%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV854-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:36:13 AM UTC 2025
% Result : Unsatisfiable 0.38s 0.57s
% Output : Proof 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 34 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 126 ( 58 ~; 54 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 102 ( 90 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Hoare__Mirabelle_Otriple__valid_type,type,
c_Hoare__Mirabelle_Otriple__valid: ( $i * $i * $i ) > $o ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Hoare__Mirabelle_Otriple_Otriple_type,type,
c_Hoare__Mirabelle_Otriple_Otriple: ( $i * $i * $i * $i ) > $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_Q_type,type,
v_Q: $i ).
tff(c_Option_Othe_type,type,
c_Option_Othe: ( $i * $i ) > $i ).
tff(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
tff(c_Com_Obody_type,type,
c_Com_Obody: $i > $i ).
tff(v_P_type,type,
v_P: $i ).
tff(v_na_type,type,
v_na: $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(v_Procs_type,type,
v_Procs: $i ).
tff(c_Com_Ocom_OBODY_type,type,
c_Com_Ocom_OBODY: $i > $i ).
tff(c_Suc_type,type,
c_Suc: $i ).
tff(1,plain,
^ [V_x: $i] :
refl(( ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) )
<=> ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_x: $i] :
( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) )
<=> ! [V_x: $i] :
( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_x: $i] :
( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) )
<=> ! [V_x: $i] :
( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [V_x: $i] :
rewrite(( ( c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a)
| ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname)) )
<=> ( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_x: $i] :
( c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a)
| ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname)) )
<=> ! [V_x: $i] :
( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [V_x: $i] :
( c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a)
| ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(7,plain,
! [V_x: $i] :
( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [V_x: $i] :
( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [V_x: $i] :
( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_x: $i] :
( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( hBOOL(c_in(v_x,v_Procs,tc_Com_Opname))
<=> hBOOL(c_in(v_x,v_Procs,tc_Com_Opname)) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
hBOOL(c_in(v_x,v_Procs,tc_Com_Opname)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(13,plain,
hBOOL(c_in(v_x,v_Procs,tc_Com_Opname)),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [V_x: $i] :
( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) )
| ~ hBOOL(c_in(v_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a) )
<=> ( ~ ! [V_x: $i] :
( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) )
| ~ hBOOL(c_in(v_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_x: $i] :
( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) )
| ~ hBOOL(c_in(v_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_x: $i] :
( ~ hBOOL(c_in(V_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,V_x),c_Option_Othe(c_Com_Obody(V_x),tc_Com_Ocom),hAPP(v_Q,V_x),t_a),t_a) )
| ~ hBOOL(c_in(v_x,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a)
<=> ~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(20,plain,
~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
refl(( ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) )
<=> ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) )
<=> ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) )
<=> ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
rewrite(( ( c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a) )
<=> ( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
( c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a) )
<=> ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
( c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Body__triple__valid__Suc_0) ).
tff(27,plain,
! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) )
| ~ c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a) )
<=> ( ~ ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) )
| ~ c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) )
| ~ c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [V_n: $i,V_Q: $i,V_pn: $i,T_a: $i,V_P: $i] :
( ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_Q,T_a),T_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,V_n),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OBODY(V_pn),V_Q,T_a),T_a) )
| ~ c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Option_Othe(c_Com_Obody(v_x),tc_Com_Ocom),hAPP(v_Q,v_x),t_a),t_a)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,30,20,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV854-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 10:58:42 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.38/0.57 % SZS status Unsatisfiable
% 0.38/0.57 % SZS output start Proof
% See solution above
% 0.38/0.61 % E exiting
%------------------------------------------------------------------------------