%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG386-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 11:49:19 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.47s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 7 unt; 5 def)
% Number of atoms : 67 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 63 ( 30 ~; 28 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f197,axiom,
v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f398,axiom,
! [V_d,V_a,V_p,V_z] :
( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(V_a,V_d,V_p),c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(V_d,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f422,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f423,negated_conjecture,
! [V_xa] :
( c_lessequals(V_xa,c_RealVector_Onorm__class_Onorm(v_x(V_xa),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f424,negated_conjecture,
! [V_xa] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f943,plain,
v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f1289,plain,
! [V_p] :
( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ! [V_d,V_a,V_z] :
( ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(V_a,V_d,V_p),c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(V_d,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
inference(miniscoping,[status(thm)],[f398]) ).
fof(f1290,plain,
! [X0,X1,X2,X3] :
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(X1,X0,X2),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f1289]) ).
fof(f1325,plain,
~ v_thesis____,
inference(cnf_transformation,[status(thm)],[f422]) ).
fof(f1326,plain,
( ! [V_xa] : c_lessequals(V_xa,c_RealVector_Onorm__class_Onorm(v_x(V_xa),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
inference(miniscoping,[status(thm)],[f423]) ).
fof(f1327,plain,
! [X0] :
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
inference(cnf_transformation,[status(thm)],[f1326]) ).
fof(f1328,plain,
( ! [V_xa] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
inference(miniscoping,[status(thm)],[f424]) ).
fof(f1329,plain,
! [X0] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
inference(cnf_transformation,[status(thm)],[f1328]) ).
fof(f1500,definition,
( sQ0_spl
<=> v_thesis____ ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1501,plain,
( ~ sQ0_spl
| v_thesis____ ),
inference(component_clause,[status(thm)],[f1500]) ).
fof(f1511,definition,
! [X0] :
( sQ3_spl
<=> c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1512,plain,
! [X0] :
( ~ sQ3_spl
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1511]) ).
fof(f1514,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1327,f1500,f1511]) ).
fof(f1515,definition,
! [X0] :
( sQ4_spl
<=> ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1516,plain,
! [X0] :
( ~ sQ4_spl
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1515]) ).
fof(f1518,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1329,f1500,f1515]) ).
fof(f1535,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1501,f1325]) ).
fof(f1536,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f1535]) ).
fof(f1726,definition,
( sQ31_spl
<=> c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_cs____ ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f1727,plain,
( ~ sQ31_spl
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_cs____ ),
inference(component_clause,[status(thm)],[f1726]) ).
fof(f1884,plain,
! [X0] :
( ~ sQ4_spl
| v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(v_c____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_cs____),c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1516,f1290]) ).
fof(f1890,definition,
! [X0] :
( sQ50_spl
<=> ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(v_c____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_cs____),c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f1891,plain,
! [X0] :
( ~ sQ50_spl
| ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(v_c____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_cs____),c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1890]) ).
fof(f1893,plain,
( ~ sQ4_spl
| sQ31_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f1884,f1890,f1726,f1515]) ).
fof(f1899,plain,
( ~ sQ3_spl
| ~ sQ50_spl
| $false ),
inference(resolution,[status(thm)],[f1891,f1512]) ).
fof(f1905,plain,
( ~ sQ3_spl
| ~ sQ50_spl ),
inference(contradiction_clause,[status(thm)],[f1899]) ).
fof(f1906,plain,
( ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1727,f943]) ).
fof(f1907,plain,
~ sQ31_spl,
inference(contradiction_clause,[status(thm)],[f1906]) ).
fof(f1908,plain,
$false,
inference(sat_refutation,[status(thm)],[f1514,f1518,f1536,f1893,f1905,f1907]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG386-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 13:18:43 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.47 % Refutation found
% 0.10/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.48 % Elapsed time: 0.117661 seconds
% 0.10/0.48 % CPU time: 0.647587 seconds
% 0.10/0.48 % Total memory used: 141.146 MB
% 0.10/0.48 % Net memory used: 140.534 MB
%------------------------------------------------------------------------------