TSTP Solution File: SWV679-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV679-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 15:24:03 EDT 2022
% Result : Unsatisfiable 0.20s 0.57s
% Output : Proof 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 45
% Syntax : Number of formulae : 88 ( 22 unt; 14 typ; 0 def)
% Number of atoms : 328 ( 121 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 411 ( 168 ~; 205 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 9 >; 9 *; 0 +; 0 <<)
% Number of predicates : 10 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 161 ( 145 !; 0 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(v_m_type,type,
v_m: $i ).
tff(v_n_type,type,
v_n: $i ).
tff(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(v_a_type,type,
v_a: $i ).
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(c_HOL_Oinverse__class_Oinverse_type,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
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_a: $i,T_a: $i] :
refl(
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
<=> ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
tff(8,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_HOL_Oinverse__class_Oinverse(v_a,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( class_Orderings_Olinorder(tc_nat)
<=> class_Orderings_Olinorder(tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
tff(18,plain,
class_Orderings_Olinorder(tc_nat),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ c_lessequals(v_n,v_m,tc_nat)
<=> ~ c_lessequals(v_n,v_m,tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
~ c_lessequals(v_n,v_m,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_False_0) ).
tff(21,plain,
~ c_lessequals(v_n,v_m,tc_nat),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(
( ( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
rewrite(
( ( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
tff(28,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Olinorder(tc_nat)
| c_lessequals(v_m,v_n,tc_nat)
| c_lessequals(v_n,v_m,tc_nat) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Olinorder(tc_nat)
| c_lessequals(v_m,v_n,tc_nat)
| c_lessequals(v_n,v_m,tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Olinorder(tc_nat)
| c_lessequals(v_m,v_n,tc_nat)
| c_lessequals(v_n,v_m,tc_nat) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) )
| ~ class_Orderings_Olinorder(tc_nat)
| c_lessequals(v_m,v_n,tc_nat)
| c_lessequals(v_n,v_m,tc_nat) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
c_lessequals(v_m,v_n,tc_nat),
inference(unit_resolution,[status(thm)],[34,31,21,18]) ).
tff(36,plain,
^ [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
refl(
( ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) )
<=> ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) )
<=> ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
^ [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
trans(
monotonicity(
rewrite(
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat) )
<=> ( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) ) )),
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
rewrite(
( ( ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ 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) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) ) )),
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__diff__inverse_0) ).
tff(42,plain,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( v_a != c_HOL_Ozero__class_Ozero(t_a) )
<=> ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,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(48,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( class_Ring__and__Field_Ofield(t_a)
<=> $true ),
inference(iff_true,[status(thm)],[2]) ).
tff(50,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
<=> $false ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,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)],[51]) ).
tff(53,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)],[52,47]) ).
tff(54,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(55,plain,
v_a != c_HOL_Ozero__class_Ozero(t_a),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
v_a != c_HOL_Ozero__class_Ozero(t_a),
inference(modus_ponens,[status(thm)],[55,46]) ).
tff(57,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(v_m,v_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) ) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(v_m,v_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ( ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(v_m,v_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) )
| ~ class_Ring__and__Field_Ofield(t_a) )
<=> ( ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(v_m,v_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(v_m,v_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) )
| ~ class_Ring__and__Field_Ofield(t_a) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(v_m,v_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) ) ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(v_m,v_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) )
| ~ class_Ring__and__Field_Ofield(t_a) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(v_m,v_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) ) ) ),
inference(transitivity,[status(thm)],[59,57]) ).
tff(61,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) )
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(v_m,v_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) )
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i,V_m: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_m,V_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) )
| ~ class_Ring__and__Field_Ofield(T_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(v_m,v_n,tc_nat)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),
inference(unit_resolution,[status(thm)],[62,56,45,3,35]) ).
tff(64,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),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),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a),
inference(transitivity,[status(thm)],[64,15]) ).
tff(66,plain,
( ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) )
<=> ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ( ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) )
| $false )
<=> ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( c_lessequals(v_n,v_m,tc_nat)
<=> $false ),
inference(iff_false,[status(thm)],[20]) ).
tff(69,plain,
( ( ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) )
| c_lessequals(v_n,v_m,tc_nat) )
<=> ( ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) )
| $false ) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( ( ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) )
| c_lessequals(v_n,v_m,tc_nat) )
<=> ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) ) ),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,axiom,
( ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) )
| c_lessequals(v_n,v_m,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(72,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a),
inference(modus_ponens,[status(thm)],[72,66]) ).
tff(74,plain,
$false,
inference(unit_resolution,[status(thm)],[73,65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV679-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 07:01:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.57 % SZS status Unsatisfiable
% 0.20/0.57 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------