%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW334+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:36:51 AM UTC 2025
% Result : Theorem 13.97s 14.18s
% Output : Proof 14.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 32 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 90 ( 33 ~; 28 |; 0 &)
% ( 26 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 3 ( 3 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; 0-2 aty)
% Number of variables : 67 ( 60 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Hoare__Mirabelle_Otriple__valid_type,type,
c_Hoare__Mirabelle_Otriple__valid: ( $i * $i * $i ) > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_Q_type,type,
v_Q: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_Com_Ocom_OBODY_type,type,
c_Com_Ocom_OBODY: $i ).
tff(v_P_type,type,
v_P: $i > $i ).
tff(c_Hoare__Mirabelle_Otriple_Otriple_type,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(v_na_type,type,
v_na: $i ).
tff(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i ).
tff(c_Com_Obody_type,type,
c_Com_Obody: $i ).
tff(c_Option_Othe_type,type,
c_Option_Othe: $i > $i ).
tff(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(v_Procs_type,type,
v_Procs: $i ).
tff(c_member_type,type,
c_member: $i > $i ).
tff(tc_Com_Opname_type,type,
tc_Com_Opname: $i ).
tff(1,plain,
^ [V_Qa_2: $i,V_pn_2: $i,V_Pa_2: $i,V_n_2: $i,T_b: $i] :
refl(( ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2))
<=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)) )
<=> ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2))
<=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_Qa_2: $i,V_pn_2: $i,V_Pa_2: $i,V_n_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2))
<=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)) )
<=> ! [V_Qa_2: $i,V_pn_2: $i,V_Pa_2: $i,V_n_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2))
<=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_Qa_2: $i,V_pn_2: $i,V_Pa_2: $i,V_n_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2))
<=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)) )
<=> ! [V_Qa_2: $i,V_pn_2: $i,V_Pa_2: $i,V_n_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2))
<=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_Qa_2: $i,V_pn_2: $i,V_Pa_2: $i,V_n_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2))
<=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Body__triple__valid__Suc) ).
tff(5,plain,
! [V_Qa_2: $i,V_pn_2: $i,V_Pa_2: $i,V_n_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2))
<=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_Qa_2: $i,V_pn_2: $i,V_Pa_2: $i,V_n_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2))
<=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_Qa_2: $i,V_pn_2: $i,V_Pa_2: $i,V_n_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2))
<=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_Qa_2: $i,V_pn_2: $i,V_Pa_2: $i,V_n_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2))
<=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)) )
| ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),v_Q(v_x)))
<=> c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),v_Q(v_x)))
<=> c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))) ),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B_x: $i] :
refl(( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) )
<=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [B_x: $i] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) )
<=> ! [B_x: $i] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [B_x: $i] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) )
<=> ! [B_x: $i] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [B_x: $i] :
rewrite(( ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) )
<=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [B_x: $i] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) )
<=> ! [B_x: $i] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [B_x: $i] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
tff(16,plain,
! [B_x: $i] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [B_x: $i] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [B_x: $i] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [B_x: $i] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs))
<=> hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs)) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(22,plain,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs)),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [B_x: $i] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),v_Q(v_x))) )
<=> ( ~ ! [B_x: $i] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),v_Q(v_x))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [B_x: $i] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),v_Q(v_x))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [B_x: $i] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),v_Q(v_x))) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),v_Q(v_x))),
inference(unit_resolution,[status(thm)],[25,22,19]) ).
tff(27,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x)))
<=> ~ c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
tff(29,plain,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),v_Q(v_x)))
<=> c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))) )
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),v_Q(v_x)))
| c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))) ),
inference(tautology,[status(thm)],[]) ).
tff(31,plain,
( ~ ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),v_Q(v_x)))
<=> c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))) )
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),v_Q(v_x))) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,26,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWW334+1 : TPTP v9.0.0. Released v5.2.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n015.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 : Fri Jun 20 11:28:40 EDT 2025
% 0.13/0.35 % CPUTime :
% 13.97/14.18 % SZS status Theorem
% 13.97/14.18 % SZS output start Proof
% See solution above
% 14.47/14.65 % E exiting
%------------------------------------------------------------------------------