TSTP Solution File: SWV674-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV674-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 15:24:01 EDT 2022
% Result : Unsatisfiable 0.41s 0.62s
% Output : Proof 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 64
% Syntax : Number of formulae : 136 ( 38 unt; 15 typ; 0 def)
% Number of atoms : 371 ( 143 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 429 ( 189 ~; 195 |; 0 &)
% ( 45 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 11 >; 9 *; 0 +; 0 <<)
% Number of predicates : 9 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 195 ( 177 !; 0 ?; 195 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_a_type,type,
v_a: $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oinverse__class_Oinverse_type,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(class_Ring__and__Field_Odivision__ring_type,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
tff(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(1,plain,
( class_Ring__and__Field_Ofield(t_a)
<=> class_Ring__and__Field_Ofield(t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_Ring__and__Field_Ofield(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
tff(3,plain,
class_Ring__and__Field_Ofield(t_a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
tff(8,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
^ [T: $i] :
refl(
( ( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) )
<=> ( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Odivision__ring) ).
tff(20,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Odivision__ring(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Odivision__ring(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Odivision__ring(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Ring__and__Field_Odivision__ring(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Ring__and__Field_Odivision__ring(t_a) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
class_Ring__and__Field_Odivision__ring(t_a),
inference(unit_resolution,[status(thm)],[25,3,22]) ).
tff(27,plain,
( ( v_a != c_HOL_Ozero__class_Ozero(t_a) )
<=> ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ( $false
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) )
<=> ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( class_Ring__and__Field_Ofield(t_a)
<=> $true ),
inference(iff_true,[status(thm)],[2]) ).
tff(31,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
<=> $false ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ( ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) )
<=> ( $false
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) )
<=> ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(transitivity,[status(thm)],[33,28]) ).
tff(35,axiom,
( ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nz_0) ).
tff(36,plain,
v_a != c_HOL_Ozero__class_Ozero(t_a),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
v_a != c_HOL_Ozero__class_Ozero(t_a),
inference(modus_ponens,[status(thm)],[36,27]) ).
tff(38,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
refl(
( ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [V_n: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
tff(44,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_Ring__and__Field_Odivision__ring(T_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( ~ class_Ring__and__Field_Odivision__ring(t_a)
| ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) ),
inference(unit_resolution,[status(thm)],[50,47,37]) ).
tff(52,plain,
c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),
inference(unit_resolution,[status(thm)],[51,26]) ).
tff(53,plain,
^ [V_m: $i] :
refl(
( ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m )
<=> ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m )
<=> ! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m )
<=> ! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,axiom,
! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
tff(57,plain,
! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
( ~ ! [V_m: $i] : ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m )
| ( c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = v_x ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = v_x,
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) = c_Power_Opower__class_Opower(v_a,v_x,t_a),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
c_Power_Opower__class_Opower(v_a,v_x,t_a) = c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),
inference(transitivity,[status(thm)],[64,52]) ).
tff(66,plain,
^ [T: $i] :
refl(
( ( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) )
<=> ( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Power_Opower) ).
tff(70,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Power_Opower(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Power_Opower(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Power_Opower(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_Power_Opower(T) )
| ~ class_Ring__and__Field_Ofield(t_a)
| class_Power_Opower(t_a) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
class_Power_Opower(t_a),
inference(unit_resolution,[status(thm)],[75,3,72]) ).
tff(77,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(78,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
tff(81,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oone__class_Oone(t_a) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oone__class_Oone(t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oone__class_Oone(t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) )
| ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oone__class_Oone(t_a) ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
( ~ class_Power_Opower(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oone__class_Oone(t_a) ) ),
inference(unit_resolution,[status(thm)],[86,83]) ).
tff(88,plain,
c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oone__class_Oone(t_a),
inference(unit_resolution,[status(thm)],[87,76]) ).
tff(89,plain,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a),
inference(monotonicity,[status(thm)],[88,65]) ).
tff(90,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),t_a),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
^ [T: $i] :
refl(
( ( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) )
<=> ( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ) )),
inference(bind,[status(th)],]) ).
tff(92,plain,
( ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,plain,
( ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
^ [T: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Omonoid__mult(T) )
<=> ( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ) )),
inference(bind,[status(th)],]) ).
tff(95,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Omonoid__mult(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Omonoid__mult(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_OrderedGroup_Omonoid__mult) ).
tff(97,plain,
! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[99,92]) ).
tff(101,plain,
( ( ~ ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_OrderedGroup_Omonoid__mult(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) )
<=> ( ~ ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_OrderedGroup_Omonoid__mult(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_OrderedGroup_Omonoid__mult(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) )
| class_OrderedGroup_Omonoid__mult(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
class_OrderedGroup_Omonoid__mult(t_a),
inference(unit_resolution,[status(thm)],[103,3,100]) ).
tff(105,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
<=> ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
tff(109,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ),
inference(skolemize,[status(sab)],[109]) ).
tff(111,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[110,106]) ).
tff(112,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) ) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),
inference(unit_resolution,[status(thm)],[114,111,104]) ).
tff(116,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),t_a),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),
inference(transitivity,[status(thm)],[116,90,15]) ).
tff(118,plain,
( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) )
<=> ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,axiom,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(120,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
$false,
inference(unit_resolution,[status(thm)],[120,117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWV674-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n012.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 06:56:18 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.41/0.62 % SZS status Unsatisfiable
% 0.41/0.62 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------