%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW234+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 : Tue May 5 05:30:47 PM UTC 2026
% Result : Theorem 23.35s 15.31s
% Output : CNFRefutation 23.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 43
% Syntax : Number of formulae : 152 ( 82 unt; 0 def)
% Number of atoms : 294 ( 45 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 257 ( 115 ~; 94 |; 14 &)
% ( 11 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 210 ( 10 sgn 123 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_linorder__not__less,axiom,
! [X21,X11,X4] :
( class_Orderings_Olinorder(X4)
=> ( ~ c_Orderings_Oord__class_Oless(X4,X11,X21)
<=> c_Orderings_Oord__class_Oless__eq(X4,X21,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(fact_less__le__not__le,axiom,
! [X21,X11,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X11,X21)
<=> ( c_Orderings_Oord__class_Oless__eq(X4,X11,X21)
& ~ c_Orderings_Oord__class_Oless__eq(X4,X21,X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_xt1_I8_J,axiom,
! [X7,X5,X13,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X13,X5)
=> ( c_Orderings_Oord__class_Oless(X4,X7,X13)
=> c_Orderings_Oord__class_Oless(X4,X7,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(fact_minus__le__self__iff,axiom,
! [X17,X4] :
( class_Groups_Olinordered__ab__group__add(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ouminus__class_Ouminus(X4,X17),X17)
<=> c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
fof(fact_complex__mod__minus__le__complex__mod,axiom,
! [X5] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X5)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(fact_real__natfloor__le,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__le) ).
fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(fact_le__natfloor__eq__one,axiom,
! [X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X11))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq__one) ).
fof(fact_natfloor__real__of__nat,axiom,
! [X46] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X46)) = X46,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__real__of__nat) ).
fof(fact_not__add__less1,axiom,
! [X9,X10] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X9),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(fact_dvd__imp__le,axiom,
! [X46,X8] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X8,X46)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X46)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8,X46) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__le) ).
fof(fact_one__dvd,axiom,
! [X14,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> c_Rings_Odvd__class_Odvd(X4,c_Groups_Oone__class_Oone(X4),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__dvd) ).
fof(fact_real__of__nat__Suc,axiom,
! [X46] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X46)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X46),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).
fof(fact_Suc__eq__plus1,axiom,
! [X46] : c_Nat_OSuc(X46) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X46,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_le__Suc__ex__iff,axiom,
! [X55,X56] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X55)
<=> ? [X29] : X55 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(fact_natceiling__le__eq__one,axiom,
! [X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X11),c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq__one) ).
fof(fact_le0,axiom,
! [X46] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X46),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_nat__add__commute,axiom,
! [X46,X40] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X46) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X46,X40),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_natfloor__mono,axiom,
! [X13,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X5),c_RComplete_Onatfloor(X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__mono) ).
fof(fact_neq0__conv,axiom,
! [X57] :
( X57 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_xt1_I6_J,axiom,
! [X7,X5,X13,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X13,X5)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X7,X13)
=> c_Orderings_Oord__class_Oless__eq(X4,X7,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_natceiling__zero,axiom,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__zero) ).
fof(fact_add__0__right,axiom,
! [X14,X4] :
( class_Groups_Omonoid__add(X4)
=> c_Groups_Oplus__class_Oplus(X4,X14,c_Groups_Ozero__class_Ozero(X4)) = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_abs__less__iff,axiom,
! [X20,X17,X4] :
( class_Rings_Olinordered__idom(X4)
=> ( c_Orderings_Oord__class_Oless(X4,c_Groups_Oabs__class_Oabs(X4,X17),X20)
<=> ( c_Orderings_Oord__class_Oless(X4,X17,X20)
& c_Orderings_Oord__class_Oless(X4,c_Groups_Ouminus__class_Ouminus(X4,X17),X20) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__less__iff) ).
fof(fact_real__natfloor__add__one__gt,axiom,
! [X5] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__add__one__gt) ).
fof(fact_real__of__nat__add,axiom,
! [X46,X40] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X46)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X40),c_RealDef_Oreal(tc_Nat_Onat,X46)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__add) ).
fof(fact_less__natfloor,axiom,
! [X46,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5,c_RealDef_Oreal(tc_Nat_Onat,X46))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X5),X46) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__natfloor) ).
fof(fact_add__le__cancel__left,axiom,
! [X20,X17,X19,X4] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oplus__class_Oplus(X4,X19,X17),c_Groups_Oplus__class_Oplus(X4,X19,X20))
<=> c_Orderings_Oord__class_Oless__eq(X4,X17,X20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(fact_real__of__nat__1,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__1) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(fact_abs__of__pos,axiom,
! [X14,X4] :
( class_Groups_Oordered__ab__group__add__abs(X4)
=> ( c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X14)
=> c_Groups_Oabs__class_Oabs(X4,X14) = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__pos) ).
fof(fact_abs__add__one__gt__zero,axiom,
! [X5] : 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_Oabs__class_Oabs(tc_RealDef_Oreal,X5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).
fof(fact_complex__mod__rcis,axiom,
! [X14,X15] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X15,X14)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__rcis) ).
fof(fact_real__of__nat__zero,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(fact_h,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_h) ).
fof(c_0_43,plain,
! [X21,X11,X4] :
( class_Orderings_Olinorder(X4)
=> ( ~ c_Orderings_Oord__class_Oless(X4,X11,X21)
<=> c_Orderings_Oord__class_Oless__eq(X4,X21,X11) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(c_0_44,plain,
! [X3200,X3201,X3202] :
( ( c_Orderings_Oord__class_Oless(X3202,X3201,X3200)
| c_Orderings_Oord__class_Oless__eq(X3202,X3200,X3201)
| ~ class_Orderings_Olinorder(X3202) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3202,X3200,X3201)
| ~ c_Orderings_Oord__class_Oless(X3202,X3201,X3200)
| ~ class_Orderings_Olinorder(X3202) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])]) ).
fof(c_0_45,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_46,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_47,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
fof(c_0_48,plain,
! [X21,X11,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X11,X21)
<=> ( c_Orderings_Oord__class_Oless__eq(X4,X11,X21)
& ~ c_Orderings_Oord__class_Oless__eq(X4,X21,X11) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(c_0_49,plain,
! [X3263,X3264,X3265,X3266] :
( ~ class_Orderings_Oorder(X3266)
| ~ c_Orderings_Oord__class_Oless__eq(X3266,X3265,X3264)
| ~ c_Orderings_Oord__class_Oless(X3266,X3263,X3265)
| c_Orderings_Oord__class_Oless(X3266,X3263,X3264) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
cnf(c_0_50,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_52,plain,
! [X3212,X3213,X3214] :
( ( c_Orderings_Oord__class_Oless__eq(X3214,X3213,X3212)
| ~ c_Orderings_Oord__class_Oless(X3214,X3213,X3212)
| ~ class_Orderings_Opreorder(X3214) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3214,X3212,X3213)
| ~ c_Orderings_Oord__class_Oless(X3214,X3213,X3212)
| ~ class_Orderings_Opreorder(X3214) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3214,X3213,X3212)
| c_Orderings_Oord__class_Oless__eq(X3214,X3212,X3213)
| c_Orderings_Oord__class_Oless(X3214,X3213,X3212)
| ~ class_Orderings_Opreorder(X3214) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])]) ).
cnf(c_0_53,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_49]) ).
cnf(c_0_54,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
fof(c_0_56,plain,
! [X3750,X3751] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3751,c_Groups_Ouminus__class_Ouminus(X3751,X3750),X3750)
| c_Orderings_Oord__class_Oless__eq(X3751,c_Groups_Ozero__class_Ozero(X3751),X3750)
| ~ class_Groups_Olinordered__ab__group__add(X3751) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3751,c_Groups_Ozero__class_Ozero(X3751),X3750)
| c_Orderings_Oord__class_Oless__eq(X3751,c_Groups_Ouminus__class_Ouminus(X3751,X3750),X3750)
| ~ class_Groups_Olinordered__ab__group__add(X3751) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])]) ).
fof(c_0_57,plain,
! [X3743] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3743)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3743)),
inference(variable_rename,[status(thm)],[fact_complex__mod__minus__le__complex__mod]) ).
cnf(c_0_58,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_59,negated_conjecture,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]) ).
cnf(c_0_60,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(c_0_61,plain,
! [X4698] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4698)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X4698)),X4698) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__natfloor__le])]) ).
cnf(c_0_62,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_63,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_64,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Olinordered__ab__group__add]) ).
fof(c_0_65,plain,
! [X4638] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X4638))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4638) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4638)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X4638)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq__one])]) ).
fof(c_0_66,plain,
! [X4673] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X4673)) = X4673,
inference(variable_rename,[status(thm)],[fact_natfloor__real__of__nat]) ).
fof(c_0_67,plain,
! [X9,X10] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X9),X10),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
cnf(c_0_68,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]) ).
cnf(c_0_69,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_70,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64])]) ).
cnf(c_0_71,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_72,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_66]) ).
fof(c_0_73,plain,
! [X5490,X5491] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5491,X5490)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5490)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5491,X5490) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__imp__le])]) ).
fof(c_0_74,plain,
! [X5226,X5227] :
( ~ class_Rings_Ocomm__semiring__1(X5227)
| c_Rings_Odvd__class_Odvd(X5227,c_Groups_Oone__class_Oone(X5227),X5226) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__dvd])]) ).
fof(c_0_75,plain,
! [X5516] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X5516)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5516),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__Suc]) ).
fof(c_0_76,plain,
! [X5362] : c_Nat_OSuc(X5362) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5362,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(c_0_77,plain,
! [X4381,X4382] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4382,X4381),X4382),
inference(variable_rename,[status(thm)],[c_0_67]) ).
fof(c_0_78,plain,
! [X4222,X4223,X4225,X4226,X4227] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4223,X4222)
| X4222 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4223,esk6_2(X4222,X4223)) )
& ( X4225 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4226,X4227)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4226,X4225) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__ex__iff])])])])]) ).
cnf(c_0_79,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]) ).
cnf(c_0_80,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_81,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_82,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_83,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]) ).
fof(c_0_84,plain,
! [X4624] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X4624),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4624,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4624,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X4624),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq__one])]) ).
fof(c_0_85,plain,
! [X4294] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4294),
inference(variable_rename,[status(thm)],[fact_le0]) ).
cnf(c_0_86,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_87,plain,
c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
fof(c_0_88,plain,
! [X4337,X4338] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4338,X4337) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4337,X4338),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
cnf(c_0_89,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_90,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk6_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
fof(c_0_91,plain,
! [X4635,X4636] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4636,X4635)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X4636),c_RComplete_Onatfloor(X4635)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__mono])]) ).
cnf(c_0_92,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_93,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83])]) ).
fof(c_0_94,plain,
! [X4358] :
( ( X4358 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4358) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4358)
| X4358 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(c_0_95,plain,
! [X3009,X3010,X3011,X3012] :
( ~ class_Orderings_Oorder(X3012)
| ~ c_Orderings_Oord__class_Oless__eq(X3012,X3011,X3010)
| ~ c_Orderings_Oord__class_Oless__eq(X3012,X3009,X3011)
| c_Orderings_Oord__class_Oless__eq(X3012,X3009,X3010) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
cnf(c_0_96,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_97,plain,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_natceiling__zero]) ).
cnf(c_0_98,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
fof(c_0_99,plain,
! [X2902,X2903] :
( ~ class_Groups_Omonoid__add(X2903)
| c_Groups_Oplus__class_Oplus(X2903,X2902,c_Groups_Ozero__class_Ozero(X2903)) = X2902 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(c_0_100,plain,
! [X3800,X3801,X3802] :
( ( c_Orderings_Oord__class_Oless(X3802,X3801,X3800)
| ~ c_Orderings_Oord__class_Oless(X3802,c_Groups_Oabs__class_Oabs(X3802,X3801),X3800)
| ~ class_Rings_Olinordered__idom(X3802) )
& ( c_Orderings_Oord__class_Oless(X3802,c_Groups_Ouminus__class_Ouminus(X3802,X3801),X3800)
| ~ c_Orderings_Oord__class_Oless(X3802,c_Groups_Oabs__class_Oabs(X3802,X3801),X3800)
| ~ class_Rings_Olinordered__idom(X3802) )
& ( ~ c_Orderings_Oord__class_Oless(X3802,X3801,X3800)
| ~ c_Orderings_Oord__class_Oless(X3802,c_Groups_Ouminus__class_Ouminus(X3802,X3801),X3800)
| c_Orderings_Oord__class_Oless(X3802,c_Groups_Oabs__class_Oabs(X3802,X3801),X3800)
| ~ class_Rings_Olinordered__idom(X3802) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__less__iff])])]) ).
fof(c_0_101,plain,
! [X4714] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4714,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X4714)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[fact_real__natfloor__add__one__gt]) ).
fof(c_0_102,plain,
! [X4682,X4683] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4683,X4682)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4683),c_RealDef_Oreal(tc_Nat_Onat,X4682)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__add]) ).
cnf(c_0_103,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_104,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_105,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_106,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_107,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_108,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_109,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
fof(c_0_110,plain,
! [X4720,X4721] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4721)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4721,c_RealDef_Oreal(tc_Nat_Onat,X4720))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X4721),X4720) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__natfloor])]) ).
cnf(c_0_111,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_95]) ).
cnf(c_0_112,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98])]) ).
fof(c_0_113,plain,
! [X2983,X2984,X2985,X2986] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2986,c_Groups_Oplus__class_Oplus(X2986,X2985,X2984),c_Groups_Oplus__class_Oplus(X2986,X2985,X2983))
| c_Orderings_Oord__class_Oless__eq(X2986,X2984,X2983)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2986) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2986,X2984,X2983)
| c_Orderings_Oord__class_Oless__eq(X2986,c_Groups_Oplus__class_Oplus(X2986,X2985,X2984),c_Groups_Oplus__class_Oplus(X2986,X2985,X2983))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2986) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
cnf(c_0_114,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_99]) ).
cnf(c_0_115,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]) ).
cnf(c_0_116,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_117,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_118,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
cnf(c_0_119,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_120,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__of__nat__1]) ).
cnf(c_0_121,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_122,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_123,negated_conjecture,
c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_124,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) ),
inference(spm,[status(thm)],[c_0_105,c_0_109]) ).
cnf(c_0_125,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_126,plain,
( 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,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_55])]) ).
cnf(c_0_127,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_128,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_114,c_0_115]) ).
cnf(c_0_129,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le]) ).
cnf(c_0_130,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118])]) ).
cnf(c_0_131,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_121]) ).
cnf(c_0_132,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
fof(c_0_133,plain,
! [X3358,X3359] :
( ~ class_Groups_Oordered__ab__group__add__abs(X3359)
| ~ c_Orderings_Oord__class_Oless(X3359,c_Groups_Ozero__class_Ozero(X3359),X3358)
| c_Groups_Oabs__class_Oabs(X3359,X3358) = X3358 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__pos])]) ).
fof(c_0_134,plain,
! [X3324] : 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_Oabs__class_Oabs(tc_RealDef_Oreal,X3324))),
inference(variable_rename,[status(thm)],[fact_abs__add__one__gt__zero]) ).
cnf(c_0_135,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_120]),c_0_126]) ).
cnf(c_0_136,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_70]),c_0_128]),c_0_129])]) ).
fof(c_0_137,plain,
! [X5128,X5129] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X5129,X5128)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5129),
inference(variable_rename,[status(thm)],[fact_complex__mod__rcis]) ).
cnf(c_0_138,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))))),
inference(rw,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_139,negated_conjecture,
( c_RComplete_Onatfloor(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(spm,[status(thm)],[c_0_132,c_0_108]) ).
cnf(c_0_140,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__of__nat__zero]) ).
cnf(c_0_141,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_142,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_Oabs__class_Oabs(tc_RealDef_Oreal,X1))),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_143,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs]) ).
cnf(c_0_144,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_145,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_146,negated_conjecture,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_140]),c_0_128]) ).
cnf(c_0_147,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_143])]) ).
cnf(c_0_148,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_149,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(split_conjunct,[status(thm)],[fact_h]) ).
cnf(c_0_150,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148]) ).
cnf(c_0_151,plain,
$false,
inference(sr,[status(thm)],[c_0_149,c_0_150]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW234+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n027.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 06:29:04 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 23.35/15.31 % Version : CSE_E---1.7
% 23.35/15.31 % Problem : theBenchmark.p
% 23.35/15.31 % SZS status Theorem for theBenchmark.p
% 23.35/15.31 % SZS output start CNFRefutation
% See solution above
% 23.35/15.39 % Total time : 11.603s
%------------------------------------------------------------------------------