%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV678-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:35:55 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.56s
% Output : Proof 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 37 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 196 ( 92 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 263 ( 112 ~; 135 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 84 ( 76 !; 0 ?; 84 :)
% 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_n_type,type,
v_n: $i ).
tff(v_m_type,type,
v_m: $i ).
tff(v_a_type,type,
v_a: $i ).
tff(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(1,plain,
( c_lessequals(v_n,v_m,tc_nat)
<=> c_lessequals(v_n,v_m,tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_lessequals(v_n,v_m,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).
tff(3,plain,
c_lessequals(v_n,v_m,tc_nat),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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(bind,[status(th)],[]) ).
tff(5,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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(quant_intro,[status(thm)],[4]) ).
tff(6,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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(7,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(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_n,V_m,tc_nat) )
<=> ( ~ c_lessequals(V_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ c_lessequals(V_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_a = c_HOL_Ozero__class_Ozero(T_a) ) ) )),
rewrite(( ( ~ c_lessequals(V_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ c_lessequals(V_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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(bind,[status(th)],[]) ).
tff(8,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(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_n,V_m,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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(quant_intro,[status(thm)],[7]) ).
tff(9,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(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_n,V_m,tc_nat)
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__diff_0) ).
tff(10,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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)],[9,8]) ).
tff(11,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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)],[10,6]) ).
tff(12,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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(skolemize,[status(sab)],[11]) ).
tff(13,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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)],[12,5]) ).
tff(14,plain,
( class_Ring__and__Field_Ofield(t_a)
<=> class_Ring__and__Field_Ofield(t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
class_Ring__and__Field_Ofield(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tff(16,plain,
class_Ring__and__Field_Ofield(t_a),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) )
<=> ( ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
( ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nz_0) ).
tff(19,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| ( v_a != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
v_a != c_HOL_Ozero__class_Ozero(t_a),
inference(unit_resolution,[status(thm)],[19,16]) ).
tff(21,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_n,v_m,tc_nat)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_n,v_m,tc_nat)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,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(22,plain,
( ( ( v_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(v_n,v_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,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_n,v_m,tc_nat)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,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(23,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(v_n,v_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_n,v_m,tc_nat)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,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)],[22]) ).
tff(24,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(v_n,v_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_n,v_m,tc_nat)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,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)],[23,21]) ).
tff(25,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_a = c_HOL_Ozero__class_Ozero(t_a) )
| ~ c_lessequals(v_n,v_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,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(quant_inst,[status(thm)],[]) ).
tff(26,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_n,V_m,tc_nat)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,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_n,v_m,tc_nat)
| ( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,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)],[25,24]) ).
tff(27,plain,
c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,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)],[26,16,20,13,3]) ).
tff(28,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(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a),
inference(symmetry,[status(thm)],[27]) ).
tff(29,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(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,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(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) )
| ~ c_lessequals(v_n,v_m,tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,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(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) )
| ~ c_lessequals(v_n,v_m,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(31,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(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) )
| ~ c_lessequals(v_n,v_m,tc_nat) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,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(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) )
| ~ c_lessequals(v_n,v_m,tc_nat) ),
inference(modus_ponens,[status(thm)],[31,29]) ).
tff(33,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(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) )
| ~ c_lessequals(v_n,v_m,tc_nat) ),
inference(modus_ponens,[status(thm)],[32,29]) ).
tff(34,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(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) )
| ~ c_lessequals(v_n,v_m,tc_nat) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,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(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) )
| ~ c_lessequals(v_n,v_m,tc_nat) ),
inference(modus_ponens,[status(thm)],[34,29]) ).
tff(36,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(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a),
inference(unit_resolution,[status(thm)],[35,3]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWV678-1 : TPTP v9.0.0. Released v4.1.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Fri Jun 20 10:39:24 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.22/0.56 % SZS status Unsatisfiable
% 0.22/0.56 % SZS output start Proof
% See solution above
% 0.43/0.60 % E exiting
%------------------------------------------------------------------------------