%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW270+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 03:10:12 PM UTC 2026
% Result : Theorem 36.63s 5.85s
% Output : CNFRefutation 36.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 73 ( 40 unt; 0 def)
% Number of atoms : 138 ( 75 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 114 ( 49 ~; 44 |; 4 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 74 ( 2 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_right__inverse__eq,axiom,
! [X27,X26,X14] :
( class_Rings_Odivision__ring(X14)
=> ( X26 != c_Groups_Ozero__class_Ozero(X14)
=> ( c_Rings_Oinverse__class_Odivide(X14,X27,X26) = c_Groups_Oone__class_Oone(X14)
<=> X27 = X26 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__inverse__eq) ).
fof(fact_sgn__of__real,axiom,
! [X11,X7] :
( class_RealVector_Oreal__normed__algebra__1(X7)
=> c_Groups_Osgn__class_Osgn(X7,c_RealVector_Oof__real(X7,X11)) = c_RealVector_Oof__real(X7,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__of__real) ).
fof(fact_real__sgn__pos,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X6) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sgn__pos) ).
fof(fact_of__real__1,axiom,
! [X7] :
( class_RealVector_Oreal__algebra__1(X7)
=> c_RealVector_Oof__real(X7,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__1) ).
fof(fact_sgn__eq,axiom,
! [X20] : c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,X20) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X20,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X20))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__eq) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(fact_x_I1_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_x_I1_J) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
fof(fact_of__real__eq__iff,axiom,
! [X15,X16,X14] :
( class_RealVector_Oreal__algebra__1(X14)
=> ( c_RealVector_Oof__real(X14,X16) = c_RealVector_Oof__real(X14,X15)
<=> X16 = X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__eq__iff) ).
fof(fact_real__zero__not__eq__one,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
fof(fact_divide__zero,axiom,
! [X18,X7] :
( class_Rings_Odivision__ring__inverse__zero(X7)
=> c_Rings_Oinverse__class_Odivide(X7,X18,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero) ).
fof(fact_of__real__eq__0__iff,axiom,
! [X16,X14] :
( class_RealVector_Oreal__algebra__1(X14)
=> ( c_RealVector_Oof__real(X14,X16) = c_Groups_Ozero__class_Ozero(X14)
<=> X16 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__eq__0__iff) ).
fof(fact_norm__mult,axiom,
! [X5,X6,X7] :
( class_RealVector_Oreal__normed__div__algebra(X7)
=> c_RealVector_Onorm__class_Onorm(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X6)),c_RealVector_Onorm__class_Onorm(X7,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult) ).
fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
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_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(fact_real__mult__le__cancel__iff2,axiom,
! [X15,X16,X24] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X24),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X24),X15))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
fof(fact__096cmod_A_Ipoly_Ads_A_Icomplex__of__real_Ax_J_J_A_060_061_Am_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),v_m____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096cmod_A_Ipoly_Ads_A_Icomplex__of__real_Ax_J_J_A_060_061_Am_096) ).
fof(fact_cth,axiom,
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_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_d____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cth) ).
fof(c_0_20,plain,
! [X27,X26,X14] :
( class_Rings_Odivision__ring(X14)
=> ( X26 != c_Groups_Ozero__class_Ozero(X14)
=> ( c_Rings_Oinverse__class_Odivide(X14,X27,X26) = c_Groups_Oone__class_Oone(X14)
<=> X27 = X26 ) ) ),
inference(fof_simplification,[status(thm)],[fact_right__inverse__eq]) ).
fof(c_0_21,plain,
! [X1231,X1232] :
( c_Groups_Osgn__class_Osgn(X1232,c_RealVector_Oof__real(X1232,X1231)) = c_RealVector_Oof__real(X1232,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1231))
| ~ class_RealVector_Oreal__normed__algebra__1(X1232) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__of__real])])]) ).
fof(c_0_22,plain,
! [X1631] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1631) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1631) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sgn__pos])])]) ).
fof(c_0_23,plain,
! [X127] :
( c_RealVector_Oof__real(X127,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X127)
| ~ class_RealVector_Oreal__algebra__1(X127) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__1])])]) ).
fof(c_0_24,plain,
! [X444,X445,X446] :
( ( ~ class_Rings_Odivision__ring(X446)
| X445 = c_Groups_Ozero__class_Ozero(X446)
| c_Rings_Oinverse__class_Odivide(X446,X444,X445) = c_Groups_Oone__class_Oone(X446)
| X444 != X445 )
& ( ~ class_Rings_Odivision__ring(X446)
| X445 = c_Groups_Ozero__class_Ozero(X446)
| X444 = X445
| c_Rings_Oinverse__class_Odivide(X446,X444,X445) != c_Groups_Oone__class_Oone(X446) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
fof(c_0_25,plain,
! [X1717] : c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,X1717) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1717,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1717))),
inference(variable_rename,[status(thm)],[fact_sgn__eq]) ).
cnf(c_0_26,plain,
( ~ class_RealVector_Oreal__normed__algebra__1(X1)
| c_Groups_Osgn__class_Osgn(X1,c_RealVector_Oof__real(X1,X2)) = c_RealVector_Oof__real(X1,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,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_28,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_x____),
inference(split_conjunct,[status(thm)],[fact_x_I1_J]) ).
cnf(c_0_30,plain,
( ~ class_RealVector_Oreal__algebra__1(X1)
| c_RealVector_Oof__real(X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__algebra__1]) ).
cnf(c_0_32,plain,
( ~ class_Rings_Odivision__ring(X1)
| c_Rings_Oinverse__class_Odivide(X1,X2,X3) != c_Groups_Oone__class_Oone(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,X1) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring]) ).
cnf(c_0_35,plain,
c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1)) = c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_36,plain,
c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_x____) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,plain,
c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_38,plain,
! [X353,X354,X355] :
( ( ~ class_RealVector_Oreal__algebra__1(X355)
| c_RealVector_Oof__real(X355,X354) = c_RealVector_Oof__real(X355,X353)
| X354 != X353 )
& ( ~ class_RealVector_Oreal__algebra__1(X355)
| X354 = X353
| c_RealVector_Oof__real(X355,X354) != c_RealVector_Oof__real(X355,X353) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__eq__iff])])])]) ).
cnf(c_0_39,plain,
( c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,X1) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)) = X1
| c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_40,plain,
c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
fof(c_0_41,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_simplification,[status(thm)],[fact_real__zero__not__eq__one]) ).
cnf(c_0_42,plain,
( ~ class_RealVector_Oreal__algebra__1(X1)
| c_RealVector_Oof__real(X1,X2) != c_RealVector_Oof__real(X1,X3)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_43,plain,
( c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_44,plain,
! [X406,X407] :
( c_Rings_Oinverse__class_Odivide(X407,X406,c_Groups_Ozero__class_Ozero(X407)) = c_Groups_Ozero__class_Ozero(X407)
| ~ class_Rings_Odivision__ring__inverse__zero(X407) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero])])]) ).
fof(c_0_45,plain,
! [X147,X148] :
( ( ~ class_RealVector_Oreal__algebra__1(X148)
| c_RealVector_Oof__real(X148,X147) = c_Groups_Ozero__class_Ozero(X148)
| X147 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ~ class_RealVector_Oreal__algebra__1(X148)
| X147 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X148,X147) != c_Groups_Ozero__class_Ozero(X148) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__eq__0__iff])])])]) ).
fof(c_0_46,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[c_0_41]) ).
fof(c_0_47,plain,
! [X103,X104,X105] :
( c_RealVector_Onorm__class_Onorm(X105,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X105),X104),X103)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X105,X104)),c_RealVector_Onorm__class_Onorm(X105,X103))
| ~ class_RealVector_Oreal__normed__div__algebra(X105) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult])])]) ).
cnf(c_0_48,plain,
( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____) != c_RealVector_Oof__real(tc_Complex_Ocomplex,X1)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = X1
| c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_31])]) ).
cnf(c_0_49,plain,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero]) ).
cnf(c_0_51,plain,
( ~ class_RealVector_Oreal__algebra__1(X1)
| c_RealVector_Oof__real(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_53,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_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_54,plain,
( ~ class_RealVector_Oreal__normed__div__algebra(X1)
| 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_47]) ).
cnf(c_0_55,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra]) ).
cnf(c_0_56,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = v_x____
| c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_57,plain,
c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_58,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_37]),c_0_31])]),c_0_52]) ).
fof(c_0_59,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_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_60,plain,
! [X363,X364,X365] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X365)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X365),X364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X365),X363))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X364,X363) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X365)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X364,X363)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X365),X364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X365),X363)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff2])])])]) ).
cnf(c_0_61,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)) = v_x____,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_56]),c_0_57]),c_0_40]),c_0_58]) ).
fof(c_0_63,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_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)),
inference(fof_nnf,[status(thm)],[c_0_59]) ).
cnf(c_0_64,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_65,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____))),v_m____),
inference(split_conjunct,[status(thm)],[fact__096cmod_A_Ipoly_Ads_A_Icomplex__of__real_Ax_J_J_A_060_061_Am_096]) ).
cnf(c_0_66,plain,
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_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_d____),
inference(split_conjunct,[status(thm)],[fact_cth]) ).
cnf(c_0_67,plain,
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_x____)),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,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_x____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_69,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),v_m____)) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_70,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_ds____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_x____)))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_d____),
inference(rw,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_71,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_d____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),v_m____)),
inference(rw,[status(thm)],[c_0_68,c_0_66]) ).
cnf(c_0_72,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_29]),c_0_70]),c_0_71]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW270+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 09:46:48 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.63/5.85 % Version: 3.5.1
% 36.63/5.85 % Preprocessing class: FMLMSMSMSSSNFFN.
% 36.63/5.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 36.63/5.85 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 36.63/5.85 % Starting new_bool_3 with 300s (1) cores
% 36.63/5.85 % Starting new_bool_1 with 300s (1) cores
% 36.63/5.85 % Starting sh5l with 300s (1) cores
% 36.63/5.85 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3988248 completed with status 0
% 36.63/5.85 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 36.63/5.85 % Preprocessing class: FMLMSMSMSSSNFFN.
% 36.63/5.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 36.63/5.85 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 36.63/5.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 36.63/5.85 % No SInE strategy applied
% 36.63/5.85 % Search class: FGHSM-SMLM32-DFFFFFNN
% 36.63/5.85 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 36.63/5.85 % Starting SubtermCWHack with 136s (1) cores
% 36.63/5.85 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 36.63/5.85 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 36.63/5.85 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 36.63/5.85 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 36.63/5.85 % G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with pid 3988257 completed with status 0
% 36.63/5.85 % Result found by G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI
% 36.63/5.85 % Preprocessing class: FMLMSMSMSSSNFFN.
% 36.63/5.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 36.63/5.85 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 36.63/5.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 36.63/5.85 % No SInE strategy applied
% 36.63/5.85 % Search class: FGHSM-SMLM32-DFFFFFNN
% 36.63/5.85 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 36.63/5.85 % Starting SubtermCWHack with 136s (1) cores
% 36.63/5.85 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 36.63/5.85 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 36.63/5.85 % Preprocessing time : 0.024 s
% 36.63/5.85
% 36.63/5.85 % Proof found!
% 36.63/5.85 % SZS status Theorem
% 36.63/5.85 % SZS output start CNFRefutation
% See solution above
% 36.63/5.85 % Parsed axioms : 1268
% 36.63/5.85 % Removed by relevancy pruning/SinE : 0
% 36.63/5.85 % Initial clauses : 1825
% 36.63/5.85 % Removed in clause preprocessing : 84
% 36.63/5.85 % Initial clauses in saturation : 1741
% 36.63/5.85 % Processed clauses : 14234
% 36.63/5.85 % ...of these trivial : 471
% 36.63/5.85 % ...subsumed : 7950
% 36.63/5.85 % ...remaining for further processing : 5813
% 36.63/5.85 % Other redundant clauses eliminated : 274
% 36.63/5.85 % Clauses deleted for lack of memory : 0
% 36.63/5.85 % Backward-subsumed : 103
% 36.63/5.85 % Backward-rewritten : 385
% 36.63/5.85 % Generated clauses : 163281
% 36.63/5.85 % ...of the previous two non-redundant : 142824
% 36.63/5.85 % ...aggressively subsumed : 0
% 36.63/5.85 % Contextual simplify-reflections : 38
% 36.63/5.85 % Paramodulations : 162962
% 36.63/5.85 % Factorizations : 27
% 36.63/5.85 % NegExts : 0
% 36.63/5.85 % Equation resolutions : 306
% 36.63/5.85 % Disequality decompositions : 0
% 36.63/5.85 % Total rewrite steps : 116548
% 36.63/5.85 % ...of those cached : 111399
% 36.63/5.85 % Propositional unsat checks : 0
% 36.63/5.85 % Propositional check models : 0
% 36.63/5.85 % Propositional check unsatisfiable : 0
% 36.63/5.85 % Propositional clauses : 0
% 36.63/5.85 % Propositional clauses after purity: 0
% 36.63/5.85 % Propositional unsat core size : 0
% 36.63/5.85 % Propositional preprocessing time : 0.000
% 36.63/5.85 % Propositional encoding time : 0.000
% 36.63/5.85 % Propositional solver time : 0.000
% 36.63/5.85 % Success case prop preproc time : 0.000
% 36.63/5.85 % Success case prop encoding time : 0.000
% 36.63/5.85 % Success case prop solver time : 0.000
% 36.63/5.85 % Current number of processed clauses : 5184
% 36.63/5.85 % Positive orientable unit clauses : 933
% 36.63/5.85 % Positive unorientable unit clauses: 13
% 36.63/5.85 % Negative unit clauses : 128
% 36.63/5.85 % Non-unit-clauses : 4110
% 36.63/5.85 % Current number of unprocessed clauses: 130182
% 36.63/5.85 % ...number of literals in the above : 354699
% 36.63/5.85 % Current number of archived formulas : 0
% 36.63/5.85 % Current number of archived clauses : 490
% 36.63/5.85 % Clause-clause subsumption calls (NU) : 2899624
% 36.63/5.85 % Rec. Clause-clause subsumption calls : 2121079
% 36.63/5.85 % Non-unit clause-clause subsumptions : 7396
% 36.63/5.85 % Unit Clause-clause subsumption calls : 129742
% 36.63/5.85 % Rewrite failures with RHS unbound : 4
% 36.63/5.85 % BW rewrite match attempts : 36410
% 36.63/5.85 % BW rewrite match successes : 509
% 36.63/5.85 % Condensation attempts : 0
% 36.63/5.85 % Condensation successes : 0
% 36.63/5.85 % Termbank termtop insertions : 4043970
% 36.63/5.85 % Search garbage collected termcells : 22882
% 36.63/5.85
% 36.63/5.85 % -------------------------------------------------
% 36.63/5.85 % User time : 5.118 s
% 36.63/5.85 % System time : 0.143 s
% 36.63/5.85 % Total time : 5.261 s
% 36.63/5.85 % Maximum resident set size: 10472 pages
% 36.63/5.85
% 36.63/5.85 % -------------------------------------------------
% 36.63/5.85 % User time : 25.031 s
% 36.63/5.85 % System time : 0.826 s
% 36.63/5.85 % Total time : 25.857 s
% 36.63/5.85 % Maximum resident set size: 6400 pages
% 36.63/5.85 % E exiting
%------------------------------------------------------------------------------