%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ALG342-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 11:50:03 AM UTC 2026
% Result : Unsatisfiable 57.77s 7.72s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG342-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 13:16:27 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.41 % Drodi V4.1.1
% 57.77/7.72 % Refutation found
% 57.77/7.72 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 57.77/7.72 % SZS output start CNFRefutation for theBenchmark
% 57.77/7.72 fof(f436,axiom,(
% 57.77/7.72 (![V_z]: (( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ) ))),
% 57.77/7.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.77/7.72 fof(f437,axiom,(
% 57.77/7.72 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
% 57.77/7.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.77/7.72 fof(f438,negated_conjecture,(
% 57.77/7.72 (![V_xa]: (( c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(V_xa),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa,tc_RealDef_Oreal) ) ))),
% 57.77/7.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.77/7.72 fof(f439,negated_conjecture,(
% 57.77/7.72 (![V_xa]: (( ~ c_lessequals(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),V_xa,tc_RealDef_Oreal)| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa,tc_RealDef_Oreal) ) ))),
% 57.77/7.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.77/7.72 fof(f1305,plain,(
% 57.77/7.72 ![X0]: (c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)|~c_lessequals(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal))),
% 57.77/7.72 inference(cnf_transformation,[status(thm)],[f436])).
% 57.77/7.72 fof(f1306,plain,(
% 57.77/7.72 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
% 57.77/7.72 inference(cnf_transformation,[status(thm)],[f437])).
% 57.77/7.72 fof(f1307,plain,(
% 57.77/7.72 ![X0]: (c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal))),
% 57.77/7.72 inference(cnf_transformation,[status(thm)],[f438])).
% 57.77/7.72 fof(f1308,plain,(
% 57.77/7.72 ![X0]: (~c_lessequals(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),X0,tc_RealDef_Oreal)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal))),
% 57.77/7.72 inference(cnf_transformation,[status(thm)],[f439])).
% 57.77/7.72 fof(f20150,plain,(
% 57.77/7.72 ~c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
% 57.77/7.74 inference(resolution,[status(thm)],[f1305,f1308])).
% 57.77/7.74 fof(f20158,definition,(
% 57.77/7.74 sQ860_spl <=> (c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal))),
% 57.77/7.74 introduced(definition,[new_symbols(definition,[sQ860_spl])],[split_symbol_definition])).
% 57.77/7.74 fof(f20160,plain,(
% 57.77/7.74 ~c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)|sQ860_spl),
% 57.77/7.74 inference(component_clause,[status(thm)],[f20158])).
% 57.77/7.74 fof(f20161,definition,(
% 57.77/7.74 sQ861_spl <=> (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))),
% 57.77/7.74 introduced(definition,[new_symbols(definition,[sQ861_spl])],[split_symbol_definition])).
% 57.77/7.74 fof(f20163,plain,(
% 57.77/7.74 ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)|sQ861_spl),
% 57.77/7.74 inference(component_clause,[status(thm)],[f20161])).
% 57.77/7.74 fof(f20164,plain,(
% 57.77/7.74 ~sQ860_spl|~sQ861_spl),
% 57.77/7.74 inference(split_clause,[status(thm)],[f20150,f20158,f20161])).
% 57.77/7.74 fof(f28032,plain,(
% 57.77/7.74 ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)|sQ860_spl),
% 57.77/7.74 inference(resolution,[status(thm)],[f20160,f1307])).
% 57.77/7.74 fof(f28042,plain,(
% 57.77/7.74 $false|sQ860_spl),
% 57.77/7.74 inference(forward_subsumption_resolution,[status(thm)],[f28032,f1306])).
% 57.77/7.74 fof(f28043,plain,(
% 57.77/7.74 sQ860_spl),
% 57.77/7.74 inference(contradiction_clause,[status(thm)],[f28042])).
% 57.77/7.74 fof(f28382,plain,(
% 57.77/7.74 $false|sQ861_spl),
% 57.77/7.74 inference(forward_subsumption_resolution,[status(thm)],[f20163,f1306])).
% 57.77/7.74 fof(f28383,plain,(
% 57.77/7.74 sQ861_spl),
% 57.77/7.74 inference(contradiction_clause,[status(thm)],[f28382])).
% 57.77/7.74 fof(f28384,plain,(
% 57.77/7.74 $false),
% 57.77/7.74 inference(sat_refutation,[status(thm)],[f20164,f28043,f28383])).
% 57.77/7.74 % SZS output end CNFRefutation for theBenchmark.p
% 57.77/7.78 % Elapsed time: 7.399237 seconds
% 57.77/7.78 % CPU time: 58.260358 seconds
% 57.77/7.78 % Total memory used: 471.652 MB
% 57.77/7.78 % Net memory used: 442.396 MB
%------------------------------------------------------------------------------