TSTP Solution File: SWW385+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWW385+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 29 20:58:27 EDT 2022

% Result   : Theorem 5.16s 3.97s
% Output   : Proof 5.61s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWW385+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sun Sep  4 16:02:55 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 5.16/3.97  % SZS status Theorem
% 5.16/3.97  % SZS output start Proof
% 5.16/3.97  tff(hBOOL_type, type, (
% 5.16/3.97     hBOOL: $i > $o)).
% 5.16/3.97  tff(hAPP_type, type, (
% 5.16/3.97     hAPP: ( $i * $i ) > $i)).
% 5.16/3.97  tff(tptp_fun_B_x_468_type, type, (
% 5.16/3.97     tptp_fun_B_x_468: $i)).
% 5.16/3.97  tff(c_Com_Ocom_OBODY_type, type, (
% 5.16/3.97     c_Com_Ocom_OBODY: $i)).
% 5.16/3.97  tff(c_Com_OWT_type, type, (
% 5.16/3.97     c_Com_OWT: $i)).
% 5.16/3.97  tff(c_Hoare__Mirabelle_Ohoare__derivs_type, type, (
% 5.16/3.97     c_Hoare__Mirabelle_Ohoare__derivs: ( $i * $i * $i ) > $o)).
% 5.16/3.97  tff(c_Orderings_Obot__class_Obot_type, type, (
% 5.16/3.97     c_Orderings_Obot__class_Obot: $i > $i)).
% 5.16/3.97  tff(tc_fun_type, type, (
% 5.16/3.97     tc_fun: ( $i * $i ) > $i)).
% 5.16/3.97  tff(tc_HOL_Obool_type, type, (
% 5.16/3.97     tc_HOL_Obool: $i)).
% 5.16/3.97  tff(tc_Hoare__Mirabelle_Otriple_type, type, (
% 5.16/3.97     tc_Hoare__Mirabelle_Otriple: $i > $i)).
% 5.16/3.97  tff(tc_Com_Ostate_type, type, (
% 5.16/3.97     tc_Com_Ostate: $i)).
% 5.16/3.97  tff(c_Hoare__Mirabelle_OMGT_type, type, (
% 5.16/3.97     c_Hoare__Mirabelle_OMGT: $i)).
% 5.16/3.97  tff(c_Set_Oinsert_type, type, (
% 5.16/3.97     c_Set_Oinsert: $i > $i)).
% 5.16/3.97  tff(c_Map_Odom_type, type, (
% 5.16/3.97     c_Map_Odom: ( $i * $i * $i ) > $i)).
% 5.16/3.97  tff(c_Com_Obodies_type, type, (
% 5.16/3.97     c_Com_Obodies: $i)).
% 5.16/3.97  tff(c_Map_Omap__of_type, type, (
% 5.16/3.97     c_Map_Omap__of: ( $i * $i ) > $i)).
% 5.16/3.97  tff(tc_Com_Ocom_type, type, (
% 5.16/3.97     tc_Com_Ocom: $i)).
% 5.16/3.97  tff(tc_Com_Opname_type, type, (
% 5.16/3.97     tc_Com_Opname: $i)).
% 5.16/3.97  tff(c_member_type, type, (
% 5.16/3.97     c_member: $i > $i)).
% 5.16/3.97  tff(c_Com_Obody_type, type, (
% 5.16/3.97     c_Com_Obody: $i)).
% 5.16/3.97  tff(c_Hoare__Mirabelle_Ostate__not__singleton_type, type, (
% 5.16/3.97     c_Hoare__Mirabelle_Ostate__not__singleton: $o)).
% 5.16/3.97  tff(c_Com_OWT__bodies_type, type, (
% 5.16/3.97     c_Com_OWT__bodies: $o)).
% 5.16/3.97  tff(c_Option_Ooption_ONone_type, type, (
% 5.16/3.97     c_Option_Ooption_ONone: $i > $i)).
% 5.16/3.97  tff(1,plain,
% 5.16/3.97      ((~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))) <=> (~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))))),
% 5.16/3.97      inference(rewrite,[status(thm)],[])).
% 5.16/3.97  tff(2,plain,
% 5.16/3.97      ((~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))) <=> (~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))))),
% 5.16/3.97      inference(rewrite,[status(thm)],[])).
% 5.16/3.97  tff(3,plain,
% 5.16/3.97      ((~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))) <=> (~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))))),
% 5.16/3.97      inference(rewrite,[status(thm)],[])).
% 5.16/3.97  tff(4,plain,
% 5.16/3.97      ((~![B_x: $i] : (hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))) => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))) <=> (~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))))),
% 5.16/3.97      inference(rewrite,[status(thm)],[])).
% 5.16/3.97  tff(5,axiom,(~![B_x: $i] : (hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))) => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_3')).
% 5.16/3.97  tff(6,plain,
% 5.16/3.97      (~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))),
% 5.16/3.97      inference(modus_ponens,[status(thm)],[5, 4])).
% 5.16/3.97  tff(7,plain,
% 5.16/3.97      (~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))),
% 5.16/3.97      inference(modus_ponens,[status(thm)],[6, 3])).
% 5.16/3.97  tff(8,plain,
% 5.16/3.97      (~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))),
% 5.16/3.97      inference(modus_ponens,[status(thm)],[7, 3])).
% 5.16/3.97  tff(9,plain,
% 5.16/3.97      (~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))),
% 5.16/3.97      inference(modus_ponens,[status(thm)],[8, 3])).
% 5.16/3.97  tff(10,plain,
% 5.16/3.97      (~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))),
% 5.16/3.97      inference(modus_ponens,[status(thm)],[9, 3])).
% 5.16/3.97  tff(11,plain,
% 5.16/3.97      (~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))),
% 5.16/3.97      inference(modus_ponens,[status(thm)],[10, 2])).
% 5.16/3.97  tff(12,plain,
% 5.16/3.97      (~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))),
% 5.16/3.97      inference(modus_ponens,[status(thm)],[11, 1])).
% 5.16/3.97  tff(13,plain,
% 5.16/3.97      (~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))),
% 5.16/3.97      inference(modus_ponens,[status(thm)],[12, 1])).
% 5.16/3.97  tff(14,plain,
% 5.16/3.97      (~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))),
% 5.16/3.97      inference(modus_ponens,[status(thm)],[13, 1])).
% 5.16/3.97  tff(15,plain,
% 5.16/3.97      (~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))),
% 5.16/3.98      inference(modus_ponens,[status(thm)],[14, 1])).
% 5.16/3.98  tff(16,plain,
% 5.16/3.98      (~![B_x: $i] : ((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))),
% 5.16/3.98      inference(modus_ponens,[status(thm)],[15, 1])).
% 5.16/3.98  tff(17,plain,(
% 5.16/3.98      ~((~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x!468), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x!468))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))),
% 5.16/3.98      inference(skolemize,[status(sab)],[16])).
% 5.16/3.98  tff(18,plain,
% 5.16/3.98      (~c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x!468))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))),
% 5.16/3.98      inference(or_elim,[status(thm)],[17])).
% 5.16/3.98  tff(19,plain,
% 5.16/3.98      (^[V_ca_2: $i] : refl((c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2)))) <=> (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2)))))),
% 5.16/3.98      inference(bind,[status(th)],[])).
% 5.16/3.98  tff(20,plain,
% 5.16/3.98      (![V_ca_2: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2)))) <=> ![V_ca_2: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))))),
% 5.16/3.98      inference(quant_intro,[status(thm)],[19])).
% 5.16/3.98  tff(21,plain,
% 5.16/3.98      (![V_ca_2: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2)))) <=> ![V_ca_2: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))))),
% 5.16/3.98      inference(rewrite,[status(thm)],[])).
% 5.16/3.98  tff(22,plain,
% 5.16/3.98      (^[V_ca_2: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(c_Com_OWT__bodies), (c_Com_OWT__bodies <=> $true)), ((~c_Com_OWT__bodies) <=> (~$true))), rewrite((~$true) <=> $false), ((~c_Com_OWT__bodies) <=> $false)), trans(monotonicity(iff_true(asserted(c_Hoare__Mirabelle_Ostate__not__singleton), (c_Hoare__Mirabelle_Ostate__not__singleton <=> $true)), ((~c_Hoare__Mirabelle_Ostate__not__singleton) <=> (~$true))), rewrite((~$true) <=> $false), ((~c_Hoare__Mirabelle_Ostate__not__singleton) <=> $false)), ((c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))) | (~c_Com_OWT__bodies) | (~c_Hoare__Mirabelle_Ostate__not__singleton)) <=> (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))) | $false | $false))), rewrite((c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))) | $false | $false) <=> (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))))), ((c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))) | (~c_Com_OWT__bodies) | (~c_Hoare__Mirabelle_Ostate__not__singleton)) <=> (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))))))),
% 5.16/3.98      inference(bind,[status(th)],[])).
% 5.16/3.98  tff(23,plain,
% 5.16/3.98      (![V_ca_2: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))) | (~c_Com_OWT__bodies) | (~c_Hoare__Mirabelle_Ostate__not__singleton)) <=> ![V_ca_2: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))))),
% 5.16/3.98      inference(quant_intro,[status(thm)],[22])).
% 5.16/3.98  tff(24,plain,
% 5.16/3.98      (^[V_ca_2: $i] : trans(monotonicity(trans(monotonicity(rewrite((hBOOL(hAPP(c_Com_OWT, V_ca_2)) => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))) <=> ((~hBOOL(hAPP(c_Com_OWT, V_ca_2))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))), ((c_Com_OWT__bodies => (hBOOL(hAPP(c_Com_OWT, V_ca_2)) => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))) <=> (c_Com_OWT__bodies => ((~hBOOL(hAPP(c_Com_OWT, V_ca_2))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))))), rewrite((c_Com_OWT__bodies => ((~hBOOL(hAPP(c_Com_OWT, V_ca_2))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))) <=> (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))) | (~c_Com_OWT__bodies))), ((c_Com_OWT__bodies => (hBOOL(hAPP(c_Com_OWT, V_ca_2)) => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))) <=> (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))) | (~c_Com_OWT__bodies)))), ((c_Hoare__Mirabelle_Ostate__not__singleton => (c_Com_OWT__bodies => (hBOOL(hAPP(c_Com_OWT, V_ca_2)) => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))))) <=> (c_Hoare__Mirabelle_Ostate__not__singleton => (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))) | (~c_Com_OWT__bodies))))), rewrite((c_Hoare__Mirabelle_Ostate__not__singleton => (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))) | (~c_Com_OWT__bodies))) <=> (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))) | (~c_Com_OWT__bodies) | (~c_Hoare__Mirabelle_Ostate__not__singleton))), ((c_Hoare__Mirabelle_Ostate__not__singleton => (c_Com_OWT__bodies => (hBOOL(hAPP(c_Com_OWT, V_ca_2)) => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))))) <=> (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))) | (~c_Com_OWT__bodies) | (~c_Hoare__Mirabelle_Ostate__not__singleton))))),
% 5.16/3.98      inference(bind,[status(th)],[])).
% 5.16/3.98  tff(25,plain,
% 5.16/3.98      (![V_ca_2: $i] : (c_Hoare__Mirabelle_Ostate__not__singleton => (c_Com_OWT__bodies => (hBOOL(hAPP(c_Com_OWT, V_ca_2)) => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))))) <=> ![V_ca_2: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))) | (~c_Com_OWT__bodies) | (~c_Hoare__Mirabelle_Ostate__not__singleton))),
% 5.16/3.98      inference(quant_intro,[status(thm)],[24])).
% 5.16/3.98  tff(26,axiom,(![V_ca_2: $i] : (c_Hoare__Mirabelle_Ostate__not__singleton => (c_Com_OWT__bodies => (hBOOL(hAPP(c_Com_OWT, V_ca_2)) => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_MGF')).
% 5.16/3.98  tff(27,plain,
% 5.16/3.98      (![V_ca_2: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))) | (~c_Com_OWT__bodies) | (~c_Hoare__Mirabelle_Ostate__not__singleton))),
% 5.16/3.98      inference(modus_ponens,[status(thm)],[26, 25])).
% 5.16/3.98  tff(28,plain,
% 5.16/3.98      (![V_ca_2: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))))),
% 5.16/3.98      inference(modus_ponens,[status(thm)],[27, 23])).
% 5.16/3.98  tff(29,plain,
% 5.16/3.98      (![V_ca_2: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))))),
% 5.16/3.98      inference(modus_ponens,[status(thm)],[28, 21])).
% 5.16/3.98  tff(30,plain,(
% 5.16/3.98      ![V_ca_2: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))))),
% 5.16/3.98      inference(skolemize,[status(sab)],[29])).
% 5.16/3.98  tff(31,plain,
% 5.16/3.98      (![V_ca_2: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))))),
% 5.16/3.98      inference(modus_ponens,[status(thm)],[30, 20])).
% 5.16/3.98  tff(32,plain,
% 5.16/3.98      (((~![V_ca_2: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))))) | (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x!468))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, B_x!468)))))) <=> ((~![V_ca_2: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x!468))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, B_x!468)))))),
% 5.16/3.98      inference(rewrite,[status(thm)],[])).
% 5.16/3.98  tff(33,plain,
% 5.16/3.98      ((~![V_ca_2: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))))) | (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x!468))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, B_x!468)))))),
% 5.16/3.98      inference(quant_inst,[status(thm)],[])).
% 5.16/3.98  tff(34,plain,
% 5.16/3.98      ((~![V_ca_2: $i] : (c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, V_ca_2)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, V_ca_2))))) | c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, B_x!468))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))) | (~hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, B_x!468))))),
% 5.16/3.98      inference(modus_ponens,[status(thm)],[33, 32])).
% 5.16/3.98  tff(35,plain,
% 5.16/3.98      (~hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, B_x!468)))),
% 5.16/3.98      inference(unit_resolution,[status(thm)],[34, 31, 18])).
% 5.16/3.98  tff(36,plain,
% 5.16/3.98      (^[V_m_2: $i, T_b: $i, V_a_2: $i, T_a: $i] : refl((hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), c_Map_Odom(T_a, T_b, V_m_2))) <=> (~(hAPP(V_m_2, V_a_2) = c_Option_Ooption_ONone(T_b)))) <=> (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), c_Map_Odom(T_a, T_b, V_m_2))) <=> (~(hAPP(V_m_2, V_a_2) = c_Option_Ooption_ONone(T_b)))))),
% 5.16/3.98      inference(bind,[status(th)],[])).
% 5.16/3.98  tff(37,plain,
% 5.16/3.98      (![V_m_2: $i, T_b: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), c_Map_Odom(T_a, T_b, V_m_2))) <=> (~(hAPP(V_m_2, V_a_2) = c_Option_Ooption_ONone(T_b)))) <=> ![V_m_2: $i, T_b: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), c_Map_Odom(T_a, T_b, V_m_2))) <=> (~(hAPP(V_m_2, V_a_2) = c_Option_Ooption_ONone(T_b))))),
% 5.16/3.98      inference(quant_intro,[status(thm)],[36])).
% 5.16/3.98  tff(38,plain,
% 5.16/3.98      (![V_m_2: $i, T_b: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), c_Map_Odom(T_a, T_b, V_m_2))) <=> (~(hAPP(V_m_2, V_a_2) = c_Option_Ooption_ONone(T_b)))) <=> ![V_m_2: $i, T_b: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), c_Map_Odom(T_a, T_b, V_m_2))) <=> (~(hAPP(V_m_2, V_a_2) = c_Option_Ooption_ONone(T_b))))),
% 5.16/3.98      inference(rewrite,[status(thm)],[])).
% 5.16/3.98  tff(39,axiom,(![V_m_2: $i, T_b: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), c_Map_Odom(T_a, T_b, V_m_2))) <=> (~(hAPP(V_m_2, V_a_2) = c_Option_Ooption_ONone(T_b))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_domIff')).
% 5.16/3.98  tff(40,plain,
% 5.16/3.98      (![V_m_2: $i, T_b: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), c_Map_Odom(T_a, T_b, V_m_2))) <=> (~(hAPP(V_m_2, V_a_2) = c_Option_Ooption_ONone(T_b))))),
% 5.16/3.98      inference(modus_ponens,[status(thm)],[39, 38])).
% 5.16/3.98  tff(41,plain,(
% 5.16/3.98      ![V_m_2: $i, T_b: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), c_Map_Odom(T_a, T_b, V_m_2))) <=> (~(hAPP(V_m_2, V_a_2) = c_Option_Ooption_ONone(T_b))))),
% 5.16/3.98      inference(skolemize,[status(sab)],[40])).
% 5.16/3.98  tff(42,plain,
% 5.16/3.98      (![V_m_2: $i, T_b: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), c_Map_Odom(T_a, T_b, V_m_2))) <=> (~(hAPP(V_m_2, V_a_2) = c_Option_Ooption_ONone(T_b))))),
% 5.16/3.98      inference(modus_ponens,[status(thm)],[41, 37])).
% 5.16/3.98  tff(43,plain,
% 5.16/3.98      ((~![V_m_2: $i, T_b: $i, V_a_2: $i, T_a: $i] : (hBOOL(hAPP(hAPP(c_member(T_a), V_a_2), c_Map_Odom(T_a, T_b, V_m_2))) <=> (~(hAPP(V_m_2, V_a_2) = c_Option_Ooption_ONone(T_b))))) | (hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x!468), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies)))) <=> (~(hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), B_x!468) = c_Option_Ooption_ONone(tc_Com_Ocom))))),
% 5.16/3.98      inference(quant_inst,[status(thm)],[])).
% 5.16/3.98  tff(44,plain,
% 5.16/3.98      (hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x!468), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies)))) <=> (~(hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), B_x!468) = c_Option_Ooption_ONone(tc_Com_Ocom)))),
% 5.16/3.98      inference(unit_resolution,[status(thm)],[43, 42])).
% 5.16/3.98  tff(45,plain,
% 5.16/3.98      (hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x!468), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))))),
% 5.16/3.98      inference(or_elim,[status(thm)],[17])).
% 5.16/3.98  tff(46,plain,
% 5.16/3.98      ((~(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x!468), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies)))) <=> (~(hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), B_x!468) = c_Option_Ooption_ONone(tc_Com_Ocom))))) | (~hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x!468), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))))) | (~(hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), B_x!468) = c_Option_Ooption_ONone(tc_Com_Ocom)))),
% 5.16/3.98      inference(tautology,[status(thm)],[])).
% 5.16/3.98  tff(47,plain,
% 5.16/3.98      ((~(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), B_x!468), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies)))) <=> (~(hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), B_x!468) = c_Option_Ooption_ONone(tc_Com_Ocom))))) | (~(hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), B_x!468) = c_Option_Ooption_ONone(tc_Com_Ocom)))),
% 5.16/3.98      inference(unit_resolution,[status(thm)],[46, 45])).
% 5.16/3.98  tff(48,plain,
% 5.16/3.98      (~(hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), B_x!468) = c_Option_Ooption_ONone(tc_Com_Ocom))),
% 5.16/3.98      inference(unit_resolution,[status(thm)],[47, 44])).
% 5.16/3.98  tff(49,plain,
% 5.16/3.98      (^[V_pn: $i] : refl((hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom))) <=> (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom))))),
% 5.16/3.98      inference(bind,[status(th)],[])).
% 5.16/3.98  tff(50,plain,
% 5.16/3.98      (![V_pn: $i] : (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom))) <=> ![V_pn: $i] : (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom)))),
% 5.16/3.98      inference(quant_intro,[status(thm)],[49])).
% 5.16/3.98  tff(51,plain,
% 5.16/3.98      (^[V_pn: $i] : rewrite((hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(c_Com_Obody, V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom))) <=> (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom))))),
% 5.16/3.98      inference(bind,[status(th)],[])).
% 5.16/3.98  tff(52,plain,
% 5.16/3.98      (![V_pn: $i] : (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(c_Com_Obody, V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom))) <=> ![V_pn: $i] : (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom)))),
% 5.16/3.98      inference(quant_intro,[status(thm)],[51])).
% 5.16/3.98  tff(53,plain,
% 5.16/3.98      (![V_pn: $i] : (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(c_Com_Obody, V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom))) <=> ![V_pn: $i] : (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(c_Com_Obody, V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom)))),
% 5.16/3.98      inference(rewrite,[status(thm)],[])).
% 5.16/3.98  tff(54,plain,
% 5.16/3.98      (^[V_pn: $i] : rewrite(((~(hAPP(c_Com_Obody, V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom))) => hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn)))) <=> (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(c_Com_Obody, V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom))))),
% 5.16/3.98      inference(bind,[status(th)],[])).
% 5.16/3.98  tff(55,plain,
% 5.16/3.98      (![V_pn: $i] : ((~(hAPP(c_Com_Obody, V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom))) => hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn)))) <=> ![V_pn: $i] : (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(c_Com_Obody, V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom)))),
% 5.16/3.98      inference(quant_intro,[status(thm)],[54])).
% 5.16/3.98  tff(56,axiom,(![V_pn: $i] : ((~(hAPP(c_Com_Obody, V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom))) => hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_WT_OBody')).
% 5.16/3.98  tff(57,plain,
% 5.16/3.98      (![V_pn: $i] : (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(c_Com_Obody, V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom)))),
% 5.16/3.98      inference(modus_ponens,[status(thm)],[56, 55])).
% 5.16/3.98  tff(58,plain,
% 5.16/3.98      (![V_pn: $i] : (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(c_Com_Obody, V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom)))),
% 5.16/3.98      inference(modus_ponens,[status(thm)],[57, 53])).
% 5.16/3.98  tff(59,plain,
% 5.16/3.98      (![V_pn: $i] : (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom)))),
% 5.16/3.98      inference(modus_ponens,[status(thm)],[58, 52])).
% 5.16/3.98  tff(60,plain,(
% 5.16/3.98      ![V_pn: $i] : (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom)))),
% 5.16/3.98      inference(skolemize,[status(sab)],[59])).
% 5.16/3.98  tff(61,plain,
% 5.16/3.98      (![V_pn: $i] : (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom)))),
% 5.16/3.98      inference(modus_ponens,[status(thm)],[60, 50])).
% 5.16/3.98  tff(62,plain,
% 5.16/3.98      (((~![V_pn: $i] : (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom)))) | (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, B_x!468))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), B_x!468) = c_Option_Ooption_ONone(tc_Com_Ocom)))) <=> ((~![V_pn: $i] : (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom)))) | hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, B_x!468))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), B_x!468) = c_Option_Ooption_ONone(tc_Com_Ocom)))),
% 5.16/3.98      inference(rewrite,[status(thm)],[])).
% 5.16/3.98  tff(63,plain,
% 5.16/3.98      ((~![V_pn: $i] : (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom)))) | (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, B_x!468))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), B_x!468) = c_Option_Ooption_ONone(tc_Com_Ocom)))),
% 5.16/3.98      inference(quant_inst,[status(thm)],[])).
% 5.16/3.98  tff(64,plain,
% 5.16/3.98      ((~![V_pn: $i] : (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, V_pn))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom)))) | hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, B_x!468))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), B_x!468) = c_Option_Ooption_ONone(tc_Com_Ocom))),
% 5.61/4.45      inference(modus_ponens,[status(thm)],[63, 62])).
% 5.61/4.45  tff(65,plain,
% 5.61/4.45      (hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, B_x!468))) | (hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies), B_x!468) = c_Option_Ooption_ONone(tc_Com_Ocom))),
% 5.61/4.45      inference(unit_resolution,[status(thm)],[64, 61])).
% 5.61/4.45  tff(66,plain,
% 5.61/4.45      ($false),
% 5.61/4.45      inference(unit_resolution,[status(thm)],[65, 48, 35])).
% 5.61/4.45  % SZS output end Proof
%------------------------------------------------------------------------------