%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV905-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 09:09:19 AM UTC 2026
% Result : Unsatisfiable 1.61s 0.68s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 12 unt; 0 def)
% Number of atoms : 37 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 19 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_4,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_141,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_3,axiom,
hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_142,plain,
hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_1,axiom,
c_Com_OWT__bodies,
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_144,plain,
c_Com_OWT__bodies,
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_145,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_MGF_0,axiom,
! [VAR_0] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_Com_OWT(VAR_0)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(VAR_0),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
file('theBenchmark.p',cls_MGF_0) ).
cnf(c_173,plain,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_Com_OWT(A)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(A),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(clausify,[status(thm)],[cls_MGF_0]) ).
cnf(c_3270,plain,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(A)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(A),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(resolve,[status(thm)],[c_144,c_173]) ).
cnf(c_174,plain,
( ~ c_Com_OWT(A)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(A),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(resolve,[status(thm)],[c_145,c_3270]) ).
fof(cls_WT_OBody_0,axiom,
! [VAR_0] :
( hAPP(c_Com_Obody,VAR_0) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Com_OWT(c_Com_Ocom_OBODY(VAR_0)) ),
file('theBenchmark.p',cls_WT_OBody_0) ).
cnf(c_189,plain,
( hAPP(c_Com_Obody,A) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Com_OWT(c_Com_Ocom_OBODY(A)) ),
inference(clausify,[status(thm)],[cls_WT_OBody_0]) ).
cnf(c_190,plain,
( c_Option_Ooption_ONone(tc_Com_Ocom) = hAPP(c_Com_Obody,A)
| c_Com_OWT(c_Com_Ocom_OBODY(A)) ),
inference(copy,[status(thm)],[c_189]) ).
fof(cls_domIff_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ hBOOL(c_in(VAR_1,c_Map_Odom(VAR_0,VAR_3,VAR_2),VAR_3))
| hAPP(VAR_0,VAR_1) != c_Option_Ooption_ONone(VAR_2) ),
file('theBenchmark.p',cls_domIff_0) ).
cnf(c_207,plain,
( ~ hBOOL(c_in(B,c_Map_Odom(A,D,C),D))
| hAPP(A,B) != c_Option_Ooption_ONone(C) ),
inference(clausify,[status(thm)],[cls_domIff_0]) ).
cnf(c_208,plain,
( ~ hBOOL(c_in(C,c_Map_Odom(B,D,A),D))
| c_Option_Ooption_ONone(A) != hAPP(B,C) ),
inference(copy,[status(thm)],[c_207]) ).
cnf(c_781,plain,
c_Option_Ooption_ONone(tc_Com_Ocom) != hAPP(c_Com_Obody,v_x),
inference(resolve,[status(thm)],[c_208,c_142]) ).
cnf(c_3250,plain,
c_Com_OWT(c_Com_Ocom_OBODY(v_x)),
inference(resolve,[status(thm)],[c_781,c_190]) ).
cnf(c_3271,plain,
c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(resolve,[status(thm)],[c_3250,c_174]) ).
cnf(c_3269,plain,
$false,
inference(resolve,[status(thm)],[c_141,c_3271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV905-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 15:08:48 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1621873 was started by sandbox2 on n019,
% 0.10/0.36 % Sat Sep 26 15:08:48 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 1.61/0.68
% 1.61/0.68 % SZS status Unsatisfiable for theBenchmark
% 1.61/0.68
% 1.61/0.68 % Proof 1 at 0.24 (+ 0.05) seconds.
% 1.61/0.68 % Length of proof is 13.
% 1.61/0.68 % Level of proof is 4.
% 1.61/0.68 % Maximum clause weight is 44.000.
% 1.61/0.68 % Given clauses 498.
% 1.61/0.68
% 1.61/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------