%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW314+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:36:49 AM UTC 2025
% Result : Theorem 14.31s 14.47s
% Output : Proof 14.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 23 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 125 ( 53 ~; 49 |; 0 &)
% ( 12 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 8 ( 8 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 68 ( 60 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Hoare__Mirabelle_Ohoare__derivs_type,type,
c_Hoare__Mirabelle_Ohoare__derivs: ( $i * $i * $i ) > $o ).
tff(v_ts_type,type,
v_ts: $i ).
tff(v_Ga_type,type,
v_Ga: $i ).
tff(t_a_type,type,
t_a: $i ).
tff(v_G_H_type,type,
v_G_H: $i ).
tff(1,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts)
<=> ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).
tff(3,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_G_H)
<=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_G_H) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_G_H),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
tff(6,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_G_H),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G_H,v_ts)
<=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G_H,v_ts) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G_H,v_ts),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(9,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G_H,v_ts),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
refl(( ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2) )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2) )
<=> ! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2) )
<=> ! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
trans(monotonicity(rewrite(( ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2)
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) )
<=> ( ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2)
| c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) )),
( ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2)
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
=> ( ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2)
| c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ) )),
rewrite(( ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
=> ( ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2)
| c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2) ) )),
( ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2)
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2)
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) )
<=> ! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2)
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut) ).
tff(16,plain,
! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2) )
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G_H,v_ts)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_G_H) )
<=> ( ~ ! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2) )
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G_H,v_ts)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_G_H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2) )
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G_H,v_ts)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_G_H) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2) )
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G_H,v_ts)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_G_H) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,19,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW314+1 : TPTP v9.0.0. Released v5.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 11:25:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 14.31/14.47 % SZS status Theorem
% 14.31/14.47 % SZS output start Proof
% See solution above
% 14.69/14.92 % E exiting
%------------------------------------------------------------------------------