TSTP Solution File: SWV911-1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV911-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 15:24:56 EDT 2022
% Result : Unsatisfiable 0.21s 0.60s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 45
% Syntax : Number of formulae : 82 ( 13 unt; 19 typ; 0 def)
% Number of atoms : 264 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 399 ( 202 ~; 173 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 9 >; 8 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-4 aty)
% Number of variables : 139 ( 129 !; 0 ?; 139 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_xa_type,type,
v_xa: $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_P_type,type,
v_P: $i ).
tff(v_xb_type,type,
v_xb: ( $i * $i ) > $i ).
tff(v_Q_type,type,
v_Q: $i ).
tff(c_Hoare__Mirabelle_Ohoare__derivs_type,type,
c_Hoare__Mirabelle_Ohoare__derivs: ( $i * $i * $i ) > $o ).
tff(t_a_type,type,
t_a: $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(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
tff(c_Hoare__Mirabelle_Otriple_Otriple_type,type,
c_Hoare__Mirabelle_Otriple_Otriple: ( $i * $i * $i * $i ) > $i ).
tff(v_c_type,type,
v_c: $i ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i ).
tff(v_G_type,type,
v_G: $i ).
tff(v_P_H_type,type,
v_P_H: $i ).
tff(v_Q_H_type,type,
v_Q_H: $i ).
tff(1,plain,
^ [V_xd: $i,V_xc: $i] :
refl(
( ( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
<=> ( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
<=> ! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
<=> ! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(5,plain,
! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
<=> c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(10,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
| ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
<=> ( ~ ! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
| ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
| ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
| ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q))),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
^ [V_xd: $i,V_xc: $i,V_Z_H: $i] :
refl(
( ( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
<=> ( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
<=> ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
<=> ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
^ [V_xd: $i,V_xc: $i,V_Z_H: $i] :
rewrite(
( ( hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd)))
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
<=> ( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd)))
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
<=> ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd)))
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(21,plain,
! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( ( ~ ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q)))
| ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) )
<=> ( ~ ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q)))
| ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q))) )
<=> ( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q)))
| ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ( ~ ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q))) )
<=> ( ~ ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q)))
| ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ( ~ ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q))) )
<=> ( ~ ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q)))
| ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ) ),
inference(transitivity,[status(thm)],[27,25]) ).
tff(29,plain,
( ~ ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q))) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q)))
| ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
~ hBOOL(hAPP(hAPP(v_P,v_x),v_xa)),
inference(unit_resolution,[status(thm)],[30,10,24,14]) ).
tff(32,plain,
^ [V_xd: $i,V_xc: $i] :
refl(
( ( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
<=> ( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
<=> ! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
<=> ! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(36,plain,
! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
<=> c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(41,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ( ~ ! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
<=> ( ~ ! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ~ ! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [V_xd: $i,V_xc: $i] :
( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(V_xc,V_xd)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) )
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H))),
inference(unit_resolution,[status(thm)],[44,41,38]) ).
tff(46,plain,
( ( ~ ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H)))
| ~ hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa)) )
<=> ( ~ ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H)))
| ~ hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H))) )
<=> ( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H)))
| ~ hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ( ~ ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H))) )
<=> ( ~ ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H)))
| ~ hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa)) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( ~ ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H))) )
<=> ( ~ ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H)))
| ~ hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa)) ) ),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,plain,
( ~ ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H))) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
( ~ ! [V_xd: $i,V_xc: $i,V_Z_H: $i] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_xc,v_c,V_xd,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_xc,V_Z_H),v_xa))
| hBOOL(hAPP(hAPP(V_xd,V_Z_H),v_xb(V_xc,V_xd))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H)))
| ~ hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa)) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
~ hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa)),
inference(unit_resolution,[status(thm)],[51,41,24,45]) ).
tff(53,plain,
( ( hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) )
<=> ( hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,axiom,
( hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(55,plain,
( hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
( hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ),
inference(modus_ponens,[status(thm)],[55,53]) ).
tff(57,plain,
( hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ),
inference(modus_ponens,[status(thm)],[56,53]) ).
tff(58,plain,
( hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ),
inference(modus_ponens,[status(thm)],[58,53]) ).
tff(60,plain,
( hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ),
inference(modus_ponens,[status(thm)],[59,53]) ).
tff(61,plain,
( hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ),
inference(modus_ponens,[status(thm)],[61,53]) ).
tff(63,plain,
$false,
inference(unit_resolution,[status(thm)],[62,52,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SWV911-1 : TPTP v8.1.0. Released v4.1.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 09:51:32 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.21/0.60 % SZS status Unsatisfiable
% 0.21/0.60 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------