%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW261+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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:10:11 PM UTC 2026
% Result : Theorem 5.57s 1.27s
% Output : CNFRefutation 5.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 24
% Syntax : Number of formulae : 83 ( 46 unt; 0 def)
% Number of atoms : 165 ( 52 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 140 ( 58 ~; 54 |; 8 &)
% ( 6 <=>; 14 =>; 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 : 95 ( 0 sgn 62 !; 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,X9,X10)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X9) ),
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)
<=> ( X8 = X7
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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(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(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_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,X7,X8)
& c_Orderings_Oord__class_Oless__eq(X6,X8,X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_w0,axiom,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_w0) ).
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(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(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_25,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)],[c_0_24]) ).
fof(c_0_26,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_nnf,[status(thm)],[c_0_25]) ).
fof(c_0_27,plain,
! [X105,X106] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X105,X106)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X106,X105) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
fof(c_0_28,plain,
! [X1995,X1996] :
( c_RealVector_Onorm__class_Onorm(X1996,c_RealVector_Oof__real(X1996,X1995)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1995)
| ~ class_RealVector_Oreal__normed__algebra__1(X1996) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__of__real])])]) ).
fof(c_0_29,plain,
! [X1925] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1925) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1925),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(c_0_30,plain,
! [X294,X295] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X295,X294)
| X295 != X294 )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X295,X294)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X295,X294) )
& ( X295 = X294
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X295,X294)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X295,X294) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])])]) ).
fof(c_0_31,plain,
! [X127] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X127) = X127,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
fof(c_0_32,plain,
! [X315,X316,X317,X318] :
( c_Orderings_Oord__class_Oless__eq(X318,X315,X316)
| ~ c_Orderings_Oord__class_Oless__eq(X318,X315,X317)
| ~ c_Orderings_Oord__class_Oless__eq(X318,X317,X316)
| ~ class_Orderings_Oorder(X318) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])])]) ).
cnf(c_0_33,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_26]) ).
cnf(c_0_34,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,plain,
( ~ class_RealVector_Oreal__normed__algebra__1(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,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_29]) ).
fof(c_0_37,plain,
! [X1947,X1948] :
( c_Groups_Oabs__class_Oabs(X1948,X1947) = X1947
| ~ c_Orderings_Oord__class_Oless__eq(X1948,c_Groups_Ozero__class_Ozero(X1948),X1947)
| ~ class_Groups_Oordered__ab__group__add__abs(X1948) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])])]) ).
cnf(c_0_38,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,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_40,plain,
! [X110,X111] :
( X111 = X110
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X110,X111)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X111,X110) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])])]) ).
cnf(c_0_41,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_42,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_31]) ).
cnf(c_0_43,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_44,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_33,c_0_34]) ).
cnf(c_0_45,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
fof(c_0_46,plain,
! [X90,X91,X92] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X92,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X92),X91),X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X92,X91)),c_RealVector_Onorm__class_Onorm(X92,X90)))
| ~ class_RealVector_Oreal__normed__algebra(X92) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__ineq])])]) ).
cnf(c_0_47,plain,
( ~ class_RealVector_Oreal__normed__algebra__1(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X2)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X2) ),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_48,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_49,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Groups_Oabs__class_Oabs(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_50,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_38,c_0_39]) ).
cnf(c_0_51,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]) ).
fof(c_0_52,plain,
! [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 ) ),
inference(fof_simplification,[status(thm)],[fact_real__mult__right__cancel]) ).
cnf(c_0_53,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_54,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_41,c_0_42]) ).
cnf(c_0_55,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____)),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_56,plain,
( ~ class_RealVector_Oreal__normed__algebra(X1)
| 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))) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_57,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_47,c_0_48]) ).
cnf(c_0_58,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_49,c_0_50]),c_0_36]),c_0_51])]) ).
cnf(c_0_59,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).
fof(c_0_60,plain,
! [X142,X143,X144] :
( ( X144 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X143),X144) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X142),X144)
| X143 != X142 )
& ( X144 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X143 = X142
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X143),X144) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X142),X144) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])]) ).
cnf(c_0_61,plain,
( ~ 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____)))
| 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(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_62,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_55,c_0_56]),c_0_57]),c_0_58]),c_0_59])]) ).
fof(c_0_63,plain,
! [X7,X8,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X8,X7)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X7,X8)
& c_Orderings_Oord__class_Oless__eq(X6,X8,X7) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
cnf(c_0_64,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_65,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_61,c_0_62])]) ).
fof(c_0_66,plain,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(fof_simplification,[status(thm)],[fact_w0]) ).
fof(c_0_67,plain,
! [X271,X272,X273] :
( ( ~ class_Orderings_Opreorder(X273)
| c_Orderings_Oord__class_Oless(X273,X272,X271)
| c_Orderings_Oord__class_Oless__eq(X273,X271,X272)
| ~ c_Orderings_Oord__class_Oless__eq(X273,X272,X271) )
& ( ~ class_Orderings_Opreorder(X273)
| ~ c_Orderings_Oord__class_Oless(X273,X272,X271)
| ~ c_Orderings_Oord__class_Oless__eq(X273,X271,X272) )
& ( ~ class_Orderings_Opreorder(X273)
| ~ c_Orderings_Oord__class_Oless(X273,X272,X271)
| c_Orderings_Oord__class_Oless__eq(X273,X272,X271) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])])]) ).
fof(c_0_68,plain,
! [X298,X299] :
( ( ~ class_RealVector_Oreal__normed__vector(X299)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X299,X298),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X298 != c_Groups_Ozero__class_Ozero(X299) )
& ( ~ class_RealVector_Oreal__normed__vector(X299)
| X298 = c_Groups_Ozero__class_Ozero(X299)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X299,X298),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff])])])]) ).
cnf(c_0_69,plain,
( 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____)
| v_t____ = X1
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
fof(c_0_70,plain,
! [X104] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X104,X104),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
fof(c_0_71,plain,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[c_0_66]) ).
cnf(c_0_72,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_73,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_74,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
cnf(c_0_75,plain,
( ~ class_RealVector_Oreal__normed__vector(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))
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_76,plain,
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v_t____
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_69,c_0_42]) ).
cnf(c_0_77,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(c_0_78,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_79,plain,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_80,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_72,c_0_73]),c_0_74])]) ).
cnf(c_0_81,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_75,c_0_76]),c_0_77]),c_0_78])]),c_0_79]) ).
cnf(c_0_82,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81]),c_0_78])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW261+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n009.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 09:44:42 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 5.57/1.27 % Version: 3.5.1
% 5.57/1.27 % Preprocessing class: FMLMSMSMSSSNFFN.
% 5.57/1.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.57/1.27 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.57/1.27 % Starting new_bool_3 with 300s (1) cores
% 5.57/1.27 % Starting new_bool_1 with 300s (1) cores
% 5.57/1.27 % Starting sh5l with 300s (1) cores
% 5.57/1.27 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1443168 completed with status 0
% 5.57/1.27 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 5.57/1.27 % Preprocessing class: FMLMSMSMSSSNFFN.
% 5.57/1.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.57/1.27 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.57/1.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.57/1.27 % No SInE strategy applied
% 5.57/1.27 % Search class: FGHSM-SSLM31-DFFFFFNN
% 5.57/1.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.57/1.27 % Starting SubtermCWHack with 136s (1) cores
% 5.57/1.27 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 5.57/1.27 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S2S with 136s (1) cores
% 5.57/1.27 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 136s (1) cores
% 5.57/1.27 % Starting G-E--_208_B07AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 5.57/1.27 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1443216 completed with status 0
% 5.57/1.27 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 5.57/1.27 % Preprocessing class: FMLMSMSMSSSNFFN.
% 5.57/1.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.57/1.27 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.57/1.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.57/1.27 % No SInE strategy applied
% 5.57/1.27 % Search class: FGHSM-SSLM31-DFFFFFNN
% 5.57/1.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.57/1.27 % Starting SubtermCWHack with 136s (1) cores
% 5.57/1.27 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 5.57/1.27 % Preprocessing time : 0.017 s
% 5.57/1.27 % Presaturation interreduction done
% 5.57/1.27
% 5.57/1.27 % Proof found!
% 5.57/1.27 % SZS status Theorem
% 5.57/1.27 % SZS output start CNFRefutation
% See solution above
% 5.57/1.27 % Parsed axioms : 1288
% 5.57/1.27 % Removed by relevancy pruning/SinE : 0
% 5.57/1.27 % Initial clauses : 1648
% 5.57/1.27 % Removed in clause preprocessing : 46
% 5.57/1.27 % Initial clauses in saturation : 1602
% 5.57/1.27 % Processed clauses : 4726
% 5.57/1.27 % ...of these trivial : 105
% 5.57/1.27 % ...subsumed : 1129
% 5.57/1.27 % ...remaining for further processing : 3492
% 5.57/1.27 % Other redundant clauses eliminated : 297
% 5.57/1.27 % Clauses deleted for lack of memory : 0
% 5.57/1.27 % Backward-subsumed : 21
% 5.57/1.27 % Backward-rewritten : 161
% 5.57/1.27 % Generated clauses : 42442
% 5.57/1.27 % ...of the previous two non-redundant : 37785
% 5.57/1.27 % ...aggressively subsumed : 0
% 5.57/1.27 % Contextual simplify-reflections : 4
% 5.57/1.27 % Paramodulations : 42128
% 5.57/1.27 % Factorizations : 10
% 5.57/1.27 % NegExts : 0
% 5.57/1.27 % Equation resolutions : 315
% 5.57/1.27 % Disequality decompositions : 0
% 5.57/1.27 % Total rewrite steps : 35847
% 5.57/1.27 % ...of those cached : 33490
% 5.57/1.27 % Propositional unsat checks : 0
% 5.57/1.27 % Propositional check models : 0
% 5.57/1.27 % Propositional check unsatisfiable : 0
% 5.57/1.27 % Propositional clauses : 0
% 5.57/1.27 % Propositional clauses after purity: 0
% 5.57/1.27 % Propositional unsat core size : 0
% 5.57/1.27 % Propositional preprocessing time : 0.000
% 5.57/1.27 % Propositional encoding time : 0.000
% 5.57/1.27 % Propositional solver time : 0.000
% 5.57/1.27 % Success case prop preproc time : 0.000
% 5.57/1.27 % Success case prop encoding time : 0.000
% 5.57/1.27 % Success case prop solver time : 0.000
% 5.57/1.27 % Current number of processed clauses : 1813
% 5.57/1.27 % Positive orientable unit clauses : 547
% 5.57/1.27 % Positive unorientable unit clauses: 8
% 5.57/1.27 % Negative unit clauses : 84
% 5.57/1.27 % Non-unit-clauses : 1174
% 5.57/1.27 % Current number of unprocessed clauses: 35941
% 5.57/1.27 % ...number of literals in the above : 99082
% 5.57/1.27 % Current number of archived formulas : 0
% 5.57/1.27 % Current number of archived clauses : 1560
% 5.57/1.27 % Clause-clause subsumption calls (NU) : 600123
% 5.57/1.27 % Rec. Clause-clause subsumption calls : 357083
% 5.57/1.27 % Non-unit clause-clause subsumptions : 631
% 5.57/1.27 % Unit Clause-clause subsumption calls : 5609
% 5.57/1.27 % Rewrite failures with RHS unbound : 0
% 5.57/1.27 % BW rewrite match attempts : 3940
% 5.57/1.27 % BW rewrite match successes : 173
% 5.57/1.27 % Condensation attempts : 0
% 5.57/1.27 % Condensation successes : 0
% 5.57/1.27 % Termbank termtop insertions : 1062120
% 5.57/1.27 % Search garbage collected termcells : 19012
% 5.57/1.27
% 5.57/1.27 % -------------------------------------------------
% 5.57/1.27 % User time : 0.750 s
% 5.57/1.27 % System time : 0.035 s
% 5.57/1.27 % Total time : 0.785 s
% 5.57/1.27 % Maximum resident set size: 9920 pages
% 5.57/1.27
% 5.57/1.27 % -------------------------------------------------
% 5.57/1.27 % User time : 3.361 s
% 5.57/1.27 % System time : 0.166 s
% 5.57/1.27 % Total time : 3.527 s
% 5.57/1.27 % Maximum resident set size: 6144 pages
% 5.57/1.27 % E exiting
%------------------------------------------------------------------------------