%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW231+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 : n009.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 03:10:07 PM UTC 2026
% Result : Theorem 218.40s 32.19s
% Output : CNFRefutation 218.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 40
% Syntax : Number of formulae : 171 ( 139 unt; 0 def)
% Number of atoms : 217 ( 192 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 79 ( 33 ~; 28 |; 7 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 6 con; 0-3 aty)
% Number of variables : 236 ( 5 sgn 126 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_complex__of__real__add__Complex,axiom,
! [X4,X5,X44] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X44),c_Complex_Ocomplex_OComplex(X5,X4)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X44,X5),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__of__real__add__Complex) ).
fof(fact_complex__of__real__def,axiom,
! [X44] : c_RealVector_Oof__real(tc_Complex_Ocomplex,X44) = c_Complex_Ocomplex_OComplex(X44,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__of__real__def) ).
fof(fact_complex__add,axiom,
! [X34,X12,X11,X9] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X9,X11),c_Complex_Ocomplex_OComplex(X12,X34)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X9,X12),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X11,X34)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__add) ).
fof(fact_cos__periodic__pi,axiom,
! [X5] : c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__periodic__pi) ).
fof(fact_Im,axiom,
! [X4,X5] : c_Complex_OIm(c_Complex_Ocomplex_OComplex(X5,X4)) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im) ).
fof(fact_cos__zero,axiom,
c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__zero) ).
fof(fact_real__sqrt__eq__1__iff,axiom,
! [X19] :
( c_NthRoot_Osqrt(X19) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
<=> X19 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__eq__1__iff) ).
fof(fact_real__sqrt__abs2,axiom,
! [X5] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5),X5)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__abs2) ).
fof(fact_sin__zero__abs__cos__one,axiom,
! [X5] :
( c_Transcendental_Osin(X5) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(X5)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sin__zero__abs__cos__one) ).
fof(fact_rcis__zero__arg,axiom,
! [X44] : c_Complex_Orcis(X44,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(tc_Complex_Ocomplex,X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rcis__zero__arg) ).
fof(fact_real__0__less__add__iff,axiom,
! [X18,X19] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X19,X18))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X19),X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).
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/sandbox/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).
fof(fact_abs__real__of__nat__cancel,axiom,
! [X5] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5)) = c_RealDef_Oreal(tc_Nat_Onat,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__real__of__nat__cancel) ).
fof(fact_sin__pi,axiom,
c_Transcendental_Osin(c_Transcendental_Opi) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sin__pi) ).
fof(fact_Im__rcis,axiom,
! [X9,X44] : c_Complex_OIm(c_Complex_Orcis(X44,X9)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X44),c_Transcendental_Osin(X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im__rcis) ).
fof(fact_real__abs__def,axiom,
! [X44] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X44,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X44) = X44 )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X44,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X44) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X44) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__abs__def) ).
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/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).
fof(fact_cos__add,axiom,
! [X4,X5] : c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,X4)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X5)),c_Transcendental_Ocos(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X5)),c_Transcendental_Osin(X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__add) ).
fof(fact_sin__zero,axiom,
c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sin__zero) ).
fof(fact_real__add__minus__iff,axiom,
! [X14,X19] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X19,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X14)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X19 = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
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/benchmark/theBenchmark.p',fact_minus__real__def) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_real__mult__1,axiom,
! [X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X17) = X17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(fact_real__add__eq__0__iff,axiom,
! [X18,X19] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X19,X18) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X18 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).
fof(fact_real__add__mult__distrib,axiom,
! [X6,X7,X8] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X8,X7)),X6) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X8),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X7),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
fof(fact_nat__mult__1,axiom,
! [X60] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X60) = X60,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(fact_real__mult__commute,axiom,
! [X6,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(conj_0,conjecture,
c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) = c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_real__mult__assoc,axiom,
! [X16,X7,X8] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X8),X7)),X16) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X7),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
fof(fact_rcis__def,axiom,
! [X9,X44] : c_Complex_Orcis(X44,X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X44)),c_Complex_Ocis(X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rcis__def) ).
fof(fact_cis__def,axiom,
! [X9] : c_Complex_Ocis(X9) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X9),c_Transcendental_Osin(X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cis__def) ).
fof(fact_real__sqrt__mult,axiom,
! [X4,X5] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(X5)),c_NthRoot_Osqrt(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__mult) ).
fof(fact_cis__mult,axiom,
! [X11,X9] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X9)),c_Complex_Ocis(X11)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X9,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cis__mult) ).
fof(fact_sin__minus,axiom,
! [X5] : c_Transcendental_Osin(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X5)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sin__minus) ).
fof(fact_sin__periodic__pi,axiom,
! [X5] : c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sin__periodic__pi) ).
fof(fact_Complex__add__complex__of__real,axiom,
! [X44,X4,X5] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X5,X4),c_RealVector_Oof__real(tc_Complex_Ocomplex,X44)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,X44),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Complex__add__complex__of__real) ).
fof(fact_rcis__mult,axiom,
! [X11,X21,X9,X22] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(X22,X9)),c_Complex_Orcis(X21,X11)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X22),X21),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X9,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rcis__mult) ).
fof(fact_cos__one__sin__zero,axiom,
! [X5] :
( c_Transcendental_Ocos(X5) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
=> c_Transcendental_Osin(X5) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__one__sin__zero) ).
fof(fact_cos__minus,axiom,
! [X5] : c_Transcendental_Ocos(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X5)) = c_Transcendental_Ocos(X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__minus) ).
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/benchmark/theBenchmark.p',fact_abs__minus__add__cancel) ).
fof(c_0_40,plain,
! [X472,X473,X474] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X474),c_Complex_Ocomplex_OComplex(X473,X472)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X474,X473),X472),
inference(variable_rename,[status(thm)],[fact_complex__of__real__add__Complex]) ).
fof(c_0_41,plain,
! [X481] : c_RealVector_Oof__real(tc_Complex_Ocomplex,X481) = c_Complex_Ocomplex_OComplex(X481,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[fact_complex__of__real__def]) ).
cnf(c_0_42,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X1),c_Complex_Ocomplex_OComplex(X2,X3)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_43,plain,
c_RealVector_Oof__real(tc_Complex_Ocomplex,X1) = c_Complex_Ocomplex_OComplex(X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_44,plain,
! [X948,X949,X950,X951] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X951,X950),c_Complex_Ocomplex_OComplex(X949,X948)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X951,X949),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X950,X948)),
inference(variable_rename,[status(thm)],[fact_complex__add]) ).
fof(c_0_45,plain,
! [X353] : c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X353,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(X353)),
inference(variable_rename,[status(thm)],[fact_cos__periodic__pi]) ).
fof(c_0_46,plain,
! [X655,X656] : c_Complex_OIm(c_Complex_Ocomplex_OComplex(X656,X655)) = X655,
inference(variable_rename,[status(thm)],[fact_Im]) ).
cnf(c_0_47,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Complex_Ocomplex_OComplex(X2,X3)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X3),
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2),c_Complex_Ocomplex_OComplex(X3,X4)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_49,plain,
c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(X1)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,plain,
c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_cos__zero]) ).
cnf(c_0_51,plain,
c_Complex_OIm(c_Complex_Ocomplex_OComplex(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,plain,
c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X3),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
fof(c_0_53,plain,
! [X445] :
( ( c_NthRoot_Osqrt(X445) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X445 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( X445 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(X445) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__1__iff])])]) ).
fof(c_0_54,plain,
! [X426] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X426),X426)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X426),
inference(variable_rename,[status(thm)],[fact_real__sqrt__abs2]) ).
fof(c_0_55,plain,
! [X644] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(X644)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Osin(X644) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sin__zero__abs__cos__one])])]) ).
fof(c_0_56,plain,
! [X99] : c_Complex_Orcis(X99,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(tc_Complex_Ocomplex,X99),
inference(variable_rename,[status(thm)],[fact_rcis__zero__arg]) ).
fof(c_0_57,plain,
! [X129,X130] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X130,X129))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X130),X129) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X130),X129)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X130,X129)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__less__add__iff])])]) ).
fof(c_0_58,plain,
! [X156] : 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,X156))),
inference(variable_rename,[status(thm)],[fact_abs__add__one__gt__zero]) ).
cnf(c_0_59,plain,
c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_60,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_51]) ).
fof(c_0_61,plain,
! [X548] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X548)) = c_RealDef_Oreal(tc_Nat_Onat,X548),
inference(variable_rename,[status(thm)],[fact_abs__real__of__nat__cancel]) ).
cnf(c_0_62,plain,
( c_NthRoot_Osqrt(X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X1 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_63,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_64,plain,
( c_Transcendental_Osin(X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(X1)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_65,plain,
c_Transcendental_Osin(c_Transcendental_Opi) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_sin__pi]) ).
fof(c_0_66,plain,
! [X107,X108] : c_Complex_OIm(c_Complex_Orcis(X108,X107)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X108),c_Transcendental_Osin(X107)),
inference(variable_rename,[status(thm)],[fact_Im__rcis]) ).
cnf(c_0_67,plain,
c_Complex_Orcis(X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(tc_Complex_Ocomplex,X1),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
fof(c_0_68,plain,
! [X44] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X44,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X44) = X44 )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X44,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X44) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X44) ) ),
inference(fof_simplification,[status(thm)],[fact_real__abs__def]) ).
cnf(c_0_69,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,X1,X2))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_70,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_58]) ).
cnf(c_0_71,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_Transcendental_Opi),
inference(rw,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_72,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)) = c_RealDef_Oreal(tc_Nat_Onat,X1),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_73,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]) ).
fof(c_0_74,plain,
! [X645,X646] : c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X646,X645)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X646)),c_Transcendental_Ocos(X645)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X646)),c_Transcendental_Osin(X645))),
inference(variable_rename,[status(thm)],[fact_cos__add]) ).
cnf(c_0_75,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_76,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(c_Transcendental_Opi)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_77,plain,
c_Complex_OIm(c_Complex_Orcis(X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Transcendental_Osin(X2)),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_78,plain,
c_Complex_Orcis(X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Complex_Ocomplex_OComplex(X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[c_0_67,c_0_43]) ).
cnf(c_0_79,plain,
c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_sin__zero]) ).
fof(c_0_80,plain,
! [X153] :
( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X153) = X153
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X153,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X153) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X153)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X153,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])])]) ).
cnf(c_0_81,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Ocos(c_Transcendental_Opi),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_82,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_83,plain,
c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(X1)),c_Transcendental_Ocos(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(X1)),c_Transcendental_Osin(X2))),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_84,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi)),c_Transcendental_Ocos(c_Transcendental_Opi)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_85,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_51]),c_0_79]) ).
fof(c_0_86,plain,
! [X119,X120] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X120,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X119)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X120 != X119 )
& ( X120 = X119
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X120,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X119)) != 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__minus__iff])])]) ).
fof(c_0_87,plain,
! [X123,X124] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X124,X123) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X124,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X123)),
inference(variable_rename,[status(thm)],[fact_minus__real__def]) ).
cnf(c_0_88,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) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_89,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Ocos(c_Transcendental_Opi),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_90,plain,
c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,c_Transcendental_Opi)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_65]),c_0_65]),c_0_85]) ).
cnf(c_0_91,plain,
( X1 != X2
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_92,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_87]) ).
cnf(c_0_93,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_76]),c_0_49]),c_0_90]) ).
fof(c_0_94,plain,
! [X364,X365] :
( X365 = X364
| hAPP(X365,esk9_2(X364,X365)) != hAPP(X364,esk9_2(X364,X365)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])]) ).
fof(c_0_95,plain,
! [X502] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X502) = X502,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
fof(c_0_96,plain,
! [X117,X118] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X118,X117) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X117 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X118) )
& ( X117 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X118)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X118,X117) != 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])])]) ).
fof(c_0_97,plain,
! [X191,X192,X193] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X193,X192)),X191) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X193),X191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X192),X191)),
inference(variable_rename,[status(thm)],[fact_real__add__mult__distrib]) ).
cnf(c_0_98,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(er,[status(thm)],[c_0_91]) ).
cnf(c_0_99,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Transcendental_Opi))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Transcendental_Ocos(X2)),
inference(spm,[status(thm)],[c_0_92,c_0_49]) ).
cnf(c_0_100,plain,
c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,c_Transcendental_Opi)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_90,c_0_93]) ).
cnf(c_0_101,plain,
( hAPP(X1,esk9_2(X2,X1)) != hAPP(X2,esk9_2(X2,X1))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_102,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_95]) ).
fof(c_0_103,plain,
! [X505] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X505) = X505,
inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).
fof(c_0_104,plain,
! [X197,X198] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X198),X197) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X197),X198),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
fof(c_0_105,negated_conjecture,
c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_106,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_107,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)),X3) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_108,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_98,c_0_92]) ).
cnf(c_0_109,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Transcendental_Ocos(c_Transcendental_Opi)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_110,plain,
( hAPP(X1,esk9_2(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) != esk9_2(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)
| X1 = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_111,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_112,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_104]) ).
fof(c_0_113,plain,
! [X194,X195,X196] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X196),X195)),X194) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X195),X194)),
inference(variable_rename,[status(thm)],[fact_real__mult__assoc]) ).
fof(c_0_114,negated_conjecture,
c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_115,plain,
! [X97,X98] : c_Complex_Orcis(X98,X97) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X98)),c_Complex_Ocis(X97)),
inference(variable_rename,[status(thm)],[fact_rcis__def]) ).
fof(c_0_116,plain,
! [X463] : c_Complex_Ocis(X463) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X463),c_Transcendental_Osin(X463)),
inference(variable_rename,[status(thm)],[fact_cis__def]) ).
cnf(c_0_117,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X1)),X2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2)) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_118,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Ocos(c_Transcendental_Opi),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_119,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_120,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_85,c_0_112]) ).
cnf(c_0_121,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
fof(c_0_122,negated_conjecture,
c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
inference(fof_nnf,[status(thm)],[c_0_114]) ).
fof(c_0_123,plain,
! [X428,X429] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X429),X428)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(X429)),c_NthRoot_Osqrt(X428)),
inference(variable_rename,[status(thm)],[fact_real__sqrt__mult]) ).
cnf(c_0_124,plain,
c_Complex_Orcis(X1,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X1)),c_Complex_Ocis(X2)),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_125,plain,
c_Complex_Ocis(X1) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X1),c_Transcendental_Osin(X1)),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
fof(c_0_126,plain,
! [X461,X462] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X462)),c_Complex_Ocis(X461)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X462,X461)),
inference(variable_rename,[status(thm)],[fact_cis__mult]) ).
cnf(c_0_127,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi)),X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119]),c_0_111]),c_0_120])]) ).
cnf(c_0_128,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi)),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_84]),c_0_102]) ).
fof(c_0_129,plain,
! [X633] : c_Transcendental_Osin(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X633)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(X633)),
inference(variable_rename,[status(thm)],[fact_sin__minus]) ).
fof(c_0_130,plain,
! [X355] : c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X355,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(X355)),
inference(variable_rename,[status(thm)],[fact_sin__periodic__pi]) ).
fof(c_0_131,plain,
! [X475,X476,X477] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X477,X476),c_RealVector_Oof__real(tc_Complex_Ocomplex,X475)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X477,X475),X476),
inference(variable_rename,[status(thm)],[fact_Complex__add__complex__of__real]) ).
cnf(c_0_132,negated_conjecture,
c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_133,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1)),c_NthRoot_Osqrt(X2)),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
fof(c_0_134,plain,
! [X93,X94,X95,X96] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(X96,X95)),c_Complex_Orcis(X94,X93)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X96),X94),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X95,X93)),
inference(variable_rename,[status(thm)],[fact_rcis__mult]) ).
cnf(c_0_135,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Complex_Ocis(X2)) = c_Complex_Orcis(X1,X2),
inference(rw,[status(thm)],[c_0_124,c_0_43]) ).
cnf(c_0_136,plain,
c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(c_Transcendental_Opi),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Complex_Ocis(c_Transcendental_Opi),
inference(spm,[status(thm)],[c_0_125,c_0_65]) ).
cnf(c_0_137,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X1)),c_Complex_Ocis(X2)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_138,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi)),X1) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
fof(c_0_139,plain,
! [X635] :
( c_Transcendental_Osin(X635) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X635) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_cos__one__sin__zero])])]) ).
fof(c_0_140,plain,
! [X684] : c_Transcendental_Ocos(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X684)) = c_Transcendental_Ocos(X684),
inference(variable_rename,[status(thm)],[fact_cos__minus]) ).
cnf(c_0_141,plain,
c_Transcendental_Osin(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(X1)),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_142,plain,
c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(X1)),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_143,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2),c_RealVector_Oof__real(tc_Complex_Ocomplex,X3)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_144,negated_conjecture,
c_Complex_Orcis(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_133]),c_0_63]) ).
cnf(c_0_145,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = 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_80]) ).
cnf(c_0_146,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(X1,X2)),c_Complex_Orcis(X3,X4)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_147,plain,
c_Complex_Orcis(c_Transcendental_Ocos(c_Transcendental_Opi),X1) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137]) ).
cnf(c_0_148,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Transcendental_Ocos(c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),
inference(spm,[status(thm)],[c_0_112,c_0_138]) ).
cnf(c_0_149,plain,
( c_Transcendental_Ocos(X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Osin(X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_150,plain,
c_Transcendental_Ocos(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Transcendental_Ocos(X1),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_151,plain,
c_Transcendental_Osin(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Transcendental_Opi)),
inference(rw,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_152,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2),c_Complex_Ocomplex_OComplex(X3,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3),X2),
inference(rw,[status(thm)],[c_0_143,c_0_43]) ).
cnf(c_0_153,negated_conjecture,
( c_Complex_Orcis(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r),v_a)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_154,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(X1,X2)),c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,X3))) = c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148]) ).
fof(c_0_155,plain,
! [X141,X142] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X142,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X141))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X141,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X142))),
inference(variable_rename,[status(thm)],[fact_abs__minus__add__cancel]) ).
cnf(c_0_156,plain,
( c_Transcendental_Ocos(X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Transcendental_Opi)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_151]) ).
cnf(c_0_157,plain,
c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_142,c_0_79]) ).
cnf(c_0_158,plain,
c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X3),
inference(rw,[status(thm)],[c_0_152,c_0_48]) ).
cnf(c_0_159,negated_conjecture,
( c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r),v_a) != c_Complex_Orcis(v_r,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[c_0_153,c_0_145]) ).
cnf(c_0_160,plain,
c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) = c_Complex_Orcis(X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_78]),c_0_135]),c_0_60]) ).
cnf(c_0_161,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_155]) ).
cnf(c_0_162,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_50]),c_0_157]) ).
cnf(c_0_163,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_158]),c_0_51]) ).
cnf(c_0_164,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_160])]) ).
cnf(c_0_165,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_161,c_0_92]),c_0_92]) ).
cnf(c_0_166,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_92,c_0_162]),c_0_163]) ).
cnf(c_0_167,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_92,c_0_60]) ).
cnf(c_0_168,negated_conjecture,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r),
inference(spm,[status(thm)],[c_0_88,c_0_164]) ).
cnf(c_0_169,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)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_167]) ).
cnf(c_0_170,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_160]),c_0_168]),c_0_169]),c_0_168]),c_0_160]),c_0_168]),c_0_160])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW231+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 09:42:28 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 218.40/32.19 % Version: 3.5.1
% 218.40/32.19 % Preprocessing class: FMLMSMSMSSSNFFN.
% 218.40/32.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 218.40/32.19 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 218.40/32.19 % Starting new_bool_3 with 300s (1) cores
% 218.40/32.19 % Starting new_bool_1 with 300s (1) cores
% 218.40/32.19 % Starting sh5l with 300s (1) cores
% 218.40/32.19 % new_bool_3 with pid 1439876 completed with status 0
% 218.40/32.19 % Result found by new_bool_3
% 218.40/32.19 % Preprocessing class: FMLMSMSMSSSNFFN.
% 218.40/32.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 218.40/32.19 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 218.40/32.19 % Starting new_bool_3 with 300s (1) cores
% 218.40/32.19 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 218.40/32.19 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 218.40/32.19 % Search class: FGHSM-FSLM31-DFFFFFNN
% 218.40/32.19 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 218.40/32.19 % Starting SubtermCWHack with 28s (1) cores
% 218.40/32.19 % SubtermCWHack with pid 1439883 completed with status 8
% 218.40/32.19 % Starting new_bool_3 with 31s (1) cores
% 218.40/32.19 % new_bool_3 with pid 1439924 completed with status 0
% 218.40/32.19 % Result found by new_bool_3
% 218.40/32.19 % Preprocessing class: FMLMSMSMSSSNFFN.
% 218.40/32.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 218.40/32.19 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 218.40/32.19 % Starting new_bool_3 with 300s (1) cores
% 218.40/32.19 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 218.40/32.19 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 218.40/32.19 % Search class: FGHSM-FSLM31-DFFFFFNN
% 218.40/32.19 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 218.40/32.19 % Starting SubtermCWHack with 28s (1) cores
% 218.40/32.19 % SubtermCWHack with pid 1439883 completed with status 8
% 218.40/32.19 % Starting new_bool_3 with 31s (1) cores
% 218.40/32.19 % Preprocessing time : 0.014 s
% 218.40/32.19 % Presaturation interreduction done
% 218.40/32.19
% 218.40/32.19 % Proof found!
% 218.40/32.19 % SZS status Theorem
% 218.40/32.19 % SZS output start CNFRefutation
% See solution above
% 218.40/32.19 % Parsed axioms : 1201
% 218.40/32.19 % Removed by relevancy pruning/SinE : 789
% 218.40/32.19 % Initial clauses : 566
% 218.40/32.19 % Removed in clause preprocessing : 14
% 218.40/32.19 % Initial clauses in saturation : 552
% 218.40/32.19 % Processed clauses : 13458
% 218.40/32.19 % ...of these trivial : 827
% 218.40/32.19 % ...subsumed : 7412
% 218.40/32.19 % ...remaining for further processing : 5218
% 218.40/32.19 % Other redundant clauses eliminated : 206
% 218.40/32.19 % Clauses deleted for lack of memory : 0
% 218.40/32.19 % Backward-subsumed : 47
% 218.40/32.19 % Backward-rewritten : 689
% 218.40/32.19 % Generated clauses : 78200
% 218.40/32.19 % ...of the previous two non-redundant : 64192
% 218.40/32.19 % ...aggressively subsumed : 0
% 218.40/32.19 % Contextual simplify-reflections : 6
% 218.40/32.19 % Paramodulations : 77962
% 218.40/32.19 % Factorizations : 10
% 218.40/32.19 % NegExts : 0
% 218.40/32.19 % Equation resolutions : 235
% 218.40/32.19 % Disequality decompositions : 0
% 218.40/32.19 % Total rewrite steps : 112982
% 218.40/32.19 % ...of those cached : 105800
% 218.40/32.19 % Propositional unsat checks : 1
% 218.40/32.19 % Propositional check models : 0
% 218.40/32.19 % Propositional check unsatisfiable : 0
% 218.40/32.19 % Propositional clauses : 0
% 218.40/32.19 % Propositional clauses after purity: 0
% 218.40/32.19 % Propositional unsat core size : 0
% 218.40/32.19 % Propositional preprocessing time : 0.000
% 218.40/32.19 % Propositional encoding time : 0.094
% 218.40/32.19 % Propositional solver time : 0.131
% 218.40/32.19 % Success case prop preproc time : 0.000
% 218.40/32.19 % Success case prop encoding time : 0.000
% 218.40/32.19 % Success case prop solver time : 0.000
% 218.40/32.19 % Current number of processed clauses : 3985
% 218.40/32.19 % Positive orientable unit clauses : 1456
% 218.40/32.19 % Positive unorientable unit clauses: 19
% 218.40/32.19 % Negative unit clauses : 613
% 218.40/32.19 % Non-unit-clauses : 1897
% 218.40/32.19 % Current number of unprocessed clauses: 50137
% 218.40/32.19 % ...number of literals in the above : 89992
% 218.40/32.19 % Current number of archived formulas : 0
% 218.40/32.19 % Current number of archived clauses : 1185
% 218.40/32.19 % Clause-clause subsumption calls (NU) : 311153
% 218.40/32.19 % Rec. Clause-clause subsumption calls : 296197
% 218.40/32.19 % Non-unit clause-clause subsumptions : 2446
% 218.40/32.19 % Unit Clause-clause subsumption calls : 124559
% 218.40/32.19 % Rewrite failures with RHS unbound : 0
% 218.40/32.19 % BW rewrite match attempts : 121203
% 218.40/32.19 % BW rewrite match successes : 772
% 218.40/32.19 % Condensation attempts : 0
% 218.40/32.19 % Condensation successes : 0
% 218.40/32.19 % Termbank termtop insertions : 1970337
% 218.40/32.19 % Search garbage collected termcells : 9808
% 218.40/32.19
% 218.40/32.19 % -------------------------------------------------
% 218.40/32.19 % User time : 30.599 s
% 218.40/32.19 % System time : 0.828 s
% 218.40/32.19 % Total time : 31.428 s
% 218.40/32.19 % Maximum resident set size: 6224 pages
% 218.40/32.19
% 218.40/32.19 % -------------------------------------------------
% 218.40/32.19 % User time : 30.639 s
% 218.40/32.19 % System time : 0.834 s
% 218.40/32.19 % Total time : 31.473 s
% 218.40/32.19 % Maximum resident set size: 6144 pages
% 218.40/32.19 % E exiting
%------------------------------------------------------------------------------