts__analz_0]) ).
fof(cls_Message_Oparts__subset__iff_0,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(VAR_0,c_Message_Oparts(VAR_1),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(VAR_0),c_Message_Oparts(VAR_1),tc_set(tc_Message_Omsg)) ),
file('theBenchmark.p',cls_Message_Oparts__subset__iff_0) ).
cnf(c_11,plain,
( c_lessequals(A,c_Message_Oparts(B),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(A),c_Message_Oparts(B),tc_set(tc_Message_Omsg)) ),
inference(clausify,[status(thm)],[cls_Message_Oparts__subset__iff_0]) ).
fof(cls_Message_Oparts__subset__iff_1,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(c_Message_Oparts(VAR_0),c_Message_Oparts(VAR_1),tc_set(tc_Message_Omsg))
| ~ c_lessequals(VAR_0,c_Message_Oparts(VAR_1),tc_set(tc_Message_Omsg)) ),
file('theBenchmark.p',cls_Message_Oparts__subset__iff_1) ).
cnf(c_12,plain,
( c_lessequals(c_Message_Oparts(A),c_Message_Oparts(B),tc_set(tc_Message_Omsg))
| ~ c_lessequals(A,c_Message_Oparts(B),tc_set(tc_Message_Omsg)) ),
inference(clausify,[status(thm)],[cls_Message_Oparts__subset__iff_1]) ).
fof(cls_Message_Oparts__synth_0,axiom,
! [VAR_0] : c_Message_Oparts(c_Message_Osynth(VAR_0)) = c_union(c_Message_Oparts(VAR_0),c_Message_Osynth(VAR_0),tc_Message_Omsg),
file('theBenchmark.p',cls_Message_Oparts__synth_0) ).
cnf(c_13,plain,
c_Message_Oparts(c_Message_Osynth(A)) = c_union(c_Message_Oparts(A),c_Message_Osynth(A),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_Message_Oparts__synth_0]) ).
cnf(c_14,plain,
c_union(c_Message_Oparts(A),c_Message_Osynth(A),tc_Message_Omsg) = c_Message_Oparts(c_Message_Osynth(A)),
inference(copy,[status(thm)],[c_13]) ).
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(D,E,C),B,tc_set(C))
| c_lessequals(c_insert(D,A,C),B,tc_set(C))
| ~ c_lessequals(A,B,tc_set(C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_23,plain,
( c_lessequals(c_insert(v_X,A,tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_H)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(A,c_Message_Osynth(c_Message_Oanalz(v_H)),tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_2364,plain,
( c_lessequals(A,c_Message_Oanalz(c_Message_Oparts(B)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(A),c_Message_Oparts(B),tc_set(tc_Message_Omsg)) ),
inference(paramod,[status(thm)],[c_8,c_9]) ).
cnf(c_25,plain,
( c_lessequals(A,c_Message_Oparts(B),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(A),c_Message_Oparts(B),tc_set(tc_Message_Omsg)) ),
inference(paramod,[status(thm)],[c_8,c_2364]) ).
cnf(c_26,plain,
c_lessequals(A,c_Message_Oparts(A),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_11,c_6]) ).
cnf(c_29,plain,
c_union(c_Message_Oparts(A),c_Message_Osynth(c_Message_Oanalz(A)),tc_Message_Omsg) = c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(A))),
inference(paramod,[status(thm)],[c_10,c_14]) ).
cnf(c_30,plain,
c_lessequals(A,c_union(A,B,C),tc_set(C)),
inference(resolve,[status(thm)],[c_17,c_6]) ).
cnf(c_34,plain,
c_lessequals(A,c_union(B,A,C),tc_set(C)),
inference(resolve,[status(thm)],[c_18,c_6]) ).
cnf(c_35,plain,
~ c_lessequals(c_union(A,c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_H)),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_18,c_7]) ).
cnf(c_39,plain,
c_lessequals(A,c_insert(B,A,C),tc_set(C)),
inference(resolve,[status(thm)],[c_20,c_6]) ).
cnf(c_42,plain,
c_lessequals(c_insert(v_X,c_Message_Osynth(c_Message_Oanalz(v_H)),tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_H)),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_23,c_6]) ).
cnf(c_132,plain,
c_lessequals(c_Message_Oparts(A),c_Message_Oparts(c_Message_Osynth(A)),tc_set(tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_14,c_30]) ).
cnf(c_2365,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_30]) ).
cnf(c_140,plain,
c_lessequals(c_union(A,B,C),c_union(B,A,C),tc_set(C)),
inference(resolve,[status(thm)],[c_2365,c_34]) ).
cnf(c_223,plain,
c_lessequals(A,c_Message_Oparts(c_Message_Osynth(A)),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_11,c_132]) ).
cnf(c_225,plain,
c_lessequals(A,c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(A))),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_25,c_223]) ).
cnf(c_2366,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_39]) ).
cnf(c_820,plain,
c_insert(v_X,c_Message_Osynth(c_Message_Oanalz(v_H)),tc_Message_Omsg) = c_Message_Osynth(c_Message_Oanalz(v_H)),
inference(resolve,[status(thm)],[c_2366,c_42]) ).
cnf(c_2367,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_140]) ).
cnf(c_1972,plain,
c_union(A,B,C) = c_union(B,A,C),
inference(resolve,[status(thm)],[c_2367,c_140]) ).
cnf(c_2368,plain,
( c_lessequals(c_union(c_union(C,B,D),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_140]) ).
cnf(c_2369,plain,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Osynth(c_Message_Oanalz(v_H)),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_2368,c_35]) ).
cnf(c_2370,plain,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_H),c_Message_Osynth(c_Message_Oanalz(v_H)),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_1972,c_2369]) ).
cnf(c_1998,plain,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))),tc_set(tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_29,c_2370]) ).
cnf(c_2354,plain,
~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_12,c_1998]) ).
cnf(c_2371,plain,
( ~ c_lessequals(c_insert(A,C,tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(B))),tc_set(tc_Message_Omsg))
| c_lessequals(c_insert(A,B,tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(B))),tc_set(tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_22,c_225]) ).
cnf(c_2355,plain,
~ c_lessequals(c_insert(v_X,A,tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))),tc_set(tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_2371,c_2354]) ).
cnf(c_2362,plain,
~ c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)),c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))),tc_set(tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_820,c_2355]) ).
cnf(c_2363,plain,
$false,
inference(resolve,[status(thm)],[c_2362,c_26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV252-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n011.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 13:22:44 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 656875 was started by sandbox2 on n011,
% 0.18/0.45 % Sat Sep 26 13:22:44 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 3.35/1.03
% 3.35/1.03 % SZS status Unsatisfiable for theBenchmark
% 3.35/1.03
% 3.35/1.03 % Proof 1 at 0.43 (+ 0.13) seconds.
% 3.35/1.03 % Length of proof is 40.
% 3.35/1.03 % Level of proof is 9.
% 3.35/1.03 % Maximum clause weight is 21.000.
% 3.35/1.03 % Given clauses 219.
% 3.35/1.03
% 3.35/1.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------