TSTP Solution File: SWW177+1 by E-SAT---3.2.0
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%------------------------------------------------------------------------------
% File : E-SAT---3.2.0
% Problem : SWW177+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d SAT
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:13:44 EDT 2024
% Result : Theorem 177.47s 23.18s
% Output : CNFRefutation 177.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 72
% Syntax : Number of formulae : 295 ( 112 unt; 0 def)
% Number of atoms : 729 ( 177 equ)
% Maximal formula atoms : 62 ( 2 avg)
% Number of connectives : 742 ( 308 ~; 306 |; 47 &)
% ( 20 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 477 ( 7 sgn 261 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_real__less__def,axiom,
! [X9,X10] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10,X9)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X9)
& X10 != X9 ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_real__less__def) ).
fof(conj_2,conjecture,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d1)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d2) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',conj_2) ).
fof(fact_mult__2__right,axiom,
! [X26,X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Otimes__class_Otimes(X5,X26,c_Int_Onumber__class_Onumber__of(X5,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X5,X26,X26) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_mult__2__right) ).
fof(fact_Bit0__def,axiom,
! [X21] : c_Int_OBit0(X21) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X21),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_Bit0__def) ).
fof(fact_Bit1__def,axiom,
! [X21] : c_Int_OBit1(X21) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X21),X21),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_Bit1__def) ).
fof(fact_add__Pls__right,axiom,
! [X21] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Int_OPls) = X21,
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_add__Pls__right) ).
fof(fact_min__less__iff__conj,axiom,
! [X9,X10,X25,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X25,c_Orderings_Oord__class_Omin(X5,X10,X9))
<=> ( c_Orderings_Oord__class_Oless(X5,X25,X10)
& c_Orderings_Oord__class_Oless(X5,X25,X9) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_min__less__iff__conj) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X10,X9)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X10,X9)
<=> X10 = X9 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_linorder__antisym__conv2) ).
fof(fact_real__le__trans,axiom,
! [X21,X41,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X42,X41)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X41,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X42,X21) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_real__le__trans) ).
fof(fact_real__mult__1,axiom,
! [X26] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X26) = X26,
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_real__mult__1) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(fact_min__max_Oless__infI1,axiom,
! [X24,X8,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X7,X8)
=> c_Orderings_Oord__class_Oless(X5,c_Orderings_Oord__class_Omin(X5,X7,X24),X8) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_min__max_Oless__infI1) ).
fof(fact_min__max_Ole__infI1,axiom,
! [X24,X8,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X7,X8)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Orderings_Oord__class_Omin(X5,X7,X24),X8) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_min__max_Ole__infI1) ).
fof(fact_sum__squares__le__zero__iff,axiom,
! [X9,X10,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,c_Groups_Otimes__class_Otimes(X5,X10,X10),c_Groups_Otimes__class_Otimes(X5,X9,X9)),c_Groups_Ozero__class_Ozero(X5))
<=> ( X10 = c_Groups_Ozero__class_Ozero(X5)
& X9 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_sum__squares__le__zero__iff) ).
fof(fact_add__0__right,axiom,
! [X7,X5] :
( class_Groups_Omonoid__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,X7,c_Groups_Ozero__class_Ozero(X5)) = X7 ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_add__0__right) ).
fof(fact_mult_Ozero__right,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> c_Groups_Otimes__class_Otimes(X5,X7,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_mult_Ozero__right) ).
fof(fact_zadd__commute,axiom,
! [X27,X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X27) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X27,X26),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_zadd__commute) ).
fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(fact_less__divide__eq,axiom,
! [X43,X11,X12,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X12,c_Rings_Oinverse__class_Odivide(X5,X11,X43))
<=> ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X43)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Otimes__class_Otimes(X5,X12,X43),X11) )
& ( ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X43)
=> ( ( c_Orderings_Oord__class_Oless(X5,X43,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,X11,c_Groups_Otimes__class_Otimes(X5,X12,X43)) )
& ( ~ c_Orderings_Oord__class_Oless(X5,X43,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ozero__class_Ozero(X5)) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_less__divide__eq) ).
fof(fact_mult_Ozero__left,axiom,
! [X24,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> c_Groups_Otimes__class_Otimes(X5,c_Groups_Ozero__class_Ozero(X5),X24) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_mult_Ozero__left) ).
fof(fact_zero__less__two,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_zero__less__two) ).
fof(fact_real__le__refl,axiom,
! [X27] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27,X27),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_real__le__refl) ).
fof(fact_zminus__zminus,axiom,
! [X26] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X26)) = X26,
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_zminus__zminus) ).
fof(fact_mult__Min,axiom,
! [X21] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,X21) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X21),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_mult__Min) ).
fof(conj_1,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d2),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',conj_1) ).
fof(fact_real__add__mult__distrib,axiom,
! [X27,X50,X51] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X51,X50),X27) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X51,X27),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X50,X27)),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_real__add__mult__distrib) ).
fof(fact_real__mult__commute,axiom,
! [X27,X26] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X26,X27) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X27,X26),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_real__mult__commute) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(fact_min__max_Oinf_Ocommute,axiom,
! [X24,X7,X5] :
( class_Orderings_Olinorder(X5)
=> c_Orderings_Oord__class_Omin(X5,X7,X24) = c_Orderings_Oord__class_Omin(X5,X24,X7) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_min__max_Oinf_Ocommute) ).
fof(fact_xt1_I8_J,axiom,
! [X26,X8,X13,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X8)
=> ( c_Orderings_Oord__class_Oless(X5,X26,X13)
=> c_Orderings_Oord__class_Oless(X5,X26,X8) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_xt1_I8_J) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X13,X8,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( X8 != X13
=> ( ~ c_Orderings_Oord__class_Oless(X5,X8,X13)
=> c_Orderings_Oord__class_Oless(X5,X13,X8) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_mult__2,axiom,
! [X26,X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Otimes__class_Otimes(X5,c_Int_Onumber__class_Onumber__of(X5,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X26) = c_Groups_Oplus__class_Oplus(X5,X26,X26) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_mult__2) ).
fof(fact_number__of__is__id,axiom,
! [X21] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X21) = X21,
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_number__of__is__id) ).
fof(conj_0,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d1),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',conj_0) ).
fof(fact_leD,axiom,
! [X8,X13,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X8)
=> ~ c_Orderings_Oord__class_Oless(X5,X8,X13) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_leD) ).
fof(fact_xt1_I6_J,axiom,
! [X26,X8,X13,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X8)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X26,X13)
=> c_Orderings_Oord__class_Oless__eq(X5,X26,X8) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_xt1_I6_J) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X23,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X7,X23) = c_Groups_Oplus__class_Oplus(X5,X23,X7) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_real__sum__of__halves,axiom,
! [X8] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X8,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X8,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X8,
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_real__sum__of__halves) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(arity_Int__Oint__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',arity_Int__Oint__Int_Onumber__ring) ).
fof(fact_real__add__less__0__iff,axiom,
! [X9,X10] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X9,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10)) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_real__add__less__0__iff) ).
fof(fact_neg__less__iff__less,axiom,
! [X12,X11,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X11),c_Groups_Ouminus__class_Ouminus(X5,X12))
<=> c_Orderings_Oord__class_Oless(X5,X12,X11) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_neg__less__iff__less) ).
fof(fact_real__diff__def,axiom,
! [X38,X6] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X6,X38) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X38)),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_real__diff__def) ).
fof(fact_add__left__cancel,axiom,
! [X43,X11,X12,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,X12,X11) = c_Groups_Oplus__class_Oplus(X5,X12,X43)
<=> X11 = X43 ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_add__left__cancel) ).
fof(fact_diff__add__cancel,axiom,
! [X24,X7,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ominus__class_Ominus(X5,X7,X24),X24) = X7 ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_diff__add__cancel) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(fact_add__0__iff,axiom,
! [X12,X11,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X11 = c_Groups_Oplus__class_Oplus(X5,X11,X12)
<=> X12 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_add__0__iff) ).
fof(fact_add__special_I2_J,axiom,
! [X27,X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Oone__class_Oone(X5),c_Int_Onumber__class_Onumber__of(X5,X27)) = c_Int_Onumber__class_Onumber__of(X5,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X27)) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_add__special_I2_J) ).
fof(fact_zadd__zminus__inverse2,axiom,
! [X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X26),X26) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_zadd__zminus__inverse2) ).
fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_Pls__def) ).
fof(fact_zless__le,axiom,
! [X15,X25] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,X15)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,X15)
& X25 != X15 ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_zless__le) ).
fof(fact_min__max_Oinf__le2,axiom,
! [X13,X8,X5] :
( class_Orderings_Olinorder(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Orderings_Oord__class_Omin(X5,X8,X13),X13) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_min__max_Oinf__le2) ).
fof(fact_less__special_I3_J,axiom,
! [X10,X5] :
( ( class_Int_Onumber__ring(X5)
& class_Rings_Olinordered__idom(X5) )
=> ( c_Orderings_Oord__class_Oless(X5,c_Int_Onumber__class_Onumber__of(X5,X10),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X10,c_Int_OPls) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_less__special_I3_J) ).
fof(fact_zmult__1__right,axiom,
! [X26] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X26,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X26,
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_zmult__1__right) ).
fof(fact_min__less__iff__disj,axiom,
! [X25,X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Orderings_Oord__class_Omin(X5,X10,X9),X25)
<=> ( c_Orderings_Oord__class_Oless(X5,X10,X25)
| c_Orderings_Oord__class_Oless(X5,X9,X25) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_min__less__iff__disj) ).
fof(fact_semiring__norm_I112_J,axiom,
! [X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Int_Onumber__class_Onumber__of(X5,c_Int_OPls) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_semiring__norm_I112_J) ).
fof(fact_order__less__trans,axiom,
! [X26,X13,X8,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X8,X13)
=> ( c_Orderings_Oord__class_Oless(X5,X13,X26)
=> c_Orderings_Oord__class_Oless(X5,X8,X26) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_order__less__trans) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(fact_real__0__less__add__iff,axiom,
! [X9,X10] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X9))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10),X9) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_real__0__less__add__iff) ).
fof(fact_minus__less__iff,axiom,
! [X11,X12,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X12),X11)
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X11),X12) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_minus__less__iff) ).
fof(fact_minus__minus,axiom,
! [X7,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ouminus__class_Ouminus(X5,X7)) = X7 ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_minus__minus) ).
fof(fact_real__add__le__0__iff,axiom,
! [X9,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10)) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_real__add__le__0__iff) ).
fof(fact_less__minus__self__iff,axiom,
! [X12,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ouminus__class_Ouminus(X5,X12))
<=> c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p',fact_less__minus__self__iff) ).
fof(c_0_72,plain,
! [X9,X10] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10,X9)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X9)
& X10 != X9 ) ),
inference(fof_simplification,[status(thm)],[fact_real__less__def]) ).
fof(c_0_73,negated_conjecture,
~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d1)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d2) ),
inference(assume_negation,[status(cth)],[conj_2]) ).
fof(c_0_74,plain,
! [X1183,X1184] :
( ~ class_Int_Onumber__ring(X1184)
| c_Groups_Otimes__class_Otimes(X1184,X1183,c_Int_Onumber__class_Onumber__of(X1184,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1184,X1183,X1183) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])])]) ).
fof(c_0_75,plain,
! [X1739] : c_Int_OBit0(X1739) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1739,X1739),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_76,plain,
! [X1888] : c_Int_OBit1(X1888) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1888),X1888),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(c_0_77,plain,
! [X795,X796] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X796,X795)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X796,X795) )
& ( X796 != X795
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X796,X795) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X796,X795)
| X796 = X795
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X796,X795) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])])])]) ).
fof(c_0_78,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d2) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_73])]) ).
cnf(c_0_79,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_80,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_81,plain,
c_Int_OBit1(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
fof(c_0_82,plain,
! [X1738] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1738,c_Int_OPls) = X1738,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
cnf(c_0_83,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
fof(c_0_84,plain,
! [X178,X179,X180,X181] :
( ( c_Orderings_Oord__class_Oless(X181,X180,X179)
| ~ c_Orderings_Oord__class_Oless(X181,X180,c_Orderings_Oord__class_Omin(X181,X179,X178))
| ~ class_Orderings_Olinorder(X181) )
& ( c_Orderings_Oord__class_Oless(X181,X180,X178)
| ~ c_Orderings_Oord__class_Oless(X181,X180,c_Orderings_Oord__class_Omin(X181,X179,X178))
| ~ class_Orderings_Olinorder(X181) )
& ( ~ c_Orderings_Oord__class_Oless(X181,X180,X179)
| ~ c_Orderings_Oord__class_Oless(X181,X180,X178)
| c_Orderings_Oord__class_Oless(X181,X180,c_Orderings_Oord__class_Omin(X181,X179,X178))
| ~ class_Orderings_Olinorder(X181) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__conj])])])]) ).
fof(c_0_85,plain,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X10,X9)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X10,X9)
<=> X10 = X9 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(c_0_86,plain,
! [X759,X760,X761] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X761,X760)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X760,X759)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X761,X759) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])])]) ).
cnf(c_0_87,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
fof(c_0_88,plain,
! [X1159] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1159) = X1159,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
cnf(c_0_89,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_81]) ).
cnf(c_0_90,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_91,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(er,[status(thm)],[c_0_83]) ).
cnf(c_0_92,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Orderings_Oord__class_Omin(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_93,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
fof(c_0_94,plain,
! [X170,X171,X172,X173] :
( ~ class_Orderings_Olinorder(X173)
| ~ c_Orderings_Oord__class_Oless(X173,X172,X171)
| c_Orderings_Oord__class_Oless(X173,c_Orderings_Oord__class_Omin(X173,X172,X170),X171) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI1])])]) ).
fof(c_0_95,plain,
! [X467,X468,X469] :
( ( c_Orderings_Oord__class_Oless(X469,X468,X467)
| X468 = X467
| ~ c_Orderings_Oord__class_Oless__eq(X469,X468,X467)
| ~ class_Orderings_Olinorder(X469) )
& ( X468 != X467
| ~ c_Orderings_Oord__class_Oless(X469,X468,X467)
| ~ c_Orderings_Oord__class_Oless__eq(X469,X468,X467)
| ~ class_Orderings_Olinorder(X469) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_85])])])]) ).
fof(c_0_96,plain,
! [X536,X537,X538,X539] :
( ~ class_Orderings_Olinorder(X539)
| ~ c_Orderings_Oord__class_Oless__eq(X539,X538,X537)
| c_Orderings_Oord__class_Oless__eq(X539,c_Orderings_Oord__class_Omin(X539,X538,X536),X537) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI1])])]) ).
cnf(c_0_97,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_98,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
fof(c_0_99,plain,
! [X855,X856,X857] :
( ( X856 = c_Groups_Ozero__class_Ozero(X857)
| ~ c_Orderings_Oord__class_Oless__eq(X857,c_Groups_Oplus__class_Oplus(X857,c_Groups_Otimes__class_Otimes(X857,X856,X856),c_Groups_Otimes__class_Otimes(X857,X855,X855)),c_Groups_Ozero__class_Ozero(X857))
| ~ class_Rings_Olinordered__ring__strict(X857) )
& ( X855 = c_Groups_Ozero__class_Ozero(X857)
| ~ c_Orderings_Oord__class_Oless__eq(X857,c_Groups_Oplus__class_Oplus(X857,c_Groups_Otimes__class_Otimes(X857,X856,X856),c_Groups_Otimes__class_Otimes(X857,X855,X855)),c_Groups_Ozero__class_Ozero(X857))
| ~ class_Rings_Olinordered__ring__strict(X857) )
& ( X856 != c_Groups_Ozero__class_Ozero(X857)
| X855 != c_Groups_Ozero__class_Ozero(X857)
| c_Orderings_Oord__class_Oless__eq(X857,c_Groups_Oplus__class_Oplus(X857,c_Groups_Otimes__class_Otimes(X857,X856,X856),c_Groups_Otimes__class_Otimes(X857,X855,X855)),c_Groups_Ozero__class_Ozero(X857))
| ~ class_Rings_Olinordered__ring__strict(X857) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff])])])]) ).
fof(c_0_100,plain,
! [X898,X899] :
( ~ class_Groups_Omonoid__add(X899)
| c_Groups_Oplus__class_Oplus(X899,X898,c_Groups_Ozero__class_Ozero(X899)) = X898 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])])]) ).
fof(c_0_101,plain,
! [X1069,X1070] :
( ~ class_RealVector_Oreal__normed__algebra(X1070)
| c_Groups_Otimes__class_Otimes(X1070,X1069,c_Groups_Ozero__class_Ozero(X1070)) = c_Groups_Ozero__class_Ozero(X1070) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__right])])]) ).
cnf(c_0_102,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_80]),c_0_80]),c_0_80]),c_0_81]),c_0_81]),c_0_81]),c_0_81]),c_0_81]),c_0_81]) ).
fof(c_0_103,plain,
! [X1710,X1711] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1711,X1710) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1710,X1711),
inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).
cnf(c_0_104,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_105,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90]),c_0_90]),c_0_90]),c_0_90]) ).
cnf(c_0_106,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).
fof(c_0_107,plain,
! [X43,X11,X12,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X12,c_Rings_Oinverse__class_Odivide(X5,X11,X43))
<=> ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X43)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Otimes__class_Otimes(X5,X12,X43),X11) )
& ( ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X43)
=> ( ( c_Orderings_Oord__class_Oless(X5,X43,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,X11,c_Groups_Otimes__class_Otimes(X5,X12,X43)) )
& ( ~ c_Orderings_Oord__class_Oless(X5,X43,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ozero__class_Ozero(X5)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__divide__eq]) ).
fof(c_0_108,plain,
! [X1063,X1064] :
( ~ class_RealVector_Oreal__normed__algebra(X1064)
| c_Groups_Otimes__class_Otimes(X1064,c_Groups_Ozero__class_Ozero(X1064),X1063) = c_Groups_Ozero__class_Ozero(X1064) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__left])])]) ).
fof(c_0_109,plain,
! [X1453] :
( ~ class_Rings_Olinordered__semidom(X1453)
| c_Orderings_Oord__class_Oless(X1453,c_Groups_Ozero__class_Ozero(X1453),c_Groups_Oplus__class_Oplus(X1453,c_Groups_Oone__class_Oone(X1453),c_Groups_Oone__class_Oone(X1453))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])])]) ).
cnf(c_0_110,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93])]) ).
cnf(c_0_111,plain,
( c_Orderings_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X1,X2,X4),X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_112,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_113,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Orderings_Oord__class_Omin(X1,X2,X4),X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
fof(c_0_114,plain,
! [X764] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X764,X764),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
fof(c_0_115,plain,
! [X692] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X692)) = X692,
inference(variable_rename,[status(thm)],[fact_zminus__zminus]) ).
fof(c_0_116,plain,
! [X1904] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,X1904) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1904),
inference(variable_rename,[status(thm)],[fact_mult__Min]) ).
cnf(c_0_117,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_118,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d2),
inference(split_conjunct,[status(thm)],[conj_1]) ).
cnf(c_0_119,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X1,X1),c_Groups_Otimes__class_Otimes(X2,X3,X3)),c_Groups_Ozero__class_Ozero(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
fof(c_0_120,plain,
! [X1038,X1039,X1040] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1040,X1039),X1038) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1040,X1038),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1039,X1038)),
inference(variable_rename,[status(thm)],[fact_real__add__mult__distrib]) ).
fof(c_0_121,plain,
! [X1025,X1026] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1026,X1025) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1025,X1026),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
cnf(c_0_122,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_123,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]) ).
cnf(c_0_124,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_125,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra]) ).
cnf(c_0_126,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),v_d2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_90]),c_0_90]),c_0_90]),c_0_90]),c_0_90]),c_0_90]),c_0_90]),c_0_90]),c_0_90]),c_0_90]),c_0_90]),c_0_90]) ).
cnf(c_0_127,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_128,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = 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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106])]) ).
fof(c_0_129,plain,
! [X1524,X1525,X1526,X1527] :
( ( ~ c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| c_Orderings_Oord__class_Oless(X1527,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524),X1525)
| ~ c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,X1525,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524))
| c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| ~ c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| ~ c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1526,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| ~ c_Orderings_Oord__class_Oless(X1527,X1525,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524))
| c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1526,c_Groups_Ozero__class_Ozero(X1527))
| ~ c_Orderings_Oord__class_Oless(X1527,X1525,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524))
| c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,c_Groups_Ozero__class_Ozero(X1527),X1524)
| ~ c_Orderings_Oord__class_Oless(X1527,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524),X1525)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| ~ c_Orderings_Oord__class_Oless(X1527,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524),X1525)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1526,c_Groups_Ozero__class_Ozero(X1527))
| c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| ~ c_Orderings_Oord__class_Oless(X1527,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524),X1525)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1524,c_Groups_Ozero__class_Ozero(X1527))
| ~ c_Orderings_Oord__class_Oless(X1527,X1525,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524))
| ~ c_Orderings_Oord__class_Oless(X1527,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524),X1525)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) )
& ( ~ c_Orderings_Oord__class_Oless(X1527,X1526,c_Groups_Ozero__class_Ozero(X1527))
| ~ c_Orderings_Oord__class_Oless(X1527,X1525,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524))
| ~ c_Orderings_Oord__class_Oless(X1527,c_Groups_Otimes__class_Otimes(X1527,X1526,X1524),X1525)
| c_Orderings_Oord__class_Oless(X1527,X1526,c_Rings_Oinverse__class_Odivide(X1527,X1525,X1524))
| ~ class_Fields_Olinordered__field__inverse__zero(X1527) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_107])])])]) ).
cnf(c_0_130,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_131,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_132,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
fof(c_0_133,plain,
! [X285,X286,X287] :
( ~ class_Orderings_Olinorder(X287)
| c_Orderings_Oord__class_Omin(X287,X286,X285) = c_Orderings_Oord__class_Omin(X287,X285,X286) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Ocommute])])]) ).
cnf(c_0_134,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_93])]) ).
cnf(c_0_135,plain,
( c_Orderings_Oord__class_Omin(X1,X2,X3) = X4
| c_Orderings_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X1,X2,X3),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Olinorder(X1) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_136,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
fof(c_0_137,plain,
! [X442,X443,X444,X445] :
( ~ class_Orderings_Oorder(X445)
| ~ c_Orderings_Oord__class_Oless__eq(X445,X444,X443)
| ~ c_Orderings_Oord__class_Oless(X445,X442,X444)
| c_Orderings_Oord__class_Oless(X445,X442,X443) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])])]) ).
fof(c_0_138,plain,
! [X13,X8,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( X8 != X13
=> ( ~ c_Orderings_Oord__class_Oless(X5,X8,X13)
=> c_Orderings_Oord__class_Oless(X5,X13,X8) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(c_0_139,plain,
! [X1185,X1186] :
( ~ class_Int_Onumber__ring(X1186)
| c_Groups_Otimes__class_Otimes(X1186,c_Int_Onumber__class_Onumber__of(X1186,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1185) = c_Groups_Oplus__class_Oplus(X1186,X1185,X1185) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2])])]) ).
cnf(c_0_140,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_141,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,X1) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
fof(c_0_142,plain,
! [X193] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X193) = X193,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
cnf(c_0_143,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d1),
inference(split_conjunct,[status(thm)],[conj_0]) ).
fof(c_0_144,plain,
! [X8,X13,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X8)
=> ~ c_Orderings_Oord__class_Oless(X5,X8,X13) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(c_0_145,plain,
! [X338,X339,X340,X341] :
( ~ class_Orderings_Oorder(X341)
| ~ c_Orderings_Oord__class_Oless__eq(X341,X340,X339)
| ~ c_Orderings_Oord__class_Oless__eq(X341,X338,X340)
| c_Orderings_Oord__class_Oless__eq(X341,X338,X339) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])])]) ).
cnf(c_0_146,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_d2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_147,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(X1))),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_119])]) ).
cnf(c_0_148,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_149,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_150,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X1,
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_151,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_152,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring__strict]) ).
fof(c_0_153,plain,
! [X1954,X1955,X1956] :
( ~ class_Rings_Ocomm__semiring__1(X1956)
| c_Groups_Oplus__class_Oplus(X1956,X1955,X1954) = c_Groups_Oplus__class_Oplus(X1956,X1954,X1955) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])])]) ).
fof(c_0_154,plain,
! [X1696] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1696,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1696,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X1696,
inference(variable_rename,[status(thm)],[fact_real__sum__of__halves]) ).
cnf(c_0_155,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128]),c_0_128]),c_0_128]) ).
cnf(c_0_156,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_157,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_130,c_0_125]) ).
cnf(c_0_158,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_159,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).
cnf(c_0_160,plain,
( c_Orderings_Oord__class_Omin(X1,X2,X3) = c_Orderings_Oord__class_Omin(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_161,plain,
( c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2) = X1
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_136]),c_0_93])]) ).
cnf(c_0_162,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_163,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
fof(c_0_164,plain,
! [X229,X230,X231] :
( ~ class_Rings_Olinordered__idom(X231)
| X230 = X229
| c_Orderings_Oord__class_Oless(X231,X230,X229)
| c_Orderings_Oord__class_Oless(X231,X229,X230) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_138])])]) ).
cnf(c_0_165,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_166,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_141]),c_0_141]) ).
cnf(c_0_167,plain,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_142]) ).
cnf(c_0_168,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]) ).
cnf(c_0_169,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_d1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[c_0_117,c_0_143]) ).
fof(c_0_170,plain,
! [X473,X474,X475] :
( ~ class_Orderings_Olinorder(X475)
| ~ c_Orderings_Oord__class_Oless__eq(X475,X474,X473)
| ~ c_Orderings_Oord__class_Oless(X475,X473,X474) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_144])])]) ).
cnf(c_0_171,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_172,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148]),c_0_149]),c_0_150]),c_0_151]),c_0_152])]) ).
fof(c_0_173,plain,
! [X1604,X1605] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1605,X1604),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1604,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1605)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1604,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1605))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1605,X1604),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__less__0__iff])])]) ).
fof(c_0_174,plain,
! [X792,X793,X794] :
( ( ~ c_Orderings_Oord__class_Oless(X794,c_Groups_Ouminus__class_Ouminus(X794,X793),c_Groups_Ouminus__class_Ouminus(X794,X792))
| c_Orderings_Oord__class_Oless(X794,X792,X793)
| ~ class_Groups_Oordered__ab__group__add(X794) )
& ( ~ c_Orderings_Oord__class_Oless(X794,X792,X793)
| c_Orderings_Oord__class_Oless(X794,c_Groups_Ouminus__class_Ouminus(X794,X793),c_Groups_Ouminus__class_Ouminus(X794,X792))
| ~ class_Groups_Oordered__ab__group__add(X794) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])])]) ).
fof(c_0_175,plain,
! [X2174,X2175] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2175,X2174) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2175,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2174)),
inference(variable_rename,[status(thm)],[fact_real__diff__def]) ).
fof(c_0_176,plain,
! [X1041,X1042,X1043,X1044] :
( ( c_Groups_Oplus__class_Oplus(X1044,X1043,X1042) != c_Groups_Oplus__class_Oplus(X1044,X1043,X1041)
| X1042 = X1041
| ~ class_Groups_Ocancel__semigroup__add(X1044) )
& ( X1042 != X1041
| c_Groups_Oplus__class_Oplus(X1044,X1043,X1042) = c_Groups_Oplus__class_Oplus(X1044,X1043,X1041)
| ~ class_Groups_Ocancel__semigroup__add(X1044) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])])]) ).
fof(c_0_177,plain,
! [X2282,X2283,X2284] :
( ~ class_Groups_Ogroup__add(X2284)
| c_Groups_Oplus__class_Oplus(X2284,c_Groups_Ominus__class_Ominus(X2284,X2283,X2282),X2282) = X2283 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])])]) ).
cnf(c_0_178,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
cnf(c_0_179,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
cnf(c_0_180,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X1,
inference(split_conjunct,[status(thm)],[c_0_154]) ).
cnf(c_0_181,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_157]),c_0_158]),c_0_159])]) ).
cnf(c_0_182,plain,
( c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2) = X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_93])]) ).
cnf(c_0_183,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_98]),c_0_163])]) ).
cnf(c_0_184,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_164]) ).
cnf(c_0_185,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
cnf(c_0_186,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_165,c_0_80]),c_0_81]),c_0_81]) ).
cnf(c_0_187,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OMin,c_Int_OMin)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_105]),c_0_167]),c_0_168])]) ).
cnf(c_0_188,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_147]),c_0_148]),c_0_149]),c_0_150]),c_0_151]),c_0_152])]) ).
cnf(c_0_189,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_190,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_163])]) ).
cnf(c_0_191,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_173]) ).
cnf(c_0_192,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_174]) ).
cnf(c_0_193,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),
inference(split_conjunct,[status(thm)],[c_0_175]) ).
cnf(c_0_194,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add]) ).
cnf(c_0_195,plain,
( X3 = X4
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X2,X4)
| ~ class_Groups_Ocancel__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
cnf(c_0_196,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__semigroup__add]) ).
cnf(c_0_197,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_177]) ).
cnf(c_0_198,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
cnf(c_0_199,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
fof(c_0_200,plain,
! [X1998,X1999,X2000] :
( ( X1999 != c_Groups_Oplus__class_Oplus(X2000,X1999,X1998)
| X1998 = c_Groups_Ozero__class_Ozero(X2000)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2000) )
& ( X1998 != c_Groups_Ozero__class_Ozero(X2000)
| X1999 = c_Groups_Oplus__class_Oplus(X2000,X1999,X1998)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2000) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])])]) ).
cnf(c_0_201,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_180,c_0_80]),c_0_80]),c_0_81]),c_0_81]),c_0_81]),c_0_81]) ).
cnf(c_0_202,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d2,v_d1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_118])]),c_0_183]) ).
cnf(c_0_203,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1) ),
inference(spm,[status(thm)],[c_0_184,c_0_185]) ).
cnf(c_0_204,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_186,c_0_90]),c_0_90]),c_0_90]),c_0_90]) ).
cnf(c_0_205,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OMin,c_Int_OMin))) = 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(rw,[status(thm)],[c_0_128,c_0_187]) ).
fof(c_0_206,plain,
! [X1179,X1180] :
( ~ class_Int_Onumber__ring(X1180)
| c_Groups_Oplus__class_Oplus(X1180,c_Groups_Oone__class_Oone(X1180),c_Int_Onumber__class_Onumber__of(X1180,X1179)) = c_Int_Onumber__class_Onumber__of(X1180,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X1179)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I2_J])])]) ).
fof(c_0_207,plain,
! [X1903] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1903),X1903) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2]) ).
cnf(c_0_208,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d1,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_188]),c_0_163])]) ).
cnf(c_0_209,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,v_d2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_161]),c_0_143])]),c_0_183]) ).
cnf(c_0_210,hypothesis,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_93])]) ).
cnf(c_0_211,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_192]),c_0_193]),c_0_194])]) ).
cnf(c_0_212,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X1) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X2) ),
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_213,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_198]),c_0_199]) ).
cnf(c_0_214,plain,
( X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(split_conjunct,[status(thm)],[c_0_200]) ).
cnf(c_0_215,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_201,c_0_90]),c_0_90]),c_0_90]),c_0_90]),c_0_90]),c_0_90]),c_0_90]),c_0_90]) ).
cnf(c_0_216,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
cnf(c_0_217,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_218,negated_conjecture,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = v_d2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d2,v_d1) ),
inference(spm,[status(thm)],[c_0_202,c_0_203]) ).
cnf(c_0_219,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_204]),c_0_106])]),c_0_187]),c_0_205]) ).
cnf(c_0_220,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_206]) ).
cnf(c_0_221,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_207]) ).
cnf(c_0_222,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_223,plain,
! [X15,X25] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,X15)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,X15)
& X25 != X15 ) ),
inference(fof_simplification,[status(thm)],[fact_zless__le]) ).
cnf(c_0_224,hypothesis,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d1,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_208]),c_0_93])]) ).
cnf(c_0_225,negated_conjecture,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = v_d1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,v_d2) ),
inference(spm,[status(thm)],[c_0_209,c_0_203]) ).
cnf(c_0_226,hypothesis,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d2,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(spm,[status(thm)],[c_0_210,c_0_211]) ).
cnf(c_0_227,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X1) = X2,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213])]) ).
cnf(c_0_228,plain,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) != X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_215]),c_0_216])]),c_0_128]),c_0_128]) ).
cnf(c_0_229,negated_conjecture,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = v_d2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_d2,v_d2),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d2,v_d1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_218]),c_0_219]),c_0_158]),c_0_159])]) ).
fof(c_0_230,plain,
! [X551,X552,X553] :
( ~ class_Orderings_Olinorder(X553)
| c_Orderings_Oord__class_Oless__eq(X553,c_Orderings_Oord__class_Omin(X553,X552,X551),X551) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le2])])]) ).
fof(c_0_231,plain,
! [X91,X92] :
( ( ~ c_Orderings_Oord__class_Oless(X92,c_Int_Onumber__class_Onumber__of(X92,X91),c_Groups_Ozero__class_Ozero(X92))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X91,c_Int_OPls)
| ~ class_Int_Onumber__ring(X92)
| ~ class_Rings_Olinordered__idom(X92) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X91,c_Int_OPls)
| c_Orderings_Oord__class_Oless(X92,c_Int_Onumber__class_Onumber__of(X92,X91),c_Groups_Ozero__class_Ozero(X92))
| ~ class_Int_Onumber__ring(X92)
| ~ class_Rings_Olinordered__idom(X92) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I3_J])])])]) ).
cnf(c_0_232,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[c_0_220,c_0_81]) ).
cnf(c_0_233,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,X1),X1) = c_Int_OPls,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_221,c_0_141]),c_0_222]) ).
fof(c_0_234,plain,
! [X1843] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1843,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1843,
inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).
fof(c_0_235,plain,
! [X718,X719] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X719,X718)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X719,X718) )
& ( X719 != X718
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X719,X718) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X719,X718)
| X719 = X718
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X719,X718) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_223])])])]) ).
cnf(c_0_236,hypothesis,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d1,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(spm,[status(thm)],[c_0_224,c_0_211]) ).
cnf(c_0_237,negated_conjecture,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = v_d1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_d1,v_d1),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,v_d2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_225]),c_0_219]),c_0_158]),c_0_159])]) ).
cnf(c_0_238,hypothesis,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_226,c_0_227]) ).
cnf(c_0_239,negated_conjecture,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_d2,v_d2),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d2,v_d1) ),
inference(spm,[status(thm)],[c_0_228,c_0_229]) ).
fof(c_0_240,plain,
! [X174,X175,X176,X177] :
( ( ~ c_Orderings_Oord__class_Oless(X177,c_Orderings_Oord__class_Omin(X177,X176,X175),X174)
| c_Orderings_Oord__class_Oless(X177,X176,X174)
| c_Orderings_Oord__class_Oless(X177,X175,X174)
| ~ class_Orderings_Olinorder(X177) )
& ( ~ c_Orderings_Oord__class_Oless(X177,X176,X174)
| c_Orderings_Oord__class_Oless(X177,c_Orderings_Oord__class_Omin(X177,X176,X175),X174)
| ~ class_Orderings_Olinorder(X177) )
& ( ~ c_Orderings_Oord__class_Oless(X177,X175,X174)
| c_Orderings_Oord__class_Oless(X177,c_Orderings_Oord__class_Omin(X177,X176,X175),X174)
| ~ class_Orderings_Olinorder(X177) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__disj])])])]) ).
cnf(c_0_241,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_242,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Orderings_Oord__class_Omin(X1,X2,X3),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_243,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_231]) ).
cnf(c_0_244,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_232,c_0_90]),c_0_90]) ).
cnf(c_0_245,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,X1)) = c_Int_OPls,
inference(rw,[status(thm)],[c_0_233,c_0_127]) ).
cnf(c_0_246,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1,
inference(split_conjunct,[status(thm)],[c_0_234]) ).
cnf(c_0_247,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_235]) ).
cnf(c_0_248,hypothesis,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d1,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_236,c_0_227]) ).
cnf(c_0_249,negated_conjecture,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_d1,v_d1),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,v_d2) ),
inference(spm,[status(thm)],[c_0_228,c_0_237]) ).
cnf(c_0_250,hypothesis,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d2,v_d1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_239]),c_0_136])]) ).
fof(c_0_251,plain,
! [X93] :
( ~ class_Int_Onumber__ring(X93)
| c_Groups_Ozero__class_Ozero(X93) = c_Int_Onumber__class_Onumber__of(X93,c_Int_OPls) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J])])]) ).
cnf(c_0_252,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X1,X2,X3),X4)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_240]) ).
cnf(c_0_253,plain,
( c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2) = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_242]),c_0_93])]) ).
cnf(c_0_254,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),c_Int_OPls)
| ~ class_Rings_Olinordered__idom(X2)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X2,X1)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Int_Onumber__ring(X2) ),
inference(spm,[status(thm)],[c_0_243,c_0_244]) ).
cnf(c_0_255,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_245]),c_0_246]) ).
cnf(c_0_256,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OPls,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_245,c_0_246]),c_0_127]) ).
cnf(c_0_257,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(er,[status(thm)],[c_0_247]) ).
cnf(c_0_258,hypothesis,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d1
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,v_d2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_249]),c_0_136])]) ).
cnf(c_0_259,hypothesis,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d2
| v_d2 = v_d1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,v_d2) ),
inference(spm,[status(thm)],[c_0_250,c_0_203]) ).
cnf(c_0_260,plain,
( c_Groups_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_251]) ).
cnf(c_0_261,plain,
( c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2) = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_253]),c_0_93])]),c_0_91]) ).
cnf(c_0_262,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Int_Onumber__ring(X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_255]),c_0_127]),c_0_256]),c_0_257]) ).
cnf(c_0_263,hypothesis,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d2
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d1
| v_d2 = v_d1 ),
inference(spm,[status(thm)],[c_0_258,c_0_259]) ).
cnf(c_0_264,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_260,c_0_106]) ).
fof(c_0_265,plain,
! [X269,X270,X271,X272] :
( ~ class_Orderings_Opreorder(X272)
| ~ c_Orderings_Oord__class_Oless(X272,X271,X270)
| ~ c_Orderings_Oord__class_Oless(X272,X270,X269)
| c_Orderings_Oord__class_Oless(X272,X271,X269) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])])]) ).
cnf(c_0_266,plain,
( c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2) = X1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_261]),c_0_93])]) ).
cnf(c_0_267,hypothesis,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d1
| v_d2 = v_d1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_262,c_0_263]),c_0_185]),c_0_264]),c_0_118]),c_0_106])]) ).
cnf(c_0_268,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_265]) ).
cnf(c_0_269,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(c_0_270,plain,
! [X1602,X1603] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1603,X1602))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1603),X1602) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1603),X1602)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1603,X1602)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__less__add__iff])])]) ).
cnf(c_0_271,negated_conjecture,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d2,v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_266]),c_0_143])]) ).
cnf(c_0_272,hypothesis,
v_d2 = v_d1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_262,c_0_267]),c_0_185]),c_0_264]),c_0_143]),c_0_106])]) ).
fof(c_0_273,plain,
! [X789,X790,X791] :
( ( ~ c_Orderings_Oord__class_Oless(X791,c_Groups_Ouminus__class_Ouminus(X791,X790),X789)
| c_Orderings_Oord__class_Oless(X791,c_Groups_Ouminus__class_Ouminus(X791,X789),X790)
| ~ class_Groups_Oordered__ab__group__add(X791) )
& ( ~ c_Orderings_Oord__class_Oless(X791,c_Groups_Ouminus__class_Ouminus(X791,X789),X790)
| c_Orderings_Oord__class_Oless(X791,c_Groups_Ouminus__class_Ouminus(X791,X790),X789)
| ~ class_Groups_Oordered__ab__group__add(X791) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])])]) ).
cnf(c_0_274,hypothesis,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_268,c_0_143]),c_0_269])]) ).
cnf(c_0_275,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
fof(c_0_276,plain,
! [X755,X756] :
( ~ class_Groups_Ogroup__add(X756)
| c_Groups_Ouminus__class_Ouminus(X756,c_Groups_Ouminus__class_Ouminus(X756,X755)) = X755 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])])]) ).
cnf(c_0_277,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_271,c_0_272]),c_0_272])]),c_0_91]) ).
fof(c_0_278,plain,
! [X1598,X1599] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1599,X1598),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1598,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1599)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1598,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1599))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1599,X1598),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__le__0__iff])])]) ).
fof(c_0_279,plain,
! [X571,X572] :
( ( ~ c_Orderings_Oord__class_Oless(X572,X571,c_Groups_Ouminus__class_Ouminus(X572,X571))
| c_Orderings_Oord__class_Oless(X572,X571,c_Groups_Ozero__class_Ozero(X572))
| ~ class_Rings_Olinordered__idom(X572) )
& ( ~ c_Orderings_Oord__class_Oless(X572,X571,c_Groups_Ozero__class_Ozero(X572))
| c_Orderings_Oord__class_Oless(X572,X571,c_Groups_Ouminus__class_Ouminus(X572,X571))
| ~ class_Rings_Olinordered__idom(X572) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])])]) ).
cnf(c_0_280,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_281,hypothesis,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_274,c_0_275]),c_0_150]) ).
cnf(c_0_282,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_283,negated_conjecture,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = v_d1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,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(spm,[status(thm)],[c_0_277,c_0_203]) ).
cnf(c_0_284,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_285,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_286,hypothesis,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_d1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_280,c_0_281]),c_0_194])]) ).
cnf(c_0_287,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = X1,
inference(spm,[status(thm)],[c_0_282,c_0_198]) ).
cnf(c_0_288,negated_conjecture,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = v_d1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_d1,v_d1),v_d1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_283]),c_0_219]),c_0_158]),c_0_159])]) ).
cnf(c_0_289,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_284]),c_0_93])]) ).
cnf(c_0_290,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_d1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_285,c_0_286]),c_0_185]),c_0_287]),c_0_143])]) ).
cnf(c_0_291,negated_conjecture,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_d1,v_d1),v_d1) ),
inference(spm,[status(thm)],[c_0_228,c_0_288]) ).
cnf(c_0_292,hypothesis,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_290]),c_0_150]) ).
cnf(c_0_293,hypothesis,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_291]),c_0_136])]) ).
cnf(c_0_294,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_292,c_0_293]),c_0_136])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWW177+1 : TPTP v8.2.0. Released v5.2.0.
% 0.08/0.13 % Command : run_E %s %d SAT
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jun 19 05:00:39 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.43/0.63 Running first-order model finding
% 0.43/0.63 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.851O4T2XAG/E---3.1_7048.p
% 177.47/23.18 # Version: 3.2.0
% 177.47/23.18 # Preprocessing class: FMLMSMSMSSSNFFN.
% 177.47/23.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 177.47/23.18 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 177.47/23.18 # Starting new_bool_3 with 300s (1) cores
% 177.47/23.18 # Starting new_bool_1 with 300s (1) cores
% 177.47/23.18 # Starting sh5l with 300s (1) cores
% 177.47/23.18 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 7132 completed with status 0
% 177.47/23.18 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 177.47/23.18 # Preprocessing class: FMLMSMSMSSSNFFN.
% 177.47/23.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 177.47/23.18 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 177.47/23.18 # No SInE strategy applied
% 177.47/23.18 # Search class: FGHSM-SMLM32-DFFFFFNN
% 177.47/23.18 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 177.47/23.18 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 113s (1) cores
% 177.47/23.18 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 177.47/23.18 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 177.47/23.18 # Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 177.47/23.18 # Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN with 113s (1) cores
% 177.47/23.18 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with pid 7139 completed with status 0
% 177.47/23.18 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y
% 177.47/23.18 # Preprocessing class: FMLMSMSMSSSNFFN.
% 177.47/23.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 177.47/23.18 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 177.47/23.18 # No SInE strategy applied
% 177.47/23.18 # Search class: FGHSM-SMLM32-DFFFFFNN
% 177.47/23.18 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 177.47/23.18 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 113s (1) cores
% 177.47/23.18 # Preprocessing time : 0.024 s
% 177.47/23.18 # Presaturation interreduction done
% 177.47/23.18
% 177.47/23.18 # Proof found!
% 177.47/23.18 # SZS status Theorem
% 177.47/23.18 # SZS output start CNFRefutation
% See solution above
% 177.47/23.18 # Parsed axioms : 1200
% 177.47/23.18 # Removed by relevancy pruning/SinE : 0
% 177.47/23.18 # Initial clauses : 1801
% 177.47/23.18 # Removed in clause preprocessing : 89
% 177.47/23.18 # Initial clauses in saturation : 1712
% 177.47/23.18 # Processed clauses : 87861
% 177.47/23.18 # ...of these trivial : 1146
% 177.47/23.18 # ...subsumed : 75361
% 177.47/23.18 # ...remaining for further processing : 11354
% 177.47/23.18 # Other redundant clauses eliminated : 4529
% 177.47/23.18 # Clauses deleted for lack of memory : 0
% 177.47/23.18 # Backward-subsumed : 322
% 177.47/23.18 # Backward-rewritten : 2906
% 177.47/23.18 # Generated clauses : 801863
% 177.47/23.18 # ...of the previous two non-redundant : 739926
% 177.47/23.18 # ...aggressively subsumed : 0
% 177.47/23.18 # Contextual simplify-reflections : 69
% 177.47/23.18 # Paramodulations : 797265
% 177.47/23.18 # Factorizations : 39
% 177.47/23.18 # NegExts : 0
% 177.47/23.18 # Equation resolutions : 4578
% 177.47/23.18 # Disequality decompositions : 0
% 177.47/23.18 # Total rewrite steps : 2419706
% 177.47/23.18 # ...of those cached : 2395727
% 177.47/23.18 # Propositional unsat checks : 2
% 177.47/23.18 # Propositional check models : 0
% 177.47/23.18 # Propositional check unsatisfiable : 0
% 177.47/23.18 # Propositional clauses : 0
% 177.47/23.18 # Propositional clauses after purity: 0
% 177.47/23.18 # Propositional unsat core size : 0
% 177.47/23.18 # Propositional preprocessing time : 0.000
% 177.47/23.18 # Propositional encoding time : 0.939
% 177.47/23.18 # Propositional solver time : 0.678
% 177.47/23.18 # Success case prop preproc time : 0.000
% 177.47/23.18 # Success case prop encoding time : 0.000
% 177.47/23.18 # Success case prop solver time : 0.000
% 177.47/23.18 # Current number of processed clauses : 6681
% 177.47/23.18 # Positive orientable unit clauses : 840
% 177.47/23.18 # Positive unorientable unit clauses: 111
% 177.47/23.18 # Negative unit clauses : 764
% 177.47/23.18 # Non-unit-clauses : 4966
% 177.47/23.18 # Current number of unprocessed clauses: 651665
% 177.47/23.18 # ...number of literals in the above : 1817798
% 177.47/23.18 # Current number of archived formulas : 0
% 177.47/23.18 # Current number of archived clauses : 4548
% 177.47/23.18 # Clause-clause subsumption calls (NU) : 4231206
% 177.47/23.18 # Rec. Clause-clause subsumption calls : 2643809
% 177.47/23.18 # Non-unit clause-clause subsumptions : 24290
% 177.47/23.18 # Unit Clause-clause subsumption calls : 303544
% 177.47/23.18 # Rewrite failures with RHS unbound : 0
% 177.47/23.18 # BW rewrite match attempts : 37571
% 177.47/23.18 # BW rewrite match successes : 1175
% 177.47/23.18 # Condensation attempts : 0
% 177.47/23.18 # Condensation successes : 0
% 177.47/23.18 # Termbank termtop insertions : 25736726
% 177.47/23.18 # Search garbage collected termcells : 20661
% 177.47/23.18
% 177.47/23.18 # -------------------------------------------------
% 177.47/23.18 # User time : 20.747 s
% 177.47/23.18 # System time : 0.545 s
% 177.47/23.18 # Total time : 21.293 s
% 177.47/23.18 # Maximum resident set size: 8072 pages
% 177.47/23.18
% 177.47/23.18 # -------------------------------------------------
% 177.47/23.18 # User time : 107.091 s
% 177.47/23.18 # System time : 2.722 s
% 177.47/23.18 # Total time : 109.813 s
% 177.47/23.18 # Maximum resident set size: 3012 pages
% 177.47/23.18 % E---3.1 exiting
% 177.47/23.18 % E exiting
%------------------------------------------------------------------------------