%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV262-2 : 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 : n006.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 09:07:11 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 41 ( 1 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_union(c_union(c_Message_Oparts(c_insert(v_X,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(v_H),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_union(c_union(c_Message_Oparts(c_insert(v_X,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(v_H),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_Message_Oparts__Un_0,axiom,
! [VAR_0,VAR_1] : c_Message_Oparts(c_union(VAR_0,VAR_1,tc_Message_Omsg)) = c_union(c_Message_Oparts(VAR_0),c_Message_Oparts(VAR_1),tc_Message_Omsg),
file('theBenchmark.p',cls_Message_Oparts__Un_0) ).
cnf(c_2,plain,
c_Message_Oparts(c_union(A,B,tc_Message_Omsg)) = c_union(c_Message_Oparts(A),c_Message_Oparts(B),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_Message_Oparts__Un_0]) ).
cnf(c_3,plain,
c_union(c_Message_Oparts(A),c_Message_Oparts(B),tc_Message_Omsg) = c_Message_Oparts(c_union(A,B,tc_Message_Omsg)),
inference(copy,[status(thm)],[c_2]) ).
fof(cls_Set_OUn__empty__left_0,axiom,
! [VAR_0,VAR_1] : c_union(c_emptyset,VAR_0,VAR_1) = VAR_0,
file('theBenchmark.p',cls_Set_OUn__empty__left_0) ).
cnf(c_4,plain,
c_union(c_emptyset,A,B) = A,
inference(clausify,[status(thm)],[cls_Set_OUn__empty__left_0]) ).
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_5,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_6,plain,
c_insert(A,c_union(B,C,D),D) = c_union(c_insert(A,B,D),C,D),
inference(copy,[status(thm)],[c_5]) ).
cnf(c_30,plain,
c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_union(c_Message_Oparts(c_union(c_insert(v_X,c_emptyset,tc_Message_Omsg),c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(v_H),tc_Message_Omsg),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_7,plain,
c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_Message_Oparts(c_union(c_union(c_insert(v_X,c_emptyset,tc_Message_Omsg),c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_3,c_30]) ).
cnf(c_31,plain,
c_insert(A,B,C) = c_union(c_insert(A,c_emptyset,C),B,C),
inference(paramod,[status(thm)],[c_4,c_6]) ).
cnf(c_9,plain,
c_union(c_insert(A,c_emptyset,B),C,B) = c_insert(A,C,B),
inference(copy,[status(thm)],[c_31]) ).
cnf(c_32,plain,
c_union(c_Message_Oparts(c_insert(A,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(B),tc_Message_Omsg) = c_Message_Oparts(c_insert(A,B,tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_12,plain,
c_Message_Oparts(c_union(c_insert(A,c_emptyset,tc_Message_Omsg),B,tc_Message_Omsg)) = c_Message_Oparts(c_insert(A,B,tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_3,c_32]) ).
cnf(c_33,plain,
c_Message_Oparts(c_insert(v_X,c_union(c_insert(v_Y,c_emptyset,tc_Message_Omsg),v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_Message_Oparts(c_union(c_union(c_insert(v_X,c_emptyset,tc_Message_Omsg),c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_9,c_7]) ).
cnf(c_17,plain,
c_Message_Oparts(c_union(c_insert(v_X,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)) != c_Message_Oparts(c_union(c_union(c_insert(v_X,c_emptyset,tc_Message_Omsg),c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_6,c_33]) ).
cnf(c_34,plain,
c_union(c_Message_Oparts(c_insert(A,B,tc_Message_Omsg)),c_Message_Oparts(C),tc_Message_Omsg) = c_Message_Oparts(c_union(c_union(c_insert(A,c_emptyset,tc_Message_Omsg),B,tc_Message_Omsg),C,tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_12,c_3]) ).
cnf(c_35,plain,
c_Message_Oparts(c_union(c_insert(A,B,tc_Message_Omsg),C,tc_Message_Omsg)) = c_Message_Oparts(c_union(c_union(c_insert(A,c_emptyset,tc_Message_Omsg),B,tc_Message_Omsg),C,tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_3,c_34]) ).
cnf(c_28,plain,
c_Message_Oparts(c_union(c_union(c_insert(A,c_emptyset,tc_Message_Omsg),B,tc_Message_Omsg),C,tc_Message_Omsg)) = c_Message_Oparts(c_union(c_insert(A,B,tc_Message_Omsg),C,tc_Message_Omsg)),
inference(copy,[status(thm)],[c_35]) ).
cnf(c_36,plain,
c_Message_Oparts(c_union(c_union(c_insert(v_X,c_emptyset,tc_Message_Omsg),c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)) != c_Message_Oparts(c_union(c_insert(v_X,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_29,plain,
$false,
inference(resolve,[status(thm)],[c_28,c_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV262-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.39 % Computer : n006.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sat Sep 26 13:24:12 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.39 % Process 1370771 was started by sandbox2 on n006,
% 0.11/0.39 % Sat Sep 26 13:24:12 2026
% 0.11/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % 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 0.00 (+ 0.00) seconds.
% 0.11/0.41 % Length of proof is 12.
% 0.11/0.41 % Level of proof is 5.
% 0.11/0.41 % Maximum clause weight is 26.000.
% 0.11/0.41 % Given clauses 7.
% 0.11/0.41
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------