TSTP Solution File: SWW315+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW315+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 : Thu Sep 29 20:58:17 EDT 2022
% Result : Theorem 5.51s 4.16s
% Output : Proof 5.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 23
% Syntax : Number of formulae : 34 ( 9 unt; 11 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 : 6 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 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_ts_H_type,type,
v_ts_H: $i ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_HOL_Obool_type,type,
tc_HOL_Obool: $i ).
tff(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $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/sandbox/benchmark/theBenchmark.p',conj_4) ).
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_ts_H)
<=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts_H) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts_H),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
tff(6,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts_H),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_ts_H))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_ts_H)) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_ts_H)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(9,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_ts_H)),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
refl(
( ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) )
<=> ! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) )
<=> ! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
trans(
monotonicity(
rewrite(
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) )
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_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_ts_H_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_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_ts_H_2)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ) )),
rewrite(
( ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) ) )),
( ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_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)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) )
<=> ! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_weaken) ).
tff(16,plain,
! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) )
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_ts_H))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts_H) )
<=> ( ~ ! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) )
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_ts_H))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts_H) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ~ ! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) )
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_ts_H))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts_H) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [V_tsa_2: $i,V_ts_H_2: $i,V_G_2: $i,T_b: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) )
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_ts_H))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts_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
% 0.03/0.12 % Problem : SWW315+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n016.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 : Sun Sep 4 14:58:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 5.51/4.16 % SZS status Theorem
% 5.51/4.16 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------