TSTP Solution File: SWW203+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SWW203+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 00:10:17 EDT 2022
% Result : Theorem 0.62s 41.82s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 19
% Syntax : Number of formulae : 74 ( 57 unt; 0 def)
% Number of atoms : 91 ( 53 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 35 ( 18 ~; 12 |; 0 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 7 con; 0-3 aty)
% Number of variables : 72 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Bit0__def,axiom,
! [X16] : c_Int_OBit0(X16) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,X16),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_Bit0__def) ).
fof(fact_complex__norm,axiom,
! [X1,X2] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X2,X1)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_complex__norm) ).
fof(fact_semiring__norm_I112_J,axiom,
! [X7] :
( class_Int_Onumber__ring(X7)
=> c_Groups_Ozero__class_Ozero(X7) = c_Int_Onumber__class_Onumber__of(X7,c_Int_OPls) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_semiring__norm_I112_J) ).
fof(fact__096sqrt_A_I_IRe_Ax_A_N_ARe_Ay_A_L_A0_J_A_094_A2_A_L_A_I0_A_L_A_IIm_Ax_A_N_AIm_Ay_J_J_A_094_A2_J_060_061_Asqrt_A_I_IRe_Ax_A_N_ARe_Ay_J_A_094_A2_A_L_A0_A_094_A2_J_A_L_Asqrt_A_I0_A_094_A2_A_L_A_IIm_Ax_A_N_AIm_Ay_J_A_094_A2_J_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact__096sqrt_A_I_IRe_Ax_A_N_ARe_Ay_A_L_A0_J_A_094_A2_A_L_A_I0_A_L_A_IIm_Ax_A_N_AIm_Ay_J_J_A_094_A2_J_060_061_Asqrt_A_I_IRe_Ax_A_N_ARe_Ay_J_A_094_A2_A_L_A0_A_094_A2_J_A_L_Asqrt_A_I0_A_094_A2_A_L_A_IIm_Ax_A_N_AIm_Ay_J_A_094_A2_J_096) ).
fof(fact_Re_Odiff,axiom,
! [X1,X2] : c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X1)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(X2),c_Complex_ORe(X1)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_Re_Odiff) ).
fof(fact_semiring__norm_I115_J,axiom,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_semiring__norm_I115_J) ).
fof(fact_Im_Odiff,axiom,
! [X1,X2] : c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X1)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X2),c_Complex_OIm(X1)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_Im_Odiff) ).
fof(fact_add__numeral__0__right,axiom,
! [X6,X7] :
( class_Int_Onumber__ring(X7)
=> c_Groups_Oplus__class_Oplus(X7,X6,c_Int_Onumber__class_Onumber__of(X7,c_Int_OPls)) = X6 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_add__numeral__0__right) ).
fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_0) ).
fof(fact_add__numeral__0,axiom,
! [X6,X7] :
( class_Int_Onumber__ring(X7)
=> c_Groups_Oplus__class_Oplus(X7,c_Int_Onumber__class_Onumber__of(X7,c_Int_OPls),X6) = X6 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_add__numeral__0) ).
fof(fact_zero__power2,axiom,
! [X7] :
( class_Rings_Osemiring__1(X7)
=> c_Power_Opower__class_Opower(X7,c_Groups_Ozero__class_Ozero(X7),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X7) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_zero__power2) ).
fof(fact_real__sqrt__abs,axiom,
! [X2] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_real__sqrt__abs) ).
fof(fact_complex__surj,axiom,
! [X17] : c_Complex_Ocomplex_OComplex(c_Complex_ORe(X17),c_Complex_OIm(X17)) = X17,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_complex__surj) ).
fof(fact_norm__of__real,axiom,
! [X44,X7] :
( class_RealVector_Oreal__normed__algebra__1(X7)
=> c_RealVector_Onorm__class_Onorm(X7,c_RealVector_Oof__real(X7,X44)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X44) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_norm__of__real) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_complex__of__real__def) ).
fof(fact_real__sqrt__power,axiom,
! [X16,X2] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,X16)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X2),X16),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_real__sqrt__power) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(arity_RealDef__Oreal__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Rings_Osemiring__1) ).
fof(c_0_19,plain,
! [X17] : c_Int_OBit0(X17) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,X17),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_20,plain,
! [X3,X4] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X4,X3)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(variable_rename,[status(thm)],[fact_complex__norm]) ).
fof(c_0_21,plain,
! [X8] :
( ~ class_Int_Onumber__ring(X8)
| c_Groups_Ozero__class_Ozero(X8) = c_Int_Onumber__class_Onumber__of(X8,c_Int_OPls) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J])]) ).
cnf(c_0_22,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(split_conjunct,[status(thm)],[fact__096sqrt_A_I_IRe_Ax_A_N_ARe_Ay_A_L_A0_J_A_094_A2_A_L_A_I0_A_L_A_IIm_Ax_A_N_AIm_Ay_J_J_A_094_A2_J_060_061_Asqrt_A_I_IRe_Ax_A_N_ARe_Ay_J_A_094_A2_A_L_A0_A_094_A2_J_A_L_Asqrt_A_I0_A_094_A2_A_L_A_IIm_Ax_A_N_AIm_Ay_J_A_094_A2_J_096]) ).
cnf(c_0_23,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_24,plain,
! [X3,X4] : c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X3)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(X4),c_Complex_ORe(X3)),
inference(variable_rename,[status(thm)],[fact_Re_Odiff]) ).
cnf(c_0_25,plain,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_semiring__norm_I115_J]) ).
fof(c_0_26,plain,
! [X3,X4] : c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4,X3)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X4),c_Complex_OIm(X3)),
inference(variable_rename,[status(thm)],[fact_Im_Odiff]) ).
cnf(c_0_27,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_28,plain,
! [X8,X9] :
( ~ class_Int_Onumber__ring(X9)
| c_Groups_Oplus__class_Oplus(X9,X8,c_Int_Onumber__class_Onumber__of(X9,c_Int_OPls)) = X8 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right])]) ).
cnf(c_0_29,plain,
( c_Groups_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).
fof(c_0_31,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_32,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]) ).
cnf(c_0_33,plain,
c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(X1),c_Complex_ORe(X2)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))),
inference(rw,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_35,plain,
c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X1),c_Complex_OIm(X2)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_23]),c_0_23]) ).
cnf(c_0_37,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_39,plain,
! [X8,X9] :
( ~ class_Int_Onumber__ring(X9)
| c_Groups_Oplus__class_Oplus(X9,c_Int_Onumber__class_Onumber__of(X9,c_Int_OPls),X8) = X8 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0])]) ).
fof(c_0_40,plain,
! [X8] :
( ~ class_Rings_Osemiring__1(X8)
| c_Power_Opower__class_Opower(X8,c_Groups_Ozero__class_Ozero(X8),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__power2])]) ).
fof(c_0_41,plain,
! [X3] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3),
inference(variable_rename,[status(thm)],[fact_real__sqrt__abs]) ).
fof(c_0_42,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
cnf(c_0_43,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]),c_0_34]),c_0_33]),c_0_34]),c_0_34]),c_0_34]),c_0_35]),c_0_34]) ).
cnf(c_0_44,plain,
c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_34]),c_0_34]) ).
cnf(c_0_45,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_37,c_0_30]),c_0_38]) ).
cnf(c_0_46,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls),X2) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_47,plain,
! [X18] : c_Complex_Ocomplex_OComplex(c_Complex_ORe(X18),c_Complex_OIm(X18)) = X18,
inference(variable_rename,[status(thm)],[fact_complex__surj]) ).
fof(c_0_48,plain,
! [X45,X46] :
( ~ class_RealVector_Oreal__normed__algebra__1(X46)
| c_RealVector_Onorm__class_Onorm(X46,c_RealVector_Oof__real(X46,X45)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X45) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__of__real])]) ).
fof(c_0_49,plain,
! [X45] : c_RealVector_Oof__real(tc_Complex_Ocomplex,X45) = c_Complex_Ocomplex_OComplex(X45,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[fact_complex__of__real__def]) ).
cnf(c_0_50,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,plain,
c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_52,plain,
! [X17,X18] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,X17)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X18),X17),
inference(variable_rename,[status(thm)],[fact_real__sqrt__power]) ).
cnf(c_0_53,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_54,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_44]),c_0_44]),c_0_45]) ).
cnf(c_0_55,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_46,c_0_30]),c_0_38]) ).
cnf(c_0_56,plain,
c_Complex_Ocomplex_OComplex(c_Complex_ORe(X1),c_Complex_OIm(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_57,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_58,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1]) ).
cnf(c_0_59,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_49]) ).
cnf(c_0_60,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(rw,[status(thm)],[c_0_50,c_0_23]) ).
cnf(c_0_61,plain,
c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(rw,[status(thm)],[c_0_51,c_0_23]) ).
cnf(c_0_62,plain,
c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,X2)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),X2),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_63,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_23]),c_0_23]) ).
cnf(c_0_64,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_65,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_66,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(rw,[status(thm)],[c_0_60,c_0_34]) ).
cnf(c_0_67,plain,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__1]) ).
cnf(c_0_68,plain,
c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_34]),c_0_62]) ).
cnf(c_0_69,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(rw,[status(thm)],[c_0_63,c_0_33]) ).
cnf(c_0_70,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))))),
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_71,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_66]),c_0_67])]),c_0_55]),c_0_62]),c_0_68]) ).
cnf(c_0_72,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_35]),c_0_34]),c_0_34]),c_0_44]),c_0_56]) ).
cnf(c_0_73,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71]),c_0_72]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWW203+1 : TPTP v8.1.0. Released v5.2.0.
% 0.08/0.14 % Command : run_ET %s %d
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 6 09:35:31 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.51/23.55 eprover: CPU time limit exceeded, terminating
% 0.51/23.55 eprover: CPU time limit exceeded, terminating
% 0.51/23.56 eprover: CPU time limit exceeded, terminating
% 0.51/23.56 eprover: CPU time limit exceeded, terminating
% 0.62/41.82 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.62/41.82
% 0.62/41.82 # Failure: Resource limit exceeded (time)
% 0.62/41.82 # OLD status Res
% 0.62/41.82 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.62/41.82 # Preprocessing time : 0.029 s
% 0.62/41.82 # Running protocol protocol_eprover_f171197f65f27d1ba69648a20c844832c84a5dd7 for 23 seconds:
% 0.62/41.82 # Preprocessing time : 0.129 s
% 0.62/41.82
% 0.62/41.82 # Proof found!
% 0.62/41.82 # SZS status Theorem
% 0.62/41.82 # SZS output start CNFRefutation
% See solution above
% 0.62/41.82 # Proof object total steps : 74
% 0.62/41.82 # Proof object clause steps : 40
% 0.62/41.82 # Proof object formula steps : 34
% 0.62/41.82 # Proof object conjectures : 7
% 0.62/41.82 # Proof object clause conjectures : 4
% 0.62/41.82 # Proof object formula conjectures : 3
% 0.62/41.82 # Proof object initial clauses used : 19
% 0.62/41.82 # Proof object initial formulas used : 19
% 0.62/41.82 # Proof object generating inferences : 5
% 0.62/41.82 # Proof object simplifying inferences : 51
% 0.62/41.82 # Training examples: 0 positive, 0 negative
% 0.62/41.82 # Parsed axioms : 1202
% 0.62/41.82 # Removed by relevancy pruning/SinE : 0
% 0.62/41.82 # Initial clauses : 1695
% 0.62/41.82 # Removed in clause preprocessing : 85
% 0.62/41.82 # Initial clauses in saturation : 1610
% 0.62/41.82 # Processed clauses : 49195
% 0.62/41.82 # ...of these trivial : 1099
% 0.62/41.82 # ...subsumed : 39878
% 0.62/41.82 # ...remaining for further processing : 8218
% 0.62/41.82 # Other redundant clauses eliminated : 762
% 0.62/41.82 # Clauses deleted for lack of memory : 315532
% 0.62/41.82 # Backward-subsumed : 791
% 0.62/41.82 # Backward-rewritten : 757
% 0.62/41.82 # Generated clauses : 562196
% 0.62/41.82 # ...of the previous two non-trivial : 493872
% 0.62/41.82 # Contextual simplify-reflections : 7909
% 0.62/41.82 # Paramodulations : 561196
% 0.62/41.82 # Factorizations : 10
% 0.62/41.82 # Equation resolutions : 987
% 0.62/41.82 # Current number of processed clauses : 6643
% 0.62/41.82 # Positive orientable unit clauses : 958
% 0.62/41.82 # Positive unorientable unit clauses: 53
% 0.62/41.82 # Negative unit clauses : 1087
% 0.62/41.82 # Non-unit-clauses : 4545
% 0.62/41.82 # Current number of unprocessed clauses: 92649
% 0.62/41.82 # ...number of literals in the above : 258195
% 0.62/41.82 # Current number of archived formulas : 0
% 0.62/41.82 # Current number of archived clauses : 1553
% 0.62/41.82 # Clause-clause subsumption calls (NU) : 8160301
% 0.62/41.82 # Rec. Clause-clause subsumption calls : 4596495
% 0.62/41.82 # Non-unit clause-clause subsumptions : 23314
% 0.62/41.82 # Unit Clause-clause subsumption calls : 272303
% 0.62/41.82 # Rewrite failures with RHS unbound : 2
% 0.62/41.82 # BW rewrite match attempts : 27868
% 0.62/41.82 # BW rewrite match successes : 1113
% 0.62/41.82 # Condensation attempts : 0
% 0.62/41.82 # Condensation successes : 0
% 0.62/41.82 # Termbank termtop insertions : 11172471
% 0.62/41.82
% 0.62/41.82 # -------------------------------------------------
% 0.62/41.82 # User time : 17.489 s
% 0.62/41.82 # System time : 0.207 s
% 0.62/41.82 # Total time : 17.696 s
% 0.62/41.82 # Maximum resident set size: 143344 pages
% 0.62/46.60 eprover: CPU time limit exceeded, terminating
% 0.62/46.61 eprover: CPU time limit exceeded, terminating
% 0.62/46.62 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/46.62 eprover: No such file or directory
% 0.62/46.62 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/46.62 eprover: No such file or directory
% 0.62/46.62 eprover: CPU time limit exceeded, terminating
% 0.62/46.63 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/46.63 eprover: No such file or directory
% 0.62/46.63 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.62/46.63 eprover: No such file or directory
% 0.62/46.63 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/46.63 eprover: No such file or directory
% 0.62/46.64 eprover: eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.62/46.64 eprover: No such file or directory
% 0.62/46.64 Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/46.64 eprover: No such file or directory
% 0.62/46.64 eprover: eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/46.64 eprover: No such file or directory
% 0.62/46.64 Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.62/46.64 eprover: No such file or directory
% 0.62/46.65 eprover: eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.pCannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/46.65
% 0.62/46.65 eprover: No such file or directory
% 0.62/46.65 eprover: No such file or directory
% 0.62/46.65 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.62/46.65 eprover: No such file or directory
% 0.62/46.65 eprover: eprover: eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.pCannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/46.65
% 0.62/46.65 eprover: No such file or directory
% 0.62/46.65 eprover: No such file or directory
% 0.62/46.65 Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.62/46.65 eprover: No such file or directory
% 0.62/46.66 eprover: eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.peprover:
% 0.62/46.66 Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.62/46.66 Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/46.66 eprover: No such file or directory
% 0.62/46.66 eprover: No such file or directory
% 0.62/46.66 eprover: No such file or directory
% 0.62/46.66 eprover: eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.peprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.62/46.66
% 0.62/46.66 Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/46.66 eprover: No such file or directory
% 0.62/46.66 eprover: No such file or directory
% 0.62/46.66 eprover: No such file or directory
% 0.62/46.67 eprover: eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.62/46.67 eprover: No such file or directory
% 0.62/46.67 Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.62/46.67 eprover: No such file or directory
% 0.62/46.67 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.62/46.67 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.62/46.67 eprover: No such file or directory
% 0.62/46.67 eprover: No such file or directory
% 0.62/46.68 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.62/46.68 eprover: No such file or directory
% 0.62/46.68 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.62/46.68 eprover: No such file or directory
% 0.62/46.68 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.62/46.68 eprover: No such file or directory
% 0.62/46.69 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.62/46.69 eprover: No such file or directory
% 0.62/46.69 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.62/46.69 eprover: No such file or directory
%------------------------------------------------------------------------------