%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG371-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 11:49:17 AM UTC 2026
% Result : Unsatisfiable 3.94s 1.36s
% Output : CNFRefutation 4.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 41 ( 15 unt; 4 def)
% Number of atoms : 72 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 59 ( 28 ~; 27 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f381,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(f385,axiom,
! [V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(V_x,V_y,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f389,axiom,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f393,axiom,
! [T_a,V_x] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f412,axiom,
! [V_z,V_w] :
( ~ c_lessequals(V_z,V_w,tc_RealDef_Oreal)
| ~ c_lessequals(V_w,V_z,tc_RealDef_Oreal)
| V_z = V_w ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f428,negated_conjecture,
c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f429,negated_conjecture,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f438,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f489,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1172,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)],[f381]) ).
fof(f1173,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)],[f1172]) ).
fof(f1179,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f385]) ).
fof(f1184,plain,
! [X0] : ~ c_HOL_Oord__class_Oless(X0,X0,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f1190,plain,
! [T_a] :
( ! [V_x] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(miniscoping,[status(thm)],[f393]) ).
fof(f1191,plain,
! [X0,X1] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[status(thm)],[f1190]) ).
fof(f1214,plain,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f412]) ).
fof(f1233,plain,
c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f428]) ).
fof(f1234,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f1243,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f438]) ).
fof(f1294,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f489]) ).
fof(f1345,plain,
c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f1179,f1233]) ).
fof(f1368,definition,
( sQ7_spl
<=> v_r = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1369,plain,
( ~ sQ7_spl
| v_r = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1368]) ).
fof(f1387,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r ),
inference(resolution,[status(thm)],[f1214,f1345]) ).
fof(f1392,definition,
( sQ12_spl
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f1395,plain,
( ~ sQ12_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f1387,f1368,f1392]) ).
fof(f1407,plain,
( ~ sQ7_spl
| c_HOL_Oord__class_Oless(v_r,v_r,tc_RealDef_Oreal) ),
inference(backward_demodulation,[status(thm)],[f1369,f1233]) ).
fof(f1411,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1407,f1184]) ).
fof(f1412,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f1411]) ).
fof(f4536,definition,
( sQ273_spl
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f4538,plain,
( sQ273_spl
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f4536]) ).
fof(f4540,plain,
( sQ273_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4538,f1294]) ).
fof(f4541,plain,
sQ273_spl,
inference(contradiction_clause,[status(thm)],[f4540]) ).
fof(f4573,plain,
! [X0] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1234,f1173]) ).
fof(f4629,definition,
( sQ279_spl
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f4631,plain,
( sQ279_spl
| ~ class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f4629]) ).
fof(f4636,plain,
( sQ279_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4631,f1243]) ).
fof(f4637,plain,
sQ279_spl,
inference(contradiction_clause,[status(thm)],[f4636]) ).
fof(f4652,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f4573,f1191]) ).
fof(f4666,plain,
( ~ sQ273_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f4652,f1392,f4536]) ).
fof(f4677,plain,
$false,
inference(sat_refutation,[status(thm)],[f1395,f1412,f4541,f4637,f4666]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG371-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.65 % Computer : n002.cluster.edu
% 0.20/0.65 % Model : x86_64 x86_64
% 0.20/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.65 % Memory : 8046.5625MB
% 0.20/0.65 % OS : Linux 6.8.0-71-generic
% 0.20/0.65 % CPULimit : 300
% 0.20/0.65 % WCLimit : 300
% 0.20/0.65 % DateTime : Mon Sep 21 13:20:48 UTC 2026
% 0.22/0.65 % CPUTime :
% 0.23/0.72 % Drodi V4.1.1
% 3.94/1.36 % Refutation found
% 3.94/1.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.94/1.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.98/1.40 % Elapsed time: 0.728871 seconds
% 4.98/1.40 % CPU time: 5.159875 seconds
% 4.98/1.40 % Total memory used: 165.010 MB
% 4.98/1.40 % Net memory used: 162.384 MB
%------------------------------------------------------------------------------