%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV250-2 : 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 : n002.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 0.38s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 15 unt; 0 def)
% Number of atoms : 31 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 37 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1,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]) ).
fof(cls_conjecture_3,axiom,
~ c_in(v_x,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_Message_Omsg),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_2,plain,
~ c_in(v_x,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_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
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_3,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__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_4,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_5,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_4]) ).
fof(cls_Set_OUn__iff_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,VAR_1,VAR_3)
| c_in(VAR_0,VAR_2,VAR_3)
| ~ c_in(VAR_0,c_union(VAR_1,VAR_2,VAR_3),VAR_3) ),
file('theBenchmark.p',cls_Set_OUn__iff_0) ).
cnf(c_6,plain,
( c_in(A,B,D)
| c_in(A,C,D)
| ~ c_in(A,c_union(B,C,D),D) ),
inference(clausify,[status(thm)],[cls_Set_OUn__iff_0]) ).
fof(cls_Set_OUn__iff_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_OUn__iff_1) ).
cnf(c_7,plain,
( c_in(A,c_union(B,D,C),C)
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_OUn__iff_1]) ).
fof(cls_Set_OUn__iff_2,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_OUn__iff_2) ).
cnf(c_8,plain,
( c_in(A,c_union(D,B,C),C)
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_OUn__iff_2]) ).
cnf(c_12,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_3,c_5]) ).
cnf(c_17,plain,
~ c_in(v_x,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_7,c_2]) ).
cnf(c_19,plain,
~ c_in(v_x,c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_8,c_2]) ).
cnf(c_29,plain,
( c_in(v_x,A,tc_Message_Omsg)
| ~ c_in(v_x,c_union(A,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_6,c_17]) ).
cnf(c_30,plain,
~ c_in(v_x,c_union(c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_29,c_19]) ).
cnf(c_31,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(paramod,[status(thm)],[c_12,c_30]) ).
cnf(c_28,plain,
$false,
inference(resolve,[status(thm)],[c_1,c_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV250-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.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
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 13:25:36 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 1837674 was started by sandbox on n002,
% 0.02/0.36 % Sat Sep 26 13:25:36 2026
% 0.02/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.37
% 0.02/0.37 % From the command line: assign(max_seconds, 300).
% 0.02/0.38
% 0.02/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.02/0.38
% 0.02/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.02/0.38 % Length of proof is 12.
% 0.02/0.38 % Level of proof is 3.
% 0.02/0.38 % Maximum clause weight is 18.000.
% 0.02/0.38 % Given clauses 11.
% 0.02/0.38
% 0.02/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------