%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : NUM923^1 : TPTP v7.0.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n151.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.625MB
% OS       : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan  8 13:12:01 EST 2018

% Result   : Timeout 300.01s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04  % Problem  : NUM923^1 : TPTP v7.0.0. Released v5.3.0.
% 0.00/0.04  % Command  : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.24  % Computer : n151.star.cs.uiowa.edu
% 0.02/0.24  % Model    : x86_64 x86_64
% 0.02/0.24  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.24  % Memory   : 32218.625MB
% 0.02/0.24  % OS       : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.24  % CPULimit : 300
% 0.02/0.24  % DateTime : Fri Jan  5 15:36:35 CST 2018
% 0.02/0.24  % CPUTime  : 
% 0.02/0.26  Python 2.7.13
% 0.08/0.52  Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.08/0.52  FOF formula (<kernel.Constant object at 0x2b7480041a28>, <kernel.Type object at 0x2b7480041368>) of role type named ty_ty_tc__Int__Oint
% 0.08/0.52  Using role type
% 0.08/0.52  Declaring int:Type
% 0.08/0.52  FOF formula (<kernel.Constant object at 0x2b747fd5a878>, <kernel.Type object at 0x2b74800419e0>) of role type named ty_ty_tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J
% 0.08/0.52  Using role type
% 0.08/0.52  Declaring product_prod_int_int:Type
% 0.08/0.52  FOF formula (<kernel.Constant object at 0x2b7480041638>, <kernel.DependentProduct object at 0x2b7480041cf8>) of role type named sy_c_All
% 0.08/0.52  Using role type
% 0.08/0.52  Declaring all:((product_prod_int_int->Prop)->Prop)
% 0.08/0.52  FOF formula (<kernel.Constant object at 0x2b7480041f38>, <kernel.DependentProduct object at 0x2b7480041dd0>) of role type named sy_c_Ex
% 0.08/0.52  Using role type
% 0.08/0.52  Declaring _TPTP_ex:((product_prod_int_int->Prop)->Prop)
% 0.08/0.52  FOF formula (<kernel.Constant object at 0x2b7480041560>, <kernel.DependentProduct object at 0x2b7480041c20>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint
% 0.08/0.52  Using role type
% 0.08/0.52  Declaring minus_minus_int:(int->(int->int))
% 0.08/0.52  FOF formula (<kernel.Constant object at 0x2b7480041c68>, <kernel.DependentProduct object at 0x2b74800417e8>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint
% 0.08/0.52  Using role type
% 0.08/0.52  Declaring plus_plus_int:(int->(int->int))
% 0.08/0.52  FOF formula (<kernel.Constant object at 0x2b7480041dd0>, <kernel.DependentProduct object at 0x2b7480041710>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint
% 0.08/0.52  Using role type
% 0.08/0.52  Declaring times_times_int:(int->(int->int))
% 0.08/0.52  FOF formula (<kernel.Constant object at 0x2b7480041c20>, <kernel.DependentProduct object at 0x2b7480041638>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Int__Oint
% 0.08/0.52  Using role type
% 0.08/0.52  Declaring ord_less_eq_int:(int->(int->Prop))
% 0.08/0.52  FOF formula (<kernel.Constant object at 0x2b74800417e8>, <kernel.DependentProduct object at 0x2b7480041cf8>) of role type named sy_c_Product__Type_OPair_000tc__Int__Oint_000tc__Int__Oint
% 0.08/0.52  Using role type
% 0.08/0.52  Declaring product_Pair_int_int:(int->(int->product_prod_int_int))
% 0.08/0.52  FOF formula (<kernel.Constant object at 0x2b7480041710>, <kernel.DependentProduct object at 0x2b7480041f38>) of role type named sy_c_Product__Type_Ocurry_000tc__Int__Oint_000tc__Int__Oint_000_Eo
% 0.08/0.52  Using role type
% 0.08/0.52  Declaring produc176579150_int_o:((product_prod_int_int->Prop)->(int->(int->Prop)))
% 0.08/0.52  FOF formula (<kernel.Constant object at 0x2b7480041638>, <kernel.DependentProduct object at 0x2b7480041c20>) of role type named sy_c_TwoSquares__Mirabelle__fqdbopfjxb_Ois__sum2sq
% 0.08/0.52  Using role type
% 0.08/0.52  Declaring twoSqu1013291560sum2sq:(int->Prop)
% 0.08/0.52  FOF formula (<kernel.Constant object at 0x2b7480041ea8>, <kernel.DependentProduct object at 0x2b7480041128>) of role type named sy_c_TwoSquares__Mirabelle__fqdbopfjxb_Osum2sq
% 0.08/0.52  Using role type
% 0.08/0.52  Declaring twoSqu1535104286sum2sq:(product_prod_int_int->int)
% 0.08/0.52  FOF formula (<kernel.Constant object at 0x2b7480041f38>, <kernel.Constant object at 0x2b7480041128>) of role type named sy_v_a
% 0.08/0.52  Using role type
% 0.08/0.52  Declaring a:int
% 0.08/0.52  FOF formula (<kernel.Constant object at 0x2b7480041638>, <kernel.Constant object at 0x2b7480041128>) of role type named sy_v_b
% 0.08/0.52  Using role type
% 0.08/0.52  Declaring b:int
% 0.08/0.52  FOF formula (<kernel.Constant object at 0x2b7480041ea8>, <kernel.Constant object at 0x2b7480041128>) of role type named sy_v_p
% 0.08/0.52  Using role type
% 0.08/0.52  Declaring p:int
% 0.08/0.52  FOF formula (<kernel.Constant object at 0x2b7480041f38>, <kernel.Constant object at 0x2b7480041128>) of role type named sy_v_q
% 0.08/0.52  Using role type
% 0.08/0.52  Declaring q:int
% 0.08/0.52  FOF formula (forall (A_42:int) (R:int) (B_39:int) (M_1:int) (C_29:int) (D_12:int) (N:int), (((eq int) ((plus_plus_int ((times_times_int ((minus_minus_int A_42) ((times_times_int R) B_39))) M_1)) ((times_times_int ((minus_minus_int C_29) ((times_times_int R) D_12))) N))) ((minus_minus_int ((plus_plus_int ((times_times_int A_42) M_1)) ((times_times_int C_29) N))) ((times_times_int R) ((plus_plus_int ((times_times_int B_39) M_1)) ((times_times_int D_12) N)))))) of role axiom named fact_0_xzgcda__linear__aux1
% 0.08/0.52  A new axiom: (forall (A_42:int) (R:int) (B_39:int) (M_1:int) (C_29:int) (D_12:int) (N:int), (((eq int) ((plus_plus_int ((times_times_int ((minus_minus_int A_42) ((times_times_int R) B_39))) M_1)) ((times_times_int ((minus_minus_int C_29) ((times_times_int R) D_12))) N))) ((minus_minus_int ((plus_plus_int ((times_times_int A_42) M_1)) ((times_times_int C_29) N))) ((times_times_int R) ((plus_plus_int ((times_times_int B_39) M_1)) ((times_times_int D_12) N))))))
% 0.08/0.53  FOF formula (forall (X_6:int) (Y_6:int) (A_45:int) (B_42:int), (((eq int) ((minus_minus_int ((times_times_int X_6) Y_6)) ((times_times_int A_45) B_42))) ((plus_plus_int ((times_times_int X_6) ((minus_minus_int Y_6) B_42))) ((times_times_int ((minus_minus_int X_6) A_45)) B_42)))) of role axiom named fact_1_mult__diff__mult
% 0.08/0.53  A new axiom: (forall (X_6:int) (Y_6:int) (A_45:int) (B_42:int), (((eq int) ((minus_minus_int ((times_times_int X_6) Y_6)) ((times_times_int A_45) B_42))) ((plus_plus_int ((times_times_int X_6) ((minus_minus_int Y_6) B_42))) ((times_times_int ((minus_minus_int X_6) A_45)) B_42))))
% 0.08/0.53  FOF formula (forall (A_44:int) (E_4:int) (C_31:int) (B_41:int) (D_11:int), ((iff (((eq int) ((plus_plus_int ((times_times_int A_44) E_4)) C_31)) ((plus_plus_int ((times_times_int B_41) E_4)) D_11))) (((eq int) C_31) ((plus_plus_int ((times_times_int ((minus_minus_int B_41) A_44)) E_4)) D_11)))) of role axiom named fact_2_eq__add__iff2
% 0.08/0.53  A new axiom: (forall (A_44:int) (E_4:int) (C_31:int) (B_41:int) (D_11:int), ((iff (((eq int) ((plus_plus_int ((times_times_int A_44) E_4)) C_31)) ((plus_plus_int ((times_times_int B_41) E_4)) D_11))) (((eq int) C_31) ((plus_plus_int ((times_times_int ((minus_minus_int B_41) A_44)) E_4)) D_11))))
% 0.08/0.53  FOF formula (forall (A_43:int) (E_3:int) (C_30:int) (B_40:int) (D_10:int), ((iff (((eq int) ((plus_plus_int ((times_times_int A_43) E_3)) C_30)) ((plus_plus_int ((times_times_int B_40) E_3)) D_10))) (((eq int) ((plus_plus_int ((times_times_int ((minus_minus_int A_43) B_40)) E_3)) C_30)) D_10))) of role axiom named fact_3_eq__add__iff1
% 0.08/0.53  A new axiom: (forall (A_43:int) (E_3:int) (C_30:int) (B_40:int) (D_10:int), ((iff (((eq int) ((plus_plus_int ((times_times_int A_43) E_3)) C_30)) ((plus_plus_int ((times_times_int B_40) E_3)) D_10))) (((eq int) ((plus_plus_int ((times_times_int ((minus_minus_int A_43) B_40)) E_3)) C_30)) D_10)))
% 0.08/0.53  FOF formula (forall (X_5:int), ((iff (twoSqu1013291560sum2sq X_5)) ((ex int) (fun (A_14:int)=> ((ex int) (fun (B_14:int)=> (((eq int) (twoSqu1535104286sum2sq ((product_Pair_int_int A_14) B_14))) X_5))))))) of role axiom named fact_4_is__sum2sq__def
% 0.08/0.53  A new axiom: (forall (X_5:int), ((iff (twoSqu1013291560sum2sq X_5)) ((ex int) (fun (A_14:int)=> ((ex int) (fun (B_14:int)=> (((eq int) (twoSqu1535104286sum2sq ((product_Pair_int_int A_14) B_14))) X_5)))))))
% 0.08/0.53  FOF formula (forall (A_42:int) (B_39:int) (C_29:int), ((((eq int) ((minus_minus_int A_42) B_39)) C_29)->(((eq int) A_42) ((plus_plus_int C_29) B_39)))) of role axiom named fact_5_Int2_Oaux1
% 0.08/0.53  A new axiom: (forall (A_42:int) (B_39:int) (C_29:int), ((((eq int) ((minus_minus_int A_42) B_39)) C_29)->(((eq int) A_42) ((plus_plus_int C_29) B_39))))
% 0.08/0.53  FOF formula (forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((minus_minus_int Z1) Z2))) ((minus_minus_int ((times_times_int W) Z1)) ((times_times_int W) Z2)))) of role axiom named fact_6_zdiff__zmult__distrib2
% 0.08/0.53  A new axiom: (forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((minus_minus_int Z1) Z2))) ((minus_minus_int ((times_times_int W) Z1)) ((times_times_int W) Z2))))
% 0.08/0.53  FOF formula (forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((minus_minus_int Z1) Z2)) W)) ((minus_minus_int ((times_times_int Z1) W)) ((times_times_int Z2) W)))) of role axiom named fact_7_zdiff__zmult__distrib
% 0.08/0.53  A new axiom: (forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((minus_minus_int Z1) Z2)) W)) ((minus_minus_int ((times_times_int Z1) W)) ((times_times_int Z2) W))))
% 0.08/0.53  FOF formula (forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((plus_plus_int Z1) Z2))) ((plus_plus_int ((times_times_int W) Z1)) ((times_times_int W) Z2)))) of role axiom named fact_8_zadd__zmult__distrib2
% 0.08/0.55  A new axiom: (forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((plus_plus_int Z1) Z2))) ((plus_plus_int ((times_times_int W) Z1)) ((times_times_int W) Z2))))
% 0.08/0.55  FOF formula (forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((plus_plus_int Z1) Z2)) W)) ((plus_plus_int ((times_times_int Z1) W)) ((times_times_int Z2) W)))) of role axiom named fact_9_zadd__zmult__distrib
% 0.08/0.55  A new axiom: (forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((plus_plus_int Z1) Z2)) W)) ((plus_plus_int ((times_times_int Z1) W)) ((times_times_int Z2) W))))
% 0.08/0.55  FOF formula (forall (A_41:int) (B_38:int), (((eq int) ((plus_plus_int ((minus_minus_int A_41) B_38)) B_38)) A_41)) of role axiom named fact_10_diff__add__cancel
% 0.08/0.55  A new axiom: (forall (A_41:int) (B_38:int), (((eq int) ((plus_plus_int ((minus_minus_int A_41) B_38)) B_38)) A_41))
% 0.08/0.55  FOF formula (forall (A_40:int) (B_37:int) (C_28:int), (((eq int) ((times_times_int ((times_times_int A_40) B_37)) C_28)) ((times_times_int A_40) ((times_times_int B_37) C_28)))) of role axiom named fact_11_ab__semigroup__mult__class_Omult__ac_I1_J
% 0.08/0.55  A new axiom: (forall (A_40:int) (B_37:int) (C_28:int), (((eq int) ((times_times_int ((times_times_int A_40) B_37)) C_28)) ((times_times_int A_40) ((times_times_int B_37) C_28))))
% 0.08/0.55  FOF formula (forall (B_36:int) (A_39:int) (C_27:int), ((((eq int) ((plus_plus_int B_36) A_39)) ((plus_plus_int C_27) A_39))->(((eq int) B_36) C_27))) of role axiom named fact_12_add__right__imp__eq
% 0.08/0.55  A new axiom: (forall (B_36:int) (A_39:int) (C_27:int), ((((eq int) ((plus_plus_int B_36) A_39)) ((plus_plus_int C_27) A_39))->(((eq int) B_36) C_27)))
% 0.08/0.55  FOF formula (forall (A_38:int) (B_35:int) (C_26:int), ((((eq int) ((plus_plus_int A_38) B_35)) ((plus_plus_int A_38) C_26))->(((eq int) B_35) C_26))) of role axiom named fact_13_add__imp__eq
% 0.08/0.55  A new axiom: (forall (A_38:int) (B_35:int) (C_26:int), ((((eq int) ((plus_plus_int A_38) B_35)) ((plus_plus_int A_38) C_26))->(((eq int) B_35) C_26)))
% 0.08/0.55  FOF formula (forall (A_37:int) (B_34:int) (C_25:int), ((((eq int) ((plus_plus_int A_37) B_34)) ((plus_plus_int A_37) C_25))->(((eq int) B_34) C_25))) of role axiom named fact_14_add__left__imp__eq
% 0.08/0.55  A new axiom: (forall (A_37:int) (B_34:int) (C_25:int), ((((eq int) ((plus_plus_int A_37) B_34)) ((plus_plus_int A_37) C_25))->(((eq int) B_34) C_25)))
% 0.08/0.55  FOF formula (forall (B_33:int) (A_36:int) (C_24:int), ((iff (((eq int) ((plus_plus_int B_33) A_36)) ((plus_plus_int C_24) A_36))) (((eq int) B_33) C_24))) of role axiom named fact_15_add__right__cancel
% 0.08/0.55  A new axiom: (forall (B_33:int) (A_36:int) (C_24:int), ((iff (((eq int) ((plus_plus_int B_33) A_36)) ((plus_plus_int C_24) A_36))) (((eq int) B_33) C_24)))
% 0.08/0.55  FOF formula (forall (A_35:int) (B_32:int) (C_23:int), ((iff (((eq int) ((plus_plus_int A_35) B_32)) ((plus_plus_int A_35) C_23))) (((eq int) B_32) C_23))) of role axiom named fact_16_add__left__cancel
% 0.08/0.55  A new axiom: (forall (A_35:int) (B_32:int) (C_23:int), ((iff (((eq int) ((plus_plus_int A_35) B_32)) ((plus_plus_int A_35) C_23))) (((eq int) B_32) C_23)))
% 0.08/0.55  FOF formula (forall (A_34:int) (B_31:int) (C_22:int), (((eq int) ((plus_plus_int ((plus_plus_int A_34) B_31)) C_22)) ((plus_plus_int A_34) ((plus_plus_int B_31) C_22)))) of role axiom named fact_17_ab__semigroup__add__class_Oadd__ac_I1_J
% 0.08/0.55  A new axiom: (forall (A_34:int) (B_31:int) (C_22:int), (((eq int) ((plus_plus_int ((plus_plus_int A_34) B_31)) C_22)) ((plus_plus_int A_34) ((plus_plus_int B_31) C_22))))
% 0.08/0.55  FOF formula (forall (A_33:int) (B_30:int) (C_21:int) (D_9:int), ((((eq int) ((minus_minus_int A_33) B_30)) ((minus_minus_int C_21) D_9))->((iff (((eq int) A_33) B_30)) (((eq int) C_21) D_9)))) of role axiom named fact_18_diff__eq__diff__eq
% 0.08/0.55  A new axiom: (forall (A_33:int) (B_30:int) (C_21:int) (D_9:int), ((((eq int) ((minus_minus_int A_33) B_30)) ((minus_minus_int C_21) D_9))->((iff (((eq int) A_33) B_30)) (((eq int) C_21) D_9))))
% 0.08/0.55  FOF formula (forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((times_times_int ((times_times_int Z1) Z2)) Z3)) ((times_times_int Z1) ((times_times_int Z2) Z3)))) of role axiom named fact_19_zmult__assoc
% 0.08/0.57  A new axiom: (forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((times_times_int ((times_times_int Z1) Z2)) Z3)) ((times_times_int Z1) ((times_times_int Z2) Z3))))
% 0.08/0.57  FOF formula (forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z))) of role axiom named fact_20_zmult__commute
% 0.08/0.57  A new axiom: (forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z)))
% 0.08/0.57  FOF formula (forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((plus_plus_int ((plus_plus_int Z1) Z2)) Z3)) ((plus_plus_int Z1) ((plus_plus_int Z2) Z3)))) of role axiom named fact_21_zadd__assoc
% 0.08/0.57  A new axiom: (forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((plus_plus_int ((plus_plus_int Z1) Z2)) Z3)) ((plus_plus_int Z1) ((plus_plus_int Z2) Z3))))
% 0.08/0.57  FOF formula (forall (X_5:int) (Y_5:int) (Z:int), (((eq int) ((plus_plus_int X_5) ((plus_plus_int Y_5) Z))) ((plus_plus_int Y_5) ((plus_plus_int X_5) Z)))) of role axiom named fact_22_zadd__left__commute
% 0.08/0.57  A new axiom: (forall (X_5:int) (Y_5:int) (Z:int), (((eq int) ((plus_plus_int X_5) ((plus_plus_int Y_5) Z))) ((plus_plus_int Y_5) ((plus_plus_int X_5) Z))))
% 0.08/0.57  FOF formula (forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z))) of role axiom named fact_23_zadd__commute
% 0.08/0.57  A new axiom: (forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z)))
% 0.08/0.57  FOF formula (forall (A_32:int) (E_2:int) (B_29:int) (C_20:int), (((eq int) ((plus_plus_int ((times_times_int A_32) E_2)) ((plus_plus_int ((times_times_int B_29) E_2)) C_20))) ((plus_plus_int ((times_times_int ((plus_plus_int A_32) B_29)) E_2)) C_20))) of role axiom named fact_24_combine__common__factor
% 0.08/0.57  A new axiom: (forall (A_32:int) (E_2:int) (B_29:int) (C_20:int), (((eq int) ((plus_plus_int ((times_times_int A_32) E_2)) ((plus_plus_int ((times_times_int B_29) E_2)) C_20))) ((plus_plus_int ((times_times_int ((plus_plus_int A_32) B_29)) E_2)) C_20)))
% 0.08/0.57  FOF formula (forall (A_31:int) (B_28:int) (C_19:int), (((eq int) ((times_times_int ((plus_plus_int A_31) B_28)) C_19)) ((plus_plus_int ((times_times_int A_31) C_19)) ((times_times_int B_28) C_19)))) of role axiom named fact_25_comm__semiring__class_Odistrib
% 0.08/0.57  A new axiom: (forall (A_31:int) (B_28:int) (C_19:int), (((eq int) ((times_times_int ((plus_plus_int A_31) B_28)) C_19)) ((plus_plus_int ((times_times_int A_31) C_19)) ((times_times_int B_28) C_19))))
% 0.08/0.57  FOF formula (forall (A_30:int) (C_18:int) (B_27:int) (D_8:int), (((eq int) ((minus_minus_int ((plus_plus_int A_30) C_18)) ((plus_plus_int B_27) D_8))) ((plus_plus_int ((minus_minus_int A_30) B_27)) ((minus_minus_int C_18) D_8)))) of role axiom named fact_26_add__diff__add
% 0.08/0.57  A new axiom: (forall (A_30:int) (C_18:int) (B_27:int) (D_8:int), (((eq int) ((minus_minus_int ((plus_plus_int A_30) C_18)) ((plus_plus_int B_27) D_8))) ((plus_plus_int ((minus_minus_int A_30) B_27)) ((minus_minus_int C_18) D_8))))
% 0.08/0.57  FOF formula (forall (A_29:int) (B_26:int), (((eq int) ((minus_minus_int ((plus_plus_int A_29) B_26)) B_26)) A_29)) of role axiom named fact_27_add__diff__cancel
% 0.08/0.57  A new axiom: (forall (A_29:int) (B_26:int), (((eq int) ((minus_minus_int ((plus_plus_int A_29) B_26)) B_26)) A_29))
% 0.08/0.57  FOF formula (forall (W_1:int) (Y_4:int) (X_4:int) (Z_2:int), ((iff (((eq int) ((plus_plus_int ((times_times_int W_1) Y_4)) ((times_times_int X_4) Z_2))) ((plus_plus_int ((times_times_int W_1) Z_2)) ((times_times_int X_4) Y_4)))) ((or (((eq int) W_1) X_4)) (((eq int) Y_4) Z_2)))) of role axiom named fact_28_crossproduct__eq
% 0.08/0.57  A new axiom: (forall (W_1:int) (Y_4:int) (X_4:int) (Z_2:int), ((iff (((eq int) ((plus_plus_int ((times_times_int W_1) Y_4)) ((times_times_int X_4) Z_2))) ((plus_plus_int ((times_times_int W_1) Z_2)) ((times_times_int X_4) Y_4)))) ((or (((eq int) W_1) X_4)) (((eq int) Y_4) Z_2))))
% 0.08/0.57  FOF formula (forall (A_28:int) (M:int) (B_25:int), (((eq int) ((plus_plus_int ((times_times_int A_28) M)) ((times_times_int B_25) M))) ((times_times_int ((plus_plus_int A_28) B_25)) M))) of role axiom named fact_29_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J
% 0.08/0.57  A new axiom: (forall (A_28:int) (M:int) (B_25:int), (((eq int) ((plus_plus_int ((times_times_int A_28) M)) ((times_times_int B_25) M))) ((times_times_int ((plus_plus_int A_28) B_25)) M)))
% 0.40/0.59  FOF formula (forall (A_27:int) (B_24:int) (C_17:int), (((eq int) ((times_times_int ((plus_plus_int A_27) B_24)) C_17)) ((plus_plus_int ((times_times_int A_27) C_17)) ((times_times_int B_24) C_17)))) of role axiom named fact_30_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J
% 0.40/0.59  A new axiom: (forall (A_27:int) (B_24:int) (C_17:int), (((eq int) ((times_times_int ((plus_plus_int A_27) B_24)) C_17)) ((plus_plus_int ((times_times_int A_27) C_17)) ((times_times_int B_24) C_17))))
% 0.40/0.59  FOF formula (forall (C_16:int) (D_7:int) (A_26:int) (B_23:int), ((iff ((and (not (((eq int) A_26) B_23))) (not (((eq int) C_16) D_7)))) (not (((eq int) ((plus_plus_int ((times_times_int A_26) C_16)) ((times_times_int B_23) D_7))) ((plus_plus_int ((times_times_int A_26) D_7)) ((times_times_int B_23) C_16)))))) of role axiom named fact_31_crossproduct__noteq
% 0.40/0.59  A new axiom: (forall (C_16:int) (D_7:int) (A_26:int) (B_23:int), ((iff ((and (not (((eq int) A_26) B_23))) (not (((eq int) C_16) D_7)))) (not (((eq int) ((plus_plus_int ((times_times_int A_26) C_16)) ((times_times_int B_23) D_7))) ((plus_plus_int ((times_times_int A_26) D_7)) ((times_times_int B_23) C_16))))))
% 0.40/0.59  FOF formula (forall (X_3:int) (Y_3:int) (Z_1:int), (((eq int) ((times_times_int X_3) ((plus_plus_int Y_3) Z_1))) ((plus_plus_int ((times_times_int X_3) Y_3)) ((times_times_int X_3) Z_1)))) of role axiom named fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J
% 0.40/0.59  A new axiom: (forall (X_3:int) (Y_3:int) (Z_1:int), (((eq int) ((times_times_int X_3) ((plus_plus_int Y_3) Z_1))) ((plus_plus_int ((times_times_int X_3) Y_3)) ((times_times_int X_3) Z_1))))
% 0.40/0.59  FOF formula (forall (A_25:int) (B_22:int) (A_24:int) (B_21:int), ((((eq product_prod_int_int) ((product_Pair_int_int A_25) B_22)) ((product_Pair_int_int A_24) B_21))->(((((eq int) A_25) A_24)->(not (((eq int) B_22) B_21)))->False))) of role axiom named fact_33_Pair__inject
% 0.40/0.59  A new axiom: (forall (A_25:int) (B_22:int) (A_24:int) (B_21:int), ((((eq product_prod_int_int) ((product_Pair_int_int A_25) B_22)) ((product_Pair_int_int A_24) B_21))->(((((eq int) A_25) A_24)->(not (((eq int) B_22) B_21)))->False)))
% 0.40/0.59  FOF formula (forall (A_23:int) (B_20:int) (A_22:int) (B_19:int), ((iff (((eq product_prod_int_int) ((product_Pair_int_int A_23) B_20)) ((product_Pair_int_int A_22) B_19))) ((and (((eq int) A_23) A_22)) (((eq int) B_20) B_19)))) of role axiom named fact_34_Pair__eq
% 0.40/0.59  A new axiom: (forall (A_23:int) (B_20:int) (A_22:int) (B_19:int), ((iff (((eq product_prod_int_int) ((product_Pair_int_int A_23) B_20)) ((product_Pair_int_int A_22) B_19))) ((and (((eq int) A_23) A_22)) (((eq int) B_20) B_19))))
% 0.40/0.59  FOF formula (forall (A_21:int) (B_18:int), (((eq int) ((times_times_int A_21) B_18)) ((times_times_int B_18) A_21))) of role axiom named fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J
% 0.40/0.59  A new axiom: (forall (A_21:int) (B_18:int), (((eq int) ((times_times_int A_21) B_18)) ((times_times_int B_18) A_21)))
% 0.40/0.59  FOF formula (forall (Lx_6:int) (Rx_6:int) (Ry_4:int), (((eq int) ((times_times_int Lx_6) ((times_times_int Rx_6) Ry_4))) ((times_times_int Rx_6) ((times_times_int Lx_6) Ry_4)))) of role axiom named fact_36_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J
% 0.40/0.59  A new axiom: (forall (Lx_6:int) (Rx_6:int) (Ry_4:int), (((eq int) ((times_times_int Lx_6) ((times_times_int Rx_6) Ry_4))) ((times_times_int Rx_6) ((times_times_int Lx_6) Ry_4))))
% 0.40/0.59  FOF formula (forall (Lx_5:int) (Rx_5:int) (Ry_3:int), (((eq int) ((times_times_int Lx_5) ((times_times_int Rx_5) Ry_3))) ((times_times_int ((times_times_int Lx_5) Rx_5)) Ry_3))) of role axiom named fact_37_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J
% 0.40/0.59  A new axiom: (forall (Lx_5:int) (Rx_5:int) (Ry_3:int), (((eq int) ((times_times_int Lx_5) ((times_times_int Rx_5) Ry_3))) ((times_times_int ((times_times_int Lx_5) Rx_5)) Ry_3)))
% 0.40/0.59  FOF formula (forall (Lx_4:int) (Ly_4:int) (Rx_4:int), (((eq int) ((times_times_int ((times_times_int Lx_4) Ly_4)) Rx_4)) ((times_times_int Lx_4) ((times_times_int Ly_4) Rx_4)))) of role axiom named fact_38_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J
% 0.40/0.61  A new axiom: (forall (Lx_4:int) (Ly_4:int) (Rx_4:int), (((eq int) ((times_times_int ((times_times_int Lx_4) Ly_4)) Rx_4)) ((times_times_int Lx_4) ((times_times_int Ly_4) Rx_4))))
% 0.40/0.61  FOF formula (forall (Lx_3:int) (Ly_3:int) (Rx_3:int), (((eq int) ((times_times_int ((times_times_int Lx_3) Ly_3)) Rx_3)) ((times_times_int ((times_times_int Lx_3) Rx_3)) Ly_3))) of role axiom named fact_39_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J
% 0.40/0.61  A new axiom: (forall (Lx_3:int) (Ly_3:int) (Rx_3:int), (((eq int) ((times_times_int ((times_times_int Lx_3) Ly_3)) Rx_3)) ((times_times_int ((times_times_int Lx_3) Rx_3)) Ly_3)))
% 0.40/0.61  FOF formula (forall (Lx_2:int) (Ly_2:int) (Rx_2:int) (Ry_2:int), (((eq int) ((times_times_int ((times_times_int Lx_2) Ly_2)) ((times_times_int Rx_2) Ry_2))) ((times_times_int Lx_2) ((times_times_int Ly_2) ((times_times_int Rx_2) Ry_2))))) of role axiom named fact_40_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J
% 0.40/0.61  A new axiom: (forall (Lx_2:int) (Ly_2:int) (Rx_2:int) (Ry_2:int), (((eq int) ((times_times_int ((times_times_int Lx_2) Ly_2)) ((times_times_int Rx_2) Ry_2))) ((times_times_int Lx_2) ((times_times_int Ly_2) ((times_times_int Rx_2) Ry_2)))))
% 0.40/0.61  FOF formula (forall (Lx_1:int) (Ly_1:int) (Rx_1:int) (Ry_1:int), (((eq int) ((times_times_int ((times_times_int Lx_1) Ly_1)) ((times_times_int Rx_1) Ry_1))) ((times_times_int Rx_1) ((times_times_int ((times_times_int Lx_1) Ly_1)) Ry_1)))) of role axiom named fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J
% 0.40/0.61  A new axiom: (forall (Lx_1:int) (Ly_1:int) (Rx_1:int) (Ry_1:int), (((eq int) ((times_times_int ((times_times_int Lx_1) Ly_1)) ((times_times_int Rx_1) Ry_1))) ((times_times_int Rx_1) ((times_times_int ((times_times_int Lx_1) Ly_1)) Ry_1))))
% 0.40/0.61  FOF formula (forall (Lx:int) (Ly:int) (Rx:int) (Ry:int), (((eq int) ((times_times_int ((times_times_int Lx) Ly)) ((times_times_int Rx) Ry))) ((times_times_int ((times_times_int Lx) Rx)) ((times_times_int Ly) Ry)))) of role axiom named fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J
% 0.40/0.61  A new axiom: (forall (Lx:int) (Ly:int) (Rx:int) (Ry:int), (((eq int) ((times_times_int ((times_times_int Lx) Ly)) ((times_times_int Rx) Ry))) ((times_times_int ((times_times_int Lx) Rx)) ((times_times_int Ly) Ry))))
% 0.40/0.61  FOF formula (forall (A_20:int) (C_15:int), (((eq int) ((plus_plus_int A_20) C_15)) ((plus_plus_int C_15) A_20))) of role axiom named fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J
% 0.40/0.61  A new axiom: (forall (A_20:int) (C_15:int), (((eq int) ((plus_plus_int A_20) C_15)) ((plus_plus_int C_15) A_20)))
% 0.40/0.61  FOF formula (forall (A_19:int) (C_14:int) (D_6:int), (((eq int) ((plus_plus_int A_19) ((plus_plus_int C_14) D_6))) ((plus_plus_int C_14) ((plus_plus_int A_19) D_6)))) of role axiom named fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J
% 0.40/0.61  A new axiom: (forall (A_19:int) (C_14:int) (D_6:int), (((eq int) ((plus_plus_int A_19) ((plus_plus_int C_14) D_6))) ((plus_plus_int C_14) ((plus_plus_int A_19) D_6))))
% 0.40/0.61  FOF formula (forall (A_18:int) (C_13:int) (D_5:int), (((eq int) ((plus_plus_int A_18) ((plus_plus_int C_13) D_5))) ((plus_plus_int ((plus_plus_int A_18) C_13)) D_5))) of role axiom named fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J
% 0.40/0.61  A new axiom: (forall (A_18:int) (C_13:int) (D_5:int), (((eq int) ((plus_plus_int A_18) ((plus_plus_int C_13) D_5))) ((plus_plus_int ((plus_plus_int A_18) C_13)) D_5)))
% 0.40/0.61  FOF formula (forall (A_17:int) (B_17:int) (C_12:int), (((eq int) ((plus_plus_int ((plus_plus_int A_17) B_17)) C_12)) ((plus_plus_int A_17) ((plus_plus_int B_17) C_12)))) of role axiom named fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J
% 0.40/0.61  A new axiom: (forall (A_17:int) (B_17:int) (C_12:int), (((eq int) ((plus_plus_int ((plus_plus_int A_17) B_17)) C_12)) ((plus_plus_int A_17) ((plus_plus_int B_17) C_12))))
% 0.40/0.61  FOF formula (forall (A_16:int) (B_16:int) (C_11:int), (((eq int) ((plus_plus_int ((plus_plus_int A_16) B_16)) C_11)) ((plus_plus_int ((plus_plus_int A_16) C_11)) B_16))) of role axiom named fact_47_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J
% 0.43/0.62  A new axiom: (forall (A_16:int) (B_16:int) (C_11:int), (((eq int) ((plus_plus_int ((plus_plus_int A_16) B_16)) C_11)) ((plus_plus_int ((plus_plus_int A_16) C_11)) B_16)))
% 0.43/0.62  FOF formula (forall (A_15:int) (B_15:int) (C_10:int) (D_4:int), (((eq int) ((plus_plus_int ((plus_plus_int A_15) B_15)) ((plus_plus_int C_10) D_4))) ((plus_plus_int ((plus_plus_int A_15) C_10)) ((plus_plus_int B_15) D_4)))) of role axiom named fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J
% 0.43/0.62  A new axiom: (forall (A_15:int) (B_15:int) (C_10:int) (D_4:int), (((eq int) ((plus_plus_int ((plus_plus_int A_15) B_15)) ((plus_plus_int C_10) D_4))) ((plus_plus_int ((plus_plus_int A_15) C_10)) ((plus_plus_int B_15) D_4))))
% 0.43/0.62  FOF formula (forall (P_2:(product_prod_int_int->Prop)), ((iff (all P_2)) (forall (A_14:int) (B_14:int), (P_2 ((product_Pair_int_int A_14) B_14))))) of role axiom named fact_49_split__paired__All
% 0.43/0.62  A new axiom: (forall (P_2:(product_prod_int_int->Prop)), ((iff (all P_2)) (forall (A_14:int) (B_14:int), (P_2 ((product_Pair_int_int A_14) B_14)))))
% 0.43/0.62  FOF formula (forall (P_1:(product_prod_int_int->Prop)), ((iff (_TPTP_ex P_1)) ((ex int) (fun (A_14:int)=> ((ex int) (fun (B_14:int)=> (P_1 ((product_Pair_int_int A_14) B_14)))))))) of role axiom named fact_50_split__paired__Ex
% 0.43/0.62  A new axiom: (forall (P_1:(product_prod_int_int->Prop)), ((iff (_TPTP_ex P_1)) ((ex int) (fun (A_14:int)=> ((ex int) (fun (B_14:int)=> (P_1 ((product_Pair_int_int A_14) B_14))))))))
% 0.43/0.62  FOF formula (forall (Y_2:product_prod_int_int), ((forall (A_14:int) (B_14:int), (not (((eq product_prod_int_int) Y_2) ((product_Pair_int_int A_14) B_14))))->False)) of role axiom named fact_51_prod_Oexhaust
% 0.43/0.62  A new axiom: (forall (Y_2:product_prod_int_int), ((forall (A_14:int) (B_14:int), (not (((eq product_prod_int_int) Y_2) ((product_Pair_int_int A_14) B_14))))->False))
% 0.43/0.62  FOF formula (forall (P:product_prod_int_int), ((forall (X_2:int) (Y_1:int), (not (((eq product_prod_int_int) P) ((product_Pair_int_int X_2) Y_1))))->False)) of role axiom named fact_52_PairE
% 0.43/0.62  A new axiom: (forall (P:product_prod_int_int), ((forall (X_2:int) (Y_1:int), (not (((eq product_prod_int_int) P) ((product_Pair_int_int X_2) Y_1))))->False))
% 0.43/0.62  FOF formula (forall (F_3:(product_prod_int_int->Prop)) (A_13:int) (B_13:int), ((F_3 ((product_Pair_int_int A_13) B_13))->(((produc176579150_int_o F_3) A_13) B_13))) of role axiom named fact_53_curryI
% 0.43/0.62  A new axiom: (forall (F_3:(product_prod_int_int->Prop)) (A_13:int) (B_13:int), ((F_3 ((product_Pair_int_int A_13) B_13))->(((produc176579150_int_o F_3) A_13) B_13)))
% 0.43/0.62  FOF formula (forall (F_2:(product_prod_int_int->Prop)) (A_12:int) (B_12:int), ((((produc176579150_int_o F_2) A_12) B_12)->(F_2 ((product_Pair_int_int A_12) B_12)))) of role axiom named fact_54_curryD
% 0.43/0.62  A new axiom: (forall (F_2:(product_prod_int_int->Prop)) (A_12:int) (B_12:int), ((((produc176579150_int_o F_2) A_12) B_12)->(F_2 ((product_Pair_int_int A_12) B_12))))
% 0.43/0.62  FOF formula (forall (F_1:(product_prod_int_int->Prop)) (A_11:int) (B_11:int), ((((produc176579150_int_o F_1) A_11) B_11)->(F_1 ((product_Pair_int_int A_11) B_11)))) of role axiom named fact_55_curryE
% 0.43/0.62  A new axiom: (forall (F_1:(product_prod_int_int->Prop)) (A_11:int) (B_11:int), ((((produc176579150_int_o F_1) A_11) B_11)->(F_1 ((product_Pair_int_int A_11) B_11))))
% 0.43/0.62  FOF formula (forall (F:(product_prod_int_int->Prop)) (A_10:int) (B_10:int), ((iff (((produc176579150_int_o F) A_10) B_10)) (F ((product_Pair_int_int A_10) B_10)))) of role axiom named fact_56_curry__conv
% 0.43/0.62  A new axiom: (forall (F:(product_prod_int_int->Prop)) (A_10:int) (B_10:int), ((iff (((produc176579150_int_o F) A_10) B_10)) (F ((product_Pair_int_int A_10) B_10))))
% 0.43/0.62  FOF formula (forall (A_9:int) (E_1:int) (C_9:int) (B_9:int) (D_3:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int A_9) E_1)) C_9)) ((plus_plus_int ((times_times_int B_9) E_1)) D_3))) ((ord_less_eq_int ((plus_plus_int ((times_times_int ((minus_minus_int A_9) B_9)) E_1)) C_9)) D_3))) of role axiom named fact_57_le__add__iff1
% 0.43/0.64  A new axiom: (forall (A_9:int) (E_1:int) (C_9:int) (B_9:int) (D_3:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int A_9) E_1)) C_9)) ((plus_plus_int ((times_times_int B_9) E_1)) D_3))) ((ord_less_eq_int ((plus_plus_int ((times_times_int ((minus_minus_int A_9) B_9)) E_1)) C_9)) D_3)))
% 0.43/0.64  FOF formula (forall (A_8:int) (E:int) (C_8:int) (B_8:int) (D_2:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int A_8) E)) C_8)) ((plus_plus_int ((times_times_int B_8) E)) D_2))) ((ord_less_eq_int C_8) ((plus_plus_int ((times_times_int ((minus_minus_int B_8) A_8)) E)) D_2)))) of role axiom named fact_58_le__add__iff2
% 0.43/0.64  A new axiom: (forall (A_8:int) (E:int) (C_8:int) (B_8:int) (D_2:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int A_8) E)) C_8)) ((plus_plus_int ((times_times_int B_8) E)) D_2))) ((ord_less_eq_int C_8) ((plus_plus_int ((times_times_int ((minus_minus_int B_8) A_8)) E)) D_2))))
% 0.43/0.64  FOF formula (forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_eq_int _TPTP_I) J)->((ord_less_eq_int ((plus_plus_int K) _TPTP_I)) ((plus_plus_int K) J)))) of role axiom named fact_59_zadd__left__mono
% 0.43/0.64  A new axiom: (forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_eq_int _TPTP_I) J)->((ord_less_eq_int ((plus_plus_int K) _TPTP_I)) ((plus_plus_int K) J))))
% 0.43/0.64  FOF formula (forall (A_7:int) (B_7:int) (C_7:int) (D_1:int), ((((eq int) ((minus_minus_int A_7) B_7)) ((minus_minus_int C_7) D_1))->((iff ((ord_less_eq_int A_7) B_7)) ((ord_less_eq_int C_7) D_1)))) of role axiom named fact_60_diff__eq__diff__less__eq
% 0.43/0.64  A new axiom: (forall (A_7:int) (B_7:int) (C_7:int) (D_1:int), ((((eq int) ((minus_minus_int A_7) B_7)) ((minus_minus_int C_7) D_1))->((iff ((ord_less_eq_int A_7) B_7)) ((ord_less_eq_int C_7) D_1))))
% 0.43/0.64  FOF formula (forall (C_6:int) (A_6:int) (B_6:int), (((ord_less_eq_int ((plus_plus_int C_6) A_6)) ((plus_plus_int C_6) B_6))->((ord_less_eq_int A_6) B_6))) of role axiom named fact_61_add__le__imp__le__left
% 0.43/0.64  A new axiom: (forall (C_6:int) (A_6:int) (B_6:int), (((ord_less_eq_int ((plus_plus_int C_6) A_6)) ((plus_plus_int C_6) B_6))->((ord_less_eq_int A_6) B_6)))
% 0.43/0.64  FOF formula (forall (A_5:int) (C_5:int) (B_5:int), (((ord_less_eq_int ((plus_plus_int A_5) C_5)) ((plus_plus_int B_5) C_5))->((ord_less_eq_int A_5) B_5))) of role axiom named fact_62_add__le__imp__le__right
% 0.43/0.64  A new axiom: (forall (A_5:int) (C_5:int) (B_5:int), (((ord_less_eq_int ((plus_plus_int A_5) C_5)) ((plus_plus_int B_5) C_5))->((ord_less_eq_int A_5) B_5)))
% 0.43/0.64  FOF formula (forall (C_4:int) (D:int) (A_4:int) (B_4:int), (((ord_less_eq_int A_4) B_4)->(((ord_less_eq_int C_4) D)->((ord_less_eq_int ((plus_plus_int A_4) C_4)) ((plus_plus_int B_4) D))))) of role axiom named fact_63_add__mono
% 0.43/0.64  A new axiom: (forall (C_4:int) (D:int) (A_4:int) (B_4:int), (((ord_less_eq_int A_4) B_4)->(((ord_less_eq_int C_4) D)->((ord_less_eq_int ((plus_plus_int A_4) C_4)) ((plus_plus_int B_4) D)))))
% 0.43/0.64  FOF formula (forall (C_3:int) (A_3:int) (B_3:int), (((ord_less_eq_int A_3) B_3)->((ord_less_eq_int ((plus_plus_int C_3) A_3)) ((plus_plus_int C_3) B_3)))) of role axiom named fact_64_add__left__mono
% 0.43/0.64  A new axiom: (forall (C_3:int) (A_3:int) (B_3:int), (((ord_less_eq_int A_3) B_3)->((ord_less_eq_int ((plus_plus_int C_3) A_3)) ((plus_plus_int C_3) B_3))))
% 0.43/0.64  FOF formula (forall (C_2:int) (A_2:int) (B_2:int), (((ord_less_eq_int A_2) B_2)->((ord_less_eq_int ((plus_plus_int A_2) C_2)) ((plus_plus_int B_2) C_2)))) of role axiom named fact_65_add__right__mono
% 0.43/0.64  A new axiom: (forall (C_2:int) (A_2:int) (B_2:int), (((ord_less_eq_int A_2) B_2)->((ord_less_eq_int ((plus_plus_int A_2) C_2)) ((plus_plus_int B_2) C_2))))
% 0.43/0.64  FOF formula (forall (C_1:int) (A_1:int) (B_1:int), ((iff ((ord_less_eq_int ((plus_plus_int C_1) A_1)) ((plus_plus_int C_1) B_1))) ((ord_less_eq_int A_1) B_1))) of role axiom named fact_66_add__le__cancel__left
% 0.43/0.64  A new axiom: (forall (C_1:int) (A_1:int) (B_1:int), ((iff ((ord_less_eq_int ((plus_plus_int C_1) A_1)) ((plus_plus_int C_1) B_1))) ((ord_less_eq_int A_1) B_1)))
% 0.43/0.64  FOF formula (forall (A:int) (C:int) (B:int), ((iff ((ord_less_eq_int ((plus_plus_int A) C)) ((plus_plus_int B) C))) ((ord_less_eq_int A) B))) of role axiom named fact_67_add__le__cancel__right
% 0.43/0.66  A new axiom: (forall (A:int) (C:int) (B:int), ((iff ((ord_less_eq_int ((plus_plus_int A) C)) ((plus_plus_int B) C))) ((ord_less_eq_int A) B)))
% 0.43/0.66  FOF formula (forall (X_1:int), ((ord_less_eq_int X_1) X_1)) of role axiom named fact_68_order__refl
% 0.43/0.66  A new axiom: (forall (X_1:int), ((ord_less_eq_int X_1) X_1))
% 0.43/0.66  FOF formula (forall (X:int) (Y:int), ((((ord_less_eq_int X) Y)->False)->((ord_less_eq_int Y) X))) of role axiom named fact_69_linorder__le__cases
% 0.43/0.66  A new axiom: (forall (X:int) (Y:int), ((((ord_less_eq_int X) Y)->False)->((ord_less_eq_int Y) X)))
% 0.43/0.66  FOF formula (forall (W:int), ((ord_less_eq_int W) W)) of role axiom named fact_70_zle__refl
% 0.43/0.66  A new axiom: (forall (W:int), ((ord_less_eq_int W) W))
% 0.43/0.66  FOF formula (forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z))) of role axiom named fact_71_zle__linear
% 0.43/0.66  A new axiom: (forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z)))
% 0.43/0.66  FOF formula (forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_eq_int _TPTP_I) J)->(((ord_less_eq_int J) K)->((ord_less_eq_int _TPTP_I) K)))) of role axiom named fact_72_zle__trans
% 0.43/0.66  A new axiom: (forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_eq_int _TPTP_I) J)->(((ord_less_eq_int J) K)->((ord_less_eq_int _TPTP_I) K))))
% 0.43/0.66  FOF formula (forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W)))) of role axiom named fact_73_zle__antisym
% 0.43/0.66  A new axiom: (forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W))))
% 0.43/0.66  FOF formula (((eq int) ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q)))) (twoSqu1535104286sum2sq ((product_Pair_int_int ((plus_plus_int ((times_times_int a) p)) ((times_times_int b) q))) ((minus_minus_int ((times_times_int a) q)) ((times_times_int b) p))))) of role conjecture named conj_0
% 0.43/0.66  Conjecture to prove = (((eq int) ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q)))) (twoSqu1535104286sum2sq ((product_Pair_int_int ((plus_plus_int ((times_times_int a) p)) ((times_times_int b) q))) ((minus_minus_int ((times_times_int a) q)) ((times_times_int b) p))))):Prop
% 0.43/0.66  Parameter product_prod_int_int_DUMMY:product_prod_int_int.
% 0.43/0.66  We need to prove ['(((eq int) ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q)))) (twoSqu1535104286sum2sq ((product_Pair_int_int ((plus_plus_int ((times_times_int a) p)) ((times_times_int b) q))) ((minus_minus_int ((times_times_int a) q)) ((times_times_int b) p)))))']
% 0.43/0.66  Parameter int:Type.
% 0.43/0.66  Parameter product_prod_int_int:Type.
% 0.43/0.66  Parameter all:((product_prod_int_int->Prop)->Prop).
% 0.43/0.66  Parameter _TPTP_ex:((product_prod_int_int->Prop)->Prop).
% 0.43/0.66  Parameter minus_minus_int:(int->(int->int)).
% 0.43/0.66  Parameter plus_plus_int:(int->(int->int)).
% 0.43/0.66  Parameter times_times_int:(int->(int->int)).
% 0.43/0.66  Parameter ord_less_eq_int:(int->(int->Prop)).
% 0.43/0.66  Parameter product_Pair_int_int:(int->(int->product_prod_int_int)).
% 0.43/0.66  Parameter produc176579150_int_o:((product_prod_int_int->Prop)->(int->(int->Prop))).
% 0.43/0.66  Parameter twoSqu1013291560sum2sq:(int->Prop).
% 0.43/0.66  Parameter twoSqu1535104286sum2sq:(product_prod_int_int->int).
% 0.43/0.66  Parameter a:int.
% 0.43/0.66  Parameter b:int.
% 0.43/0.66  Parameter p:int.
% 0.43/0.66  Parameter q:int.
% 0.43/0.66  Axiom fact_0_xzgcda__linear__aux1:(forall (A_42:int) (R:int) (B_39:int) (M_1:int) (C_29:int) (D_12:int) (N:int), (((eq int) ((plus_plus_int ((times_times_int ((minus_minus_int A_42) ((times_times_int R) B_39))) M_1)) ((times_times_int ((minus_minus_int C_29) ((times_times_int R) D_12))) N))) ((minus_minus_int ((plus_plus_int ((times_times_int A_42) M_1)) ((times_times_int C_29) N))) ((times_times_int R) ((plus_plus_int ((times_times_int B_39) M_1)) ((times_times_int D_12) N)))))).
% 0.43/0.66  Axiom fact_1_mult__diff__mult:(forall (X_6:int) (Y_6:int) (A_45:int) (B_42:int), (((eq int) ((minus_minus_int ((times_times_int X_6) Y_6)) ((times_times_int A_45) B_42))) ((plus_plus_int ((times_times_int X_6) ((minus_minus_int Y_6) B_42))) ((times_times_int ((minus_minus_int X_6) A_45)) B_42)))).
% 0.43/0.66  Axiom fact_2_eq__add__iff2:(forall (A_44:int) (E_4:int) (C_31:int) (B_41:int) (D_11:int), ((iff (((eq int) ((plus_plus_int ((times_times_int A_44) E_4)) C_31)) ((plus_plus_int ((times_times_int B_41) E_4)) D_11))) (((eq int) C_31) ((plus_plus_int ((times_times_int ((minus_minus_int B_41) A_44)) E_4)) D_11)))).
% 0.43/0.66  Axiom fact_3_eq__add__iff1:(forall (A_43:int) (E_3:int) (C_30:int) (B_40:int) (D_10:int), ((iff (((eq int) ((plus_plus_int ((times_times_int A_43) E_3)) C_30)) ((plus_plus_int ((times_times_int B_40) E_3)) D_10))) (((eq int) ((plus_plus_int ((times_times_int ((minus_minus_int A_43) B_40)) E_3)) C_30)) D_10))).
% 0.43/0.66  Axiom fact_4_is__sum2sq__def:(forall (X_5:int), ((iff (twoSqu1013291560sum2sq X_5)) ((ex int) (fun (A_14:int)=> ((ex int) (fun (B_14:int)=> (((eq int) (twoSqu1535104286sum2sq ((product_Pair_int_int A_14) B_14))) X_5))))))).
% 0.43/0.66  Axiom fact_5_Int2_Oaux1:(forall (A_42:int) (B_39:int) (C_29:int), ((((eq int) ((minus_minus_int A_42) B_39)) C_29)->(((eq int) A_42) ((plus_plus_int C_29) B_39)))).
% 0.43/0.66  Axiom fact_6_zdiff__zmult__distrib2:(forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((minus_minus_int Z1) Z2))) ((minus_minus_int ((times_times_int W) Z1)) ((times_times_int W) Z2)))).
% 0.43/0.66  Axiom fact_7_zdiff__zmult__distrib:(forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((minus_minus_int Z1) Z2)) W)) ((minus_minus_int ((times_times_int Z1) W)) ((times_times_int Z2) W)))).
% 0.43/0.66  Axiom fact_8_zadd__zmult__distrib2:(forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((plus_plus_int Z1) Z2))) ((plus_plus_int ((times_times_int W) Z1)) ((times_times_int W) Z2)))).
% 0.43/0.66  Axiom fact_9_zadd__zmult__distrib:(forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((plus_plus_int Z1) Z2)) W)) ((plus_plus_int ((times_times_int Z1) W)) ((times_times_int Z2) W)))).
% 0.43/0.66  Axiom fact_10_diff__add__cancel:(forall (A_41:int) (B_38:int), (((eq int) ((plus_plus_int ((minus_minus_int A_41) B_38)) B_38)) A_41)).
% 0.43/0.66  Axiom fact_11_ab__semigroup__mult__class_Omult__ac_I1_J:(forall (A_40:int) (B_37:int) (C_28:int), (((eq int) ((times_times_int ((times_times_int A_40) B_37)) C_28)) ((times_times_int A_40) ((times_times_int B_37) C_28)))).
% 0.43/0.66  Axiom fact_12_add__right__imp__eq:(forall (B_36:int) (A_39:int) (C_27:int), ((((eq int) ((plus_plus_int B_36) A_39)) ((plus_plus_int C_27) A_39))->(((eq int) B_36) C_27))).
% 0.43/0.66  Axiom fact_13_add__imp__eq:(forall (A_38:int) (B_35:int) (C_26:int), ((((eq int) ((plus_plus_int A_38) B_35)) ((plus_plus_int A_38) C_26))->(((eq int) B_35) C_26))).
% 0.43/0.66  Axiom fact_14_add__left__imp__eq:(forall (A_37:int) (B_34:int) (C_25:int), ((((eq int) ((plus_plus_int A_37) B_34)) ((plus_plus_int A_37) C_25))->(((eq int) B_34) C_25))).
% 0.43/0.66  Axiom fact_15_add__right__cancel:(forall (B_33:int) (A_36:int) (C_24:int), ((iff (((eq int) ((plus_plus_int B_33) A_36)) ((plus_plus_int C_24) A_36))) (((eq int) B_33) C_24))).
% 0.43/0.66  Axiom fact_16_add__left__cancel:(forall (A_35:int) (B_32:int) (C_23:int), ((iff (((eq int) ((plus_plus_int A_35) B_32)) ((plus_plus_int A_35) C_23))) (((eq int) B_32) C_23))).
% 0.43/0.66  Axiom fact_17_ab__semigroup__add__class_Oadd__ac_I1_J:(forall (A_34:int) (B_31:int) (C_22:int), (((eq int) ((plus_plus_int ((plus_plus_int A_34) B_31)) C_22)) ((plus_plus_int A_34) ((plus_plus_int B_31) C_22)))).
% 0.43/0.66  Axiom fact_18_diff__eq__diff__eq:(forall (A_33:int) (B_30:int) (C_21:int) (D_9:int), ((((eq int) ((minus_minus_int A_33) B_30)) ((minus_minus_int C_21) D_9))->((iff (((eq int) A_33) B_30)) (((eq int) C_21) D_9)))).
% 0.43/0.66  Axiom fact_19_zmult__assoc:(forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((times_times_int ((times_times_int Z1) Z2)) Z3)) ((times_times_int Z1) ((times_times_int Z2) Z3)))).
% 0.43/0.66  Axiom fact_20_zmult__commute:(forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z))).
% 0.43/0.66  Axiom fact_21_zadd__assoc:(forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((plus_plus_int ((plus_plus_int Z1) Z2)) Z3)) ((plus_plus_int Z1) ((plus_plus_int Z2) Z3)))).
% 0.43/0.66  Axiom fact_22_zadd__left__commute:(forall (X_5:int) (Y_5:int) (Z:int), (((eq int) ((plus_plus_int X_5) ((plus_plus_int Y_5) Z))) ((plus_plus_int Y_5) ((plus_plus_int X_5) Z)))).
% 0.43/0.66  Axiom fact_23_zadd__commute:(forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z))).
% 0.43/0.66  Axiom fact_24_combine__common__factor:(forall (A_32:int) (E_2:int) (B_29:int) (C_20:int), (((eq int) ((plus_plus_int ((times_times_int A_32) E_2)) ((plus_plus_int ((times_times_int B_29) E_2)) C_20))) ((plus_plus_int ((times_times_int ((plus_plus_int A_32) B_29)) E_2)) C_20))).
% 0.43/0.66  Axiom fact_25_comm__semiring__class_Odistrib:(forall (A_31:int) (B_28:int) (C_19:int), (((eq int) ((times_times_int ((plus_plus_int A_31) B_28)) C_19)) ((plus_plus_int ((times_times_int A_31) C_19)) ((times_times_int B_28) C_19)))).
% 0.43/0.66  Axiom fact_26_add__diff__add:(forall (A_30:int) (C_18:int) (B_27:int) (D_8:int), (((eq int) ((minus_minus_int ((plus_plus_int A_30) C_18)) ((plus_plus_int B_27) D_8))) ((plus_plus_int ((minus_minus_int A_30) B_27)) ((minus_minus_int C_18) D_8)))).
% 0.43/0.66  Axiom fact_27_add__diff__cancel:(forall (A_29:int) (B_26:int), (((eq int) ((minus_minus_int ((plus_plus_int A_29) B_26)) B_26)) A_29)).
% 0.43/0.66  Axiom fact_28_crossproduct__eq:(forall (W_1:int) (Y_4:int) (X_4:int) (Z_2:int), ((iff (((eq int) ((plus_plus_int ((times_times_int W_1) Y_4)) ((times_times_int X_4) Z_2))) ((plus_plus_int ((times_times_int W_1) Z_2)) ((times_times_int X_4) Y_4)))) ((or (((eq int) W_1) X_4)) (((eq int) Y_4) Z_2)))).
% 0.43/0.66  Axiom fact_29_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J:(forall (A_28:int) (M:int) (B_25:int), (((eq int) ((plus_plus_int ((times_times_int A_28) M)) ((times_times_int B_25) M))) ((times_times_int ((plus_plus_int A_28) B_25)) M))).
% 0.43/0.66  Axiom fact_30_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J:(forall (A_27:int) (B_24:int) (C_17:int), (((eq int) ((times_times_int ((plus_plus_int A_27) B_24)) C_17)) ((plus_plus_int ((times_times_int A_27) C_17)) ((times_times_int B_24) C_17)))).
% 0.43/0.66  Axiom fact_31_crossproduct__noteq:(forall (C_16:int) (D_7:int) (A_26:int) (B_23:int), ((iff ((and (not (((eq int) A_26) B_23))) (not (((eq int) C_16) D_7)))) (not (((eq int) ((plus_plus_int ((times_times_int A_26) C_16)) ((times_times_int B_23) D_7))) ((plus_plus_int ((times_times_int A_26) D_7)) ((times_times_int B_23) C_16)))))).
% 0.43/0.66  Axiom fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J:(forall (X_3:int) (Y_3:int) (Z_1:int), (((eq int) ((times_times_int X_3) ((plus_plus_int Y_3) Z_1))) ((plus_plus_int ((times_times_int X_3) Y_3)) ((times_times_int X_3) Z_1)))).
% 0.43/0.66  Axiom fact_33_Pair__inject:(forall (A_25:int) (B_22:int) (A_24:int) (B_21:int), ((((eq product_prod_int_int) ((product_Pair_int_int A_25) B_22)) ((product_Pair_int_int A_24) B_21))->(((((eq int) A_25) A_24)->(not (((eq int) B_22) B_21)))->False))).
% 0.43/0.66  Axiom fact_34_Pair__eq:(forall (A_23:int) (B_20:int) (A_22:int) (B_19:int), ((iff (((eq product_prod_int_int) ((product_Pair_int_int A_23) B_20)) ((product_Pair_int_int A_22) B_19))) ((and (((eq int) A_23) A_22)) (((eq int) B_20) B_19)))).
% 0.43/0.66  Axiom fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J:(forall (A_21:int) (B_18:int), (((eq int) ((times_times_int A_21) B_18)) ((times_times_int B_18) A_21))).
% 0.43/0.66  Axiom fact_36_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J:(forall (Lx_6:int) (Rx_6:int) (Ry_4:int), (((eq int) ((times_times_int Lx_6) ((times_times_int Rx_6) Ry_4))) ((times_times_int Rx_6) ((times_times_int Lx_6) Ry_4)))).
% 0.43/0.66  Axiom fact_37_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J:(forall (Lx_5:int) (Rx_5:int) (Ry_3:int), (((eq int) ((times_times_int Lx_5) ((times_times_int Rx_5) Ry_3))) ((times_times_int ((times_times_int Lx_5) Rx_5)) Ry_3))).
% 0.43/0.66  Axiom fact_38_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J:(forall (Lx_4:int) (Ly_4:int) (Rx_4:int), (((eq int) ((times_times_int ((times_times_int Lx_4) Ly_4)) Rx_4)) ((times_times_int Lx_4) ((times_times_int Ly_4) Rx_4)))).
% 0.43/0.66  Axiom fact_39_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J:(forall (Lx_3:int) (Ly_3:int) (Rx_3:int), (((eq int) ((times_times_int ((times_times_int Lx_3) Ly_3)) Rx_3)) ((times_times_int ((times_times_int Lx_3) Rx_3)) Ly_3))).
% 0.43/0.66  Axiom fact_40_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J:(forall (Lx_2:int) (Ly_2:int) (Rx_2:int) (Ry_2:int), (((eq int) ((times_times_int ((times_times_int Lx_2) Ly_2)) ((times_times_int Rx_2) Ry_2))) ((times_times_int Lx_2) ((times_times_int Ly_2) ((times_times_int Rx_2) Ry_2))))).
% 0.43/0.66  Axiom fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J:(forall (Lx_1:int) (Ly_1:int) (Rx_1:int) (Ry_1:int), (((eq int) ((times_times_int ((times_times_int Lx_1) Ly_1)) ((times_times_int Rx_1) Ry_1))) ((times_times_int Rx_1) ((times_times_int ((times_times_int Lx_1) Ly_1)) Ry_1)))).
% 0.43/0.66  Axiom fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J:(forall (Lx:int) (Ly:int) (Rx:int) (Ry:int), (((eq int) ((times_times_int ((times_times_int Lx) Ly)) ((times_times_int Rx) Ry))) ((times_times_int ((times_times_int Lx) Rx)) ((times_times_int Ly) Ry)))).
% 0.43/0.66  Axiom fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A_20:int) (C_15:int), (((eq int) ((plus_plus_int A_20) C_15)) ((plus_plus_int C_15) A_20))).
% 0.43/0.66  Axiom fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_19:int) (C_14:int) (D_6:int), (((eq int) ((plus_plus_int A_19) ((plus_plus_int C_14) D_6))) ((plus_plus_int C_14) ((plus_plus_int A_19) D_6)))).
% 0.43/0.66  Axiom fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_18:int) (C_13:int) (D_5:int), (((eq int) ((plus_plus_int A_18) ((plus_plus_int C_13) D_5))) ((plus_plus_int ((plus_plus_int A_18) C_13)) D_5))).
% 0.43/0.66  Axiom fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_17:int) (B_17:int) (C_12:int), (((eq int) ((plus_plus_int ((plus_plus_int A_17) B_17)) C_12)) ((plus_plus_int A_17) ((plus_plus_int B_17) C_12)))).
% 0.43/0.66  Axiom fact_47_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_16:int) (B_16:int) (C_11:int), (((eq int) ((plus_plus_int ((plus_plus_int A_16) B_16)) C_11)) ((plus_plus_int ((plus_plus_int A_16) C_11)) B_16))).
% 0.43/0.66  Axiom fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_15:int) (B_15:int) (C_10:int) (D_4:int), (((eq int) ((plus_plus_int ((plus_plus_int A_15) B_15)) ((plus_plus_int C_10) D_4))) ((plus_plus_int ((plus_plus_int A_15) C_10)) ((plus_plus_int B_15) D_4)))).
% 0.43/0.66  Axiom fact_49_split__paired__All:(forall (P_2:(product_prod_int_int->Prop)), ((iff (all P_2)) (forall (A_14:int) (B_14:int), (P_2 ((product_Pair_int_int A_14) B_14))))).
% 0.43/0.66  Axiom fact_50_split__paired__Ex:(forall (P_1:(product_prod_int_int->Prop)), ((iff (_TPTP_ex P_1)) ((ex int) (fun (A_14:int)=> ((ex int) (fun (B_14:int)=> (P_1 ((product_Pair_int_int A_14) B_14)))))))).
% 0.43/0.66  Axiom fact_51_prod_Oexhaust:(forall (Y_2:product_prod_int_int), ((forall (A_14:int) (B_14:int), (not (((eq product_prod_int_int) Y_2) ((product_Pair_int_int A_14) B_14))))->False)).
% 0.43/0.66  Axiom fact_52_PairE:(forall (P:product_prod_int_int), ((forall (X_2:int) (Y_1:int), (not (((eq product_prod_int_int) P) ((product_Pair_int_int X_2) Y_1))))->False)).
% 0.43/0.66  Axiom fact_53_curryI:(forall (F_3:(product_prod_int_int->Prop)) (A_13:int) (B_13:int), ((F_3 ((product_Pair_int_int A_13) B_13))->(((produc176579150_int_o F_3) A_13) B_13))).
% 0.43/0.66  Axiom fact_54_curryD:(forall (F_2:(product_prod_int_int->Prop)) (A_12:int) (B_12:int), ((((produc176579150_int_o F_2) A_12) B_12)->(F_2 ((product_Pair_int_int A_12) B_12)))).
% 0.43/0.66  Axiom fact_55_curryE:(forall (F_1:(product_prod_int_int->Prop)) (A_11:int) (B_11:int), ((((produc176579150_int_o F_1) A_11) B_11)->(F_1 ((product_Pair_int_int A_11) B_11)))).
% 0.43/0.66  Axiom fact_56_curry__conv:(forall (F:(product_prod_int_int->Prop)) (A_10:int) (B_10:int), ((iff (((produc176579150_int_o F) A_10) B_10)) (F ((product_Pair_int_int A_10) B_10)))).
% 0.43/0.66  Axiom fact_57_le__add__iff1:(forall (A_9:int) (E_1:int) (C_9:int) (B_9:int) (D_3:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int A_9) E_1)) C_9)) ((plus_plus_int ((times_times_int B_9) E_1)) D_3))) ((ord_less_eq_int ((plus_plus_int ((times_times_int ((minus_minus_int A_9) B_9)) E_1)) C_9)) D_3))).
% 127.32/127.57  Axiom fact_58_le__add__iff2:(forall (A_8:int) (E:int) (C_8:int) (B_8:int) (D_2:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int A_8) E)) C_8)) ((plus_plus_int ((times_times_int B_8) E)) D_2))) ((ord_less_eq_int C_8) ((plus_plus_int ((times_times_int ((minus_minus_int B_8) A_8)) E)) D_2)))).
% 127.32/127.57  Axiom fact_59_zadd__left__mono:(forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_eq_int _TPTP_I) J)->((ord_less_eq_int ((plus_plus_int K) _TPTP_I)) ((plus_plus_int K) J)))).
% 127.32/127.57  Axiom fact_60_diff__eq__diff__less__eq:(forall (A_7:int) (B_7:int) (C_7:int) (D_1:int), ((((eq int) ((minus_minus_int A_7) B_7)) ((minus_minus_int C_7) D_1))->((iff ((ord_less_eq_int A_7) B_7)) ((ord_less_eq_int C_7) D_1)))).
% 127.32/127.57  Axiom fact_61_add__le__imp__le__left:(forall (C_6:int) (A_6:int) (B_6:int), (((ord_less_eq_int ((plus_plus_int C_6) A_6)) ((plus_plus_int C_6) B_6))->((ord_less_eq_int A_6) B_6))).
% 127.32/127.57  Axiom fact_62_add__le__imp__le__right:(forall (A_5:int) (C_5:int) (B_5:int), (((ord_less_eq_int ((plus_plus_int A_5) C_5)) ((plus_plus_int B_5) C_5))->((ord_less_eq_int A_5) B_5))).
% 127.32/127.57  Axiom fact_63_add__mono:(forall (C_4:int) (D:int) (A_4:int) (B_4:int), (((ord_less_eq_int A_4) B_4)->(((ord_less_eq_int C_4) D)->((ord_less_eq_int ((plus_plus_int A_4) C_4)) ((plus_plus_int B_4) D))))).
% 127.32/127.57  Axiom fact_64_add__left__mono:(forall (C_3:int) (A_3:int) (B_3:int), (((ord_less_eq_int A_3) B_3)->((ord_less_eq_int ((plus_plus_int C_3) A_3)) ((plus_plus_int C_3) B_3)))).
% 127.32/127.57  Axiom fact_65_add__right__mono:(forall (C_2:int) (A_2:int) (B_2:int), (((ord_less_eq_int A_2) B_2)->((ord_less_eq_int ((plus_plus_int A_2) C_2)) ((plus_plus_int B_2) C_2)))).
% 127.32/127.57  Axiom fact_66_add__le__cancel__left:(forall (C_1:int) (A_1:int) (B_1:int), ((iff ((ord_less_eq_int ((plus_plus_int C_1) A_1)) ((plus_plus_int C_1) B_1))) ((ord_less_eq_int A_1) B_1))).
% 127.32/127.57  Axiom fact_67_add__le__cancel__right:(forall (A:int) (C:int) (B:int), ((iff ((ord_less_eq_int ((plus_plus_int A) C)) ((plus_plus_int B) C))) ((ord_less_eq_int A) B))).
% 127.32/127.57  Axiom fact_68_order__refl:(forall (X_1:int), ((ord_less_eq_int X_1) X_1)).
% 127.32/127.57  Axiom fact_69_linorder__le__cases:(forall (X:int) (Y:int), ((((ord_less_eq_int X) Y)->False)->((ord_less_eq_int Y) X))).
% 127.32/127.57  Axiom fact_70_zle__refl:(forall (W:int), ((ord_less_eq_int W) W)).
% 127.32/127.57  Axiom fact_71_zle__linear:(forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z))).
% 127.32/127.57  Axiom fact_72_zle__trans:(forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_eq_int _TPTP_I) J)->(((ord_less_eq_int J) K)->((ord_less_eq_int _TPTP_I) K)))).
% 127.32/127.57  Axiom fact_73_zle__antisym:(forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W)))).
% 127.32/127.57  Trying to prove (((eq int) ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q)))) (twoSqu1535104286sum2sq ((product_Pair_int_int ((plus_plus_int ((times_times_int a) p)) ((times_times_int b) q))) ((minus_minus_int ((times_times_int a) q)) ((times_times_int b) p)))))
% 127.32/127.57  Found x2:(P ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q))))
% 127.32/127.57  Found (fun (x2:(P ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q)))))=> x2) as proof of (P ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q))))
% 127.32/127.57  Found (fun (x2:(P ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q)))))=> x2) as proof of (P0 ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q))))
% 127.32/127.57  Found eq_ref00:=(eq_ref0 b0):(((eq int) b0) b0)
% 127.32/127.57  Found (eq_ref0 b0) as proof of (((eq int) b0) (twoSqu1535104286sum2sq ((product_Pair_int_int ((plus_plus_int ((times_times_int a) p)) ((times_times_int b) q))) ((minus_minus_int ((times_times_int a) q)) ((times_times_int b) p)))))
% 127.32/127.57  Found ((eq_ref int) b0) as proof of (((eq int) b0) (twoSqu1535104286sum2sq ((product_Pair_int_int ((plus_plus_int ((times_times_int a) p)) ((times_times_int b) q))) ((minus_minus_int ((times_times_int a) q)) ((times_times_int b) p)))))
% 279.64/279.97  Found ((eq_ref int) b0) as proof of (((eq int) b0) (twoSqu1535104286sum2sq ((product_Pair_int_int ((plus_plus_int ((times_times_int a) p)) ((times_times_int b) q))) ((minus_minus_int ((times_times_int a) q)) ((times_times_int b) p)))))
% 279.64/279.97  Found ((eq_ref int) b0) as proof of (((eq int) b0) (twoSqu1535104286sum2sq ((product_Pair_int_int ((plus_plus_int ((times_times_int a) p)) ((times_times_int b) q))) ((minus_minus_int ((times_times_int a) q)) ((times_times_int b) p)))))
% 279.64/279.97  Found fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J00:=(fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J0 (twoSqu1535104286sum2sq ((product_Pair_int_int p) q))):(((eq int) ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q)))) ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int p) q))) (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))))
% 279.64/279.97  Found (fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J0 (twoSqu1535104286sum2sq ((product_Pair_int_int p) q))) as proof of (((eq int) ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q)))) b0)
% 279.64/279.97  Found ((fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q))) as proof of (((eq int) ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q)))) b0)
% 279.64/279.97  Found ((fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q))) as proof of (((eq int) ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q)))) b0)
% 279.64/279.97  Found ((fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q))) as proof of (((eq int) ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q)))) b0)
% 279.64/279.97  Found fact_23_zadd__commute001:=(fact_23_zadd__commute00 (fun (x:int)=> (P ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q)))))):((P ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q))))->(P ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q)))))
% 279.64/279.97  Found (fact_23_zadd__commute00 (fun (x:int)=> (P ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q)))))) as proof of (P0 ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q))))
% 279.64/279.97  Found (fact_23_zadd__commute00 (fun (x:int)=> (P ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q)))))) as proof of (P0 ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q))))
% 279.64/279.97  Found fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J001:=(fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J00 (fun (x:int)=> (P ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q)))))):((P ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) q))))->(P ((times_times_int (twoSqu1535104286sum2sq ((product_Pair_int_int a) b))) (twoSqu1535104286sum2sq ((product_Pair_int_int p) 
%------------------------------------------------------------------------------