%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG395-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 11:49:20 AM UTC 2026
% Result : Unsatisfiable 114.12s 34.92s
% Output : CNFRefutation 114.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 10 unt; 2 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 27 ~; 20 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 38 ( 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f722,axiom,
! [V_w,V_z] : c_lessequals(c_RealVector_Onorm__class_Onorm(V_w,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(V_w,V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f733,axiom,
! [V_p,V_r,V_w] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_w,tc_Complex_Ocomplex),V_r,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(V_p,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1(V_p,V_r),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(V_p,V_w,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f742,axiom,
! [V_i,V_k,V_j] :
( ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal)
| ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal)
| c_lessequals(V_i,V_k,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f749,axiom,
! [V_p,V_w] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(V_p,v_sko__CHAINED__1(V_p),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(V_p,V_w,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f750,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f751,negated_conjecture,
! [V_xa] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,V_xa,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,hAPP(v_x,V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2094,plain,
! [X0,X1] : c_lessequals(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f722]) ).
fof(f2108,plain,
! [V_r,V_w] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_w,tc_Complex_Ocomplex),V_r,tc_RealDef_Oreal)
| ! [V_p] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(V_p,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1(V_p,V_r),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(V_p,V_w,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(miniscoping,[status(thm)],[f733]) ).
fof(f2109,plain,
! [X0,X1,X2] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X2,tc_Complex_Ocomplex),X1,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X0,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1(X0,X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f2108]) ).
fof(f2122,plain,
! [V_i,V_j] :
( ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal)
| ! [V_k] :
( ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal)
| c_lessequals(V_i,V_k,tc_RealDef_Oreal) ) ),
inference(miniscoping,[status(thm)],[f742]) ).
fof(f2123,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X0,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f2122]) ).
fof(f2132,plain,
! [X0,X1] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X0,v_sko__CHAINED__1(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f749]) ).
fof(f2133,plain,
~ v_thesis____,
inference(cnf_transformation,[status(thm)],[f750]) ).
fof(f2134,plain,
( ! [V_xa] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,V_xa,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,hAPP(v_x,V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
inference(miniscoping,[status(thm)],[f751]) ).
fof(f2135,plain,
! [X0] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
inference(cnf_transformation,[status(thm)],[f2134]) ).
fof(f2284,definition,
( sQ0_spl
<=> v_thesis____ ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f2285,plain,
( ~ sQ0_spl
| v_thesis____ ),
inference(component_clause,[status(thm)],[f2284]) ).
fof(f2291,definition,
! [X0] :
( sQ2_spl
<=> ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f2292,plain,
! [X0] :
( ~ sQ2_spl
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f2291]) ).
fof(f2294,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f2135,f2284,f2291]) ).
fof(f2299,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2285,f2133]) ).
fof(f2300,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f2299]) ).
fof(f2312,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,hAPP(v_x,X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f2292,f2123]) ).
fof(f5996,plain,
! [X0,X1,X2] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X0,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1(X0,c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(X2,tc_Complex_Ocomplex),tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f2109,f2094]) ).
fof(f6231,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,hAPP(v_x,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1(v_pa____,c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal))),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f5996,f2312]) ).
fof(f9581,plain,
( ~ sQ2_spl
| $false ),
inference(resolution,[status(thm)],[f2132,f6231]) ).
fof(f9659,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f9581]) ).
fof(f9660,plain,
$false,
inference(sat_refutation,[status(thm)],[f2294,f2300,f9659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG395-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.13/20.50 % CPULimit : 300
% 0.13/20.50 % WCLimit : 300
% 0.13/20.50 % DateTime : Mon Sep 21 13:18:58 UTC 2026
% 0.37/20.50 % CPUTime :
% 0.37/20.56 % Drodi V4.1.1
% 114.12/34.92 % Refutation found
% 114.12/34.92 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 114.12/34.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 117.00/36.11 % Elapsed time: 15.397260 seconds
% 117.00/36.11 % CPU time: 111.832121 seconds
% 117.00/36.11 % Total memory used: 454.166 MB
% 117.00/36.11 % Net memory used: 414.607 MB
%------------------------------------------------------------------------------