%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV907-1 : 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 : n020.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 9.94s 11.72s
% Output : CNFRefutation 9.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 19 unt; 0 def)
% Number of atoms : 66 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 68 ( 36 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-5 aty)
% Number of variables : 46 ( 1 sgn 13 !; 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_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_124,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_1,axiom,
c_Com_OWT__bodies,
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_128,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_129,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_image__image_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : c_Set_Oimage(VAR_0,c_Set_Oimage(VAR_1,VAR_2,VAR_3,VAR_4),VAR_4,VAR_5) = c_Set_Oimage(c_COMBB(VAR_0,VAR_1,VAR_4,VAR_5,VAR_3),VAR_2,VAR_3,VAR_5),
file('theBenchmark.p',cls_image__image_0) ).
cnf(c_141,plain,
c_Set_Oimage(A,c_Set_Oimage(B,C,D,E),E,F) = c_Set_Oimage(c_COMBB(A,B,E,F,D),C,D,F),
inference(clausify,[status(thm)],[cls_image__image_0]) ).
cnf(c_142,plain,
c_Set_Oimage(c_COMBB(A,B,C,D,E),F,E,D) = c_Set_Oimage(A,c_Set_Oimage(B,F,E,C),C,D),
inference(copy,[status(thm)],[c_141]) ).
fof(cls_MGF__lemma2__simult_0,axiom,
! [VAR_0] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_lessequals(VAR_0,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),VAR_0,tc_Com_Ostate) ),
file('theBenchmark.p',cls_MGF__lemma2__simult_0) ).
cnf(c_150,plain,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_lessequals(A,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),A,tc_Com_Ostate) ),
inference(clausify,[status(thm)],[cls_MGF__lemma2__simult_0]) ).
cnf(c_5754,plain,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_lessequals(A,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),A,tc_Com_Ostate) ),
inference(paramod,[status(thm)],[c_142,c_150]) ).
cnf(c_5755,plain,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_lessequals(A,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),A,tc_Com_Ostate) ),
inference(paramod,[status(thm)],[c_142,c_5754]) ).
cnf(c_5756,plain,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_lessequals(A,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Option_Othe(tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),A,tc_Com_Ostate) ),
inference(paramod,[status(thm)],[c_142,c_5755]) ).
cnf(c_5757,plain,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_lessequals(A,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Option_Othe(tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),A,tc_Com_Ostate) ),
inference(resolve,[status(thm)],[c_128,c_5756]) ).
cnf(c_151,plain,
( ~ c_lessequals(A,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Option_Othe(tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),A,tc_Com_Ostate) ),
inference(resolve,[status(thm)],[c_129,c_5757]) ).
fof(cls_finite__dom__body_0,axiom,
c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
file('theBenchmark.p',cls_finite__dom__body_0) ).
cnf(c_158,plain,
c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
inference(clausify,[status(thm)],[cls_finite__dom__body_0]) ).
fof(cls_MGT__Body_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(VAR_0,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),VAR_1,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),VAR_1,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Finite__Set_Ofinite(VAR_1,tc_Com_Opname)
| c_Hoare__Mirabelle_Ohoare__derivs(VAR_0,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),VAR_1,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
file('theBenchmark.p',cls_MGT__Body_0) ).
cnf(c_167,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(A,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),B,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),B,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Finite__Set_Ofinite(B,tc_Com_Opname)
| c_Hoare__Mirabelle_Ohoare__derivs(A,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),B,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(clausify,[status(thm)],[cls_MGT__Body_0]) ).
cnf(c_5758,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(A,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),B,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),B,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Finite__Set_Ofinite(B,tc_Com_Opname)
| c_Hoare__Mirabelle_Ohoare__derivs(A,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,B,tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(paramod,[status(thm)],[c_142,c_167]) ).
cnf(c_5759,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(A,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,B,tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),B,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Finite__Set_Ofinite(B,tc_Com_Opname)
| c_Hoare__Mirabelle_Ohoare__derivs(A,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,B,tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(paramod,[status(thm)],[c_142,c_5758]) ).
cnf(c_5760,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(A,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,B,tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),B,tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Finite__Set_Ofinite(B,tc_Com_Opname)
| c_Hoare__Mirabelle_Ohoare__derivs(A,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,B,tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(paramod,[status(thm)],[c_142,c_5759]) ).
cnf(c_168,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(A,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,B,tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Option_Othe(tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,B,tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Finite__Set_Ofinite(B,tc_Com_Opname)
| c_Hoare__Mirabelle_Ohoare__derivs(A,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,B,tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(paramod,[status(thm)],[c_142,c_5760]) ).
fof(cls_subset__refl_0,axiom,
! [VAR_0,VAR_1] : c_lessequals(VAR_0,VAR_0,tc_fun(VAR_1,tc_bool)),
file('theBenchmark.p',cls_subset__refl_0) ).
cnf(c_279,plain,
c_lessequals(A,A,tc_fun(B,tc_bool)),
inference(clausify,[status(thm)],[cls_subset__refl_0]) ).
fof(cls_Un__empty__left_0,axiom,
! [VAR_0,VAR_1] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(VAR_0,tc_bool)),VAR_1,tc_fun(VAR_0,tc_bool)) = VAR_1,
file('theBenchmark.p',cls_Un__empty__left_0) ).
cnf(c_365,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B,tc_fun(A,tc_bool)) = B,
inference(clausify,[status(thm)],[cls_Un__empty__left_0]) ).
cnf(c_678,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(paramod,[status(thm)],[c_142,c_124]) ).
cnf(c_816,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(A,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Option_Othe(tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| c_Hoare__Mirabelle_Ohoare__derivs(A,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(resolve,[status(thm)],[c_168,c_158]) ).
cnf(c_1007,plain,
c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Option_Othe(tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(resolve,[status(thm)],[c_279,c_151]) ).
cnf(c_5761,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Option_Othe(tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(paramod,[status(thm)],[c_365,c_816]) ).
cnf(c_5762,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Option_Othe(tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(resolve,[status(thm)],[c_678,c_5761]) ).
cnf(c_5753,plain,
$false,
inference(resolve,[status(thm)],[c_1007,c_5762]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV907-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/10.44 % Computer : n020.cluster.edu
% 0.16/10.44 % Model : x86_64 x86_64
% 0.16/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/10.44 % Memory : 8046.5625MB
% 0.16/10.44 % OS : Linux 6.8.0-71-generic
% 0.16/10.44 % CPULimit : 300
% 0.16/10.44 % WCLimit : 300
% 0.16/10.44 % DateTime : Sat Sep 26 15:10:00 UTC 2026
% 0.16/10.45 % CPUTime :
% 0.16/10.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/10.45 % Process 1867049 was started by sandbox2 on n020,
% 0.16/10.45 % Sat Sep 26 15:10:00 2026
% 0.16/10.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/10.47
% 0.16/10.47 % From the command line: assign(max_seconds, 300).
% 9.94/11.72
% 9.94/11.72 % given #500 (I,wt=40): 678 -c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate). [back_rewrite(124),rewrite([142(20)])].
% 9.94/11.72
% 9.94/11.72 % SZS status Unsatisfiable for theBenchmark
% 9.94/11.72
% 9.94/11.72 % Proof 1 at 0.96 (+ 0.27) seconds.
% 9.94/11.72 % Length of proof is 16.
% 9.94/11.72 % Level of proof is 4.
% 9.94/11.72 % Maximum clause weight is 82.000.
% 9.94/11.72 % Given clauses 873.
% 9.94/11.72
% 9.94/11.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------