%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG341-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 11:49:14 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.49s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 11 unt; 2 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 19 ~; 15 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f464,axiom,
! [V_w] : c_lessequals(V_w,V_w,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f465,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/sandbox/benchmark/theBenchmark.p') ).
fof(f472,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f473,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f474,negated_conjecture,
~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1398,plain,
! [X0] : c_lessequals(X0,X0,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f464]) ).
fof(f1399,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)],[f465]) ).
fof(f1400,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X0,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f1399]) ).
fof(f1409,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f472]) ).
fof(f1410,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f473]) ).
fof(f1411,plain,
~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f474]) ).
fof(f1534,plain,
! [X0] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1400,f1411]) ).
fof(f1535,plain,
! [X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1534,f1400]) ).
fof(f1829,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(v_r,v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1535,f1410]) ).
fof(f1896,definition,
( sQ41_spl
<=> c_lessequals(v_r,v_r,tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f1898,plain,
( sQ41_spl
| ~ c_lessequals(v_r,v_r,tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1896]) ).
fof(f1946,definition,
( sQ52_spl
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1948,plain,
( sQ52_spl
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1946]) ).
fof(f1949,plain,
( ~ sQ52_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f1829,f1896,f1946]) ).
fof(f2031,plain,
( sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1898,f1398]) ).
fof(f2032,plain,
sQ41_spl,
inference(contradiction_clause,[status(thm)],[f2031]) ).
fof(f2035,plain,
( sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1948,f1409]) ).
fof(f2036,plain,
sQ52_spl,
inference(contradiction_clause,[status(thm)],[f2035]) ).
fof(f2037,plain,
$false,
inference(sat_refutation,[status(thm)],[f1949,f2032,f2036]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG341-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 13:17:23 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.42 % Drodi V4.1.1
% 0.11/0.49 % Refutation found
% 0.11/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.54 % Elapsed time: 0.153506 seconds
% 0.11/0.54 % CPU time: 0.572448 seconds
% 0.11/0.54 % Total memory used: 90.043 MB
% 0.11/0.54 % Net memory used: 89.486 MB
%------------------------------------------------------------------------------