TSTP Solution File: ALG369-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG369-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 : Tue Sep 6 16:09:58 EDT 2022
% Result : Unsatisfiable 0.43s 0.56s
% Output : Proof 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 22
% Syntax : Number of formulae : 35 ( 10 unt; 9 typ; 0 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 229 ( 117 ~; 95 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 5 >; 5 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 21 ( 18 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(v_sko__CHAINED__1_type,type,
v_sko__CHAINED__1: ( $i * $i ) > $i ).
tff(v_m_____type,type,
v_m____: $i ).
tff(v_e_type,type,
v_e: $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(v_thesis_____type,type,
v_thesis____: $o ).
tff(1,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_e,v_m____),tc_RealDef_Oreal)
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_e,v_m____),tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_e,v_m____),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(3,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_e,v_m____),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).
tff(6,plain,
c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_2) ).
tff(9,plain,
c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_d: $i] :
refl(
( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [V_d: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ! [V_d: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_d: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ! [V_d: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [V_d: $i] :
trans(
monotonicity(
iff_false(asserted(~ v_thesis____),
( v_thesis____
<=> $false )),
( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| v_thesis____
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| $false
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ) )),
rewrite(
( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| $false
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ) )),
( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| v_thesis____
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [V_d: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| v_thesis____
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ! [V_d: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
^ [V_d: $i] :
trans(
monotonicity(
rewrite(
( ( v_thesis____
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( v_thesis____
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ) )),
( ( v_thesis____
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal) )
<=> ( v_thesis____
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal) ) )),
rewrite(
( ( v_thesis____
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal) )
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| v_thesis____
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ) )),
( ( v_thesis____
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal) )
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| v_thesis____
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [V_d: $i] :
( v_thesis____
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal) )
<=> ! [V_d: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| v_thesis____
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,axiom,
! [V_d: $i] :
( v_thesis____
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).
tff(18,plain,
! [V_d: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| v_thesis____
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [V_d: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
! [V_d: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
! [V_d: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [V_d: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[21,11]) ).
tff(23,plain,
( ( ~ ! [V_d: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_e,v_m____),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( ~ ! [V_d: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_e,v_m____),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [V_d: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_e,v_m____),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [V_d: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_e,v_m____),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,22,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG369-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 29 16:19:02 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.43/0.56 % SZS status Unsatisfiable
% 0.43/0.56 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------