%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW236+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 : 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 03:10:08 PM UTC 2026
% Result : Theorem 14.28s 2.72s
% Output : CNFRefutation 14.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 29 unt; 0 def)
% Number of atoms : 125 ( 14 equ)
% Maximal formula atoms : 62 ( 3 avg)
% Number of connectives : 141 ( 55 ~; 56 |; 16 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 43 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_real__norm__def,axiom,
! [X20] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X20) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X7,X8,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X8),X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X7),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_divide__le__eq,axiom,
! [X16,X17,X15,X6] :
( class_Fields_Olinordered__field__inverse__zero(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Rings_Oinverse__class_Odivide(X6,X15,X17),X16)
<=> ( ( ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X17)
=> ( ( ~ c_Orderings_Oord__class_Oless(X6,X17,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X16) )
& ( c_Orderings_Oord__class_Oless(X6,X17,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X16),X17),X15) ) ) )
& ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X17)
=> c_Orderings_Oord__class_Oless__eq(X6,X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X16),X17)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(fact_norm__mult,axiom,
! [X4,X5,X6] :
( class_RealVector_Oreal__normed__div__algebra(X6)
=> 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) ).
fof(fact_h,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_h) ).
fof(fact_real__mult__commute,axiom,
! [X11,X9] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X11),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(fact__0960_A_060_Acmod_Ac_096,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0960_A_060_Acmod_Ac_096) ).
fof(fact_real__of__nat__zero,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(c_0_12,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_13,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_14,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
inference(fof_nnf,[status(thm)],[c_0_13]) ).
fof(c_0_15,plain,
! [X211] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X211) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X211),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
cnf(c_0_16,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,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_15]) ).
fof(c_0_18,plain,
! [X1096,X1097,X1098] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1098),X1097),X1096) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1098),X1096),X1097)
| ~ class_Rings_Ocomm__semiring__1(X1098) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])])]) ).
fof(c_0_19,plain,
! [X16,X17,X15,X6] :
( class_Fields_Olinordered__field__inverse__zero(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Rings_Oinverse__class_Odivide(X6,X15,X17),X16)
<=> ( ( ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X17)
=> ( ( ~ c_Orderings_Oord__class_Oless(X6,X17,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X16) )
& ( c_Orderings_Oord__class_Oless(X6,X17,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X16),X17),X15) ) ) )
& ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X17)
=> c_Orderings_Oord__class_Oless__eq(X6,X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X16),X17)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__le__eq]) ).
cnf(c_0_20,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
fof(c_0_23,plain,
! [X125,X126,X127] :
( c_RealVector_Onorm__class_Onorm(X127,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X127),X126),X125)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X127,X126)),c_RealVector_Onorm__class_Onorm(X127,X125))
| ~ class_RealVector_Oreal__normed__div__algebra(X127) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult])])]) ).
fof(c_0_24,plain,
! [X1155,X1156,X1157,X1158] :
( ( ~ class_Fields_Olinordered__field__inverse__zero(X1158)
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
| ~ c_Orderings_Oord__class_Oless__eq(X1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156),X1157)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Groups_Ozero__class_Ozero(X1158),X1155) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1158)
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
| ~ c_Orderings_Oord__class_Oless__eq(X1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156),X1157)
| ~ c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158)) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1158)
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
| c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
| ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Groups_Ozero__class_Ozero(X1158),X1155) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1158)
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
| c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
| ~ c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158)) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1158)
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
| ~ c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1158)
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156),X1157)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Groups_Ozero__class_Ozero(X1158),X1155) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1158)
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156),X1157)
| ~ c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158)) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1158)
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
| c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
| ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Groups_Ozero__class_Ozero(X1158),X1155) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1158)
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
| c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
| ~ c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158)) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1158)
| c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
| ~ c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1158)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
| c_Orderings_Oord__class_Oless__eq(X1158,c_Groups_Ozero__class_Ozero(X1158),X1155)
| c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158)) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1158)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
| c_Orderings_Oord__class_Oless__eq(X1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156),X1157)
| ~ c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158)) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1158)
| ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
| c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
| ~ c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
cnf(c_0_25,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(split_conjunct,[status(thm)],[fact_h]) ).
fof(c_0_26,plain,
! [X142,X143] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X143),X142) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X142),X143),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
cnf(c_0_27,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,v_c____)),
inference(split_conjunct,[status(thm)],[fact__0960_A_060_Acmod_Ac_096]) ).
cnf(c_0_28,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__of__nat__zero]) ).
cnf(c_0_29,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_c____),v_z____))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_30,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_23]) ).
cnf(c_0_31,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_32,plain,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(rw,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_34,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).
cnf(c_0_37,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_38,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_28]),c_0_35]),c_0_36])]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW236+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n003.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Mon Sep 21 09:44:18 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.53 Running first-order theorem proving
% 0.24/0.53 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
% 14.28/2.72 % Version: 3.5.1
% 14.28/2.72 % Preprocessing class: FMLMSMSMSSSNFFN.
% 14.28/2.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.28/2.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.28/2.72 % Starting new_bool_3 with 300s (1) cores
% 14.28/2.72 % Starting new_bool_1 with 300s (1) cores
% 14.28/2.72 % Starting sh5l with 300s (1) cores
% 14.28/2.72 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3984635 completed with status 0
% 14.28/2.72 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 14.28/2.72 % Preprocessing class: FMLMSMSMSSSNFFN.
% 14.28/2.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.28/2.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.28/2.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.28/2.72 % No SInE strategy applied
% 14.28/2.72 % Search class: FGHSM-SMLM32-DFFFFFNN
% 14.28/2.72 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 14.28/2.72 % Starting SubtermCWHack with 136s (1) cores
% 14.28/2.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 14.28/2.72 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 14.28/2.72 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 14.28/2.72 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 14.28/2.72 % G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 3984645 completed with status 0
% 14.28/2.72 % Result found by G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 14.28/2.72 % Preprocessing class: FMLMSMSMSSSNFFN.
% 14.28/2.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.28/2.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.28/2.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.28/2.72 % No SInE strategy applied
% 14.28/2.72 % Search class: FGHSM-SMLM32-DFFFFFNN
% 14.28/2.72 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 14.28/2.72 % Starting SubtermCWHack with 136s (1) cores
% 14.28/2.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 14.28/2.72 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 14.28/2.72 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 14.28/2.72 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 14.28/2.72 % Preprocessing time : 0.023 s
% 14.28/2.72 % Presaturation interreduction done
% 14.28/2.72
% 14.28/2.72 % Proof found!
% 14.28/2.72 % SZS status Theorem
% 14.28/2.72 % SZS output start CNFRefutation
% See solution above
% 14.28/2.72 % Parsed axioms : 1266
% 14.28/2.72 % Removed by relevancy pruning/SinE : 0
% 14.28/2.72 % Initial clauses : 1785
% 14.28/2.72 % Removed in clause preprocessing : 59
% 14.28/2.72 % Initial clauses in saturation : 1726
% 14.28/2.72 % Processed clauses : 10368
% 14.28/2.72 % ...of these trivial : 214
% 14.28/2.72 % ...subsumed : 5959
% 14.28/2.72 % ...remaining for further processing : 4195
% 14.28/2.72 % Other redundant clauses eliminated : 721
% 14.28/2.72 % Clauses deleted for lack of memory : 0
% 14.28/2.72 % Backward-subsumed : 43
% 14.28/2.72 % Backward-rewritten : 117
% 14.28/2.72 % Generated clauses : 94096
% 14.28/2.72 % ...of the previous two non-redundant : 84271
% 14.28/2.72 % ...aggressively subsumed : 0
% 14.28/2.72 % Contextual simplify-reflections : 4
% 14.28/2.72 % Paramodulations : 93367
% 14.28/2.72 % Factorizations : 10
% 14.28/2.72 % NegExts : 0
% 14.28/2.72 % Equation resolutions : 740
% 14.28/2.72 % Disequality decompositions : 0
% 14.28/2.72 % Total rewrite steps : 76487
% 14.28/2.72 % ...of those cached : 73531
% 14.28/2.72 % Propositional unsat checks : 0
% 14.28/2.72 % Propositional check models : 0
% 14.28/2.72 % Propositional check unsatisfiable : 0
% 14.28/2.72 % Propositional clauses : 0
% 14.28/2.72 % Propositional clauses after purity: 0
% 14.28/2.72 % Propositional unsat core size : 0
% 14.28/2.72 % Propositional preprocessing time : 0.000
% 14.28/2.72 % Propositional encoding time : 0.000
% 14.28/2.72 % Propositional solver time : 0.000
% 14.28/2.72 % Success case prop preproc time : 0.000
% 14.28/2.72 % Success case prop encoding time : 0.000
% 14.28/2.72 % Success case prop solver time : 0.000
% 14.28/2.72 % Current number of processed clauses : 2454
% 14.28/2.72 % Positive orientable unit clauses : 583
% 14.28/2.72 % Positive unorientable unit clauses: 22
% 14.28/2.72 % Negative unit clauses : 311
% 14.28/2.72 % Non-unit-clauses : 1538
% 14.28/2.72 % Current number of unprocessed clauses: 76869
% 14.28/2.72 % ...number of literals in the above : 186410
% 14.28/2.72 % Current number of archived formulas : 0
% 14.28/2.72 % Current number of archived clauses : 1599
% 14.28/2.72 % Clause-clause subsumption calls (NU) : 385131
% 14.28/2.72 % Rec. Clause-clause subsumption calls : 277487
% 14.28/2.72 % Non-unit clause-clause subsumptions : 2769
% 14.28/2.72 % Unit Clause-clause subsumption calls : 57749
% 14.28/2.72 % Rewrite failures with RHS unbound : 0
% 14.28/2.72 % BW rewrite match attempts : 22418
% 14.28/2.72 % BW rewrite match successes : 303
% 14.28/2.72 % Condensation attempts : 0
% 14.28/2.72 % Condensation successes : 0
% 14.28/2.72 % Termbank termtop insertions : 1944584
% 14.28/2.72 % Search garbage collected termcells : 21898
% 14.28/2.72
% 14.28/2.72 % -------------------------------------------------
% 14.28/2.72 % User time : 1.968 s
% 14.28/2.72 % System time : 0.075 s
% 14.28/2.72 % Total time : 2.043 s
% 14.28/2.72 % Maximum resident set size: 10204 pages
% 14.28/2.72
% 14.28/2.72 % -------------------------------------------------
% 14.28/2.72 % User time : 9.468 s
% 14.28/2.72 % System time : 0.371 s
% 14.28/2.72 % Total time : 9.839 s
% 14.28/2.72 % Maximum resident set size: 6144 pages
% 14.28/2.72 % E exiting
%------------------------------------------------------------------------------