%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG372-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 0.14s 5.88s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 11 unt; 3 def)
% Number of atoms : 55 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 20 ~; 20 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 9 ( 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f684,axiom,
! [T_a] :
( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f699,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f744,axiom,
! [T_a,V_b] :
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f754,negated_conjecture,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f855,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f880,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2131,plain,
! [X0] :
( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[status(thm)],[f684]) ).
fof(f2155,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f699]) ).
fof(f2211,plain,
! [T_a] :
( ! [V_b] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
inference(miniscoping,[status(thm)],[f744]) ).
fof(f2212,plain,
! [X0,X1] :
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1
| ~ class_OrderedGroup_Ogroup__add(X0) ),
inference(cnf_transformation,[status(thm)],[f2211]) ).
fof(f2226,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f754]) ).
fof(f2327,plain,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f855]) ).
fof(f2352,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f880]) ).
fof(f2432,definition,
( sQ2_spl
<=> c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f2434,plain,
( sQ2_spl
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f2432]) ).
fof(f2435,definition,
( sQ3_spl
<=> c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f2437,plain,
( sQ3_spl
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f2435]) ).
fof(f2438,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f2226,f2432,f2435]) ).
fof(f3330,definition,
( sQ20_spl
<=> c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f3331,plain,
( ~ sQ20_spl
| c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f3330]) ).
fof(f3332,plain,
( sQ20_spl
| c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f3330]) ).
fof(f3503,plain,
( sQ3_spl
| ~ sQ20_spl
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f3331,f2437]) ).
fof(f3504,plain,
( sQ3_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3503,f2155]) ).
fof(f3505,plain,
( sQ3_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f3504]) ).
fof(f4343,plain,
! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0,
inference(resolution,[status(thm)],[f2212,f2327]) ).
fof(f4345,plain,
( sQ2_spl
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(backward_demodulation,[status(thm)],[f4343,f2434]) ).
fof(f4348,plain,
( sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f4345]) ).
fof(f4349,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f4348]) ).
fof(f6405,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f2131,f2352]) ).
fof(f6407,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6405,f3332]) ).
fof(f6408,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f6407]) ).
fof(f6409,plain,
$false,
inference(sat_refutation,[status(thm)],[f2438,f3505,f4349,f6408]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG372-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n001.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 13:23:35 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.14/5.43 % Drodi V4.1.1
% 0.14/5.88 % Refutation found
% 0.14/5.88 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.90 % Elapsed time: 0.530535 seconds
% 0.14/5.90 % CPU time: 3.662959 seconds
% 0.14/5.90 % Total memory used: 188.957 MB
% 0.14/5.90 % Net memory used: 187.251 MB
%------------------------------------------------------------------------------