%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW222+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 03:10:06 PM UTC 2026
% Result : Theorem 6.41s 6.27s
% Output : CNFRefutation 6.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 49 ( 31 unt; 0 def)
% Number of atoms : 83 ( 34 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 62 ( 28 ~; 22 |; 3 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-3 aty)
% Number of variables : 45 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_abs__minus__add__cancel,axiom,
! [X23,X9] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X9,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X23))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X23,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X9))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__add__cancel) ).
fof(fact_minus__real__def,axiom,
! [X23,X9] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X9,X23) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X9,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__real__def) ).
fof(fact_real__norm__def,axiom,
! [X22] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X22) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact__0960_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_061_061_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096,axiom,
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)),v_d____)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____))) )
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0960_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_061_061_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096) ).
fof(fact_zero__less__norm__iff,axiom,
! [X15,X7] :
( class_RealVector_Oreal__normed__vector(X7)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X15))
<=> X15 != c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).
fof(fact_w,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)),v_d____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_w) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(fact_right__minus__eq,axiom,
! [X11,X12,X7] :
( class_Groups_Ogroup__add(X7)
=> ( c_Groups_Ominus__class_Ominus(X7,X12,X11) = c_Groups_Ozero__class_Ozero(X7)
<=> X12 = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).
fof(fact_diff__self,axiom,
! [X8,X7] :
( class_Groups_Ogroup__add(X7)
=> c_Groups_Ominus__class_Ominus(X7,X8,X8) = c_Groups_Ozero__class_Ozero(X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).
fof(fact_norm__zero,axiom,
! [X7] :
( class_RealVector_Oreal__normed__vector(X7)
=> c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__zero) ).
fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(fact_e2,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_e2) ).
fof(c_0_13,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_14,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_15,plain,
! [X683,X684] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X684,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X683))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X683,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X684))),
inference(variable_rename,[status(thm)],[fact_abs__minus__add__cancel]) ).
fof(c_0_16,plain,
! [X679,X680] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X680,X679) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X680,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X679)),
inference(variable_rename,[status(thm)],[fact_minus__real__def]) ).
fof(c_0_17,plain,
! [X674] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X674) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X674),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(c_0_18,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
cnf(c_0_19,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_15]) ).
cnf(c_0_20,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_16]) ).
cnf(c_0_21,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)),v_d____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____))) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__0960_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_061_061_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096])]) ).
fof(c_0_23,plain,
! [X15,X7] :
( class_RealVector_Oreal__normed__vector(X7)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X15))
<=> X15 != c_Groups_Ozero__class_Ozero(X7) ) ),
inference(fof_simplification,[status(thm)],[fact_zero__less__norm__iff]) ).
cnf(c_0_24,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_20]),c_0_21]) ).
cnf(c_0_26,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)),v_d____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)),v_d____),
inference(split_conjunct,[status(thm)],[fact_w]) ).
fof(c_0_28,plain,
! [X998,X999] :
( ( ~ class_RealVector_Oreal__normed__vector(X999)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X999,X998))
| X998 = c_Groups_Ozero__class_Ozero(X999) )
& ( ~ class_RealVector_Oreal__normed__vector(X999)
| X998 != c_Groups_Ozero__class_Ozero(X999)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X999,X998)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
cnf(c_0_29,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_21]),c_0_25]) ).
cnf(c_0_30,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_21]),c_0_25]),c_0_27])]) ).
cnf(c_0_31,plain,
( ~ class_RealVector_Oreal__normed__vector(X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1))
| X1 = c_Groups_Ozero__class_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
fof(c_0_33,plain,
! [X1800,X1801,X1802] :
( ( ~ class_Groups_Ogroup__add(X1802)
| c_Groups_Ominus__class_Ominus(X1802,X1801,X1800) = c_Groups_Ozero__class_Ozero(X1802)
| X1801 != X1800 )
& ( ~ class_Groups_Ogroup__add(X1802)
| X1801 = X1800
| c_Groups_Ominus__class_Ominus(X1802,X1801,X1800) != c_Groups_Ozero__class_Ozero(X1802) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])])]) ).
cnf(c_0_34,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_36,plain,
! [X1798,X1799] :
( c_Groups_Ominus__class_Ominus(X1799,X1798,X1798) = c_Groups_Ozero__class_Ozero(X1799)
| ~ class_Groups_Ogroup__add(X1799) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])])]) ).
fof(c_0_37,plain,
! [X995] :
( c_RealVector_Onorm__class_Onorm(X995,c_Groups_Ozero__class_Ozero(X995)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X995) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__zero])])]) ).
cnf(c_0_38,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,negated_conjecture,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]) ).
cnf(c_0_41,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(split_conjunct,[status(thm)],[fact_e2]) ).
cnf(c_0_44,negated_conjecture,
v_wa____ = v_z____,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_45,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_41,c_0_40]) ).
cnf(c_0_46,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_42,c_0_32]) ).
cnf(c_0_47,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_21]),c_0_25]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_44]),c_0_45]),c_0_46]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWW222+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/5.31 % Computer : n012.cluster.edu
% 0.04/5.31 % Model : x86_64 x86_64
% 0.04/5.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/5.31 % Memory : 8046.5625MB
% 0.04/5.31 % OS : Linux 6.8.0-71-generic
% 0.04/5.31 % CPULimit : 300
% 0.04/5.31 % WCLimit : 300
% 0.04/5.31 % DateTime : Mon Sep 21 09:42:28 UTC 2026
% 0.04/5.31 % CPUTime :
% 0.04/5.31 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/5.34 Running first-order theorem proving
% 0.04/5.34 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 6.41/6.27 % Version: 3.5.1
% 6.41/6.27 % Preprocessing class: FMLMSMSMSSSNFFN.
% 6.41/6.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.41/6.27 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.41/6.27 % Starting new_bool_3 with 300s (1) cores
% 6.41/6.27 % Starting new_bool_1 with 300s (1) cores
% 6.41/6.27 % Starting sh5l with 300s (1) cores
% 6.41/6.27 % sh5l with pid 2098869 completed with status 0
% 6.41/6.27 % Result found by sh5l
% 6.41/6.27 % Preprocessing class: FMLMSMSMSSSNFFN.
% 6.41/6.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.41/6.27 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.41/6.27 % Starting new_bool_3 with 300s (1) cores
% 6.41/6.27 % Starting new_bool_1 with 300s (1) cores
% 6.41/6.27 % Starting sh5l with 300s (1) cores
% 6.41/6.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 6.41/6.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 6.41/6.27 % Search class: FGHSM-SSLM31-DFFFFFNN
% 6.41/6.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 6.41/6.27 % Starting SubtermCWHack with 28s (1) cores
% 6.41/6.27 % SubtermCWHack with pid 2098872 completed with status 0
% 6.41/6.27 % Result found by SubtermCWHack
% 6.41/6.27 % Preprocessing class: FMLMSMSMSSSNFFN.
% 6.41/6.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.41/6.27 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.41/6.27 % Starting new_bool_3 with 300s (1) cores
% 6.41/6.27 % Starting new_bool_1 with 300s (1) cores
% 6.41/6.27 % Starting sh5l with 300s (1) cores
% 6.41/6.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 6.41/6.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 6.41/6.27 % Search class: FGHSM-SSLM31-DFFFFFNN
% 6.41/6.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 6.41/6.27 % Starting SubtermCWHack with 28s (1) cores
% 6.41/6.27 % Preprocessing time : 0.010 s
% 6.41/6.27
% 6.41/6.27 % Proof found!
% 6.41/6.27 % SZS status Theorem
% 6.41/6.27 % SZS output start CNFRefutation
% See solution above
% 6.41/6.27 % Parsed axioms : 1251
% 6.41/6.27 % Removed by relevancy pruning/SinE : 182
% 6.41/6.27 % Initial clauses : 1614
% 6.41/6.27 % Removed in clause preprocessing : 64
% 6.41/6.27 % Initial clauses in saturation : 1550
% 6.41/6.27 % Processed clauses : 13476
% 6.41/6.27 % ...of these trivial : 798
% 6.41/6.27 % ...subsumed : 9077
% 6.41/6.27 % ...remaining for further processing : 3601
% 6.41/6.27 % Other redundant clauses eliminated : 537
% 6.41/6.27 % Clauses deleted for lack of memory : 0
% 6.41/6.27 % Backward-subsumed : 47
% 6.41/6.27 % Backward-rewritten : 105
% 6.41/6.27 % Generated clauses : 78263
% 6.41/6.27 % ...of the previous two non-redundant : 62906
% 6.41/6.27 % ...aggressively subsumed : 0
% 6.41/6.27 % Contextual simplify-reflections : 4
% 6.41/6.27 % Paramodulations : 77703
% 6.41/6.27 % Factorizations : 22
% 6.41/6.27 % NegExts : 0
% 6.41/6.27 % Equation resolutions : 559
% 6.41/6.27 % Disequality decompositions : 0
% 6.41/6.27 % Total rewrite steps : 67114
% 6.41/6.27 % ...of those cached : 62705
% 6.41/6.27 % Propositional unsat checks : 0
% 6.41/6.27 % Propositional check models : 0
% 6.41/6.27 % Propositional check unsatisfiable : 0
% 6.41/6.27 % Propositional clauses : 0
% 6.41/6.27 % Propositional clauses after purity: 0
% 6.41/6.27 % Propositional unsat core size : 0
% 6.41/6.27 % Propositional preprocessing time : 0.000
% 6.41/6.27 % Propositional encoding time : 0.000
% 6.41/6.27 % Propositional solver time : 0.000
% 6.41/6.27 % Success case prop preproc time : 0.000
% 6.41/6.27 % Success case prop encoding time : 0.000
% 6.41/6.27 % Success case prop solver time : 0.000
% 6.41/6.27 % Current number of processed clauses : 3322
% 6.41/6.27 % Positive orientable unit clauses : 1000
% 6.41/6.27 % Positive unorientable unit clauses: 16
% 6.41/6.27 % Negative unit clauses : 585
% 6.41/6.27 % Non-unit-clauses : 1721
% 6.41/6.27 % Current number of unprocessed clauses: 50715
% 6.41/6.27 % ...number of literals in the above : 122507
% 6.41/6.27 % Current number of archived formulas : 0
% 6.41/6.27 % Current number of archived clauses : 152
% 6.41/6.27 % Clause-clause subsumption calls (NU) : 467527
% 6.41/6.27 % Rec. Clause-clause subsumption calls : 320783
% 6.41/6.27 % Non-unit clause-clause subsumptions : 3461
% 6.41/6.27 % Unit Clause-clause subsumption calls : 16932
% 6.41/6.27 % Rewrite failures with RHS unbound : 0
% 6.41/6.27 % BW rewrite match attempts : 31221
% 6.41/6.27 % BW rewrite match successes : 161
% 6.41/6.27 % Condensation attempts : 0
% 6.41/6.27 % Condensation successes : 0
% 6.41/6.27 % Termbank termtop insertions : 1248342
% 6.41/6.27 % Search garbage collected termcells : 18698
% 6.41/6.27
% 6.41/6.27 % -------------------------------------------------
% 6.41/6.27 % User time : 0.841 s
% 6.41/6.27 % System time : 0.041 s
% 6.41/6.27 % Total time : 0.882 s
% 6.41/6.27 % Maximum resident set size: 9580 pages
% 6.41/6.27
% 6.41/6.27 % -------------------------------------------------
% 6.41/6.27 % User time : 0.858 s
% 6.41/6.27 % System time : 0.045 s
% 6.41/6.27 % Total time : 0.903 s
% 6.41/6.27 % Maximum resident set size: 6144 pages
% 6.41/6.27 % E exiting
%------------------------------------------------------------------------------