%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW261+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:30:49 PM UTC 2026
% Result : Theorem 14.02s 8.94s
% Output : CNFRefutation 14.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 78 ( 42 unt; 0 def)
% Number of atoms : 158 ( 47 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 133 ( 53 ~; 54 |; 8 &)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_real__le__linear,axiom,
! [X9,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X9)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(fact_norm__of__real,axiom,
! [X25,X6] :
( class_RealVector_Oreal__normed__algebra__1(X6)
=> c_RealVector_Onorm__class_Onorm(X6,c_RealVector_Oof__real(X6,X25)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X25) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__of__real) ).
fof(fact_real__norm__def,axiom,
! [X25] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X25) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact_less__eq__real__def,axiom,
! [X7,X8] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8,X7)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X8,X7)
| X8 = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(fact_real__mult__1,axiom,
! [X10] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X10) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(fact_xt1_I6_J,axiom,
! [X10,X5,X4,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X4,X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X10,X4)
=> c_Orderings_Oord__class_Oless__eq(X6,X10,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_abs__of__nonneg,axiom,
! [X22,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X22)
=> c_Groups_Oabs__class_Oabs(X6,X22) = X22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
fof(fact_t_I1_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_t_I1_J) ).
fof(fact_real__le__antisym,axiom,
! [X9,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X10)
=> X10 = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(fact__096t_A_K_Acmod_Aw_A_060_061_A1_A_K_Acmod_Aw_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096t_A_K_Acmod_Aw_A_060_061_A1_A_K_Acmod_Aw_096) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(fact_norm__mult__ineq,axiom,
! [X4,X5,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X6,X5)),c_RealVector_Onorm__class_Onorm(X6,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(fact_real__mult__right__cancel,axiom,
! [X17,X18,X19] :
( X19 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X18),X19) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X19)
<=> X18 = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
fof(fact_less__le__not__le,axiom,
! [X7,X8,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X8,X7)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X8,X7)
& ~ c_Orderings_Oord__class_Oless__eq(X6,X7,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_norm__le__zero__iff,axiom,
! [X8,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X8),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X8 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).
fof(fact_real__le__refl,axiom,
! [X9] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).
fof(fact_t_I2_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_t_I2_J) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
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_w0,axiom,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_w0) ).
fof(c_0_24,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(c_0_25,plain,
! [X2833,X2834] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2834,X2833)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2833,X2834) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
fof(c_0_26,plain,
! [X4723,X4724] :
( ~ class_RealVector_Oreal__normed__algebra__1(X4724)
| c_RealVector_Onorm__class_Onorm(X4724,c_RealVector_Oof__real(X4724,X4723)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4723) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__of__real])]) ).
fof(c_0_27,plain,
! [X4653] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X4653) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4653),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(c_0_28,plain,
! [X3022,X3023] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3023,X3022)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3023,X3022)
| X3023 = X3022 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3023,X3022)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3023,X3022) )
& ( X3023 != X3022
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3023,X3022) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).
fof(c_0_29,plain,
! [X2855] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X2855) = X2855,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
fof(c_0_30,plain,
! [X3043,X3044,X3045,X3046] :
( ~ class_Orderings_Oorder(X3046)
| ~ c_Orderings_Oord__class_Oless__eq(X3046,X3045,X3044)
| ~ c_Orderings_Oord__class_Oless__eq(X3046,X3043,X3045)
| c_Orderings_Oord__class_Oless__eq(X3046,X3043,X3044) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
cnf(c_0_31,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,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_26]) ).
cnf(c_0_34,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_27]) ).
fof(c_0_35,plain,
! [X4675,X4676] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4676)
| ~ c_Orderings_Oord__class_Oless__eq(X4676,c_Groups_Ozero__class_Ozero(X4676),X4675)
| c_Groups_Oabs__class_Oabs(X4676,X4675) = X4675 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])]) ).
cnf(c_0_36,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),
inference(split_conjunct,[status(thm)],[fact_t_I1_J]) ).
fof(c_0_38,plain,
! [X2838,X2839] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2839,X2838)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2838,X2839)
| X2839 = X2838 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])]) ).
cnf(c_0_39,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))),
inference(split_conjunct,[status(thm)],[fact__096t_A_K_Acmod_Aw_A_060_061_A1_A_K_Acmod_Aw_096]) ).
cnf(c_0_40,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_29]) ).
cnf(c_0_41,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_42,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_43,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
fof(c_0_44,plain,
! [X2818,X2819,X2820] :
( ~ class_RealVector_Oreal__normed__algebra(X2820)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2820,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2820),X2819),X2818)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2820,X2819)),c_RealVector_Onorm__class_Onorm(X2820,X2818))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__ineq])]) ).
cnf(c_0_45,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X2)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X2)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_46,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_47,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_48,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_49,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs]) ).
cnf(c_0_50,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_51,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_52,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_53,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_54,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X1)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_55,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_t____) = v_t____,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_34]),c_0_49])]) ).
cnf(c_0_56,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).
fof(c_0_57,plain,
! [X2870,X2871,X2872] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2871),X2872) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2870),X2872)
| X2871 = X2870
| X2872 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X2871 != X2870
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2871),X2872) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2870),X2872)
| X2872 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__right__cancel])])]) ).
cnf(c_0_58,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_59,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_55]),c_0_56])]) ).
fof(c_0_60,plain,
! [X7,X8,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X8,X7)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X8,X7)
& ~ c_Orderings_Oord__class_Oless__eq(X6,X7,X8) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
cnf(c_0_61,plain,
( X1 = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_62,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]) ).
fof(c_0_63,plain,
! [X2999,X3000,X3001] :
( ( c_Orderings_Oord__class_Oless__eq(X3001,X3000,X2999)
| ~ c_Orderings_Oord__class_Oless(X3001,X3000,X2999)
| ~ class_Orderings_Opreorder(X3001) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3001,X2999,X3000)
| ~ c_Orderings_Oord__class_Oless(X3001,X3000,X2999)
| ~ class_Orderings_Opreorder(X3001) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3001,X3000,X2999)
| c_Orderings_Oord__class_Oless__eq(X3001,X2999,X3000)
| c_Orderings_Oord__class_Oless(X3001,X3000,X2999)
| ~ class_Orderings_Opreorder(X3001) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])]) ).
fof(c_0_64,plain,
! [X3026,X3027] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3027,X3026),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X3026 = c_Groups_Ozero__class_Ozero(X3027)
| ~ class_RealVector_Oreal__normed__vector(X3027) )
& ( X3026 != c_Groups_Ozero__class_Ozero(X3027)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3027,X3026),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X3027) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff])])]) ).
cnf(c_0_65,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = v_t____
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
fof(c_0_66,plain,
! [X2832] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2832,X2832),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
cnf(c_0_67,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_68,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[fact_t_I2_J]) ).
cnf(c_0_69,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
cnf(c_0_70,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_71,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v_t____ ),
inference(spm,[status(thm)],[c_0_65,c_0_40]) ).
cnf(c_0_72,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(c_0_73,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_74,plain,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_w0]) ).
cnf(c_0_75,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_t____),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69])]) ).
cnf(c_0_76,plain,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v_t____,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]),c_0_73])]),c_0_74]) ).
cnf(c_0_77,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76]),c_0_73])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWW261+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Tue May 5 06:29:45 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 14.02/8.94 % Version : CSE_E---1.7
% 14.02/8.94 % Problem : theBenchmark.p
% 14.02/8.94 % SZS status Theorem for theBenchmark.p
% 14.02/8.94 % SZS output start CNFRefutation
% See solution above
% 14.02/9.00 % Total time : 6.488s
%------------------------------------------------------------------------------