%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG405-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:46:55 AM UTC 2026
% Result : Unsatisfiable 8.66s 7.74s
% Output : Refutation 8.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 11 ( 10 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 753 ( 7 ~; 1 |; 0 &; 745 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_HOL_Oplus__class_Oplus_decl,type,
c_HOL_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(c_HOL_Oone__class_Oone_decl,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(tc_Complex_Ocomplex_decl,type,
tc_Complex_Ocomplex: $i ).
thf(c_HOL_Otimes__class_Otimes_decl,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(c_Power_Opower__class_Opower_decl,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(c_RealVector_Oof__real_decl,type,
c_RealVector_Oof__real: $i > $i > $i ).
thf(v_t_____decl,type,
v_t____: $i ).
thf(v_w_____decl,type,
v_w____: $i ).
thf(v_k_____decl,type,
v_k____: $i ).
thf(v_a_____decl,type,
v_a____: $i ).
thf(c_Polynomial_Opoly_decl,type,
c_Polynomial_Opoly: $i > $i > $i > $i ).
thf(v_s_____decl,type,
v_s____: $i ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(tc_RealDef_Oreal_decl,type,
tc_RealDef_Oreal: $i ).
thf(c_RealVector_Onorm__class_Onorm_decl,type,
c_RealVector_Onorm__class_Onorm: $i > $i > $i ).
thf(1,negated_conjecture,
( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_a____ @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( v_k____ @ ( v_t____ @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Oof__real ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(771,plain,
( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_a____ @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( v_k____ @ ( v_t____ @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Oof__real ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(773,plain,
( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_a____ @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( v_k____ @ ( v_t____ @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Oof__real ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(lifteq,[status(thm)],[771]) ).
thf(2,negated_conjecture,
( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_a____ @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( v_k____ @ ( v_t____ @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Oof__real ) @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(772,plain,
( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_a____ @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( v_k____ @ ( v_t____ @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Oof__real ) @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(774,plain,
( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_a____ @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( v_k____ @ ( v_t____ @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Oof__real ) @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) ) ),
inference(polarity_switch,[status(thm)],[772]) ).
thf(775,plain,
( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_a____ @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( v_k____ @ ( v_t____ @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Oof__real ) @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) ) ),
inference(lifteq,[status(thm)],[774]) ).
thf(2493,plain,
( ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_a____ @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_a____ @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( v_k____ @ ( v_t____ @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Oof__real ) @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( v_k____ @ ( v_t____ @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Ominus__class_Ominus ) ) @ c_RealVector_Oof__real ) @ c_HOL_Oplus__class_Oplus ) ) @ c_RealVector_Onorm__class_Onorm ) ) ) ),
inference(paramod_ordered,[status(thm)],[773,775]) ).
thf(2494,plain,
( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_a____ @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_s____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( v_a____ @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ ( v_k____ @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_t____ @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(simp,[status(thm)],[2493]) ).
thf(2495,plain,
$false,
inference(pattern_uni,[status(thm)],[2494:[]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG405-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.05/5.33 % Computer : n012.cluster.edu
% 0.05/5.33 % Model : x86_64 x86_64
% 0.05/5.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/5.33 % Memory : 8046.5625MB
% 0.05/5.33 % OS : Linux 6.8.0-71-generic
% 0.05/5.33 % CPULimit : 300
% 0.05/5.33 % WCLimit : 300
% 0.05/5.33 % DateTime : Sat Sep 26 21:58:02 UTC 2026
% 0.05/5.33 % CPUTime :
% 0.05/5.33 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/5.61 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.09/5.81 % [INFO] Parsing done (194ms).
% 0.09/5.82 % [INFO] Running in sequential loop mode.
% 0.09/5.99 % [INFO] eprover registered as external prover.
% 0.09/6.00 % [INFO] Scanning for conjecture ...
% 1.56/6.10 % [INFO] Found a conjecture (or negated_conjecture) and 802 axioms. Running axiom selection ...
% 2.30/6.24 % [INFO] Axiom selection finished. Selected 768 axioms (removed 34 axioms).
% 2.76/6.39 % [INFO] Problem is propositional (TPTP CNF).
% 2.76/6.40 % [INFO] Type checking passed.
% 2.76/6.40 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 8.66/7.74 % [INFO] Killing All external provers ...
% 8.66/7.74 % Time passed: 2324ms (effective reasoning time: 1917ms)
% 8.66/7.74 % Axioms used in derivation (0):
% 8.66/7.74 % No. of inferences in proof: 10
% 8.66/7.74 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2324 ms resp. 1917 ms w/o parsing
% 8.66/7.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.66/7.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------