%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW216+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:36:38 AM UTC 2025
% Result : Theorem 0.52s 0.68s
% Output : Proof 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 18
% Syntax : Number of formulae : 35 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 373 ( 0 equ)
% Maximal formula atoms : 36 ( 10 avg)
% Number of connectives : 570 ( 241 ~; 216 |; 36 &)
% ( 51 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 84 ( 72 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_Rings_Oinverse__class_Odivide_type,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(v_m_____type,type,
v_m____: $i ).
tff(v_e_type,type,
v_e: $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(v_da_____type,type,
v_da____: $i ).
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: ( $i * $i ) > $i ).
tff(class_Fields_Olinordered__field__inverse__zero_type,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(1,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e)
<=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(3,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_m_I1_J) ).
tff(6,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) ),
inference(tautology,[status(thm)],[]) ).
tff(8,plain,
~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) ),
inference(unit_resolution,[status(thm)],[7,6,3]) ).
tff(9,plain,
( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____)) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) ),
inference(tautology,[status(thm)],[]) ).
tff(10,plain,
( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____)) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ) ),
inference(unit_resolution,[status(thm)],[9,8]) ).
tff(11,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_H_I3_J) ).
tff(13,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____)) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) )
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____)) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
inference(tautology,[status(thm)],[]) ).
tff(15,plain,
( ( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____)) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
inference(unit_resolution,[status(thm)],[14,13,10]) ).
tff(16,plain,
( class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal)
<=> class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
tff(18,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
^ [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
refl(( ( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ~ ( ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) )
<=> ( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ~ ( ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ~ ( ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) )
<=> ! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ~ ( ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
^ [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
rewrite(( ( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) )
<=> ( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ~ ( ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) )
<=> ! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ~ ( ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) )
<=> ! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
=> ( ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) )),
( ( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
=> ( ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) )
<=> ( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) )),
rewrite(( ( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) )
<=> ( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) )),
( ( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
=> ( ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) )
<=> ( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
=> ( ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) )
<=> ! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
=> ( ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq) ).
tff(27,plain,
! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ~ ( ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ~ ( ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) ),
inference(modus_ponens,[status(thm)],[30,20]) ).
tff(32,plain,
( ( ~ ! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ~ ( ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal)
| ~ ( ( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____)) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ) )
<=> ( ~ ! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ~ ( ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal)
| ~ ( ( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____)) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ~ ( ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal)
| ~ ( ( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____)) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Fields_Olinordered__field__inverse__zero(T_a)
| ~ ( ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
| ~ ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal)
| ~ ( ( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ ( ~ ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____)) )
| ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
$false,
inference(unit_resolution,[status(thm)],[34,31,18,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW216+1 : TPTP v9.0.0. Released v5.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.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 11:17:39 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.52/0.68 % SZS status Theorem
% 0.52/0.68 % SZS output start Proof
% See solution above
% 0.59/0.76 % E exiting
%------------------------------------------------------------------------------