%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW208+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:07:26 PM UTC 2026
% Result : Theorem 0.42s 0.83s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 401
% Syntax : Number of formulae : 1280 ( 160 unt; 302 def)
% Number of atoms : 3205 ( 279 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 3423 (1498 ~;1512 |; 31 &)
% ( 317 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 318 ( 316 usr; 303 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 10 con; 0-2 aty)
% Number of variables : 1808 (1807 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,B_n)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [V_x] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))
<=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( V_x != V_y
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)
=> V_b = V_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
=> V_b = V_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [V_c_2,V_a_2,V_b_2,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)
<=> V_b_2 = V_c_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oab__semigroup__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [V_w,V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
=> V_z = V_w ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [V_w,V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_w)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [V_b_2,V_a_2,V_c_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [V_b_2,V_c_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
<=> ( V_x_2 = V_y_2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
<=> ( V_x_2 != V_y_2
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [V_z,V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_x)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f101,axiom,
! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f164,axiom,
! [V_y,V_x] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f165,axiom,
! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f166,axiom,
! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f175,axiom,
! [V_j,V_i] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f176,axiom,
! [V_i,V_j] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f177,axiom,
! [V_m,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f178,axiom,
! [V_m,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f182,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f183,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f184,axiom,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f185,axiom,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f186,axiom,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f187,axiom,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f190,axiom,
! [V_l,V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f207,axiom,
! [V_n,V_m] :
( ( V_m = V_n
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f216,axiom,
! [V_t,V_s] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s),V_t))
=> V_s != V_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f223,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f358,axiom,
! [V_n,V_m] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
=> V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f362,axiom,
! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f365,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f381,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f391,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f395,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f469,axiom,
! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f660,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f662,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f675,axiom,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1020,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1021,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1025,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1026,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1027,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1028,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1029,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1037,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1042,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1046,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1048,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1059,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1073,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1074,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1077,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1078,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1079,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1082,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1087,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1090,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1098,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1111,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1112,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1120,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1121,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1123,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1124,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1125,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1135,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1138,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1142,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1147,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1149,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1269,conjecture,
( ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,B_n)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1270,negated_conjecture,
~ ( ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,B_n)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(negated_conjecture,[status(cth)],[f1269]) ).
fof(f1274,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f1276,plain,
! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X0)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f1280,plain,
! [X0] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X0)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f1281,plain,
! [T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f1282,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),c_Groups_Oone__class_Oone(X0)),c_Groups_Oone__class_Oone(X0))))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(cnf_transformation,[status(thm)],[f1281]) ).
fof(f1283,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f1284,plain,
! [T_a] :
( ! [V_a] :
( ! [V_b] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) )
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(miniscoping,[status(thm)],[f1283]) ).
fof(f1285,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0)),X1))
| ~ class_Groups_Oordered__comm__monoid__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1284]) ).
fof(f1286,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f1287,plain,
! [T_a] :
( ! [V_a] :
( ! [V_b] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) )
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(miniscoping,[status(thm)],[f1286]) ).
fof(f1288,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0)),X1))
| ~ class_Groups_Oordered__comm__monoid__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1287]) ).
fof(f1289,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f1290,plain,
! [T_a] :
( ! [V_a] :
( ! [V_c,V_b] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) )
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(miniscoping,[status(thm)],[f1289]) ).
fof(f1291,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0)),X1))
| ~ class_Groups_Oordered__comm__monoid__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1290]) ).
fof(f1292,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f1293,plain,
! [T_a] :
( ! [V_a] :
( ! [V_c,V_b] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) )
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(miniscoping,[status(thm)],[f1292]) ).
fof(f1294,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0)),X1))
| ~ class_Groups_Oordered__comm__monoid__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1293]) ).
fof(f1295,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f1296,plain,
! [T_a] :
( ! [V_a] :
( ! [V_b] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) )
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(miniscoping,[status(thm)],[f1295]) ).
fof(f1297,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2)),c_Groups_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,X2),c_Groups_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X1),c_Groups_Ozero__class_Ozero(X0)))
| ~ class_Groups_Oordered__comm__monoid__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1296]) ).
fof(f1298,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f1299,plain,
! [T_a] :
( ! [V_a] :
( ! [V_b] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) )
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(miniscoping,[status(thm)],[f1298]) ).
fof(f1300,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2)),c_Groups_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X2),c_Groups_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,X1),c_Groups_Ozero__class_Ozero(X0)))
| ~ class_Groups_Oordered__comm__monoid__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1299]) ).
fof(f1301,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f1302,plain,
! [T_a] :
( ! [V_b,V_a] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(miniscoping,[status(thm)],[f1301]) ).
fof(f1303,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oabs__class_Oabs(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),c_Groups_Oabs__class_Oabs(X0,X1)),c_Groups_Oabs__class_Oabs(X0,X2))))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f1302]) ).
fof(f1304,plain,
! [V_a,T_a] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f1305,plain,
! [T_a] :
( ! [V_a] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(miniscoping,[status(thm)],[f1304]) ).
fof(f1306,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Oabs__class_Oabs(X0,X1)),c_Groups_Ozero__class_Ozero(X0)))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f1305]) ).
fof(f1307,plain,
! [V_a_2,T_a] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))
<=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f1308,plain,
! [V_a_2,T_a] :
( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2))) )
& ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(NNF_transformation,[status(thm)],[f1307]) ).
fof(f1309,plain,
! [T_a] :
( ( ! [V_a_2] :
( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2))) )
& ! [V_a_2] :
( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(miniscoping,[status(thm)],[f1308]) ).
fof(f1310,plain,
! [X0,X1] :
( X1 != c_Groups_Ozero__class_Ozero(X0)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oabs__class_Oabs(X0,X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f1309]) ).
fof(f1311,plain,
! [X0,X1] :
( X1 = c_Groups_Ozero__class_Ozero(X0)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oabs__class_Oabs(X0,X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f1309]) ).
fof(f1319,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| V_x = V_y
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f1320,plain,
! [T_a] :
( ! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| V_x = V_y )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(miniscoping,[status(thm)],[f1319]) ).
fof(f1321,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X1),X2))
| X1 = X2
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f1320]) ).
fof(f1322,plain,
! [V_c,V_a,V_b,T_a] :
( V_b = V_c
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f1323,plain,
! [T_a] :
( ! [V_c,V_b] :
( V_b = V_c
| ! [V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) )
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(miniscoping,[status(thm)],[f1322]) ).
fof(f1324,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X3),X2)
| ~ class_Groups_Ocancel__semigroup__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1323]) ).
fof(f1328,plain,
! [V_c,V_b,V_a,T_a] :
( V_b = V_c
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f1329,plain,
! [T_a] :
( ! [V_c,V_b] :
( V_b = V_c
| ! [V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) )
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(miniscoping,[status(thm)],[f1328]) ).
fof(f1330,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X3)
| ~ class_Groups_Ocancel__semigroup__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1329]) ).
fof(f1331,plain,
! [V_c_2,V_a_2,V_b_2,T_a] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)
<=> V_b_2 = V_c_2 )
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f1332,plain,
! [V_c_2,V_a_2,V_b_2,T_a] :
( ( ( V_b_2 != V_c_2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2) )
& ( V_b_2 = V_c_2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(NNF_transformation,[status(thm)],[f1331]) ).
fof(f1333,plain,
! [T_a] :
( ( ! [V_c_2,V_b_2] :
( V_b_2 != V_c_2
| ! [V_a_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2) )
& ! [V_c_2,V_b_2] :
( V_b_2 = V_c_2
| ! [V_a_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(miniscoping,[status(thm)],[f1332]) ).
fof(f1334,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X3),X2)
| ~ class_Groups_Ocancel__semigroup__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1333]) ).
fof(f1341,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))
| ~ class_Groups_Oab__semigroup__add(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f1342,plain,
! [T_a] :
( ! [V_c,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))
| ~ class_Groups_Oab__semigroup__add(T_a) ),
inference(miniscoping,[status(thm)],[f1341]) ).
fof(f1343,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X2),X3))
| ~ class_Groups_Oab__semigroup__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1342]) ).
fof(f1349,plain,
! [V_w,V_z] :
( V_z = V_w
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w)) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f1350,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f1349]) ).
fof(f1351,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j)) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f1352,plain,
! [V_j,V_i] :
( ! [V_k] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j)) ),
inference(miniscoping,[status(thm)],[f1351]) ).
fof(f1353,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f1352]) ).
fof(f1354,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f1355,plain,
! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X0)),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f1356,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f1357,plain,
! [T_a] :
( ! [V_a] : c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(miniscoping,[status(thm)],[f1356]) ).
fof(f1358,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X0,c_Groups_Oabs__class_Oabs(X0,X1)) = c_Groups_Oabs__class_Oabs(X0,X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f1357]) ).
fof(f1365,plain,
! [V_a_2,T_a] :
( ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f1366,plain,
! [V_a_2,T_a] :
( ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ozero__class_Ozero(T_a) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(NNF_transformation,[status(thm)],[f1365]) ).
fof(f1367,plain,
! [T_a] :
( ( ! [V_a_2] :
( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) )
& ! [V_a_2] :
( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ozero__class_Ozero(T_a) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(miniscoping,[status(thm)],[f1366]) ).
fof(f1368,plain,
! [X0,X1] :
( X1 = c_Groups_Ozero__class_Ozero(X0)
| c_Groups_Ozero__class_Ozero(X0) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X1)
| ~ class_Groups_Olinordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1367]) ).
fof(f1376,plain,
! [V_b,V_a,V_c,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f1377,plain,
! [T_a] :
( ! [V_b,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ! [V_c] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(miniscoping,[status(thm)],[f1376]) ).
fof(f1378,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X0) ),
inference(cnf_transformation,[status(thm)],[f1377]) ).
fof(f1379,plain,
! [V_b,V_c,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f1380,plain,
! [T_a] :
( ! [V_b,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ! [V_c] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(miniscoping,[status(thm)],[f1379]) ).
fof(f1381,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X3),X2)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X0) ),
inference(cnf_transformation,[status(thm)],[f1380]) ).
fof(f1382,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f1383,plain,
! [T_a] :
( ! [V_b,V_a] :
( ! [V_d,V_c] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) )
| ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
inference(miniscoping,[status(thm)],[f1382]) ).
fof(f1384,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,X1),X2))
| ~ class_Groups_Oordered__ab__semigroup__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1383]) ).
fof(f1391,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f1392,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(NNF_transformation,[status(thm)],[f1391]) ).
fof(f1393,plain,
! [T_a] :
( ( ! [V_b_2,V_a_2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
| ! [V_c_2] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))) )
& ! [V_b_2,V_a_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
| ! [V_c_2] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(miniscoping,[status(thm)],[f1392]) ).
fof(f1395,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X0) ),
inference(cnf_transformation,[status(thm)],[f1393]) ).
fof(f1396,plain,
! [V_b_2,V_c_2,V_a_2,T_a] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f1397,plain,
! [V_b_2,V_c_2,V_a_2,T_a] :
( ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(NNF_transformation,[status(thm)],[f1396]) ).
fof(f1398,plain,
! [T_a] :
( ( ! [V_b_2,V_a_2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
| ! [V_c_2] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))) )
& ! [V_b_2,V_a_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
| ! [V_c_2] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(miniscoping,[status(thm)],[f1397]) ).
fof(f1400,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,X1),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X3),X2)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X0) ),
inference(cnf_transformation,[status(thm)],[f1398]) ).
fof(f1401,plain,
! [V_b,V_a,V_c,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f1402,plain,
! [T_a] :
( ! [V_b,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ! [V_c] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(miniscoping,[status(thm)],[f1401]) ).
fof(f1403,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X0) ),
inference(cnf_transformation,[status(thm)],[f1402]) ).
fof(f1404,plain,
! [V_b,V_c,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f1405,plain,
! [T_a] :
( ! [V_b,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ! [V_c] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(miniscoping,[status(thm)],[f1404]) ).
fof(f1406,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X3),X2)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X0) ),
inference(cnf_transformation,[status(thm)],[f1405]) ).
fof(f1407,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f1408,plain,
! [T_a] :
( ! [V_b,V_a] :
( ! [V_d,V_c] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) )
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(miniscoping,[status(thm)],[f1407]) ).
fof(f1409,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X2),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X1),X2))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1408]) ).
fof(f1410,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f1411,plain,
! [T_a] :
( ! [V_b,V_a] :
( ! [V_c] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) )
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(miniscoping,[status(thm)],[f1410]) ).
fof(f1412,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X3),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X1),X2))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1411]) ).
fof(f1443,plain,
! [V_y_2,V_x_2] :
( ( ( V_x_2 != V_y_2
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) )
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) )
& ( V_x_2 = V_y_2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ),
inference(NNF_transformation,[status(thm)],[f60]) ).
fof(f1444,plain,
( ! [V_y_2,V_x_2] :
( ( V_x_2 != V_y_2
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) )
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) )
& ! [V_y_2,V_x_2] :
( V_x_2 = V_y_2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ),
inference(miniscoping,[status(thm)],[f1443]) ).
fof(f1445,plain,
! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f1444]) ).
fof(f1446,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f1444]) ).
fof(f1448,plain,
! [V_y_2,V_x_2] :
( ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) )
& ( ( V_x_2 != V_y_2
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ),
inference(NNF_transformation,[status(thm)],[f61]) ).
fof(f1449,plain,
( ! [V_y_2,V_x_2] :
( V_x_2 = V_y_2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) )
& ! [V_y_2,V_x_2] :
( ( V_x_2 != V_y_2
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ),
inference(miniscoping,[status(thm)],[f1448]) ).
fof(f1451,plain,
! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f1449]) ).
fof(f1458,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f1459,plain,
! [V_z,V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_x)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_y)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y)) ),
inference(pre_NNF_transformation,[status(thm)],[f65]) ).
fof(f1460,plain,
! [V_y,V_x] :
( ! [V_z] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_x)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_y)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y)) ),
inference(miniscoping,[status(thm)],[f1459]) ).
fof(f1461,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f1460]) ).
fof(f1580,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f1798,plain,
! [X0,X1] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X0)),hAPP(c_Complex_OIm,X1)),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f1799,plain,
! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),
inference(cnf_transformation,[status(thm)],[f165]) ).
fof(f1800,plain,
! [X0] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f1826,plain,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X0)),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f1827,plain,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X1)),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f1828,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0))),
inference(cnf_transformation,[status(thm)],[f177]) ).
fof(f1829,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1))),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f1844,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) ) ),
inference(NNF_transformation,[status(thm)],[f182]) ).
fof(f1845,plain,
( ! [V_n_2,V_m_2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| ! [V_k_2] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) )
& ! [V_n_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| ! [V_k_2] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) ) ),
inference(miniscoping,[status(thm)],[f1844]) ).
fof(f1846,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2))) ),
inference(cnf_transformation,[status(thm)],[f1845]) ).
fof(f1848,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) ) ),
inference(NNF_transformation,[status(thm)],[f183]) ).
fof(f1849,plain,
( ! [V_n_2,V_m_2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
| ! [V_k_2] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) )
& ! [V_n_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
| ! [V_k_2] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) ) ),
inference(miniscoping,[status(thm)],[f1848]) ).
fof(f1851,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2))) ),
inference(cnf_transformation,[status(thm)],[f1849]) ).
fof(f1852,plain,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) ),
inference(pre_NNF_transformation,[status(thm)],[f184]) ).
fof(f1853,plain,
! [V_j,V_i] :
( ! [V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) ),
inference(miniscoping,[status(thm)],[f1852]) ).
fof(f1854,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f1853]) ).
fof(f1855,plain,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) ),
inference(pre_NNF_transformation,[status(thm)],[f185]) ).
fof(f1856,plain,
! [V_j,V_i] :
( ! [V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) ),
inference(miniscoping,[status(thm)],[f1855]) ).
fof(f1857,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f1856]) ).
fof(f1858,plain,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) ),
inference(pre_NNF_transformation,[status(thm)],[f186]) ).
fof(f1859,plain,
! [V_j,V_i] :
( ! [V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) ),
inference(miniscoping,[status(thm)],[f1858]) ).
fof(f1860,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f1859]) ).
fof(f1861,plain,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) ),
inference(pre_NNF_transformation,[status(thm)],[f187]) ).
fof(f1862,plain,
! [V_j,V_i] :
( ! [V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) ),
inference(miniscoping,[status(thm)],[f1861]) ).
fof(f1863,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f1862]) ).
fof(f1870,plain,
! [V_l,V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) ),
inference(pre_NNF_transformation,[status(thm)],[f190]) ).
fof(f1871,plain,
! [V_j,V_i] :
( ! [V_l,V_k] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) ),
inference(miniscoping,[status(thm)],[f1870]) ).
fof(f1872,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f1871]) ).
fof(f1925,plain,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
| ( V_m != V_n
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f207]) ).
fof(f1926,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f1925]) ).
fof(f1927,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f1925]) ).
fof(f1948,plain,
! [V_t,V_s] :
( V_s != V_t
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s),V_t)) ),
inference(pre_NNF_transformation,[status(thm)],[f216]) ).
fof(f1949,plain,
! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f1948]) ).
fof(f1968,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f223]) ).
fof(f2436,plain,
! [V_n,V_m] :
( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) != V_m ),
inference(pre_NNF_transformation,[status(thm)],[f358]) ).
fof(f2437,plain,
! [V_n] :
( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) != V_m ),
inference(miniscoping,[status(thm)],[f2436]) ).
fof(f2438,plain,
! [X0,X1] :
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) != X0 ),
inference(cnf_transformation,[status(thm)],[f2437]) ).
fof(f2451,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[status(thm)],[f362]) ).
fof(f2458,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[status(thm)],[f365]) ).
fof(f2515,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0),
inference(cnf_transformation,[status(thm)],[f381]) ).
fof(f2531,plain,
! [V_n_2,V_m_2] :
( ( V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(NNF_transformation,[status(thm)],[f391]) ).
fof(f2532,plain,
( ! [V_n_2,V_m_2] :
( V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [V_n_2,V_m_2] :
( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(miniscoping,[status(thm)],[f2531]) ).
fof(f2533,plain,
! [X0,X1] :
( X0 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(cnf_transformation,[status(thm)],[f2532]) ).
fof(f2543,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[status(thm)],[f395]) ).
fof(f2768,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0)) = c_RealDef_Oreal(tc_Nat_Onat,X0),
inference(cnf_transformation,[status(thm)],[f469]) ).
fof(f3319,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
inference(cnf_transformation,[status(thm)],[f660]) ).
fof(f3324,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0) = X0,
inference(cnf_transformation,[status(thm)],[f662]) ).
fof(f3348,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0),
inference(cnf_transformation,[status(thm)],[f675]) ).
fof(f4305,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f1020]) ).
fof(f4306,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f1021]) ).
fof(f4310,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f1025]) ).
fof(f4311,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f1026]) ).
fof(f4312,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f1027]) ).
fof(f4313,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f1028]) ).
fof(f4314,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f1029]) ).
fof(f4322,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f1037]) ).
fof(f4327,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f1042]) ).
fof(f4331,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f1046]) ).
fof(f4333,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f1048]) ).
fof(f4344,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f1059]) ).
fof(f4358,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f1073]) ).
fof(f4359,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f1074]) ).
fof(f4362,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f1077]) ).
fof(f4363,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f1078]) ).
fof(f4364,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f1079]) ).
fof(f4367,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f1082]) ).
fof(f4372,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f1087]) ).
fof(f4375,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f1090]) ).
fof(f4383,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f1098]) ).
fof(f4396,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1111]) ).
fof(f4397,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1112]) ).
fof(f4405,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1120]) ).
fof(f4406,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1121]) ).
fof(f4408,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1123]) ).
fof(f4409,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1124]) ).
fof(f4410,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1125]) ).
fof(f4420,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1135]) ).
fof(f4423,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1138]) ).
fof(f4427,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1142]) ).
fof(f4432,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1147]) ).
fof(f4434,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1149]) ).
fof(f4607,plain,
( ? [B_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,B_n)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(pre_NNF_transformation,[status(thm)],[f1270]) ).
fof(f4608,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sK73_skl)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73_skl]),skolemize(B_n,sK73_skl)],[f4607]) ).
fof(f4609,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sK73_skl)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(cnf_transformation,[status(thm)],[f4608]) ).
fof(f4655,definition,
( sQ0_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f4657,plain,
( sQ0_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(component_clause,[status(thm)],[f4655]) ).
fof(f4658,definition,
( sQ1_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sK73_skl)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f4660,plain,
( sQ1_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sK73_skl)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(component_clause,[status(thm)],[f4658]) ).
fof(f4661,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f4609,f4655,f4658]) ).
fof(f4662,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oabs__class_Oabs(X0,c_Groups_Ozero__class_Ozero(X0))))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f1310]) ).
fof(f4666,plain,
! [X0] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X0)),
inference(destructive_equality_resolution,[status(thm)],[f1451]) ).
fof(f4691,plain,
! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X0)),
inference(destructive_equality_resolution,[status(thm)],[f1927]) ).
fof(f4693,plain,
! [X0] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X0)),
inference(destructive_equality_resolution,[status(thm)],[f1949]) ).
fof(f4796,plain,
! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X0)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(forward_demodulation,[status(thm)],[f1580,f1276]) ).
fof(f4799,plain,
! [X0] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X0)),
inference(forward_demodulation,[status(thm)],[f1580,f1280]) ).
fof(f4809,definition,
( sQ3_spl
<=> v_r = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f4810,plain,
( ~ sQ3_spl
| v_r = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f4809]) ).
fof(f4817,plain,
( sQ0_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1285,f4657]) ).
fof(f4818,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1285]) ).
fof(f4819,definition,
( sQ4_spl
<=> class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f4821,plain,
( sQ4_spl
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f4819]) ).
fof(f4822,definition,
( sQ5_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f4823,plain,
( ~ sQ5_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ),
inference(component_clause,[status(thm)],[f4822]) ).
fof(f4825,definition,
( sQ6_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f4827,plain,
( sQ6_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(component_clause,[status(thm)],[f4825]) ).
fof(f4828,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f4817,f4819,f4822,f4825,f4655]) ).
fof(f4829,definition,
( sQ7_spl
<=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f4831,plain,
( sQ7_spl
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(component_clause,[status(thm)],[f4829]) ).
fof(f4832,definition,
! [X0] :
( sQ8_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f4835,definition,
( sQ9_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f4837,plain,
( sQ9_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(component_clause,[status(thm)],[f4835]) ).
fof(f4838,plain,
( ~ sQ9_spl
| sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4818,f4829,f4832,f4835]) ).
fof(f4839,plain,
( sQ1_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sK73_skl)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(forward_demodulation,[status(thm)],[f1580,f4660]) ).
fof(f4840,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4839,f4796]) ).
fof(f4841,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f4840]) ).
fof(f4842,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4837,f1799]) ).
fof(f4843,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f4842]) ).
fof(f4845,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1288]) ).
fof(f4846,definition,
! [X0] :
( sQ10_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f4847,plain,
! [X0] :
( ~ sQ10_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ),
inference(component_clause,[status(thm)],[f4846]) ).
fof(f4849,definition,
( sQ11_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f4852,plain,
( ~ sQ11_spl
| sQ10_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4845,f4829,f4846,f4849]) ).
fof(f4853,plain,
! [X0] :
( ~ sQ10_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f4847,f1799]) ).
fof(f4854,plain,
( sQ0_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f4657,f1288]) ).
fof(f4856,definition,
( sQ12_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f4858,plain,
( sQ12_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ),
inference(component_clause,[status(thm)],[f4856]) ).
fof(f4859,definition,
( sQ13_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f4861,plain,
( sQ13_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(component_clause,[status(thm)],[f4859]) ).
fof(f4862,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f4854,f4819,f4856,f4859,f4655]) ).
fof(f4878,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0)) = c_RealDef_Oreal(tc_Nat_Onat,X0),
inference(forward_demodulation,[status(thm)],[f1580,f2768]) ).
fof(f4887,definition,
( sQ14_spl
<=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f4889,plain,
( sQ14_spl
| ~ class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f4887]) ).
fof(f4904,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4889,f4312]) ).
fof(f4905,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f4904]) ).
fof(f4918,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X0 != X0 ),
inference(paramodulation,[status(thm)],[f2451,f2438]) ).
fof(f4919,definition,
! [X0] :
( sQ19_spl
<=> X0 != X0 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f4920,plain,
! [X0] :
( ~ sQ19_spl
| X0 != X0 ),
inference(component_clause,[status(thm)],[f4919]) ).
fof(f4922,definition,
( sQ20_spl
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f4925,plain,
( sQ20_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f4918,f4919,f4922]) ).
fof(f4926,plain,
( ~ sQ19_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f4920]) ).
fof(f4927,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f4926]) ).
fof(f4930,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ),
inference(resolution,[status(thm)],[f1445,f1274]) ).
fof(f4933,plain,
( sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f4930,f4822,f4809]) ).
fof(f4935,plain,
( ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(resolution,[status(thm)],[f1446,f1282]) ).
fof(f4936,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))) ),
inference(resolution,[status(thm)],[f1446,f1288]) ).
fof(f4937,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))) ),
inference(resolution,[status(thm)],[f1446,f1285]) ).
fof(f4938,definition,
( sQ21_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f4941,definition,
( sQ22_spl
<=> class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f4943,plain,
( sQ22_spl
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f4941]) ).
fof(f4944,plain,
( ~ sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f4935,f4938,f4941]) ).
fof(f4945,definition,
! [X0,X1] :
( sQ23_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f4948,plain,
( ~ sQ4_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f4936,f4945,f4819]) ).
fof(f4949,definition,
! [X0,X1] :
( sQ24_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f4952,plain,
( ~ sQ4_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f4937,f4949,f4819]) ).
fof(f4953,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1291,f4693]) ).
fof(f4955,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1291,f4799]) ).
fof(f4956,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1291,f1446]) ).
fof(f4957,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1291,f4666]) ).
fof(f4959,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1291]) ).
fof(f4961,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1291]) ).
fof(f4962,definition,
! [X0,X1] :
( sQ25_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f4965,plain,
( sQ25_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4953,f4829,f4962]) ).
fof(f4967,definition,
! [X0,X1] :
( sQ26_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f4970,plain,
( sQ26_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f4955,f4819,f4967]) ).
fof(f4971,definition,
! [X0,X1,X2] :
( sQ27_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f4974,plain,
( sQ27_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f4956,f4819,f4971]) ).
fof(f4975,definition,
! [X0,X1] :
( sQ28_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f4978,plain,
( sQ28_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f4957,f4819,f4975]) ).
fof(f4983,definition,
! [X0,X1] :
( sQ30_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f4986,plain,
( sQ30_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f4959,f4887,f4983]) ).
fof(f4991,definition,
! [X0,X1] :
( sQ32_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f4994,plain,
( sQ32_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4961,f4829,f4991]) ).
fof(f4995,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1294,f4693]) ).
fof(f4997,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1294,f4799]) ).
fof(f4998,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1294,f1446]) ).
fof(f4999,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1294,f4666]) ).
fof(f5001,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1294]) ).
fof(f5002,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1294]) ).
fof(f5003,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1294]) ).
fof(f5004,definition,
! [X0,X1] :
( sQ33_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f5007,plain,
( sQ33_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4995,f4829,f5004]) ).
fof(f5009,definition,
! [X0,X1] :
( sQ34_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f5012,plain,
( sQ34_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f4997,f4819,f5009]) ).
fof(f5013,definition,
! [X0,X1,X2] :
( sQ35_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f5016,plain,
( sQ35_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f4998,f4819,f5013]) ).
fof(f5017,definition,
! [X0,X1] :
( sQ36_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f5020,plain,
( sQ36_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f4999,f4819,f5017]) ).
fof(f5025,definition,
! [X0,X1] :
( sQ38_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f5028,plain,
( sQ38_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f5001,f4887,f5025]) ).
fof(f5029,definition,
! [X0,X1] :
( sQ39_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f5032,plain,
( sQ39_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5002,f4829,f4835,f5029]) ).
fof(f5033,definition,
! [X0,X1] :
( sQ40_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f5036,plain,
( sQ40_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5003,f4829,f5033]) ).
fof(f5038,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1297,f4799]) ).
fof(f5039,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1297,f1446]) ).
fof(f5043,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1297]) ).
fof(f5044,definition,
! [X0] :
( sQ41_spl
<=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f5047,definition,
! [X1] :
( sQ42_spl
<=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f5048,plain,
! [X0] :
( ~ sQ42_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(component_clause,[status(thm)],[f5047]) ).
fof(f5051,definition,
( sQ43_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f5054,definition,
( sQ44_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f5056,plain,
( sQ44_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(component_clause,[status(thm)],[f5054]) ).
fof(f5057,plain,
( ~ sQ44_spl
| ~ sQ43_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5038,f4819,f5051,f5054]) ).
fof(f5058,definition,
! [X0,X1] :
( sQ45_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f5061,plain,
( sQ45_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5039,f4819,f5058]) ).
fof(f5070,definition,
! [X0] :
( sQ48_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f5071,plain,
! [X0] :
( ~ sQ48_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(component_clause,[status(thm)],[f5070]) ).
fof(f5074,definition,
! [X0] :
( sQ49_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f5077,plain,
( ~ sQ9_spl
| sQ49_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5043,f4829,f5074,f4835]) ).
fof(f5094,plain,
( ~ sQ5_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ),
inference(resolution,[status(thm)],[f4823,f1446]) ).
fof(f5096,plain,
! [X0] :
( ~ sQ5_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(resolution,[status(thm)],[f5094,f1353]) ).
fof(f5100,plain,
! [X0] :
( ~ sQ5_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r)) ),
inference(resolution,[status(thm)],[f5096,f1354]) ).
fof(f5102,plain,
( ~ sQ5_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ),
inference(resolution,[status(thm)],[f5100,f5096]) ).
fof(f5106,plain,
( ~ sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f5102,f4856,f4822]) ).
fof(f5119,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1300,f4799]) ).
fof(f5120,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1300,f1446]) ).
fof(f5126,definition,
( sQ52_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f5128,plain,
( sQ52_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(component_clause,[status(thm)],[f5126]) ).
fof(f5129,definition,
( sQ53_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f5132,plain,
( ~ sQ53_spl
| ~ sQ52_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5119,f4819,f5126,f5129]) ).
fof(f5133,definition,
! [X0,X1] :
( sQ54_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f5136,plain,
( sQ54_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5120,f4819,f5133]) ).
fof(f5141,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1303,f1445]) ).
fof(f5142,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1303,f1353]) ).
fof(f5143,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1303,f1350]) ).
fof(f5144,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1580,f1303]) ).
fof(f5145,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1303]) ).
fof(f5146,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1303]) ).
fof(f5149,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1580,f1303]) ).
fof(f5150,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1580,f1303]) ).
fof(f5151,definition,
( sQ55_spl
<=> class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f5153,plain,
( sQ55_spl
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f5151]) ).
fof(f5154,definition,
! [X0,X1] :
( sQ56_spl
<=> ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)))) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f5157,plain,
( sQ56_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f5141,f5151,f5154]) ).
fof(f5158,definition,
! [X0,X1,X2] :
( sQ57_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)))) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f5161,plain,
( sQ57_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f5142,f5151,f5158]) ).
fof(f5162,definition,
! [X0,X1] :
( sQ58_spl
<=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1)))) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f5165,plain,
( sQ58_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f5143,f5151,f5162]) ).
fof(f5166,definition,
! [X0,X1] :
( sQ59_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f5169,plain,
( sQ59_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f5144,f5151,f5166]) ).
fof(f5170,definition,
( sQ60_spl
<=> class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f5172,plain,
( sQ60_spl
| ~ class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f5170]) ).
fof(f5173,definition,
! [X0] :
( sQ61_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0)))) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f5176,plain,
( sQ61_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f5145,f5170,f5173]) ).
fof(f5177,definition,
! [X0] :
( sQ62_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f5180,plain,
( sQ62_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f5146,f5170,f5177]) ).
fof(f5192,definition,
! [X0,X1] :
( sQ66_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f5195,plain,
( sQ66_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f5149,f5151,f5192]) ).
fof(f5196,definition,
! [X0,X1] :
( sQ67_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f5199,plain,
( sQ67_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f5150,f5151,f5196]) ).
fof(f5200,plain,
( sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5172,f4311]) ).
fof(f5201,plain,
sQ60_spl,
inference(contradiction_clause,[status(thm)],[f5200]) ).
fof(f5202,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1580,f1306]) ).
fof(f5203,definition,
! [X0] :
( sQ68_spl
<=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f5204,plain,
! [X0] :
( ~ sQ68_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(component_clause,[status(thm)],[f5203]) ).
fof(f5206,plain,
( sQ68_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f5202,f5151,f5203]) ).
fof(f5313,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1580,f4662]) ).
fof(f5319,definition,
( sQ83_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f5321,plain,
( sQ83_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) ),
inference(component_clause,[status(thm)],[f5319]) ).
fof(f5322,plain,
( ~ sQ83_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f5313,f5151,f5319]) ).
fof(f5333,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)))
| X0 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1311,f1446]) ).
fof(f5336,plain,
! [X0] :
( X0 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1580,f1311]) ).
fof(f5337,definition,
! [X0] :
( sQ85_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)))
| X0 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f5340,plain,
( sQ85_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f5333,f5151,f5337]) ).
fof(f5345,definition,
! [X0] :
( sQ87_spl
<=> ( X0 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f5348,plain,
( sQ87_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f5336,f5151,f5345]) ).
fof(f5370,definition,
( sQ88_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),v_r)) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f5371,plain,
( ~ sQ88_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),v_r)) ),
inference(component_clause,[status(thm)],[f5370]) ).
fof(f5373,definition,
( sQ89_spl
<=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v_r ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f5374,plain,
( ~ sQ89_spl
| c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v_r ),
inference(component_clause,[status(thm)],[f5373]) ).
fof(f5377,definition,
( sQ90_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f5379,plain,
( sQ90_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(component_clause,[status(thm)],[f5377]) ).
fof(f5381,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(forward_demodulation,[status(thm)],[f4810,f4657]) ).
fof(f5382,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f5381,f1294]) ).
fof(f5384,definition,
( sQ91_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f5386,plain,
( sQ91_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(component_clause,[status(thm)],[f5384]) ).
fof(f5387,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ91_spl
| ~ sQ12_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5382,f4819,f4856,f5384,f4809,f4655]) ).
fof(f5393,plain,
( sQ90_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),v_r)) ),
inference(resolution,[status(thm)],[f5379,f1354]) ).
fof(f5394,plain,
( ~ sQ88_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),v_r)) ),
inference(resolution,[status(thm)],[f5371,f1446]) ).
fof(f5406,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1)))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1303]) ).
fof(f5407,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1300]) ).
fof(f5408,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1297]) ).
fof(f5409,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(c_Complex_OIm,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(c_Complex_OIm,X0)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1294]) ).
fof(f5410,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_OIm,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(c_Complex_OIm,X0)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1291]) ).
fof(f5411,definition,
! [X0,X1] :
( sQ92_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1))))) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f5414,plain,
( sQ92_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f5406,f5151,f5411]) ).
fof(f5415,definition,
! [X0,X1] :
( sQ93_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f5418,plain,
( sQ93_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5407,f4819,f5415]) ).
fof(f5419,definition,
! [X0,X1] :
( sQ94_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f5422,plain,
( sQ94_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5408,f4819,f5419]) ).
fof(f5423,definition,
! [X0,X1,X2] :
( sQ95_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(c_Complex_OIm,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(c_Complex_OIm,X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f5426,plain,
( sQ95_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5409,f4819,f5423]) ).
fof(f5427,definition,
! [X0,X1,X2] :
( sQ96_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_OIm,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(c_Complex_OIm,X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f5430,plain,
( sQ96_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5410,f4819,f5427]) ).
fof(f5442,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4363,f4831]) ).
fof(f5443,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f5442]) ).
fof(f5448,plain,
( sQ91_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),v_r))
| c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v_r
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1321,f5386]) ).
fof(f5450,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| X0 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1321,f4799]) ).
fof(f5451,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1))
| X0 = X1
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1321,f1446]) ).
fof(f5452,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X0))
| X0 = X0
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1321,f4666]) ).
fof(f5455,definition,
( sQ97_spl
<=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f5457,plain,
( sQ97_spl
| ~ class_Rings_Olinordered__idom(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f5455]) ).
fof(f5458,definition,
( sQ98_spl
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f5473,definition,
( sQ102_spl
<=> class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f5475,plain,
( sQ102_spl
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f5473]) ).
fof(f5476,plain,
( sQ91_spl
| sQ88_spl
| sQ89_spl
| ~ sQ102_spl ),
inference(split_clause,[status(thm)],[f5448,f5473,f5373,f5370,f5384]) ).
fof(f5478,definition,
! [X0] :
( sQ103_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| X0 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f5481,plain,
( sQ103_spl
| ~ sQ102_spl ),
inference(split_clause,[status(thm)],[f5450,f5473,f5478]) ).
fof(f5482,definition,
! [X0,X1] :
( sQ104_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1))
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f5485,plain,
( sQ104_spl
| ~ sQ102_spl ),
inference(split_clause,[status(thm)],[f5451,f5473,f5482]) ).
fof(f5486,definition,
! [X0] :
( sQ105_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X0))
| X0 = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f5489,plain,
( sQ105_spl
| ~ sQ102_spl ),
inference(split_clause,[status(thm)],[f5452,f5473,f5486]) ).
fof(f5491,plain,
( sQ97_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5457,f4333]) ).
fof(f5492,plain,
sQ97_spl,
inference(contradiction_clause,[status(thm)],[f5491]) ).
fof(f5493,plain,
! [X0] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0
| ~ class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
inference(resolution,[status(thm)],[f1324,f3319]) ).
fof(f5494,plain,
! [X0] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| ~ class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1324,f2451]) ).
fof(f5497,plain,
! [X0,X1,X2] :
( hAPP(c_Complex_OIm,X0) = X2
| hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),hAPP(c_Complex_OIm,X1))
| ~ class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1324]) ).
fof(f5498,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0)
| ~ class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1324]) ).
fof(f5499,plain,
! [X0,X1] :
( X0 = X1
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1324]) ).
fof(f5500,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| ~ class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1324]) ).
fof(f5501,plain,
! [X0,X1] :
( X0 = X1
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1324]) ).
fof(f5508,definition,
( sQ106_spl
<=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f5510,plain,
( sQ106_spl
| ~ class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f5508]) ).
fof(f5511,definition,
! [X0] :
( sQ107_spl
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0 ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f5514,plain,
( sQ107_spl
| ~ sQ106_spl ),
inference(split_clause,[status(thm)],[f5493,f5508,f5511]) ).
fof(f5515,definition,
( sQ108_spl
<=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f5517,plain,
( sQ108_spl
| ~ class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
inference(component_clause,[status(thm)],[f5515]) ).
fof(f5518,definition,
! [X0] :
( sQ109_spl
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f5521,plain,
( sQ109_spl
| ~ sQ108_spl ),
inference(split_clause,[status(thm)],[f5494,f5515,f5518]) ).
fof(f5524,definition,
( sQ110_spl
<=> class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f5526,plain,
( sQ110_spl
| ~ class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f5524]) ).
fof(f5527,definition,
! [X0,X1,X2] :
( sQ111_spl
<=> ( hAPP(c_Complex_OIm,X0) = X2
| hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),hAPP(c_Complex_OIm,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f5530,plain,
( sQ111_spl
| ~ sQ110_spl ),
inference(split_clause,[status(thm)],[f5497,f5524,f5527]) ).
fof(f5531,definition,
! [X0,X1] :
( sQ112_spl
<=> ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f5532,plain,
! [X0,X1] :
( ~ sQ112_spl
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0) ),
inference(component_clause,[status(thm)],[f5531]) ).
fof(f5534,plain,
( sQ112_spl
| ~ sQ106_spl ),
inference(split_clause,[status(thm)],[f5498,f5508,f5531]) ).
fof(f5535,definition,
! [X0,X1] :
( sQ113_spl
<=> ( X0 = X1
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f5538,plain,
( sQ113_spl
| ~ sQ106_spl ),
inference(split_clause,[status(thm)],[f5499,f5508,f5535]) ).
fof(f5539,definition,
! [X0,X1] :
( sQ114_spl
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f5542,plain,
( sQ114_spl
| ~ sQ108_spl ),
inference(split_clause,[status(thm)],[f5500,f5515,f5539]) ).
fof(f5543,definition,
! [X0,X1] :
( sQ115_spl
<=> ( X0 = X1
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f5546,plain,
( sQ115_spl
| ~ sQ108_spl ),
inference(split_clause,[status(thm)],[f5501,f5515,f5543]) ).
fof(f5552,definition,
! [X0] :
( sQ116_spl
<=> ~ class_Groups_Ocancel__semigroup__add(X0) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f5553,plain,
! [X0] :
( ~ sQ116_spl
| ~ class_Groups_Ocancel__semigroup__add(X0) ),
inference(component_clause,[status(thm)],[f5552]) ).
fof(f5555,definition,
! [X1] :
( sQ117_spl
<=> X1 = X1 ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f5559,plain,
( sQ108_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5517,f4367]) ).
fof(f5560,plain,
sQ108_spl,
inference(contradiction_clause,[status(thm)],[f5559]) ).
fof(f5561,plain,
( sQ106_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5510,f4322]) ).
fof(f5562,plain,
sQ106_spl,
inference(contradiction_clause,[status(thm)],[f5561]) ).
fof(f5578,definition,
( sQ118_spl
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f5580,plain,
( sQ118_spl
| ~ class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f5578]) ).
fof(f5581,definition,
! [X0] :
( sQ119_spl
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0) = X0 ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f5585,definition,
( sQ120_spl
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f5587,plain,
( sQ120_spl
| ~ class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(component_clause,[status(thm)],[f5585]) ).
fof(f5588,definition,
! [X0] :
( sQ121_spl
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0 ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f5594,definition,
( sQ122_spl
<=> class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f5596,plain,
( sQ122_spl
| ~ class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f5594]) ).
fof(f5597,definition,
! [X0,X1,X2] :
( sQ123_spl
<=> ( hAPP(c_Complex_OIm,X1) = X2
| hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X0)),X2) ) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f5601,definition,
! [X0,X1] :
( sQ124_spl
<=> ( X0 = X1
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f5605,definition,
! [X0,X1] :
( sQ125_spl
<=> ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f5609,definition,
! [X0,X1] :
( sQ126_spl
<=> ( X0 = X1
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f5613,definition,
! [X0,X1] :
( sQ127_spl
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f5622,definition,
! [X0] :
( sQ128_spl
<=> ~ class_Groups_Ocancel__ab__semigroup__add(X0) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f5623,plain,
! [X0] :
( ~ sQ128_spl
| ~ class_Groups_Ocancel__ab__semigroup__add(X0) ),
inference(component_clause,[status(thm)],[f5622]) ).
fof(f5626,plain,
( sQ120_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5587,f4364]) ).
fof(f5627,plain,
sQ120_spl,
inference(contradiction_clause,[status(thm)],[f5626]) ).
fof(f5628,plain,
( sQ118_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5580,f4314]) ).
fof(f5629,plain,
sQ118_spl,
inference(contradiction_clause,[status(thm)],[f5628]) ).
fof(f5658,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1826,f1300]) ).
fof(f5660,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1826,f1294]) ).
fof(f5661,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1826,f1291]) ).
fof(f5665,plain,
( sQ41_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5658,f4829,f4835,f5044]) ).
fof(f5667,definition,
! [X0,X1,X2] :
( sQ133_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f5670,plain,
( sQ133_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5660,f4829,f5667]) ).
fof(f5671,definition,
! [X0,X1,X2] :
( sQ134_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f5674,plain,
( sQ134_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5661,f4829,f5671]) ).
fof(f5680,plain,
( ~ sQ116_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f4367,f5553]) ).
fof(f5682,plain,
~ sQ116_spl,
inference(contradiction_clause,[status(thm)],[f5680]) ).
fof(f5683,plain,
( ~ sQ128_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f4364,f5623]) ).
fof(f5685,plain,
~ sQ128_spl,
inference(contradiction_clause,[status(thm)],[f5683]) ).
fof(f5686,plain,
! [X0] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0) = X0
| ~ class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
inference(resolution,[status(thm)],[f1330,f3324]) ).
fof(f5687,plain,
! [X0] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0
| ~ class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1330,f2458]) ).
fof(f5690,plain,
! [X0,X1,X2] :
( hAPP(c_Complex_OIm,X1) = X2
| hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X0)),X2)
| ~ class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1330]) ).
fof(f5691,plain,
! [X0,X1] :
( X0 = X1
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)
| ~ class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1330]) ).
fof(f5692,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)
| ~ class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1330]) ).
fof(f5693,plain,
! [X0,X1] :
( X0 = X1
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1330]) ).
fof(f5694,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)
| ~ class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1330]) ).
fof(f5701,plain,
( sQ119_spl
| ~ sQ106_spl ),
inference(split_clause,[status(thm)],[f5686,f5508,f5581]) ).
fof(f5702,plain,
( sQ121_spl
| ~ sQ108_spl ),
inference(split_clause,[status(thm)],[f5687,f5515,f5588]) ).
fof(f5705,plain,
( sQ123_spl
| ~ sQ110_spl ),
inference(split_clause,[status(thm)],[f5690,f5524,f5597]) ).
fof(f5706,plain,
( sQ124_spl
| ~ sQ106_spl ),
inference(split_clause,[status(thm)],[f5691,f5508,f5601]) ).
fof(f5707,plain,
( sQ125_spl
| ~ sQ106_spl ),
inference(split_clause,[status(thm)],[f5692,f5508,f5605]) ).
fof(f5708,plain,
( sQ126_spl
| ~ sQ108_spl ),
inference(split_clause,[status(thm)],[f5693,f5515,f5609]) ).
fof(f5709,plain,
( sQ127_spl
| ~ sQ108_spl ),
inference(split_clause,[status(thm)],[f5694,f5515,f5613]) ).
fof(f5788,plain,
! [X0] :
( ~ sQ48_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(forward_subsumption_resolution,[status(thm)],[f5071,f1800]) ).
fof(f5792,plain,
( sQ44_spl
| ~ sQ3_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),v_r)) ),
inference(forward_demodulation,[status(thm)],[f4810,f5056]) ).
fof(f5793,plain,
( sQ44_spl
| ~ sQ3_spl
| sQ90_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5792,f5393]) ).
fof(f5794,plain,
( sQ44_spl
| ~ sQ3_spl
| sQ90_spl ),
inference(contradiction_clause,[status(thm)],[f5793]) ).
fof(f5821,plain,
( ~ sQ42_spl
| $false ),
inference(resolution,[status(thm)],[f5048,f1799]) ).
fof(f5823,plain,
~ sQ42_spl,
inference(contradiction_clause,[status(thm)],[f5821]) ).
fof(f5824,plain,
( ~ sQ48_spl
| $false ),
inference(resolution,[status(thm)],[f5788,f1799]) ).
fof(f5826,plain,
~ sQ48_spl,
inference(contradiction_clause,[status(thm)],[f5824]) ).
fof(f5827,plain,
( ~ sQ10_spl
| $false ),
inference(resolution,[status(thm)],[f4853,f1800]) ).
fof(f5830,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f5827]) ).
fof(f5833,plain,
( ~ sQ88_spl
| v_r = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(resolution,[status(thm)],[f5394,f1350]) ).
fof(f5835,plain,
( ~ sQ88_spl
| sQ89_spl
| ~ sQ90_spl ),
inference(split_clause,[status(thm)],[f5833,f5377,f5373,f5370]) ).
fof(f5841,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1827,f1294]) ).
fof(f5842,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1827,f1291]) ).
fof(f5848,definition,
! [X0,X1,X2] :
( sQ136_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f5851,plain,
( sQ136_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5841,f4829,f5848]) ).
fof(f5852,definition,
! [X0,X1,X2] :
( sQ137_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2))),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f5855,plain,
( sQ137_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5842,f4829,f5852]) ).
fof(f5863,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1343]) ).
fof(f5864,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1343]) ).
fof(f5865,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1))),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),X2))
| ~ class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1343]) ).
fof(f5866,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1))
| ~ class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1343]) ).
fof(f5867,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1343]) ).
fof(f5868,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1))
| ~ class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1343]) ).
fof(f5869,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1343]) ).
fof(f5870,definition,
( sQ139_spl
<=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f5872,plain,
( sQ139_spl
| ~ class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f5870]) ).
fof(f5873,definition,
! [X0,X1] :
( sQ140_spl
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f5876,plain,
( sQ140_spl
| ~ sQ139_spl ),
inference(split_clause,[status(thm)],[f5863,f5870,f5873]) ).
fof(f5877,definition,
( sQ141_spl
<=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f5879,plain,
( sQ141_spl
| ~ class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
inference(component_clause,[status(thm)],[f5877]) ).
fof(f5880,definition,
! [X0,X1] :
( sQ142_spl
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f5883,plain,
( sQ142_spl
| ~ sQ141_spl ),
inference(split_clause,[status(thm)],[f5864,f5877,f5880]) ).
fof(f5884,definition,
( sQ143_spl
<=> class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f5886,plain,
( sQ143_spl
| ~ class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f5884]) ).
fof(f5887,definition,
! [X0,X1,X2] :
( sQ144_spl
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1))),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),X2)) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f5890,plain,
( sQ144_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f5865,f5884,f5887]) ).
fof(f5891,definition,
! [X0,X1] :
( sQ145_spl
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f5894,plain,
( sQ145_spl
| ~ sQ139_spl ),
inference(split_clause,[status(thm)],[f5866,f5870,f5891]) ).
fof(f5895,definition,
! [X0,X1] :
( sQ146_spl
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f5898,plain,
( sQ146_spl
| ~ sQ139_spl ),
inference(split_clause,[status(thm)],[f5867,f5870,f5895]) ).
fof(f5899,definition,
! [X0,X1] :
( sQ147_spl
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f5902,plain,
( sQ147_spl
| ~ sQ141_spl ),
inference(split_clause,[status(thm)],[f5868,f5877,f5899]) ).
fof(f5903,definition,
! [X0,X1] :
( sQ148_spl
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f5906,plain,
( sQ148_spl
| ~ sQ141_spl ),
inference(split_clause,[status(thm)],[f5869,f5877,f5903]) ).
fof(f5907,plain,
( sQ141_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5879,f4372]) ).
fof(f5908,plain,
sQ141_spl,
inference(contradiction_clause,[status(thm)],[f5907]) ).
fof(f5909,plain,
( sQ139_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5872,f4327]) ).
fof(f5910,plain,
sQ139_spl,
inference(contradiction_clause,[status(thm)],[f5909]) ).
fof(f5911,plain,
! [X0] :
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1580,f1358]) ).
fof(f5912,plain,
! [X0] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1580,f1358]) ).
fof(f5913,definition,
! [X0] :
( sQ149_spl
<=> c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f5916,plain,
( sQ149_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f5911,f5151,f5913]) ).
fof(f5917,definition,
! [X0] :
( sQ150_spl
<=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f5920,plain,
( sQ150_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f5912,f5151,f5917]) ).
fof(f5933,definition,
( sQ151_spl
<=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f5935,plain,
( sQ151_spl
| ~ class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
inference(component_clause,[status(thm)],[f5933]) ).
fof(f5937,definition,
( sQ152_spl
<=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f5939,plain,
( sQ152_spl
| ~ class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f5937]) ).
fof(f5944,definition,
( sQ153_spl
<=> class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f5946,plain,
( sQ153_spl
| ~ class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f5944]) ).
fof(f5951,plain,
( sQ151_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5935,f4375]) ).
fof(f5952,plain,
sQ151_spl,
inference(contradiction_clause,[status(thm)],[f5951]) ).
fof(f5953,plain,
( sQ152_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5939,f4331]) ).
fof(f5954,plain,
sQ152_spl,
inference(contradiction_clause,[status(thm)],[f5953]) ).
fof(f6026,plain,
! [X0] :
( ~ sQ112_spl
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X0 != X0 ),
inference(paramodulation,[status(thm)],[f3324,f5532]) ).
fof(f6029,plain,
( ~ sQ112_spl
| sQ98_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f6026,f4919,f5458,f5531]) ).
fof(f6048,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ),
inference(resolution,[status(thm)],[f1846,f1294]) ).
fof(f6049,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ),
inference(resolution,[status(thm)],[f1846,f1291]) ).
fof(f6055,definition,
! [X0,X1,X2] :
( sQ160_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f6058,plain,
( ~ sQ7_spl
| sQ160_spl ),
inference(split_clause,[status(thm)],[f6048,f6055,f4829]) ).
fof(f6059,definition,
! [X0,X1,X2] :
( sQ161_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f6062,plain,
( ~ sQ7_spl
| sQ161_spl ),
inference(split_clause,[status(thm)],[f6049,f6059,f4829]) ).
fof(f6068,plain,
( sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4406,f5153]) ).
fof(f6069,plain,
sQ55_spl,
inference(contradiction_clause,[status(thm)],[f6068]) ).
fof(f6070,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4408,f4821]) ).
fof(f6071,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f6070]) ).
fof(f6073,plain,
( sQ12_spl
| ~ sQ3_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),v_r)) ),
inference(forward_demodulation,[status(thm)],[f4810,f4858]) ).
fof(f6074,plain,
( sQ12_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6073,f1355]) ).
fof(f6075,plain,
( sQ12_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f6074]) ).
fof(f6089,definition,
( sQ163_spl
<=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f6091,plain,
( sQ163_spl
| ~ class_Groups_Omonoid__add(tc_Nat_Onat) ),
inference(component_clause,[status(thm)],[f6089]) ).
fof(f6093,definition,
( sQ164_spl
<=> class_Groups_Omonoid__add(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f6095,plain,
( sQ164_spl
| ~ class_Groups_Omonoid__add(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f6093]) ).
fof(f6113,plain,
! [X0] :
( hAPP(c_Complex_OIm,X0) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X0))
| ~ class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1368]) ).
fof(f6118,definition,
( sQ166_spl
<=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f6120,plain,
( sQ166_spl
| ~ class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f6118]) ).
fof(f6128,definition,
( sQ168_spl
<=> class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f6130,plain,
( sQ168_spl
| ~ class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f6128]) ).
fof(f6131,definition,
! [X0] :
( sQ169_spl
<=> ( hAPP(c_Complex_OIm,X0) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f6134,plain,
( sQ169_spl
| ~ sQ168_spl ),
inference(split_clause,[status(thm)],[f6113,f6128,f6131]) ).
fof(f6139,plain,
( sQ168_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6130,f4409]) ).
fof(f6140,plain,
sQ168_spl,
inference(contradiction_clause,[status(thm)],[f6139]) ).
fof(f6304,plain,
( sQ110_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4420,f5526]) ).
fof(f6305,plain,
sQ110_spl,
inference(contradiction_clause,[status(thm)],[f6304]) ).
fof(f6306,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4423,f4943]) ).
fof(f6307,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f6306]) ).
fof(f6308,plain,
( sQ143_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4427,f5886]) ).
fof(f6309,plain,
sQ143_spl,
inference(contradiction_clause,[status(thm)],[f6308]) ).
fof(f6310,plain,
( sQ153_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4432,f5946]) ).
fof(f6311,plain,
sQ153_spl,
inference(contradiction_clause,[status(thm)],[f6310]) ).
fof(f6318,plain,
( sQ102_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4434,f5475]) ).
fof(f6319,plain,
sQ102_spl,
inference(contradiction_clause,[status(thm)],[f6318]) ).
fof(f6320,plain,
( sQ164_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6095,f4344]) ).
fof(f6321,plain,
sQ164_spl,
inference(contradiction_clause,[status(thm)],[f6320]) ).
fof(f6322,plain,
( sQ163_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6091,f4383]) ).
fof(f6323,plain,
sQ163_spl,
inference(contradiction_clause,[status(thm)],[f6322]) ).
fof(f6324,plain,
( sQ166_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6120,f4313]) ).
fof(f6325,plain,
sQ166_spl,
inference(contradiction_clause,[status(thm)],[f6324]) ).
fof(f6326,plain,
( sQ122_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5596,f4410]) ).
fof(f6327,plain,
sQ122_spl,
inference(contradiction_clause,[status(thm)],[f6326]) ).
fof(f6367,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1378,f1828]) ).
fof(f6368,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X0))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1378,f4691]) ).
fof(f6369,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1378,f1461]) ).
fof(f6370,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X0)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1378,f1354]) ).
fof(f6371,plain,
! [X0] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X0))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1378,f1355]) ).
fof(f6372,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X0)),X2)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1378]) ).
fof(f6373,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1378]) ).
fof(f6374,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1378]) ).
fof(f6375,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1378]) ).
fof(f6376,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1378]) ).
fof(f6377,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_OIm,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X0)),X1)),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X2))))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1378]) ).
fof(f6378,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1378]) ).
fof(f6379,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X0))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1378]) ).
fof(f6380,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1378]) ).
fof(f6381,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X0))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1378]) ).
fof(f6382,definition,
( sQ187_spl
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f6384,plain,
( sQ187_spl
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(component_clause,[status(thm)],[f6382]) ).
fof(f6385,definition,
! [X0,X1] :
( sQ188_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0))) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f6388,plain,
( sQ188_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f6367,f6382,f6385]) ).
fof(f6389,definition,
! [X0] :
( sQ189_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X0)) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f6392,plain,
( sQ189_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f6368,f6382,f6389]) ).
fof(f6393,definition,
( sQ190_spl
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f6395,plain,
( sQ190_spl
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f6393]) ).
fof(f6396,definition,
! [X0,X1] :
( sQ191_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f6399,plain,
( sQ191_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f6369,f6393,f6396]) ).
fof(f6400,definition,
! [X0,X1,X2] :
( sQ192_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X0)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f6403,plain,
( sQ192_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f6370,f6393,f6400]) ).
fof(f6404,definition,
! [X0] :
( sQ193_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X0)) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f6407,plain,
( sQ193_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f6371,f6393,f6404]) ).
fof(f6408,definition,
! [X0,X1,X2] :
( sQ194_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X0)),X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f6411,plain,
( sQ194_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f6372,f6393,f6408]) ).
fof(f6412,definition,
( sQ195_spl
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f6414,plain,
( sQ195_spl
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f6412]) ).
fof(f6415,definition,
! [X0,X1] :
( sQ196_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f6418,plain,
( sQ196_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f6373,f6412,f6415]) ).
fof(f6419,definition,
! [X0,X1] :
( sQ197_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f6422,plain,
( sQ197_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f6374,f6412,f6419]) ).
fof(f6423,definition,
! [X0,X1] :
( sQ198_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f6426,plain,
( sQ198_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f6375,f6382,f6423]) ).
fof(f6427,definition,
! [X0,X1] :
( sQ199_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f6430,plain,
( sQ199_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f6376,f6382,f6427]) ).
fof(f6431,definition,
! [X0,X1,X2] :
( sQ200_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_OIm,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X0)),X1)),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X2)))) ) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f6434,plain,
( sQ200_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f6377,f6393,f6431]) ).
fof(f6435,definition,
! [X0,X1] :
( sQ201_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f6438,plain,
( sQ201_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f6378,f6412,f6435]) ).
fof(f6439,definition,
! [X0,X1] :
( sQ202_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f6442,plain,
( sQ202_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f6379,f6412,f6439]) ).
fof(f6443,definition,
! [X0,X1] :
( sQ203_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f6446,plain,
( sQ203_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f6380,f6382,f6443]) ).
fof(f6447,definition,
! [X0,X1] :
( sQ204_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f6450,plain,
( sQ204_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f6381,f6382,f6447]) ).
fof(f6451,plain,
( sQ187_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6384,f4359]) ).
fof(f6452,plain,
sQ187_spl,
inference(contradiction_clause,[status(thm)],[f6451]) ).
fof(f6453,plain,
( sQ190_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6395,f4397]) ).
fof(f6454,plain,
sQ190_spl,
inference(contradiction_clause,[status(thm)],[f6453]) ).
fof(f6455,plain,
( sQ195_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6414,f4306]) ).
fof(f6456,plain,
sQ195_spl,
inference(contradiction_clause,[status(thm)],[f6455]) ).
fof(f6461,plain,
( ~ sQ89_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f5374,f1282]) ).
fof(f6466,plain,
( ~ sQ89_spl
| sQ0_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f6461,f4941,f4655,f5373]) ).
fof(f6495,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1)) ),
inference(resolution,[status(thm)],[f1851,f1378]) ).
fof(f6500,definition,
! [X0,X1] :
( sQ207_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f6503,plain,
( ~ sQ187_spl
| sQ207_spl ),
inference(split_clause,[status(thm)],[f6495,f6500,f6382]) ).
fof(f6511,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1381,f1829]) ).
fof(f6514,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1381,f1354]) ).
fof(f6516,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),hAPP(c_Complex_OIm,X1))))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1381]) ).
fof(f6517,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1381]) ).
fof(f6518,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1381]) ).
fof(f6519,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1381]) ).
fof(f6520,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1381]) ).
fof(f6521,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),hAPP(c_Complex_OIm,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),hAPP(c_Complex_OIm,X1))),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X2),X1))))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1381]) ).
fof(f6522,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1381]) ).
fof(f6523,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1381]) ).
fof(f6524,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1381]) ).
fof(f6525,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1381]) ).
fof(f6530,definition,
! [X0,X1] :
( sQ209_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1))) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f6533,plain,
( sQ209_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f6511,f6382,f6530]) ).
fof(f6539,definition,
! [X0,X1,X2] :
( sQ211_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f6542,plain,
( sQ211_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f6514,f6393,f6539]) ).
fof(f6544,definition,
! [X0,X1,X2] :
( sQ212_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),hAPP(c_Complex_OIm,X1)))) ) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f6547,plain,
( sQ212_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f6516,f6393,f6544]) ).
fof(f6548,definition,
! [X0,X1] :
( sQ213_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f6551,plain,
( sQ213_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f6517,f6412,f6548]) ).
fof(f6552,definition,
! [X0,X1] :
( sQ214_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f6555,plain,
( sQ214_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f6518,f6412,f6552]) ).
fof(f6556,definition,
! [X0,X1] :
( sQ215_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f6559,plain,
( sQ215_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f6519,f6382,f6556]) ).
fof(f6560,definition,
! [X0,X1] :
( sQ216_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f6563,plain,
( sQ216_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f6520,f6382,f6560]) ).
fof(f6564,definition,
! [X0,X1,X2] :
( sQ217_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),hAPP(c_Complex_OIm,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),hAPP(c_Complex_OIm,X1))),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X2),X1)))) ) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f6567,plain,
( sQ217_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f6521,f6393,f6564]) ).
fof(f6568,definition,
! [X0,X1] :
( sQ218_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f6571,plain,
( sQ218_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f6522,f6412,f6568]) ).
fof(f6572,definition,
! [X0,X1] :
( sQ219_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f6575,plain,
( sQ219_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f6523,f6412,f6572]) ).
fof(f6576,definition,
! [X0,X1] :
( sQ220_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f6579,plain,
( sQ220_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f6524,f6382,f6576]) ).
fof(f6580,definition,
! [X0,X1] :
( sQ221_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f6583,plain,
( sQ221_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f6525,f6382,f6580]) ).
fof(f6585,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1384,f1445]) ).
fof(f6586,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1384,f1353]) ).
fof(f6587,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1384,f1350]) ).
fof(f6590,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X2)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0)),X1))
| ~ class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1384]) ).
fof(f6591,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ~ class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1384]) ).
fof(f6592,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1384]) ).
fof(f6593,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1384]) ).
fof(f6594,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1384]) ).
fof(f6595,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X3))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),hAPP(c_Complex_OIm,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),hAPP(c_Complex_OIm,X1)))
| ~ class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1384]) ).
fof(f6596,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1384]) ).
fof(f6597,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1384]) ).
fof(f6598,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1384]) ).
fof(f6599,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1384]) ).
fof(f6600,definition,
( sQ222_spl
<=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f6602,plain,
( sQ222_spl
| ~ class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
inference(component_clause,[status(thm)],[f6600]) ).
fof(f6604,definition,
( sQ223_spl
<=> class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f6606,plain,
( sQ223_spl
| ~ class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f6604]) ).
fof(f6607,definition,
! [X0,X1,X2,X3] :
( sQ224_spl
<=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f6610,plain,
( sQ224_spl
| ~ sQ223_spl ),
inference(split_clause,[status(thm)],[f6585,f6604,f6607]) ).
fof(f6611,definition,
! [X0,X1,X2,X3,X4] :
( sQ225_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f6614,plain,
( sQ225_spl
| ~ sQ223_spl ),
inference(split_clause,[status(thm)],[f6586,f6604,f6611]) ).
fof(f6615,definition,
! [X0,X1,X2,X3] :
( sQ226_spl
<=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f6618,plain,
( sQ226_spl
| ~ sQ223_spl ),
inference(split_clause,[status(thm)],[f6587,f6604,f6615]) ).
fof(f6619,definition,
! [X0,X1,X2,X3] :
( sQ227_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X2)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f6622,plain,
( sQ227_spl
| ~ sQ223_spl ),
inference(split_clause,[status(thm)],[f6590,f6604,f6619]) ).
fof(f6623,definition,
( sQ228_spl
<=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f6625,plain,
( sQ228_spl
| ~ class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f6623]) ).
fof(f6626,definition,
! [X0,X1,X2] :
( sQ229_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f6629,plain,
( sQ229_spl
| ~ sQ228_spl ),
inference(split_clause,[status(thm)],[f6591,f6623,f6626]) ).
fof(f6630,definition,
! [X0,X1,X2] :
( sQ230_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f6633,plain,
( sQ230_spl
| ~ sQ228_spl ),
inference(split_clause,[status(thm)],[f6592,f6623,f6630]) ).
fof(f6634,definition,
! [X0,X1,X2] :
( sQ231_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f6637,plain,
( sQ231_spl
| ~ sQ222_spl ),
inference(split_clause,[status(thm)],[f6593,f6600,f6634]) ).
fof(f6638,definition,
! [X0,X1,X2] :
( sQ232_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f6641,plain,
( sQ232_spl
| ~ sQ222_spl ),
inference(split_clause,[status(thm)],[f6594,f6600,f6638]) ).
fof(f6642,definition,
! [X0,X1,X2,X3] :
( sQ233_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X3))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),hAPP(c_Complex_OIm,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),hAPP(c_Complex_OIm,X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f6645,plain,
( sQ233_spl
| ~ sQ223_spl ),
inference(split_clause,[status(thm)],[f6595,f6604,f6642]) ).
fof(f6646,definition,
! [X0,X1,X2] :
( sQ234_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f6649,plain,
( sQ234_spl
| ~ sQ228_spl ),
inference(split_clause,[status(thm)],[f6596,f6623,f6646]) ).
fof(f6650,definition,
! [X0,X1,X2] :
( sQ235_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f6653,plain,
( sQ235_spl
| ~ sQ228_spl ),
inference(split_clause,[status(thm)],[f6597,f6623,f6650]) ).
fof(f6654,definition,
! [X0,X1,X2] :
( sQ236_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f6657,plain,
( sQ236_spl
| ~ sQ222_spl ),
inference(split_clause,[status(thm)],[f6598,f6600,f6654]) ).
fof(f6658,definition,
! [X0,X1,X2] :
( sQ237_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f6661,plain,
( sQ237_spl
| ~ sQ222_spl ),
inference(split_clause,[status(thm)],[f6599,f6600,f6658]) ).
fof(f6662,plain,
( sQ222_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6602,f4362]) ).
fof(f6663,plain,
sQ222_spl,
inference(contradiction_clause,[status(thm)],[f6662]) ).
fof(f6664,plain,
( sQ223_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6606,f4405]) ).
fof(f6665,plain,
sQ223_spl,
inference(contradiction_clause,[status(thm)],[f6664]) ).
fof(f6666,plain,
( sQ228_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6625,f4310]) ).
fof(f6667,plain,
sQ228_spl,
inference(contradiction_clause,[status(thm)],[f6666]) ).
fof(f6687,definition,
! [X0,X1,X2] :
( sQ238_spl
<=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f6691,definition,
! [X0,X1,X2,X3] :
( sQ239_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X3),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X3),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f6695,definition,
! [X0,X1,X2] :
( sQ240_spl
<=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X0)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f6699,definition,
! [X0,X1,X2] :
( sQ241_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X2),X0))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X2)),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f6703,definition,
! [X0,X1] :
( sQ242_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f6707,definition,
! [X0,X1] :
( sQ243_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f6711,definition,
! [X0,X1] :
( sQ244_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f6715,definition,
! [X0,X1] :
( sQ245_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f6719,definition,
! [X0,X1,X2] :
( sQ246_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X2)),X0)),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X2),X1))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),hAPP(c_Complex_OIm,X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f6723,definition,
! [X0,X1] :
( sQ247_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f6727,definition,
! [X0,X1] :
( sQ248_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f6731,definition,
! [X0,X1] :
( sQ249_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f6735,definition,
! [X0,X1] :
( sQ250_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f6741,plain,
( sQ6_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(resolution,[status(thm)],[f4827,f1354]) ).
fof(f6744,plain,
( sQ13_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f4861,f1321]) ).
fof(f6745,definition,
( sQ251_spl
<=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f6746,plain,
( ~ sQ251_spl
| c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f6745]) ).
fof(f6748,plain,
( sQ13_spl
| sQ53_spl
| sQ251_spl
| ~ sQ102_spl ),
inference(split_clause,[status(thm)],[f6744,f5473,f6745,f5129,f4859]) ).
fof(f6749,plain,
( ~ sQ251_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6746,f1458]) ).
fof(f6750,plain,
~ sQ251_spl,
inference(contradiction_clause,[status(thm)],[f6749]) ).
fof(f6757,plain,
! [X0] :
( ~ sQ68_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f5204,f1321]) ).
fof(f6759,plain,
! [X0] :
( ~ sQ68_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(paramodulation,[status(thm)],[f4878,f5204]) ).
fof(f6760,definition,
! [X0] :
( sQ252_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0)))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f6763,plain,
( ~ sQ68_spl
| sQ252_spl
| ~ sQ102_spl ),
inference(split_clause,[status(thm)],[f6757,f5473,f6760,f5203]) ).
fof(f6764,plain,
! [X0] :
( ~ sQ68_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X0)))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,X0)
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f6759,f1321]) ).
fof(f6765,definition,
! [X0] :
( sQ253_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X0)))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f6768,plain,
( ~ sQ68_spl
| sQ253_spl
| ~ sQ102_spl ),
inference(split_clause,[status(thm)],[f6764,f5473,f6765,f5203]) ).
fof(f6776,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X2))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X2)) ),
inference(resolution,[status(thm)],[f1860,f1381]) ).
fof(f6777,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X0)) ),
inference(resolution,[status(thm)],[f1860,f1378]) ).
fof(f6780,definition,
! [X0,X1,X2] :
( sQ254_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f6783,plain,
( ~ sQ187_spl
| sQ254_spl ),
inference(split_clause,[status(thm)],[f6776,f6780,f6382]) ).
fof(f6784,definition,
! [X0,X1,X2] :
( sQ255_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f6787,plain,
( ~ sQ187_spl
| sQ255_spl ),
inference(split_clause,[status(thm)],[f6777,f6784,f6382]) ).
fof(f6805,definition,
! [X0,X1,X2] :
( sQ256_spl
<=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f6809,definition,
! [X0,X1,X2,X3] :
( sQ257_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f6813,definition,
! [X0,X1,X2] :
( sQ258_spl
<=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f6817,definition,
! [X0,X1,X2] :
( sQ259_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),hAPP(c_Complex_OIm,X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f6821,definition,
! [X0,X1] :
( sQ260_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f6825,definition,
! [X0,X1] :
( sQ261_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f6829,definition,
! [X0,X1] :
( sQ262_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f6833,definition,
! [X0,X1] :
( sQ263_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f6837,definition,
! [X0,X1,X2] :
( sQ264_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),hAPP(c_Complex_OIm,X2))),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),hAPP(c_Complex_OIm,X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f6841,definition,
! [X0,X1] :
( sQ265_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f6845,definition,
! [X0,X1] :
( sQ266_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f6849,definition,
! [X0,X1] :
( sQ267_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f6853,definition,
! [X0,X1] :
( sQ268_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f6858,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1395,f1445]) ).
fof(f6859,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X3),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X3),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1395,f1353]) ).
fof(f6860,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X0)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1395,f1350]) ).
fof(f6863,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X0)),X2)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1395]) ).
fof(f6864,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1395]) ).
fof(f6865,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1395]) ).
fof(f6866,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1395]) ).
fof(f6867,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1395]) ).
fof(f6868,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_OIm,X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X0)),X1)),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X2))))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1395]) ).
fof(f6869,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1395]) ).
fof(f6870,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X0))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1395]) ).
fof(f6871,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1395]) ).
fof(f6872,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X0))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1395]) ).
fof(f6874,plain,
( sQ238_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f6858,f6393,f6687]) ).
fof(f6875,plain,
( sQ239_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f6859,f6393,f6691]) ).
fof(f6876,plain,
( sQ240_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f6860,f6393,f6695]) ).
fof(f6878,plain,
( sQ241_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f6863,f6393,f6699]) ).
fof(f6879,plain,
( sQ242_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f6864,f6412,f6703]) ).
fof(f6880,plain,
( sQ243_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f6865,f6412,f6707]) ).
fof(f6881,plain,
( sQ244_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f6866,f6382,f6711]) ).
fof(f6882,plain,
( sQ245_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f6867,f6382,f6715]) ).
fof(f6883,plain,
( sQ246_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f6868,f6393,f6719]) ).
fof(f6884,plain,
( sQ247_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f6869,f6412,f6723]) ).
fof(f6885,plain,
( sQ248_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f6870,f6412,f6727]) ).
fof(f6886,plain,
( sQ249_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f6871,f6382,f6731]) ).
fof(f6887,plain,
( sQ250_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f6872,f6382,f6735]) ).
fof(f7034,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X0 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2543,f2533]) ).
fof(f7036,definition,
! [X0] :
( sQ287_spl
<=> X0 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f7037,plain,
! [X0] :
( ~ sQ287_spl
| X0 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(component_clause,[status(thm)],[f7036]) ).
fof(f7039,definition,
( sQ288_spl
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f7042,plain,
( sQ288_spl
| sQ287_spl ),
inference(split_clause,[status(thm)],[f7034,f7036,f7039]) ).
fof(f7043,plain,
( ~ sQ287_spl
| $false ),
inference(destructive_equality_resolution,[status(thm)],[f7037]) ).
fof(f7044,plain,
~ sQ287_spl,
inference(contradiction_clause,[status(thm)],[f7043]) ).
fof(f7054,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(resolution,[status(thm)],[f1926,f1300]) ).
fof(f7055,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(resolution,[status(thm)],[f1926,f1297]) ).
fof(f7058,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) ),
inference(resolution,[status(thm)],[f1926,f1294]) ).
fof(f7059,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) ),
inference(resolution,[status(thm)],[f1926,f1291]) ).
fof(f7061,definition,
! [X0,X1] :
( sQ289_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(definition,[new_symbols(definition,[sQ289_spl])],[split_symbol_definition]) ).
fof(f7064,plain,
( ~ sQ7_spl
| sQ289_spl ),
inference(split_clause,[status(thm)],[f7054,f7061,f4829]) ).
fof(f7065,definition,
! [X0,X1] :
( sQ290_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f7068,plain,
( ~ sQ7_spl
| sQ290_spl ),
inference(split_clause,[status(thm)],[f7055,f7065,f4829]) ).
fof(f7080,definition,
! [X0,X1,X2] :
( sQ294_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f7083,plain,
( ~ sQ7_spl
| sQ294_spl ),
inference(split_clause,[status(thm)],[f7058,f7080,f4829]) ).
fof(f7084,definition,
! [X0,X1,X2] :
( sQ295_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f7087,plain,
( ~ sQ7_spl
| sQ295_spl ),
inference(split_clause,[status(thm)],[f7059,f7084,f4829]) ).
fof(f7094,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X2))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X1)) ),
inference(resolution,[status(thm)],[f1863,f1381]) ).
fof(f7095,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X2)) ),
inference(resolution,[status(thm)],[f1863,f1378]) ).
fof(f7098,definition,
! [X0,X1,X2] :
( sQ297_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f7101,plain,
( ~ sQ187_spl
| sQ297_spl ),
inference(split_clause,[status(thm)],[f7094,f7098,f6382]) ).
fof(f7102,definition,
! [X0,X1,X2] :
( sQ298_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f7105,plain,
( ~ sQ187_spl
| sQ298_spl ),
inference(split_clause,[status(thm)],[f7095,f7102,f6382]) ).
fof(f7114,definition,
! [X0] :
( sQ299_spl
<=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X0)) ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f7117,definition,
! [X1] :
( sQ300_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X1)) ),
introduced(definition,[new_symbols(definition,[sQ300_spl])],[split_symbol_definition]) ).
fof(f7118,plain,
! [X0] :
( ~ sQ300_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X0)) ),
inference(component_clause,[status(thm)],[f7117]) ).
fof(f7122,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1400,f1445]) ).
fof(f7123,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1400,f1353]) ).
fof(f7124,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1400,f1350]) ).
fof(f7127,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),hAPP(c_Complex_OIm,X1))))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1400]) ).
fof(f7128,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1400]) ).
fof(f7129,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1400]) ).
fof(f7130,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1400]) ).
fof(f7131,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1400]) ).
fof(f7132,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),hAPP(c_Complex_OIm,X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),hAPP(c_Complex_OIm,X1))),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X2),X1))))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1400]) ).
fof(f7133,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1400]) ).
fof(f7134,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1400]) ).
fof(f7135,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1400]) ).
fof(f7136,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1400]) ).
fof(f7138,plain,
( sQ256_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f7122,f6393,f6805]) ).
fof(f7139,plain,
( sQ257_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f7123,f6393,f6809]) ).
fof(f7140,plain,
( sQ258_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f7124,f6393,f6813]) ).
fof(f7142,plain,
( sQ259_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f7127,f6393,f6817]) ).
fof(f7143,plain,
( sQ260_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7128,f6412,f6821]) ).
fof(f7144,plain,
( sQ261_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7129,f6412,f6825]) ).
fof(f7145,plain,
( sQ262_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7130,f6382,f6829]) ).
fof(f7146,plain,
( sQ263_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7131,f6382,f6833]) ).
fof(f7147,plain,
( sQ264_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f7132,f6393,f6837]) ).
fof(f7148,plain,
( sQ265_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7133,f6412,f6841]) ).
fof(f7149,plain,
( sQ266_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7134,f6412,f6845]) ).
fof(f7150,plain,
( sQ267_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7135,f6382,f6849]) ).
fof(f7151,plain,
( sQ268_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7136,f6382,f6853]) ).
fof(f7154,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1403,f1857]) ).
fof(f7155,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1403,f1854]) ).
fof(f7159,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X0)),X2)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1403]) ).
fof(f7160,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1403]) ).
fof(f7161,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1403]) ).
fof(f7162,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1403]) ).
fof(f7163,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1403]) ).
fof(f7164,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(c_Complex_OIm,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X0)),X1)),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X2))))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1403]) ).
fof(f7165,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1403]) ).
fof(f7166,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X0))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1403]) ).
fof(f7167,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1403]) ).
fof(f7168,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X0))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1403]) ).
fof(f7171,definition,
! [X0,X1,X2] :
( sQ301_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ301_spl])],[split_symbol_definition]) ).
fof(f7174,plain,
( sQ301_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7154,f6382,f7171]) ).
fof(f7175,definition,
! [X0,X1,X2] :
( sQ302_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f7178,plain,
( sQ302_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7155,f6382,f7175]) ).
fof(f7179,definition,
! [X0,X1,X2] :
( sQ303_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X0)),X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f7182,plain,
( sQ303_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f7159,f6393,f7179]) ).
fof(f7183,definition,
! [X0,X1] :
( sQ304_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f7186,plain,
( sQ304_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7160,f6412,f7183]) ).
fof(f7187,definition,
! [X0,X1] :
( sQ305_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition]) ).
fof(f7190,plain,
( sQ305_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7161,f6412,f7187]) ).
fof(f7191,definition,
! [X0,X1] :
( sQ306_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ306_spl])],[split_symbol_definition]) ).
fof(f7194,plain,
( sQ306_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7162,f6382,f7191]) ).
fof(f7195,definition,
! [X0,X1] :
( sQ307_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f7198,plain,
( sQ307_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7163,f6382,f7195]) ).
fof(f7199,definition,
! [X0,X1,X2] :
( sQ308_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(c_Complex_OIm,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X0)),X1)),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X2)))) ) ),
introduced(definition,[new_symbols(definition,[sQ308_spl])],[split_symbol_definition]) ).
fof(f7202,plain,
( sQ308_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f7164,f6393,f7199]) ).
fof(f7203,definition,
! [X0,X1] :
( sQ309_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ309_spl])],[split_symbol_definition]) ).
fof(f7206,plain,
( sQ309_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7165,f6412,f7203]) ).
fof(f7207,definition,
! [X0,X1] :
( sQ310_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition]) ).
fof(f7210,plain,
( sQ310_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7166,f6412,f7207]) ).
fof(f7211,definition,
! [X0,X1] :
( sQ311_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition]) ).
fof(f7214,plain,
( sQ311_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7167,f6382,f7211]) ).
fof(f7215,definition,
! [X0,X1] :
( sQ312_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f7218,plain,
( sQ312_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7168,f6382,f7215]) ).
fof(f7219,plain,
( ~ sQ300_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7118,f4693]) ).
fof(f7220,plain,
~ sQ300_spl,
inference(contradiction_clause,[status(thm)],[f7219]) ).
fof(f7238,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X0))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))) ),
inference(resolution,[status(thm)],[f1968,f1381]) ).
fof(f7239,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2))) ),
inference(resolution,[status(thm)],[f1968,f1378]) ).
fof(f7240,definition,
! [X0,X1,X2] :
( sQ313_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X0))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ313_spl])],[split_symbol_definition]) ).
fof(f7243,plain,
( ~ sQ187_spl
| sQ313_spl ),
inference(split_clause,[status(thm)],[f7238,f7240,f6382]) ).
fof(f7244,definition,
! [X0,X1,X2] :
( sQ314_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ314_spl])],[split_symbol_definition]) ).
fof(f7247,plain,
( ~ sQ187_spl
| sQ314_spl ),
inference(split_clause,[status(thm)],[f7239,f7244,f6382]) ).
fof(f7248,plain,
! [X0] :
( X0 = X0
| ~ class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f2515,f1334]) ).
fof(f7286,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0))
| ~ class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2515,f1343]) ).
fof(f7290,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2515,f1403]) ).
fof(f7291,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2515,f1403]) ).
fof(f7292,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2515,f1400]) ).
fof(f7293,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2515,f1400]) ).
fof(f7300,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2515,f1384]) ).
fof(f7302,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2515,f1381]) ).
fof(f7303,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2515,f1381]) ).
fof(f7306,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2))
| ~ class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2515,f1343]) ).
fof(f7307,plain,
! [X0,X1,X2] :
( X0 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
| ~ class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2515,f1334]) ).
fof(f7312,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2515,f1300]) ).
fof(f7313,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2515,f1297]) ).
fof(f7314,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2515,f1294]) ).
fof(f7315,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2515,f1291]) ).
fof(f7372,plain,
( sQ117_spl
| ~ sQ108_spl ),
inference(split_clause,[status(thm)],[f7248,f5515,f5555]) ).
fof(f7378,definition,
! [X0,X1,X2] :
( sQ315_spl
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)) ),
introduced(definition,[new_symbols(definition,[sQ315_spl])],[split_symbol_definition]) ).
fof(f7381,plain,
( sQ315_spl
| ~ sQ141_spl ),
inference(split_clause,[status(thm)],[f7286,f5877,f7378]) ).
fof(f7388,definition,
! [X0,X1,X2] :
( sQ317_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ317_spl])],[split_symbol_definition]) ).
fof(f7391,plain,
( sQ317_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7290,f6382,f7388]) ).
fof(f7392,definition,
! [X0,X1,X2] :
( sQ318_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition]) ).
fof(f7395,plain,
( sQ318_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7291,f6382,f7392]) ).
fof(f7396,definition,
! [X0,X1,X2] :
( sQ319_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ319_spl])],[split_symbol_definition]) ).
fof(f7399,plain,
( sQ319_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7292,f6382,f7396]) ).
fof(f7400,definition,
! [X0,X1,X2] :
( sQ320_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f7403,plain,
( sQ320_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7293,f6382,f7400]) ).
fof(f7410,definition,
! [X0,X1,X2,X3] :
( sQ321_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ321_spl])],[split_symbol_definition]) ).
fof(f7413,plain,
( sQ321_spl
| ~ sQ222_spl ),
inference(split_clause,[status(thm)],[f7300,f6600,f7410]) ).
fof(f7415,definition,
! [X0,X1,X2] :
( sQ322_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f7418,plain,
( sQ322_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7302,f6382,f7415]) ).
fof(f7419,definition,
! [X0,X1,X2] :
( sQ323_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ323_spl])],[split_symbol_definition]) ).
fof(f7422,plain,
( sQ323_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7303,f6382,f7419]) ).
fof(f7425,definition,
! [X0,X1,X2] :
( sQ324_spl
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)) ),
introduced(definition,[new_symbols(definition,[sQ324_spl])],[split_symbol_definition]) ).
fof(f7428,plain,
( sQ324_spl
| ~ sQ141_spl ),
inference(split_clause,[status(thm)],[f7306,f5877,f7425]) ).
fof(f7429,definition,
! [X0,X1,X2] :
( sQ325_spl
<=> ( X0 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) ) ),
introduced(definition,[new_symbols(definition,[sQ325_spl])],[split_symbol_definition]) ).
fof(f7432,plain,
( sQ325_spl
| ~ sQ108_spl ),
inference(split_clause,[status(thm)],[f7307,f5515,f7429]) ).
fof(f7437,definition,
! [X0,X1] :
( sQ326_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(definition,[new_symbols(definition,[sQ326_spl])],[split_symbol_definition]) ).
fof(f7440,plain,
( sQ326_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f7312,f4829,f7437]) ).
fof(f7441,definition,
! [X0,X1] :
( sQ327_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(definition,[new_symbols(definition,[sQ327_spl])],[split_symbol_definition]) ).
fof(f7444,plain,
( sQ327_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f7313,f4829,f7441]) ).
fof(f7445,definition,
! [X0,X1,X2] :
( sQ328_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ328_spl])],[split_symbol_definition]) ).
fof(f7448,plain,
( sQ328_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f7314,f4829,f7445]) ).
fof(f7449,definition,
! [X0,X1,X2] :
( sQ329_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f7452,plain,
( sQ329_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f7315,f4829,f7449]) ).
fof(f7503,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0))
| ~ class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1343]) ).
fof(f7504,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1303]) ).
fof(f7507,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1403]) ).
fof(f7508,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1403]) ).
fof(f7509,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1400]) ).
fof(f7510,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1400]) ).
fof(f7517,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1384]) ).
fof(f7519,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1381]) ).
fof(f7520,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1381]) ).
fof(f7523,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2))
| ~ class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1343]) ).
fof(f7524,plain,
! [X0,X1,X2] :
( X0 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)
| ~ class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1334]) ).
fof(f7529,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1300]) ).
fof(f7530,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1297]) ).
fof(f7531,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1294]) ).
fof(f7532,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ~ class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1291]) ).
fof(f7575,definition,
! [X0,X1,X2] :
( sQ330_spl
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0)) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f7578,plain,
( sQ330_spl
| ~ sQ139_spl ),
inference(split_clause,[status(thm)],[f7503,f5870,f7575]) ).
fof(f7579,definition,
! [X0,X1] :
( sQ331_spl
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0)))) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f7582,plain,
( sQ331_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f7504,f5170,f7579]) ).
fof(f7585,definition,
! [X0,X1,X2] :
( sQ332_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f7588,plain,
( sQ332_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7507,f6412,f7585]) ).
fof(f7589,definition,
! [X0,X1,X2] :
( sQ333_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f7592,plain,
( sQ333_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7508,f6412,f7589]) ).
fof(f7593,definition,
! [X0,X1,X2] :
( sQ334_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f7596,plain,
( sQ334_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7509,f6412,f7593]) ).
fof(f7597,definition,
! [X0,X1,X2] :
( sQ335_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f7600,plain,
( sQ335_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7510,f6412,f7597]) ).
fof(f7607,definition,
! [X0,X1,X2,X3] :
( sQ336_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition]) ).
fof(f7610,plain,
( sQ336_spl
| ~ sQ228_spl ),
inference(split_clause,[status(thm)],[f7517,f6623,f7607]) ).
fof(f7612,definition,
! [X0,X1,X2] :
( sQ337_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).
fof(f7615,plain,
( sQ337_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7519,f6412,f7612]) ).
fof(f7616,definition,
! [X0,X1,X2] :
( sQ338_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).
fof(f7619,plain,
( sQ338_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7520,f6412,f7616]) ).
fof(f7622,definition,
! [X0,X1,X2] :
( sQ339_spl
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)) ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f7625,plain,
( sQ339_spl
| ~ sQ139_spl ),
inference(split_clause,[status(thm)],[f7523,f5870,f7622]) ).
fof(f7626,definition,
! [X0,X1,X2] :
( sQ340_spl
<=> ( X0 = X2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2) ) ),
introduced(definition,[new_symbols(definition,[sQ340_spl])],[split_symbol_definition]) ).
fof(f7629,plain,
( sQ340_spl
| ~ sQ106_spl ),
inference(split_clause,[status(thm)],[f7524,f5508,f7626]) ).
fof(f7634,definition,
! [X0,X1] :
( sQ341_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
introduced(definition,[new_symbols(definition,[sQ341_spl])],[split_symbol_definition]) ).
fof(f7637,plain,
( sQ341_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f7529,f4887,f7634]) ).
fof(f7638,definition,
! [X0,X1] :
( sQ342_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
introduced(definition,[new_symbols(definition,[sQ342_spl])],[split_symbol_definition]) ).
fof(f7641,plain,
( sQ342_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f7530,f4887,f7638]) ).
fof(f7642,definition,
! [X0,X1,X2] :
( sQ343_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ343_spl])],[split_symbol_definition]) ).
fof(f7645,plain,
( sQ343_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f7531,f4887,f7642]) ).
fof(f7646,definition,
! [X0,X1,X2] :
( sQ344_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ344_spl])],[split_symbol_definition]) ).
fof(f7649,plain,
( sQ344_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f7532,f4887,f7646]) ).
fof(f7700,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X0)) ),
inference(resolution,[status(thm)],[f1872,f4693]) ).
fof(f7711,plain,
sQ299_spl,
inference(split_clause,[status(thm)],[f7700,f7114]) ).
fof(f7716,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1406,f1857]) ).
fof(f7717,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1406,f1854]) ).
fof(f7721,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),hAPP(c_Complex_OIm,X1))))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1406]) ).
fof(f7722,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1406]) ).
fof(f7723,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1406]) ).
fof(f7726,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1406]) ).
fof(f7727,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1406]) ).
fof(f7730,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),hAPP(c_Complex_OIm,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),hAPP(c_Complex_OIm,X1))),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X2),X1))))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1406]) ).
fof(f7731,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1406]) ).
fof(f7732,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1406]) ).
fof(f7735,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1406]) ).
fof(f7736,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1406]) ).
fof(f7742,definition,
! [X0,X1,X2] :
( sQ345_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ345_spl])],[split_symbol_definition]) ).
fof(f7745,plain,
( sQ345_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7716,f6382,f7742]) ).
fof(f7746,definition,
! [X0,X1,X2] :
( sQ346_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ346_spl])],[split_symbol_definition]) ).
fof(f7749,plain,
( sQ346_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7717,f6382,f7746]) ).
fof(f7750,definition,
! [X0,X1,X2] :
( sQ347_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),hAPP(c_Complex_OIm,X1)))) ) ),
introduced(definition,[new_symbols(definition,[sQ347_spl])],[split_symbol_definition]) ).
fof(f7753,plain,
( sQ347_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f7721,f6393,f7750]) ).
fof(f7754,definition,
! [X0,X1] :
( sQ348_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ348_spl])],[split_symbol_definition]) ).
fof(f7757,plain,
( sQ348_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7722,f6412,f7754]) ).
fof(f7758,definition,
! [X0,X1] :
( sQ349_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ),
introduced(definition,[new_symbols(definition,[sQ349_spl])],[split_symbol_definition]) ).
fof(f7761,plain,
( sQ349_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7723,f6412,f7758]) ).
fof(f7764,definition,
! [X0,X1] :
( sQ350_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f7767,plain,
( sQ350_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7726,f6382,f7764]) ).
fof(f7768,definition,
! [X0,X1] :
( sQ351_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition]) ).
fof(f7771,plain,
( sQ351_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7727,f6382,f7768]) ).
fof(f7774,definition,
! [X0,X1,X2] :
( sQ352_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),hAPP(c_Complex_OIm,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),hAPP(c_Complex_OIm,X1))),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X2),X1)))) ) ),
introduced(definition,[new_symbols(definition,[sQ352_spl])],[split_symbol_definition]) ).
fof(f7777,plain,
( sQ352_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f7730,f6393,f7774]) ).
fof(f7778,definition,
! [X0,X1] :
( sQ353_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ353_spl])],[split_symbol_definition]) ).
fof(f7781,plain,
( sQ353_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7731,f6412,f7778]) ).
fof(f7782,definition,
! [X0,X1] :
( sQ354_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f7785,plain,
( sQ354_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f7732,f6412,f7782]) ).
fof(f7788,definition,
! [X0,X1] :
( sQ355_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ355_spl])],[split_symbol_definition]) ).
fof(f7791,plain,
( sQ355_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7735,f6382,f7788]) ).
fof(f7792,definition,
! [X0,X1] :
( sQ356_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ356_spl])],[split_symbol_definition]) ).
fof(f7795,plain,
( sQ356_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f7736,f6382,f7792]) ).
fof(f7799,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1409,f1827]) ).
fof(f7800,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X0))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1409,f1826]) ).
fof(f7801,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1409,f1926]) ).
fof(f7803,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1409,f1446]) ).
fof(f7804,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X0))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1409,f4666]) ).
fof(f7807,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X2)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0)),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1409]) ).
fof(f7808,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1409]) ).
fof(f7809,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1409]) ).
fof(f7810,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1409]) ).
fof(f7812,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1409]) ).
fof(f7813,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1409]) ).
fof(f7814,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2515,f1409]) ).
fof(f7816,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X3))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),hAPP(c_Complex_OIm,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),hAPP(c_Complex_OIm,X1)))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1409]) ).
fof(f7817,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1409]) ).
fof(f7818,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1409]) ).
fof(f7821,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1409]) ).
fof(f7822,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1409]) ).
fof(f7825,definition,
( sQ357_spl
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(definition,[new_symbols(definition,[sQ357_spl])],[split_symbol_definition]) ).
fof(f7827,plain,
( sQ357_spl
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(component_clause,[status(thm)],[f7825]) ).
fof(f7829,definition,
! [X0,X1,X2] :
( sQ358_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ358_spl])],[split_symbol_definition]) ).
fof(f7832,plain,
( sQ358_spl
| ~ sQ357_spl ),
inference(split_clause,[status(thm)],[f7799,f7825,f7829]) ).
fof(f7833,definition,
! [X0,X1,X2] :
( sQ359_spl
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f7836,plain,
( sQ359_spl
| ~ sQ357_spl ),
inference(split_clause,[status(thm)],[f7800,f7825,f7833]) ).
fof(f7837,definition,
! [X0,X1,X2,X3] :
( sQ360_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ360_spl])],[split_symbol_definition]) ).
fof(f7840,plain,
( sQ360_spl
| ~ sQ357_spl ),
inference(split_clause,[status(thm)],[f7801,f7825,f7837]) ).
fof(f7842,definition,
( sQ361_spl
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ361_spl])],[split_symbol_definition]) ).
fof(f7844,plain,
( sQ361_spl
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f7842]) ).
fof(f7845,definition,
! [X0,X1,X2,X3] :
( sQ362_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ362_spl])],[split_symbol_definition]) ).
fof(f7848,plain,
( sQ362_spl
| ~ sQ361_spl ),
inference(split_clause,[status(thm)],[f7803,f7842,f7845]) ).
fof(f7849,definition,
! [X0] :
( sQ363_spl
<=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X0)) ),
introduced(definition,[new_symbols(definition,[sQ363_spl])],[split_symbol_definition]) ).
fof(f7852,plain,
( sQ363_spl
| ~ sQ361_spl ),
inference(split_clause,[status(thm)],[f7804,f7842,f7849]) ).
fof(f7853,definition,
! [X0,X1,X2,X3] :
( sQ364_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X0),X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X2)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ364_spl])],[split_symbol_definition]) ).
fof(f7856,plain,
( sQ364_spl
| ~ sQ361_spl ),
inference(split_clause,[status(thm)],[f7807,f7842,f7853]) ).
fof(f7857,definition,
( sQ365_spl
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition]) ).
fof(f7859,plain,
( sQ365_spl
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
inference(component_clause,[status(thm)],[f7857]) ).
fof(f7860,definition,
! [X0,X1,X2] :
( sQ366_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f7863,plain,
( sQ366_spl
| ~ sQ365_spl ),
inference(split_clause,[status(thm)],[f7808,f7857,f7860]) ).
fof(f7864,definition,
! [X0,X1,X2] :
( sQ367_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f7867,plain,
( sQ367_spl
| ~ sQ365_spl ),
inference(split_clause,[status(thm)],[f7809,f7857,f7864]) ).
fof(f7868,definition,
! [X0,X1,X2,X3] :
( sQ368_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ368_spl])],[split_symbol_definition]) ).
fof(f7871,plain,
( sQ368_spl
| ~ sQ365_spl ),
inference(split_clause,[status(thm)],[f7810,f7857,f7868]) ).
fof(f7873,definition,
! [X0,X1,X2] :
( sQ369_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ369_spl])],[split_symbol_definition]) ).
fof(f7876,plain,
( sQ369_spl
| ~ sQ357_spl ),
inference(split_clause,[status(thm)],[f7812,f7825,f7873]) ).
fof(f7877,definition,
! [X0,X1,X2] :
( sQ370_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ370_spl])],[split_symbol_definition]) ).
fof(f7880,plain,
( sQ370_spl
| ~ sQ357_spl ),
inference(split_clause,[status(thm)],[f7813,f7825,f7877]) ).
fof(f7881,definition,
! [X0,X1,X2,X3] :
( sQ371_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ371_spl])],[split_symbol_definition]) ).
fof(f7884,plain,
( sQ371_spl
| ~ sQ357_spl ),
inference(split_clause,[status(thm)],[f7814,f7825,f7881]) ).
fof(f7886,definition,
! [X0,X1,X2,X3] :
( sQ372_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X0),X2)),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X1),X3))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),hAPP(c_Complex_OIm,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),hAPP(c_Complex_OIm,X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ372_spl])],[split_symbol_definition]) ).
fof(f7889,plain,
( sQ372_spl
| ~ sQ361_spl ),
inference(split_clause,[status(thm)],[f7816,f7842,f7886]) ).
fof(f7890,definition,
! [X0,X1,X2] :
( sQ373_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
introduced(definition,[new_symbols(definition,[sQ373_spl])],[split_symbol_definition]) ).
fof(f7893,plain,
( sQ373_spl
| ~ sQ365_spl ),
inference(split_clause,[status(thm)],[f7817,f7857,f7890]) ).
fof(f7894,definition,
! [X0,X1,X2] :
( sQ374_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f7897,plain,
( sQ374_spl
| ~ sQ365_spl ),
inference(split_clause,[status(thm)],[f7818,f7857,f7894]) ).
fof(f7900,definition,
! [X0,X1,X2] :
( sQ375_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition]) ).
fof(f7903,plain,
( sQ375_spl
| ~ sQ357_spl ),
inference(split_clause,[status(thm)],[f7821,f7825,f7900]) ).
fof(f7904,definition,
! [X0,X1,X2] :
( sQ376_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ376_spl])],[split_symbol_definition]) ).
fof(f7907,plain,
( sQ376_spl
| ~ sQ357_spl ),
inference(split_clause,[status(thm)],[f7822,f7825,f7904]) ).
fof(f7910,plain,
( sQ357_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7827,f4358]) ).
fof(f7911,plain,
sQ357_spl,
inference(contradiction_clause,[status(thm)],[f7910]) ).
fof(f7912,plain,
( sQ365_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7859,f4305]) ).
fof(f7913,plain,
sQ365_spl,
inference(contradiction_clause,[status(thm)],[f7912]) ).
fof(f7914,plain,
( sQ361_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7844,f4396]) ).
fof(f7915,plain,
sQ361_spl,
inference(contradiction_clause,[status(thm)],[f7914]) ).
fof(f7917,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1412,f1827]) ).
fof(f7918,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(resolution,[status(thm)],[f1412,f1926]) ).
fof(f7920,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1412,f1446]) ).
fof(f7924,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X2),X0))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X2)),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0)),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1412]) ).
fof(f7925,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1412]) ).
fof(f7926,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1412]) ).
fof(f7927,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1412]) ).
fof(f7929,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1412]) ).
fof(f7930,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1412]) ).
fof(f7931,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2515,f1412]) ).
fof(f7933,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X2)),X0)),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X2),X1))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),hAPP(c_Complex_OIm,X1)))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1798,f1412]) ).
fof(f7934,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3324,f1412]) ).
fof(f7935,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3319,f1412]) ).
fof(f7936,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
inference(paramodulation,[status(thm)],[f3348,f1412]) ).
fof(f7938,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2458,f1412]) ).
fof(f7939,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2451,f1412]) ).
fof(f7940,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f2515,f1412]) ).
fof(f7943,definition,
! [X0,X1] :
( sQ377_spl
<=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)),X1)) ),
introduced(definition,[new_symbols(definition,[sQ377_spl])],[split_symbol_definition]) ).
fof(f7946,plain,
( sQ377_spl
| ~ sQ357_spl ),
inference(split_clause,[status(thm)],[f7917,f7825,f7943]) ).
fof(f7947,definition,
! [X0,X1,X2] :
( sQ378_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ378_spl])],[split_symbol_definition]) ).
fof(f7950,plain,
( sQ378_spl
| ~ sQ357_spl ),
inference(split_clause,[status(thm)],[f7918,f7825,f7947]) ).
fof(f7952,definition,
! [X0,X1,X2] :
( sQ379_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X2),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ379_spl])],[split_symbol_definition]) ).
fof(f7955,plain,
( sQ379_spl
| ~ sQ361_spl ),
inference(split_clause,[status(thm)],[f7920,f7842,f7952]) ).
fof(f7957,definition,
! [X0,X1,X2] :
( sQ380_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X2),X0))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X2)),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ380_spl])],[split_symbol_definition]) ).
fof(f7960,plain,
( sQ380_spl
| ~ sQ361_spl ),
inference(split_clause,[status(thm)],[f7924,f7842,f7957]) ).
fof(f7961,definition,
! [X0,X1] :
( sQ381_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ381_spl])],[split_symbol_definition]) ).
fof(f7964,plain,
( sQ381_spl
| ~ sQ365_spl ),
inference(split_clause,[status(thm)],[f7925,f7857,f7961]) ).
fof(f7965,definition,
! [X0,X1] :
( sQ382_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ382_spl])],[split_symbol_definition]) ).
fof(f7968,plain,
( sQ382_spl
| ~ sQ365_spl ),
inference(split_clause,[status(thm)],[f7926,f7857,f7965]) ).
fof(f7969,definition,
! [X0,X1,X2] :
( sQ383_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ383_spl])],[split_symbol_definition]) ).
fof(f7972,plain,
( sQ383_spl
| ~ sQ365_spl ),
inference(split_clause,[status(thm)],[f7927,f7857,f7969]) ).
fof(f7974,definition,
! [X0,X1] :
( sQ384_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ384_spl])],[split_symbol_definition]) ).
fof(f7977,plain,
( sQ384_spl
| ~ sQ357_spl ),
inference(split_clause,[status(thm)],[f7929,f7825,f7974]) ).
fof(f7978,definition,
! [X0,X1] :
( sQ385_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ385_spl])],[split_symbol_definition]) ).
fof(f7981,plain,
( sQ385_spl
| ~ sQ357_spl ),
inference(split_clause,[status(thm)],[f7930,f7825,f7978]) ).
fof(f7982,definition,
! [X0,X1,X2] :
( sQ386_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ386_spl])],[split_symbol_definition]) ).
fof(f7985,plain,
( sQ386_spl
| ~ sQ357_spl ),
inference(split_clause,[status(thm)],[f7931,f7825,f7982]) ).
fof(f7987,definition,
! [X0,X1,X2] :
( sQ387_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X2)),X0)),hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),X2),X1))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),hAPP(c_Complex_OIm,X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ387_spl])],[split_symbol_definition]) ).
fof(f7990,plain,
( sQ387_spl
| ~ sQ361_spl ),
inference(split_clause,[status(thm)],[f7933,f7842,f7987]) ).
fof(f7991,definition,
! [X0,X1] :
( sQ388_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ388_spl])],[split_symbol_definition]) ).
fof(f7994,plain,
( sQ388_spl
| ~ sQ365_spl ),
inference(split_clause,[status(thm)],[f7934,f7857,f7991]) ).
fof(f7995,definition,
! [X0,X1] :
( sQ389_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f7998,plain,
( sQ389_spl
| ~ sQ365_spl ),
inference(split_clause,[status(thm)],[f7935,f7857,f7995]) ).
fof(f7999,definition,
! [X0,X1,X2] :
( sQ390_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ390_spl])],[split_symbol_definition]) ).
fof(f8002,plain,
( sQ390_spl
| ~ sQ365_spl ),
inference(split_clause,[status(thm)],[f7936,f7857,f7999]) ).
fof(f8004,definition,
! [X0,X1] :
( sQ391_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ391_spl])],[split_symbol_definition]) ).
fof(f8007,plain,
( sQ391_spl
| ~ sQ357_spl ),
inference(split_clause,[status(thm)],[f7938,f7825,f8004]) ).
fof(f8008,definition,
! [X0,X1] :
( sQ392_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(definition,[new_symbols(definition,[sQ392_spl])],[split_symbol_definition]) ).
fof(f8011,plain,
( sQ392_spl
| ~ sQ357_spl ),
inference(split_clause,[status(thm)],[f7939,f7825,f8008]) ).
fof(f8012,definition,
! [X0,X1,X2] :
( sQ393_spl
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ393_spl])],[split_symbol_definition]) ).
fof(f8015,plain,
( sQ393_spl
| ~ sQ357_spl ),
inference(split_clause,[status(thm)],[f7940,f7825,f8012]) ).
fof(f8033,plain,
( sQ83_spl
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f5321,f1321]) ).
fof(f8034,definition,
( sQ395_spl
<=> c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ395_spl])],[split_symbol_definition]) ).
fof(f8035,plain,
( ~ sQ395_spl
| c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f8034]) ).
fof(f8037,plain,
( sQ83_spl
| sQ43_spl
| sQ395_spl
| ~ sQ102_spl ),
inference(split_clause,[status(thm)],[f8033,f5473,f8034,f5051,f5319]) ).
fof(f8038,plain,
( sQ44_spl
| sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5056,f6741]) ).
fof(f8039,plain,
( sQ44_spl
| sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f8038]) ).
fof(f8043,plain,
( sQ52_spl
| ~ sQ395_spl
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(forward_demodulation,[status(thm)],[f8035,f5128]) ).
fof(f8044,plain,
( sQ52_spl
| ~ sQ395_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8043,f1355]) ).
fof(f8045,plain,
( sQ52_spl
| ~ sQ395_spl ),
inference(contradiction_clause,[status(thm)],[f8044]) ).
fof(f8046,plain,
$false,
inference(sat_refutation,[status(thm)],[f4661,f4828,f4838,f4841,f4843,f4852,f4862,f4905,f4925,f4927,f4933,f4944,f4948,f4952,f4965,f4970,f4974,f4978,f4986,f4994,f5007,f5012,f5016,f5020,f5028,f5032,f5036,f5057,f5061,f5077,f5106,f5132,f5136,f5157,f5161,f5165,f5169,f5176,f5180,f5195,f5199,f5201,f5206,f5322,f5340,f5348,f5387,f5414,f5418,f5422,f5426,f5430,f5443,f5476,f5481,f5485,f5489,f5492,f5514,f5521,f5530,f5534,f5538,f5542,f5546,f5560,f5562,f5627,f5629,f5665,f5670,f5674,f5682,f5685,f5701,f5702,f5705,f5706,f5707,f5708,f5709,f5794,f5823,f5826,f5830,f5835,f5851,f5855,f5876,f5883,f5890,f5894,f5898,f5902,f5906,f5908,f5910,f5916,f5920,f5952,f5954,f6029,f6058,f6062,f6069,f6071,f6075,f6134,f6140,f6305,f6307,f6309,f6311,f6319,f6321,f6323,f6325,f6327,f6388,f6392,f6399,f6403,f6407,f6411,f6418,f6422,f6426,f6430,f6434,f6438,f6442,f6446,f6450,f6452,f6454,f6456,f6466,f6503,f6533,f6542,f6547,f6551,f6555,f6559,f6563,f6567,f6571,f6575,f6579,f6583,f6610,f6614,f6618,f6622,f6629,f6633,f6637,f6641,f6645,f6649,f6653,f6657,f6661,f6663,f6665,f6667,f6748,f6750,f6763,f6768,f6783,f6787,f6874,f6875,f6876,f6878,f6879,f6880,f6881,f6882,f6883,f6884,f6885,f6886,f6887,f7042,f7044,f7064,f7068,f7083,f7087,f7101,f7105,f7138,f7139,f7140,f7142,f7143,f7144,f7145,f7146,f7147,f7148,f7149,f7150,f7151,f7174,f7178,f7182,f7186,f7190,f7194,f7198,f7202,f7206,f7210,f7214,f7218,f7220,f7243,f7247,f7372,f7381,f7391,f7395,f7399,f7403,f7413,f7418,f7422,f7428,f7432,f7440,f7444,f7448,f7452,f7578,f7582,f7588,f7592,f7596,f7600,f7610,f7615,f7619,f7625,f7629,f7637,f7641,f7645,f7649,f7711,f7745,f7749,f7753,f7757,f7761,f7767,f7771,f7777,f7781,f7785,f7791,f7795,f7832,f7836,f7840,f7848,f7852,f7856,f7863,f7867,f7871,f7876,f7880,f7884,f7889,f7893,f7897,f7903,f7907,f7911,f7913,f7915,f7946,f7950,f7955,f7960,f7964,f7968,f7972,f7977,f7981,f7985,f7990,f7994,f7998,f8002,f8007,f8011,f8015,f8037,f8039,f8045]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW208+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n008.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 09:42:10 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.27/0.61 % Drodi V4.1.1
% 0.42/0.83 % Refutation found
% 0.42/0.83 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.42/0.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.42/0.89 % Elapsed time: 0.440491 seconds
% 0.42/0.89 % CPU time: 2.024119 seconds
% 0.42/0.89 % Total memory used: 228.195 MB
% 0.42/0.89 % Net memory used: 227.014 MB
%------------------------------------------------------------------------------