%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV857-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 0.19s 0.52s
% Output : Proof 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of formulae : 40 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 163 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 225 ( 106 ~; 101 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 101 ( 91 !; 0 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_Ga_type,type,
v_Ga: $i ).
tff(v_xa_type,type,
v_xa: $i ).
tff(c_in_type,type,
c_in: $i > $i ).
tff(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Hoare__Mirabelle_Otriple__valid_type,type,
c_Hoare__Mirabelle_Otriple__valid: ( $i * $i * $i ) > $o ).
tff(v_x_type,type,
v_x: $i ).
tff(v_tsa_type,type,
v_tsa: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(1,plain,
^ [V_xb: $i] :
refl(( ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) )
<=> ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) )
<=> ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [V_xb: $i] :
rewrite(( ( c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_xb: $i] :
( c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga)) )
<=> ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [V_xb: $i] :
( c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(7,plain,
! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a)
<=> ~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(13,plain,
~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a) )
<=> ( ~ ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_xb: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xb),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,V_xb,t_a) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_Ga))
| c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_Ga)),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
<=> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa)) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(20,plain,
hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa)),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
<=> c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(23,plain,
c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
refl(( ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
rewrite(( ( hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
tff(30,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| ~ c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| ~ c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ( ~ c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_Ga)) )
<=> ( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| ~ c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
| ~ c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_Ga)) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| ~ c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
| ~ c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_Ga)) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| ~ c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
| ~ c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_Ga)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_t: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) )
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa))
| ~ c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
$false,
inference(unit_resolution,[status(thm)],[39,33,23,20,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV857-1 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 10:58:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.52 % SZS status Unsatisfiable
% 0.19/0.52 % SZS output start Proof
% See solution above
% 0.37/0.55 % E exiting
%------------------------------------------------------------------------------