TSTP Solution File: SWW180+1 by E---3.2.0
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%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : SWW180+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.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 18:11:11 EDT 2024
% Result : Theorem 10.11s 1.92s
% Output : CNFRefutation 10.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of formulae : 109 ( 50 unt; 0 def)
% Number of atoms : 212 ( 64 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 181 ( 78 ~; 69 |; 14 &)
% ( 5 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 149 ( 1 sgn 78 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X9,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X9,c_Groups_Ozero__class_Ozero(X6)) = X9 ),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_real__add__eq__0__iff,axiom,
! [X12,X13] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,X12) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X12 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13) ),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_real__add__eq__0__iff) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(fact_real__abs__def,axiom,
! [X20] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X20,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X20) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X20) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X20,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X20) = X20 ) ),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_real__abs__def) ).
fof(fact_abs__minus__add__cancel,axiom,
! [X4,X5] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X5))),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_abs__minus__add__cancel) ).
fof(fact_minus__real__def,axiom,
! [X4,X5] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5,X4) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4)),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_minus__real__def) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X9,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Ozero__class_Ozero(X6),X9) = X9 ),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
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/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_complex__mod__minus__le__complex__mod) ).
fof(fact_abs__le__interval__iff,axiom,
! [X62,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X13),X62)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X62),X13)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X62) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_abs__le__interval__iff) ).
fof(fact_real__le__refl,axiom,
! [X27] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27,X27),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_real__le__refl) ).
fof(fact_real__less__def,axiom,
! [X12,X13] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X12)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X12)
& X13 != X12 ) ),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_real__less__def) ).
fof(fact_real__le__trans,axiom,
! [X37,X38,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X39,X38)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X38,X37)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X39,X37) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_real__le__trans) ).
fof(fact_real__le__antisym,axiom,
! [X27,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,X27)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27,X16)
=> X16 = X27 ) ),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_real__le__antisym) ).
fof(fact_H,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_H) ).
fof(fact_abs__less__iff,axiom,
! [X18,X14,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oabs__class_Oabs(X6,X14),X18)
<=> ( c_Orderings_Oord__class_Oless(X6,X14,X18)
& c_Orderings_Oord__class_Oless(X6,c_Groups_Ouminus__class_Ouminus(X6,X14),X18) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_abs__less__iff) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(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,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',conj_0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X15,X9,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X9,X15) = c_Groups_Oplus__class_Oplus(X6,X15,X9) ),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(fact_abs__add__one__not__less__self,axiom,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X5),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_abs__add__one__not__less__self) ).
fof(fact_abs__mult__pos,axiom,
! [X4,X5,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oabs__class_Oabs(X6,X4)),X5) = c_Groups_Oabs__class_Oabs(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X4),X5)) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_abs__mult__pos) ).
fof(fact_real__add__left__mono,axiom,
! [X16,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X4)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X16,X5),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X16,X4)) ),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_real__add__left__mono) ).
fof(fact_real__le__linear,axiom,
! [X27,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,X27)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27,X16) ),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_real__le__linear) ).
fof(fact_th,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),v_z____)),v_m____),
file('/export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p',fact_th) ).
fof(c_0_23,plain,
! [X981,X982] :
( ~ class_Rings_Ocomm__semiring__1(X982)
| c_Groups_Oplus__class_Oplus(X982,X981,c_Groups_Ozero__class_Ozero(X982)) = X981 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])])]) ).
fof(c_0_24,plain,
! [X500,X501] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X501,X500) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X500 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X501) )
& ( X500 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X501)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X501,X500) = 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__eq__0__iff])])]) ).
cnf(c_0_25,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_26,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
fof(c_0_27,plain,
! [X20] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X20,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X20) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X20) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X20,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X20) = X20 ) ),
inference(fof_simplification,[status(thm)],[fact_real__abs__def]) ).
fof(c_0_28,plain,
! [X283,X284] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X284,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X283))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X283,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X284))),
inference(variable_rename,[status(thm)],[fact_abs__minus__add__cancel]) ).
fof(c_0_29,plain,
! [X524,X525] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X525,X524) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X525,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X524)),
inference(variable_rename,[status(thm)],[fact_minus__real__def]) ).
cnf(c_0_30,plain,
( X2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)
| 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_24]) ).
cnf(c_0_31,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_25,c_0_26]) ).
fof(c_0_32,plain,
! [X983,X984] :
( ~ class_Rings_Ocomm__semiring__1(X984)
| c_Groups_Oplus__class_Oplus(X984,c_Groups_Ozero__class_Ozero(X984),X983) = X983 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])])]) ).
fof(c_0_33,plain,
! [X420] : 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,X420)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X420)),
inference(variable_rename,[status(thm)],[fact_complex__mod__minus__le__complex__mod]) ).
fof(c_0_34,plain,
! [X285] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X285,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X285) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X285) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X285,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X285) = X285 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
fof(c_0_35,plain,
! [X281,X282] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X281),X282)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X282),X281) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X282,X281)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X282),X281) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X281),X282)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X282,X281)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X282),X281) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__interval__iff])])])]) ).
fof(c_0_36,plain,
! [X406] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X406,X406),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
fof(c_0_37,plain,
! [X12,X13] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X12)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X12)
& X13 != X12 ) ),
inference(fof_simplification,[status(thm)],[fact_real__less__def]) ).
cnf(c_0_38,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,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_29]) ).
cnf(c_0_40,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_41,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_42,plain,
! [X409,X410,X411] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X411,X410)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X410,X409)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X411,X409) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])])]) ).
fof(c_0_43,plain,
! [X412,X413] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X413,X412)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X412,X413)
| X413 = X412 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])])]) ).
cnf(c_0_44,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_33]) ).
cnf(c_0_45,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_46,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_47,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_48,plain,
! [X414,X415] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X415,X414)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X415,X414) )
& ( X415 != X414
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X415,X414) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X415,X414)
| X415 = X414
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X415,X414) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])]) ).
cnf(c_0_49,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_39]) ).
cnf(c_0_50,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_31]) ).
cnf(c_0_51,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = X1,
inference(spm,[status(thm)],[c_0_41,c_0_26]) ).
cnf(c_0_52,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_42]) ).
cnf(c_0_53,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r),
inference(split_conjunct,[status(thm)],[fact_H]) ).
cnf(c_0_54,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_56,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_57,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_58,plain,
! [X278,X279,X280] :
( ( c_Orderings_Oord__class_Oless(X280,X279,X278)
| ~ c_Orderings_Oord__class_Oless(X280,c_Groups_Oabs__class_Oabs(X280,X279),X278)
| ~ class_Rings_Olinordered__idom(X280) )
& ( c_Orderings_Oord__class_Oless(X280,c_Groups_Ouminus__class_Ouminus(X280,X279),X278)
| ~ c_Orderings_Oord__class_Oless(X280,c_Groups_Oabs__class_Oabs(X280,X279),X278)
| ~ class_Rings_Olinordered__idom(X280) )
& ( ~ c_Orderings_Oord__class_Oless(X280,X279,X278)
| ~ c_Orderings_Oord__class_Oless(X280,c_Groups_Ouminus__class_Ouminus(X280,X279),X278)
| c_Orderings_Oord__class_Oless(X280,c_Groups_Oabs__class_Oabs(X280,X279),X278)
| ~ class_Rings_Olinordered__idom(X280) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__less__iff])])])]) ).
cnf(c_0_59,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_48]) ).
cnf(c_0_60,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_61,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),
inference(spm,[status(thm)],[c_0_39,c_0_51]) ).
cnf(c_0_62,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_63,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(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,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(c_0_64,plain,
! [X1040,X1041,X1042] :
( ~ class_Rings_Ocomm__semiring__1(X1042)
| c_Groups_Oplus__class_Oplus(X1042,X1041,X1040) = c_Groups_Oplus__class_Oplus(X1042,X1040,X1041) ),
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])])]) ).
cnf(c_0_65,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_r)
| ~ 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_52,c_0_53]) ).
cnf(c_0_66,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_67,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]),c_0_57]) ).
cnf(c_0_68,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_69,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = X1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)) ),
inference(spm,[status(thm)],[c_0_59,c_0_56]) ).
cnf(c_0_70,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(rw,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_71,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
cnf(c_0_72,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(er,[status(thm)],[c_0_62]) ).
fof(c_0_73,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(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,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(fof_nnf,[status(thm)],[c_0_63]) ).
cnf(c_0_74,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_64]) ).
cnf(c_0_75,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),v_r)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]) ).
cnf(c_0_76,plain,
( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)) ),
inference(sr,[status(thm)],[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_68,c_0_69]),c_0_70]),c_0_70]),c_0_71]),c_0_70])]),c_0_72]) ).
fof(c_0_77,plain,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X5),
inference(fof_simplification,[status(thm)],[fact_abs__add__one__not__less__self]) ).
cnf(c_0_78,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(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,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_79,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_74,c_0_26]) ).
fof(c_0_80,plain,
! [X262,X263,X264] :
( ~ class_Rings_Olinordered__idom(X264)
| ~ c_Orderings_Oord__class_Oless__eq(X264,c_Groups_Ozero__class_Ozero(X264),X263)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X264),c_Groups_Oabs__class_Oabs(X264,X262)),X263) = c_Groups_Oabs__class_Oabs(X264,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X264),X262),X263)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__pos])])]) ).
cnf(c_0_81,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r),v_r),
inference(spm,[status(thm)],[c_0_75,c_0_53]) ).
cnf(c_0_82,plain,
( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = X1 ),
inference(spm,[status(thm)],[c_0_76,c_0_69]) ).
cnf(c_0_83,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_56]) ).
fof(c_0_84,plain,
! [X258] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X258),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X258),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_77])]) ).
cnf(c_0_85,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79]),c_0_79]) ).
cnf(c_0_86,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),X2) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_87,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) = v_r,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]) ).
fof(c_0_88,plain,
! [X183,X184,X185] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X185,X184)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X183,X185),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X183,X184)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__left__mono])])]) ).
fof(c_0_89,plain,
! [X407,X408] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X408,X407)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X407,X408) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
cnf(c_0_90,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_91,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_71])]),c_0_87]) ).
cnf(c_0_92,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_93,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_94,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
inference(spm,[status(thm)],[c_0_90,c_0_67]) ).
cnf(c_0_95,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_96,plain,
( X1 = X2
| 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_59,c_0_93]) ).
cnf(c_0_97,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_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
inference(rw,[status(thm)],[c_0_94,c_0_79]) ).
cnf(c_0_98,negated_conjecture,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]) ).
cnf(c_0_99,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_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[c_0_66,c_0_40]) ).
cnf(c_0_100,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_98]),c_0_47])]) ).
cnf(c_0_101,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(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_67]),c_0_93]) ).
cnf(c_0_102,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_100,c_0_93]) ).
cnf(c_0_103,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[c_0_54,c_0_101]) ).
cnf(c_0_104,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_m____) ),
inference(spm,[status(thm)],[c_0_52,c_0_102]) ).
cnf(c_0_105,negated_conjecture,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_m____) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_106,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),v_z____)),v_m____),
inference(split_conjunct,[status(thm)],[fact_th]) ).
cnf(c_0_107,negated_conjecture,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),v_z____)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_108,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_107]),c_0_100]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SWW180+1 : TPTP v8.2.0. Released v5.2.0.
% 0.05/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Jun 19 07:38:53 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.38/0.57 Running first-order theorem proving
% 0.38/0.57 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.ZPpcmUOJFM/E---3.1_29409.p
% 10.11/1.92 # Version: 3.2.0
% 10.11/1.92 # Preprocessing class: FMLMSMSMSSSNFFN.
% 10.11/1.92 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.11/1.92 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 10.11/1.92 # Starting new_bool_3 with 300s (1) cores
% 10.11/1.92 # Starting new_bool_1 with 300s (1) cores
% 10.11/1.92 # Starting sh5l with 300s (1) cores
% 10.11/1.92 # new_bool_1 with pid 29489 completed with status 0
% 10.11/1.92 # Result found by new_bool_1
% 10.11/1.92 # Preprocessing class: FMLMSMSMSSSNFFN.
% 10.11/1.92 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.11/1.92 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 10.11/1.92 # Starting new_bool_3 with 300s (1) cores
% 10.11/1.92 # Starting new_bool_1 with 300s (1) cores
% 10.11/1.92 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 10.11/1.92 # Search class: FGHSM-FSLM31-DFFFFFNN
% 10.11/1.92 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 10.11/1.92 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 10.11/1.92 # G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 29491 completed with status 0
% 10.11/1.92 # Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 10.11/1.92 # Preprocessing class: FMLMSMSMSSSNFFN.
% 10.11/1.92 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.11/1.92 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 10.11/1.92 # Starting new_bool_3 with 300s (1) cores
% 10.11/1.92 # Starting new_bool_1 with 300s (1) cores
% 10.11/1.92 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 10.11/1.92 # Search class: FGHSM-FSLM31-DFFFFFNN
% 10.11/1.92 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 10.11/1.92 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 10.11/1.92 # Preprocessing time : 0.009 s
% 10.11/1.92 # Presaturation interreduction done
% 10.11/1.92
% 10.11/1.92 # Proof found!
% 10.11/1.92 # SZS status Theorem
% 10.11/1.92 # SZS output start CNFRefutation
% See solution above
% 10.11/1.92 # Parsed axioms : 1275
% 10.11/1.92 # Removed by relevancy pruning/SinE : 784
% 10.11/1.92 # Initial clauses : 684
% 10.11/1.92 # Removed in clause preprocessing : 35
% 10.11/1.92 # Initial clauses in saturation : 649
% 10.11/1.92 # Processed clauses : 9632
% 10.11/1.92 # ...of these trivial : 117
% 10.11/1.92 # ...subsumed : 6940
% 10.11/1.92 # ...remaining for further processing : 2575
% 10.11/1.92 # Other redundant clauses eliminated : 307
% 10.11/1.92 # Clauses deleted for lack of memory : 0
% 10.11/1.92 # Backward-subsumed : 105
% 10.11/1.92 # Backward-rewritten : 269
% 10.11/1.92 # Generated clauses : 54346
% 10.11/1.92 # ...of the previous two non-redundant : 46363
% 10.11/1.92 # ...aggressively subsumed : 0
% 10.11/1.92 # Contextual simplify-reflections : 29
% 10.11/1.92 # Paramodulations : 54026
% 10.11/1.92 # Factorizations : 12
% 10.11/1.92 # NegExts : 0
% 10.11/1.92 # Equation resolutions : 318
% 10.11/1.92 # Disequality decompositions : 0
% 10.11/1.92 # Total rewrite steps : 53081
% 10.11/1.92 # ...of those cached : 50001
% 10.11/1.92 # Propositional unsat checks : 0
% 10.11/1.92 # Propositional check models : 0
% 10.11/1.92 # Propositional check unsatisfiable : 0
% 10.11/1.92 # Propositional clauses : 0
% 10.11/1.92 # Propositional clauses after purity: 0
% 10.11/1.92 # Propositional unsat core size : 0
% 10.11/1.92 # Propositional preprocessing time : 0.000
% 10.11/1.92 # Propositional encoding time : 0.000
% 10.11/1.92 # Propositional solver time : 0.000
% 10.11/1.92 # Success case prop preproc time : 0.000
% 10.11/1.92 # Success case prop encoding time : 0.000
% 10.11/1.92 # Success case prop solver time : 0.000
% 10.11/1.92 # Current number of processed clauses : 1637
% 10.11/1.92 # Positive orientable unit clauses : 326
% 10.11/1.92 # Positive unorientable unit clauses: 17
% 10.11/1.92 # Negative unit clauses : 237
% 10.11/1.92 # Non-unit-clauses : 1057
% 10.11/1.92 # Current number of unprocessed clauses: 37454
% 10.11/1.92 # ...number of literals in the above : 86706
% 10.11/1.92 # Current number of archived formulas : 0
% 10.11/1.92 # Current number of archived clauses : 868
% 10.11/1.92 # Clause-clause subsumption calls (NU) : 229770
% 10.11/1.92 # Rec. Clause-clause subsumption calls : 150655
% 10.11/1.92 # Non-unit clause-clause subsumptions : 3609
% 10.11/1.92 # Unit Clause-clause subsumption calls : 9285
% 10.11/1.92 # Rewrite failures with RHS unbound : 0
% 10.11/1.92 # BW rewrite match attempts : 4934
% 10.11/1.92 # BW rewrite match successes : 350
% 10.11/1.92 # Condensation attempts : 0
% 10.11/1.92 # Condensation successes : 0
% 10.11/1.92 # Termbank termtop insertions : 1054721
% 10.11/1.92 # Search garbage collected termcells : 12243
% 10.11/1.92
% 10.11/1.92 # -------------------------------------------------
% 10.11/1.92 # User time : 1.191 s
% 10.11/1.92 # System time : 0.056 s
% 10.11/1.92 # Total time : 1.247 s
% 10.11/1.92 # Maximum resident set size: 4828 pages
% 10.11/1.92
% 10.11/1.92 # -------------------------------------------------
% 10.11/1.92 # User time : 1.226 s
% 10.11/1.92 # System time : 0.059 s
% 10.11/1.92 # Total time : 1.285 s
% 10.11/1.92 # Maximum resident set size: 3112 pages
% 10.11/1.92 % E---3.1 exiting
% 10.11/1.92 % E exiting
%------------------------------------------------------------------------------