%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV905-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 : Sat Jun 21 05:36:18 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.52s
% Output : Proof 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 24
% Syntax : Number of formulae : 48 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 231 ( 37 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 315 ( 148 ~; 143 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 82 ( 75 !; 0 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Com_OWT_type,type,
c_Com_OWT: $i > $o ).
tff(c_Com_Ocom_OBODY_type,type,
c_Com_Ocom_OBODY: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_Option_Ooption_ONone_type,type,
c_Option_Ooption_ONone: $i > $i ).
tff(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Com_Obody_type,type,
c_Com_Obody: $i ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $i ).
tff(tc_Com_Opname_type,type,
tc_Com_Opname: $i ).
tff(c_Map_Odom_type,type,
c_Map_Odom: ( $i * $i * $i ) > $i ).
tff(c_Hoare__Mirabelle_Ohoare__derivs_type,type,
c_Hoare__Mirabelle_Ohoare__derivs: ( $i * $i * $i ) > $o ).
tff(tc_Com_Ostate_type,type,
tc_Com_Ostate: $i ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
tff(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(c_Hoare__Mirabelle_OMGT_type,type,
c_Hoare__Mirabelle_OMGT: $i > $i ).
tff(c_Com_OWT__bodies_type,type,
c_Com_OWT__bodies: $o ).
tff(c_Hoare__Mirabelle_Ostate__not__singleton_type,type,
c_Hoare__Mirabelle_Ostate__not__singleton: $o ).
tff(1,plain,
( hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname))
<=> hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(3,plain,
hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
refl(( ( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a)) )
<=> ( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a)) )
<=> ! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a)) )
<=> ! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domIff_0) ).
tff(8,plain,
! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a)) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a)) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a)) )
| ( hAPP(c_Com_Obody,v_x) != c_Option_Ooption_ONone(tc_Com_Ocom) )
| ~ hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)) )
<=> ( ~ ! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a)) )
| ( hAPP(c_Com_Obody,v_x) != c_Option_Ooption_ONone(tc_Com_Ocom) )
| ~ hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a)) )
| ( hAPP(c_Com_Obody,v_x) != c_Option_Ooption_ONone(tc_Com_Ocom) )
| ~ hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [T_b: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b) )
| ~ hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a)) )
| ( hAPP(c_Com_Obody,v_x) != c_Option_Ooption_ONone(tc_Com_Ocom) )
| ~ hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
hAPP(c_Com_Obody,v_x) != c_Option_Ooption_ONone(tc_Com_Ocom),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [V_pn: $i] :
refl(( ( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
<=> ( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
<=> ! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
<=> ! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OBody_0) ).
tff(19,plain,
! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
| c_Com_OWT(c_Com_Ocom_OBODY(v_x))
| ( hAPP(c_Com_Obody,v_x) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
<=> ( ~ ! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
| c_Com_OWT(c_Com_Ocom_OBODY(v_x))
| ( hAPP(c_Com_Obody,v_x) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
| c_Com_OWT(c_Com_Ocom_OBODY(v_x))
| ( hAPP(c_Com_Obody,v_x) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [V_pn: $i] :
( c_Com_OWT(c_Com_Ocom_OBODY(V_pn))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
| c_Com_OWT(c_Com_Ocom_OBODY(v_x))
| ( hAPP(c_Com_Obody,v_x) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
c_Com_OWT(c_Com_Ocom_OBODY(v_x)),
inference(unit_resolution,[status(thm)],[24,21,14]) ).
tff(26,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)
<=> ~ 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(rewrite,[status(thm)],[]) ).
tff(27,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(28,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(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( c_Com_OWT__bodies
<=> c_Com_OWT__bodies ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
c_Com_OWT__bodies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(31,plain,
c_Com_OWT__bodies,
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( c_Hoare__Mirabelle_Ostate__not__singleton
<=> c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(34,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
^ [V_c: $i] :
refl(( ( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(V_c)
| 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(V_c),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) )
<=> ( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(V_c)
| 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(V_c),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(bind,[status(th)],[]) ).
tff(36,plain,
( ! [V_c: $i] :
( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(V_c)
| 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(V_c),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) )
<=> ! [V_c: $i] :
( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(V_c)
| 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(V_c),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(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [V_c: $i] :
( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(V_c)
| 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(V_c),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) )
<=> ! [V_c: $i] :
( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(V_c)
| 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(V_c),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(rewrite,[status(thm)],[]) ).
tff(38,plain,
^ [V_c: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( 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(V_c),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)
| ~ c_Com_OWT(V_c) )
<=> ( ~ c_Com_OWT(V_c)
| 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(V_c),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) ) )),
( ( 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(V_c),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)
| ~ c_Com_OWT(V_c)
| ~ c_Com_OWT__bodies )
<=> ( ~ c_Com_OWT(V_c)
| 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(V_c),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)
| ~ c_Com_OWT__bodies ) )),
rewrite(( ( ~ c_Com_OWT(V_c)
| 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(V_c),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)
| ~ c_Com_OWT__bodies )
<=> ( ~ c_Com_OWT__bodies
| ~ c_Com_OWT(V_c)
| 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(V_c),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) ) )),
( ( 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(V_c),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)
| ~ c_Com_OWT(V_c)
| ~ c_Com_OWT__bodies )
<=> ( ~ c_Com_OWT__bodies
| ~ c_Com_OWT(V_c)
| 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(V_c),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) ) )),
( ( 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(V_c),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)
| ~ c_Com_OWT(V_c)
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
<=> ( ~ c_Com_OWT__bodies
| ~ c_Com_OWT(V_c)
| 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(V_c),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)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) )),
rewrite(( ( ~ c_Com_OWT__bodies
| ~ c_Com_OWT(V_c)
| 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(V_c),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)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
<=> ( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(V_c)
| 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(V_c),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) ) )),
( ( 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(V_c),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)
| ~ c_Com_OWT(V_c)
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
<=> ( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(V_c)
| 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(V_c),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(bind,[status(th)],[]) ).
tff(39,plain,
( ! [V_c: $i] :
( 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(V_c),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)
| ~ c_Com_OWT(V_c)
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
<=> ! [V_c: $i] :
( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(V_c)
| 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(V_c),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(quant_intro,[status(thm)],[38]) ).
tff(40,axiom,
! [V_c: $i] :
( 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(V_c),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)
| ~ c_Com_OWT(V_c)
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGF_0) ).
tff(41,plain,
! [V_c: $i] :
( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(V_c)
| 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(V_c),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(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [V_c: $i] :
( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(V_c)
| 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(V_c),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(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [V_c: $i] :
( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(V_c)
| 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(V_c),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(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [V_c: $i] :
( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(V_c)
| 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(V_c),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(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( ( ~ ! [V_c: $i] :
( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(V_c)
| 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(V_c),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) )
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(c_Com_Ocom_OBODY(v_x))
| 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) )
<=> ( ~ ! [V_c: $i] :
( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(V_c)
| 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(V_c),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) )
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(c_Com_Ocom_OBODY(v_x))
| 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(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [V_c: $i] :
( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(V_c)
| 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(V_c),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) )
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(c_Com_Ocom_OBODY(v_x))
| 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(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [V_c: $i] :
( ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(V_c)
| 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(V_c),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) )
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(c_Com_Ocom_OBODY(v_x))
| 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(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
$false,
inference(unit_resolution,[status(thm)],[47,44,34,31,28,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV905-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 11:01:48 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.52 % SZS status Unsatisfiable
% 0.20/0.52 % SZS output start Proof
% See solution above
% 0.38/0.55 % E exiting
%------------------------------------------------------------------------------