TSTP Solution File: ANA016-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ANA016-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 16:23:25 EDT 2022
% Result : Unsatisfiable 1.16s 1.07s
% Output : Proof 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 65
% Syntax : Number of formulae : 126 ( 31 unt; 21 typ; 0 def)
% Number of atoms : 382 ( 144 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 440 ( 184 ~; 210 |; 0 &)
% ( 46 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 21 ( 21 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 11 >; 6 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-3 aty)
% Number of variables : 191 ( 168 !; 0 ?; 191 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_times_type,type,
c_times: ( $i * $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(v_g_type,type,
v_g: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_HOL_Oinverse_type,type,
c_HOL_Oinverse: ( $i * $i ) > $i ).
tff(v_c_type,type,
v_c: $i ).
tff(class_OrderedGroup_Osemigroup__mult_type,type,
class_OrderedGroup_Osemigroup__mult: $i > $o ).
tff(class_Ring__and__Field_Oordered__field_type,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(c_Suc_type,type,
c_Suc: $i > $i ).
tff(c_Nat_Osize_type,type,
c_Nat_Osize: ( $i * $i ) > $i ).
tff(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
tff(c_Product__Type_OUnity_type,type,
c_Product__Type_OUnity: $i ).
tff(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(c_0_type,type,
c_0: $i ).
tff(c_Numeral_Onumber__of_type,type,
c_Numeral_Onumber__of: ( $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Numeral_OBit_type,type,
c_Numeral_OBit: ( $i * $i ) > $i ).
tff(c_Numeral_Obit_OB1_type,type,
c_Numeral_Obit_OB1: $i ).
tff(c_Numeral_OPls_type,type,
c_Numeral_OPls: $i ).
tff(c_1_type,type,
c_1: $i ).
tff(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(1,plain,
( class_Ring__and__Field_Oordered__field(t_a)
<=> class_Ring__and__Field_Oordered__field(t_a) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tff(3,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [T: $i] :
refl(
( ( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) )
<=> ( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [T: $i] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [T: $i] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [T: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Osemigroup__mult(T) )
<=> ( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Osemigroup__mult(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Osemigroup__mult(T) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_24) ).
tff(10,plain,
! [T: $i] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [T: $i] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [T: $i] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [T: $i] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [T: $i] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) )
| class_OrderedGroup_Osemigroup__mult(t_a)
| ~ class_Ring__and__Field_Oordered__field(t_a) )
<=> ( ~ ! [T: $i] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) )
| class_OrderedGroup_Osemigroup__mult(t_a)
| ~ class_Ring__and__Field_Oordered__field(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) )
| class_OrderedGroup_Osemigroup__mult(t_a)
| ~ class_Ring__and__Field_Oordered__field(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__field(T) )
| class_OrderedGroup_Osemigroup__mult(t_a)
| ~ class_Ring__and__Field_Oordered__field(t_a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
class_OrderedGroup_Osemigroup__mult(t_a),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) )
<=> ( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0) ).
tff(22,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Osemigroup__mult(t_a)
| ( c_times(c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),v_g(v_x),t_a) = c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Osemigroup__mult(t_a)
| ( c_times(c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),v_g(v_x),t_a) = c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Osemigroup__mult(t_a)
| ( c_times(c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),v_g(v_x),t_a) = c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) )
| ~ class_OrderedGroup_Osemigroup__mult(t_a)
| ( c_times(c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),v_g(v_x),t_a) = c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ class_OrderedGroup_Osemigroup__mult(t_a)
| ( c_times(c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),v_g(v_x),t_a) = c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) ) ),
inference(unit_resolution,[status(thm)],[27,24]) ).
tff(29,plain,
c_times(c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),v_g(v_x),t_a) = c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),
inference(unit_resolution,[status(thm)],[28,17]) ).
tff(30,plain,
^ [T: $i] :
refl(
( ( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) )
<=> ( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [T: $i] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) )
<=> ! [T: $i] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [T: $i] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) )
<=> ! [T: $i] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
^ [T: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) )
<=> ( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) )
<=> ! [T: $i] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_0) ).
tff(36,plain,
! [T: $i] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [T: $i] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [T: $i] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [T: $i] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ( ~ ! [T: $i] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) )
| class_Ring__and__Field_Ofield(t_a)
| ~ class_Ring__and__Field_Oordered__field(t_a) )
<=> ( ~ ! [T: $i] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) )
| class_Ring__and__Field_Ofield(t_a)
| ~ class_Ring__and__Field_Oordered__field(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ~ ! [T: $i] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) )
| class_Ring__and__Field_Ofield(t_a)
| ~ class_Ring__and__Field_Oordered__field(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
( ~ ! [T: $i] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) )
| class_Ring__and__Field_Ofield(t_a)
| ~ class_Ring__and__Field_Oordered__field(t_a) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
class_Ring__and__Field_Ofield(t_a),
inference(unit_resolution,[status(thm)],[42,39,3]) ).
tff(44,plain,
( ( v_c != c_0 )
<=> ( v_c != c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( v_c != c_0 )
<=> ( v_c != c_0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
v_c != c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(47,plain,
v_c != c_0,
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
v_c != c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),
inference(modus_ponens,[status(thm)],[47,44]) ).
tff(49,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) )
<=> ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
^ [V_a: $i,T_a: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat) ) )
<=> ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
^ [V_a: $i,T_a: $i] :
trans(
monotonicity(
rewrite(
( ( V_a = c_0 )
<=> ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ) )),
rewrite(
( ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1 )
<=> ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat) ) )),
( ( ( V_a = c_0 )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1 ) )
<=> ( ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat) ) ) )),
rewrite(
( ( ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat) ) )
<=> ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat) ) ) )),
( ( ( V_a = c_0 )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1 ) )
<=> ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat) ) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1 ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1 ) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
^ [V_a: $i,T_a: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_0 )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1 ) )
<=> ( ( V_a = c_0 )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1 ) ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_0 )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1 ) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1 ) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_0 )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Ring__and__Field_Oright__inverse_0) ).
tff(59,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1 ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1 ) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[60,54]) ).
tff(62,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) ),
inference(modus_ponens,[status(thm)],[61,52]) ).
tff(63,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) ),
inference(modus_ponens,[status(thm)],[63,50]) ).
tff(65,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_c = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_c = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_c = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_c = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) )
| ( c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| ( c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) ) ),
inference(unit_resolution,[status(thm)],[67,64,48]) ).
tff(69,plain,
c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a) = c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),
inference(unit_resolution,[status(thm)],[68,43]) ).
tff(70,plain,
c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)) = c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),v_g(v_x),t_a) = c_times(c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),v_g(v_x),t_a),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
^ [T: $i] :
refl(
( ( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Omonoid__mult(T) )
<=> ( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Omonoid__mult(T) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Omonoid__mult(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Omonoid__mult(T) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Omonoid__mult(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Omonoid__mult(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Omonoid__mult(T) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__field_15) ).
tff(76,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Omonoid__mult(T) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Omonoid__mult(T) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Omonoid__mult(T) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Omonoid__mult(T) )
| ~ class_Ring__and__Field_Oordered__field(t_a)
| class_OrderedGroup_Omonoid__mult(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Omonoid__mult(T) )
| ~ class_Ring__and__Field_Oordered__field(t_a)
| class_OrderedGroup_Omonoid__mult(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Omonoid__mult(T) )
| ~ class_Ring__and__Field_Oordered__field(t_a)
| class_OrderedGroup_Omonoid__mult(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Omonoid__mult(T) )
| ~ class_Ring__and__Field_Oordered__field(t_a)
| class_OrderedGroup_Omonoid__mult(t_a) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
class_OrderedGroup_Omonoid__mult(t_a),
inference(unit_resolution,[status(thm)],[81,78,3]) ).
tff(83,plain,
^ [T_a: $i,V_y: $i] :
refl(
( ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),V_y,T_a) = V_y ) )
<=> ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),V_y,T_a) = V_y ) ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),V_y,T_a) = V_y ) )
<=> ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),V_y,T_a) = V_y ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
^ [T_a: $i,V_y: $i] :
rewrite(
( ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat),V_y,T_a) = V_y ) )
<=> ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),V_y,T_a) = V_y ) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat),V_y,T_a) = V_y ) )
<=> ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),V_y,T_a) = V_y ) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
^ [T_a: $i,V_y: $i] :
rewrite(
( ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_1,V_y,T_a) = V_y ) )
<=> ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat),V_y,T_a) = V_y ) ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_1,V_y,T_a) = V_y ) )
<=> ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat),V_y,T_a) = V_y ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_1,V_y,T_a) = V_y ) )
<=> ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_1,V_y,T_a) = V_y ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,axiom,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_1,V_y,T_a) = V_y ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
tff(91,plain,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_1,V_y,T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat),V_y,T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[91,88]) ).
tff(93,plain,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),V_y,T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[92,86]) ).
tff(94,plain,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),V_y,T_a) = V_y ) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),V_y,T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[94,84]) ).
tff(96,plain,
( ( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),v_g(v_x),t_a) = v_g(v_x) ) )
<=> ( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),v_g(v_x),t_a) = v_g(v_x) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),v_g(v_x),t_a) = v_g(v_x) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
( ~ ! [T_a: $i,V_y: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),V_y,T_a) = V_y ) )
| ~ class_OrderedGroup_Omonoid__mult(t_a)
| ( c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),v_g(v_x),t_a) = v_g(v_x) ) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),v_g(v_x),t_a) = v_g(v_x),
inference(unit_resolution,[status(thm)],[98,95,82]) ).
tff(100,plain,
v_g(v_x) = c_times(c_Suc(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit)),v_g(v_x),t_a),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
v_g(v_x) = c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),
inference(transitivity,[status(thm)],[100,71,29]) ).
tff(102,plain,
( ( v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) )
<=> ( v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,axiom,
v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(104,plain,
v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
$false,
inference(unit_resolution,[status(thm)],[104,101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA016-1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n001.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon Aug 29 19:07:15 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 1.16/1.07 % SZS status Unsatisfiable
% 1.16/1.07 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------