%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWW207+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:11:44 PM UTC 2026
% Result : Theorem 19.84s 3.50s
% Output : CNFRefutation 19.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 32
% Syntax : Number of formulae : 133 ( 79 unt; 0 def)
% Number of atoms : 212 ( 78 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 142 ( 63 ~; 55 |; 8 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 11 con; 0-3 aty)
% Number of variables : 154 ( 5 sgn 80 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Im__cis,axiom,
! [X4] : hAPP(c_Complex_OIm,c_Complex_Ocis(X4)) = c_Transcendental_Osin(X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im__cis) ).
fof(fact_cis__rcis__eq,axiom,
! [X4] : c_Complex_Ocis(X4) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cis__rcis__eq) ).
fof(fact_Re__cis,axiom,
! [X4] : hAPP(c_Complex_ORe,c_Complex_Ocis(X4)) = c_Transcendental_Ocos(X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Re__cis) ).
fof(fact_less__le__not__le,axiom,
! [X9,X10,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X9),X10))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_cmod__unit__one,axiom,
! [X4] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X4),c_Transcendental_Osin(X4))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cmod__unit__one) ).
fof(fact_complex__mod__rcis,axiom,
! [X4,X23] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X23,X4)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__rcis) ).
fof(fact_real__norm__def,axiom,
! [X23] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X23) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [X27] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X27)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(fact_Suc__eq__plus1,axiom,
! [X29] : c_Nat_OSuc(X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_cis__zero,axiom,
c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cis__zero) ).
fof(fact_complex__surj,axiom,
! [X14] : c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X14),hAPP(c_Complex_OIm,X14)) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__surj) ).
fof(fact_le__natfloor__eq__one,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X10)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__natfloor__eq__one) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X29] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29) = X29,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(fact_natfloor__mono,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X7)),c_RComplete_Onatfloor(X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__mono) ).
fof(fact_Re_Obounded,axiom,
? [X37] :
! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3)),X37))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Re_Obounded) ).
fof(fact_real__mult__commute,axiom,
! [X16,X14] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X16) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(fact_complex__Im__i,axiom,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Im__i) ).
fof(fact_complex__Re__i,axiom,
hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Re__i) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_diff__is__0__eq,axiom,
! [X27,X31] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X31,X27) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
fof(fact_natfloor__zero,axiom,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__zero) ).
fof(fact_leI,axiom,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_complex__Re__one,axiom,
hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Re__one) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(fact_minus__nat_Odiff__0,axiom,
! [X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X30,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(conj_0,conjecture,
? [X37] :
( ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,X8)))))),X37))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_gr0I,axiom,
! [X29] :
( X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_real__le__trans,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19),X17)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(fact_real__le__linear,axiom,
! [X16,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16),X14))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(fact_th,axiom,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X8)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(c_0_32,plain,
! [X1982] : hAPP(c_Complex_OIm,c_Complex_Ocis(X1982)) = c_Transcendental_Osin(X1982),
inference(variable_rename,[status(thm)],[fact_Im__cis]) ).
fof(c_0_33,plain,
! [X1966] : c_Complex_Ocis(X1966) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1966),
inference(variable_rename,[status(thm)],[fact_cis__rcis__eq]) ).
fof(c_0_34,plain,
! [X1983] : hAPP(c_Complex_ORe,c_Complex_Ocis(X1983)) = c_Transcendental_Ocos(X1983),
inference(variable_rename,[status(thm)],[fact_Re__cis]) ).
fof(c_0_35,plain,
! [X9,X10,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X9),X10))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(c_0_36,plain,
! [X2606] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X2606),c_Transcendental_Osin(X2606))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(variable_rename,[status(thm)],[fact_cmod__unit__one]) ).
cnf(c_0_37,plain,
hAPP(c_Complex_OIm,c_Complex_Ocis(X1)) = c_Transcendental_Osin(X1),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
c_Complex_Ocis(X1) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,plain,
hAPP(c_Complex_ORe,c_Complex_Ocis(X1)) = c_Transcendental_Ocos(X1),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_40,plain,
! [X1723,X1724] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X1724,X1723)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1724),
inference(variable_rename,[status(thm)],[fact_complex__mod__rcis]) ).
fof(c_0_41,plain,
! [X400] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X400) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X400),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(c_0_42,plain,
! [X1915] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1915) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1915)),
inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(c_0_43,plain,
! [X1900] : c_Nat_OSuc(X1900) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1900),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(c_0_44,plain,
! [X330,X331,X332] :
( ( ~ class_Orderings_Opreorder(X332)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X332,X331),X330))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X332,X330),X331))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X332,X331),X330)) )
& ( ~ class_Orderings_Opreorder(X332)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X332,X331),X330))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X332,X330),X331)) )
& ( ~ class_Orderings_Opreorder(X332)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X332,X331),X330))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X332,X331),X330)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])]) ).
cnf(c_0_45,plain,
c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_cis__zero]) ).
cnf(c_0_46,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X1),c_Transcendental_Osin(X1))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_47,plain,
hAPP(c_Complex_OIm,c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)) = c_Transcendental_Osin(X1),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_48,plain,
hAPP(c_Complex_ORe,c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)) = c_Transcendental_Ocos(X1),
inference(rw,[status(thm)],[c_0_39,c_0_38]) ).
fof(c_0_49,plain,
! [X2568] : c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X2568),hAPP(c_Complex_OIm,X2568)) = X2568,
inference(variable_rename,[status(thm)],[fact_complex__surj]) ).
cnf(c_0_50,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_40]) ).
cnf(c_0_51,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_52,plain,
! [X1342] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1342)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1342)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1342))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1342))) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq__one])])]) ).
cnf(c_0_53,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_54,plain,
c_Nat_OSuc(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_55,plain,
! [X629] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X629) = X629,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
cnf(c_0_56,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_57,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).
fof(c_0_58,plain,
! [X1071,X1072] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1072)),c_RComplete_Onatfloor(X1071)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1072),X1071)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__mono])])]) ).
fof(c_0_59,plain,
! [X1661] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1661))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1661)),esk33_0))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_Re_Obounded])]) ).
fof(c_0_60,plain,
! [X1387,X1388] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1388),X1387) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1387),X1388),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
cnf(c_0_61,plain,
c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[c_0_45,c_0_38]) ).
cnf(c_0_62,plain,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_complex__Im__i]) ).
cnf(c_0_63,plain,
hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_complex__Re__i]) ).
cnf(c_0_64,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)),hAPP(c_Complex_OIm,c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_65,plain,
c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X1),hAPP(c_Complex_OIm,X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_66,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X2)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1),
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
fof(c_0_67,plain,
! [X1003,X1004] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1004),X1003),c_Groups_Oone__class_Oone(X1004)) = X1003
| ~ class_Rings_Ocomm__semiring__1(X1004) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])])]) ).
fof(c_0_68,plain,
! [X2196,X2197] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2197,X2196) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2197),X2196)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2197),X2196))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2197,X2196) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq])])]) ).
cnf(c_0_69,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| hBOOL(hAPP(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_52]) ).
cnf(c_0_70,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rw,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_71,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_72,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_73,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_74,plain,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_natfloor__zero]) ).
fof(c_0_75,plain,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7)) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
cnf(c_0_76,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),esk33_0))),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_77,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_78,plain,
c_Complex_Orcis(hAPP(c_Complex_OIm,c_Complex_Oii),hAPP(c_Complex_ORe,c_Complex_Oii)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_79,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)) = hAPP(c_Complex_OIm,c_Complex_Oii),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_62]),c_0_62]),c_0_65]),c_0_66]),c_0_62]) ).
cnf(c_0_80,plain,
hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_complex__Re__one]) ).
cnf(c_0_81,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_82,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
cnf(c_0_83,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_84,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1))) ),
inference(rw,[status(thm)],[c_0_69,c_0_62]) ).
cnf(c_0_85,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
fof(c_0_86,plain,
! [X2106] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2106,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2106,
inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0]) ).
fof(c_0_87,negated_conjecture,
~ ? [X37] :
( ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,X8)))))),X37))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37)) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_88,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2))) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_89,plain,
c_RComplete_Onatfloor(hAPP(c_Complex_ORe,c_Complex_Oii)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rw,[status(thm)],[c_0_74,c_0_63]) ).
fof(c_0_90,plain,
! [X324,X325,X326] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X326,X324),X325))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X326,X325),X324))
| ~ class_Orderings_Olinorder(X326) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])]) ).
cnf(c_0_91,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1)))
| hBOOL(hAPP(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_52]) ).
fof(c_0_92,plain,
! [X29] :
( X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29)) ),
inference(fof_simplification,[status(thm)],[fact_gr0I]) ).
fof(c_0_93,plain,
! [X270,X271,X272] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X272),X270))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X271),X270))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X272),X271)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])])]) ).
cnf(c_0_94,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),esk33_0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)))),
inference(rw,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_95,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(c_Complex_OIm,c_Complex_Oii),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_78]),c_0_79]) ).
cnf(c_0_96,plain,
hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(c_Complex_OIm,c_Complex_Oii),
inference(rw,[status(thm)],[c_0_80,c_0_62]) ).
cnf(c_0_97,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),hAPP(c_Complex_OIm,c_Complex_Oii)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_62]) ).
cnf(c_0_98,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(spm,[status(thm)],[c_0_72,c_0_83]) ).
cnf(c_0_99,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(X1))) ),
inference(rw,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_100,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_86]) ).
fof(c_0_101,plain,
! [X273,X274] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X273),X274))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X274),X273)) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
fof(c_0_102,negated_conjecture,
! [X2833] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk72_1(X2833))))))),X2833))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2833)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_87])])])]) ).
fof(c_0_103,plain,
! [X362] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X362)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(variable_rename,[status(thm)],[fact_th]) ).
cnf(c_0_104,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_ORe,c_Complex_Oii)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(X1))) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_105,plain,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_106,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
cnf(c_0_107,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),X1)) ),
inference(rw,[status(thm)],[c_0_91,c_0_62]) ).
fof(c_0_108,plain,
! [X701] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X701))
| X701 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_92])]) ).
cnf(c_0_109,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_110,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),esk33_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]),c_0_79]),c_0_97]) ).
cnf(c_0_111,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),X1))
| c_RComplete_Onatfloor(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]) ).
cnf(c_0_112,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_113,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk72_1(X1))))))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_114,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X1)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_115,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_ORe,c_Complex_Oii))) ),
inference(spm,[status(thm)],[c_0_104,c_0_99]) ).
cnf(c_0_116,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2)) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_117,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),X1)) ),
inference(rw,[status(thm)],[c_0_107,c_0_85]) ).
cnf(c_0_118,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_119,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_OIm,c_Complex_Oii)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),esk33_0)) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_120,plain,
( c_RComplete_Onatfloor(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_OIm,c_Complex_Oii))) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_121,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk72_1(X1))))))),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_63]),c_0_51]) ).
cnf(c_0_122,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X1)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),hAPP(c_Complex_OIm,c_Complex_Oii)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_51]),c_0_62]) ).
cnf(c_0_123,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),X1)) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_124,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),X1))
| c_RComplete_Onatfloor(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_125,plain,
( c_RComplete_Onatfloor(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),esk33_0)) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_126,negated_conjecture,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),hAPP(c_Complex_OIm,c_Complex_Oii)))),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_127,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),X1))
| c_RComplete_Onatfloor(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_128,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| c_RComplete_Onatfloor(X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),esk33_0)) ),
inference(spm,[status(thm)],[c_0_109,c_0_125]) ).
cnf(c_0_129,negated_conjecture,
c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),hAPP(c_Complex_OIm,c_Complex_Oii))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_130,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X1)))),esk33_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_122]),c_0_129])]) ).
cnf(c_0_131,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),esk33_0)),
inference(spm,[status(thm)],[c_0_123,c_0_110]) ).
cnf(c_0_132,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_130]),c_0_131])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW207+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n015.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Mon Sep 21 09:44:36 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.54 Running first-order theorem proving
% 0.24/0.54 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/benchmark/theBenchmark.p
% 19.16/3.50 % Version: 3.5.1
% 19.16/3.50 % Preprocessing class: FMLMSMSMSSSNFFN.
% 19.16/3.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.16/3.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.16/3.50 % Starting new_bool_3 with 300s (1) cores
% 19.16/3.50 % Starting new_bool_1 with 300s (1) cores
% 19.16/3.50 % Starting sh5l with 300s (1) cores
% 19.16/3.50 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1163546 completed with status 0
% 19.16/3.50 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 19.16/3.50 % Preprocessing class: FMLMSMSMSSSNFFN.
% 19.16/3.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.16/3.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.16/3.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 19.16/3.50 % No SInE strategy applied
% 19.16/3.50 % Search class: FGHSM-SSLM32-DFFFFFNN
% 19.16/3.50 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 19.16/3.50 % Starting SubtermCWHack with 136s (1) cores
% 19.16/3.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 19.16/3.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 19.84/3.50 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 19.84/3.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 19.84/3.50 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 1163557 completed with status 0
% 19.84/3.50 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 19.84/3.50 % Preprocessing class: FMLMSMSMSSSNFFN.
% 19.84/3.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.84/3.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.84/3.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 19.84/3.50 % No SInE strategy applied
% 19.84/3.50 % Search class: FGHSM-SSLM32-DFFFFFNN
% 19.84/3.50 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 19.84/3.50 % Starting SubtermCWHack with 136s (1) cores
% 19.84/3.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 19.84/3.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 19.84/3.50 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 19.84/3.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 19.84/3.50 % Preprocessing time : 0.050 s
% 19.84/3.50 % Presaturation interreduction done
% 19.84/3.50
% 19.84/3.50 % Proof found!
% 19.84/3.50 % SZS status Theorem
% 19.84/3.50 % SZS output start CNFRefutation
% See solution above
% 19.84/3.50 % Parsed axioms : 1269
% 19.84/3.50 % Removed by relevancy pruning/SinE : 0
% 19.84/3.50 % Initial clauses : 1712
% 19.84/3.50 % Removed in clause preprocessing : 48
% 19.84/3.50 % Initial clauses in saturation : 1664
% 19.84/3.50 % Processed clauses : 7935
% 19.84/3.50 % ...of these trivial : 118
% 19.84/3.50 % ...subsumed : 3625
% 19.84/3.50 % ...remaining for further processing : 4192
% 19.84/3.50 % Other redundant clauses eliminated : 211
% 19.84/3.50 % Clauses deleted for lack of memory : 0
% 19.84/3.50 % Backward-subsumed : 46
% 19.84/3.50 % Backward-rewritten : 28
% 19.84/3.50 % Generated clauses : 25401
% 19.84/3.50 % ...of the previous two non-redundant : 20462
% 19.84/3.50 % ...aggressively subsumed : 0
% 19.84/3.50 % Contextual simplify-reflections : 2
% 19.84/3.50 % Paramodulations : 25186
% 19.84/3.50 % Factorizations : 10
% 19.84/3.50 % NegExts : 0
% 19.84/3.50 % Equation resolutions : 222
% 19.84/3.50 % Disequality decompositions : 0
% 19.84/3.50 % Total rewrite steps : 16234
% 19.84/3.50 % ...of those cached : 14735
% 19.84/3.50 % Propositional unsat checks : 0
% 19.84/3.50 % Propositional check models : 0
% 19.84/3.50 % Propositional check unsatisfiable : 0
% 19.84/3.50 % Propositional clauses : 0
% 19.84/3.50 % Propositional clauses after purity: 0
% 19.84/3.50 % Propositional unsat core size : 0
% 19.84/3.50 % Propositional preprocessing time : 0.000
% 19.84/3.50 % Propositional encoding time : 0.000
% 19.84/3.50 % Propositional solver time : 0.000
% 19.84/3.50 % Success case prop preproc time : 0.000
% 19.84/3.50 % Success case prop encoding time : 0.000
% 19.84/3.50 % Success case prop solver time : 0.000
% 19.84/3.50 % Current number of processed clauses : 2597
% 19.84/3.50 % Positive orientable unit clauses : 727
% 19.84/3.50 % Positive unorientable unit clauses: 14
% 19.84/3.50 % Negative unit clauses : 578
% 19.84/3.50 % Non-unit-clauses : 1278
% 19.84/3.50 % Current number of unprocessed clauses: 15500
% 19.84/3.50 % ...number of literals in the above : 31912
% 19.84/3.50 % Current number of archived formulas : 0
% 19.84/3.50 % Current number of archived clauses : 1466
% 19.84/3.50 % Clause-clause subsumption calls (NU) : 506684
% 19.84/3.50 % Rec. Clause-clause subsumption calls : 301633
% 19.84/3.50 % Non-unit clause-clause subsumptions : 989
% 19.84/3.50 % Unit Clause-clause subsumption calls : 37153
% 19.84/3.50 % Rewrite failures with RHS unbound : 0
% 19.84/3.50 % BW rewrite match attempts : 7702
% 19.84/3.50 % BW rewrite match successes : 243
% 19.84/3.50 % Condensation attempts : 0
% 19.84/3.50 % Condensation successes : 0
% 19.84/3.50 % Termbank termtop insertions : 694205
% 19.84/3.50 % Search garbage collected termcells : 19484
% 19.84/3.50
% 19.84/3.50 % -------------------------------------------------
% 19.84/3.50 % User time : 1.943 s
% 19.84/3.50 % System time : 0.080 s
% 19.84/3.50 % Total time : 2.023 s
% 19.84/3.50 % Maximum resident set size: 10800 pages
% 19.84/3.50
% 19.84/3.50 % -------------------------------------------------
% 19.84/3.50 % User time : 11.517 s
% 19.84/3.50 % System time : 0.439 s
% 19.84/3.50 % Total time : 11.956 s
% 19.84/3.50 % Maximum resident set size: 6144 pages
% 19.84/3.50 % E exiting
%------------------------------------------------------------------------------