%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV889-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:36:17 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of formulae : 17 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 54 ( 26 ~; 22 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 36 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
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(v_ts_type,type,
v_ts: $i ).
tff(v_G_type,type,
v_G: $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(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
tff(1,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,v_ts,tc_Com_Ostate)
<=> ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,v_ts,tc_Com_Ostate) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,v_ts,tc_Com_Ostate),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(3,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,v_ts,tc_Com_Ostate),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_lessequals(v_ts,v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
<=> c_lessequals(v_ts,v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_lessequals(v_ts,v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(6,plain,
c_lessequals(v_ts,v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_ts: $i,T_a: $i,V_G: $i] :
refl(( ( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_ts,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)) )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_ts,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_ts: $i,T_a: $i,V_G: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_ts,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)) )
<=> ! [V_ts: $i,T_a: $i,V_G: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_ts,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_ts: $i,T_a: $i,V_G: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_ts,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)) )
<=> ! [V_ts: $i,T_a: $i,V_G: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_ts,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
! [V_ts: $i,T_a: $i,V_G: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_ts,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_asm_0) ).
tff(11,plain,
! [V_ts: $i,T_a: $i,V_G: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_ts,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)) ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [V_ts: $i,T_a: $i,V_G: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_ts,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_ts: $i,T_a: $i,V_G: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_ts,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
( ( ~ ! [V_ts: $i,T_a: $i,V_G: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_ts,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)) )
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,v_ts,tc_Com_Ostate)
| ~ c_lessequals(v_ts,v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)) )
<=> ( ~ ! [V_ts: $i,T_a: $i,V_G: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_ts,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)) )
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,v_ts,tc_Com_Ostate)
| ~ c_lessequals(v_ts,v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_ts: $i,T_a: $i,V_G: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_ts,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)) )
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,v_ts,tc_Com_Ostate)
| ~ c_lessequals(v_ts,v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_ts: $i,T_a: $i,V_G: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_ts,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)) )
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,v_ts,tc_Com_Ostate)
| ~ c_lessequals(v_ts,v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
$false,
inference(unit_resolution,[status(thm)],[16,13,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWV889-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 10:59:48 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.52 % SZS status Unsatisfiable
% 0.19/0.52 % SZS output start Proof
% See solution above
% 0.19/0.54 % E exiting
%------------------------------------------------------------------------------