%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG354-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 11:49:15 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.42s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 10 unt; 5 def)
% Number of atoms : 58 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 25 ~; 21 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 5 ( 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f370,axiom,
! [V_z] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(V_z,v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_thesis____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f372,axiom,
c_HOL_Oord__class_Oless(v_m____,v_na____,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f373,axiom,
v_m____ != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f374,axiom,
( ~ c_HOL_Oord__class_Oless(v_m____,v_na____,tc_nat)
| v_m____ = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(v_sko__CHAINED__1(v_b,v_m____),v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f375,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1098,plain,
( ! [V_z] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(V_z,v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_thesis____ ),
inference(miniscoping,[status(thm)],[f370]) ).
fof(f1099,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(X0,v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_thesis____ ),
inference(cnf_transformation,[status(thm)],[f1098]) ).
fof(f1102,plain,
c_HOL_Oord__class_Oless(v_m____,v_na____,tc_nat),
inference(cnf_transformation,[status(thm)],[f372]) ).
fof(f1103,plain,
v_m____ != c_HOL_Ozero__class_Ozero(tc_nat),
inference(cnf_transformation,[status(thm)],[f373]) ).
fof(f1104,plain,
( ~ c_HOL_Oord__class_Oless(v_m____,v_na____,tc_nat)
| v_m____ = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(v_sko__CHAINED__1(v_b,v_m____),v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f374]) ).
fof(f1105,plain,
~ v_thesis____,
inference(cnf_transformation,[status(thm)],[f375]) ).
fof(f1210,definition,
( sQ0_spl
<=> v_thesis____ ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1211,plain,
( ~ sQ0_spl
| v_thesis____ ),
inference(component_clause,[status(thm)],[f1210]) ).
fof(f1213,definition,
! [X0] :
( sQ1_spl
<=> ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(X0,v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1214,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(X0,v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1213]) ).
fof(f1216,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1099,f1210,f1213]) ).
fof(f1217,definition,
( sQ2_spl
<=> c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(v_sko__CHAINED__1(v_b,v_m____),v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1218,plain,
( ~ sQ2_spl
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(v_sko__CHAINED__1(v_b,v_m____),v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1217]) ).
fof(f1220,definition,
( sQ3_spl
<=> v_m____ = c_HOL_Ozero__class_Ozero(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1221,plain,
( ~ sQ3_spl
| v_m____ = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(component_clause,[status(thm)],[f1220]) ).
fof(f1223,definition,
( sQ4_spl
<=> c_HOL_Oord__class_Oless(v_m____,v_na____,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1225,plain,
( sQ4_spl
| ~ c_HOL_Oord__class_Oless(v_m____,v_na____,tc_nat) ),
inference(component_clause,[status(thm)],[f1223]) ).
fof(f1226,plain,
( ~ sQ4_spl
| sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1104,f1217,f1220,f1223]) ).
fof(f1228,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1211,f1105]) ).
fof(f1229,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f1228]) ).
fof(f1230,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1225,f1102]) ).
fof(f1231,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f1230]) ).
fof(f1232,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1218,f1214]) ).
fof(f1233,plain,
( ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1232]) ).
fof(f1234,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1221,f1103]) ).
fof(f1235,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f1234]) ).
fof(f1236,plain,
$false,
inference(sat_refutation,[status(thm)],[f1216,f1226,f1229,f1231,f1233,f1235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG354-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n018.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 13:19:14 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.42 % Refutation found
% 0.11/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.47 % Elapsed time: 0.090054 seconds
% 0.11/0.47 % CPU time: 0.355488 seconds
% 0.11/0.47 % Total memory used: 128.107 MB
% 0.11/0.47 % Net memory used: 127.715 MB
%------------------------------------------------------------------------------