%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG340-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 9 unt; 2 def)
% Number of atoms : 105 ( 22 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 101 ( 47 ~; 52 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 56 ( 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f211,axiom,
! [V_x] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),tc_RealDef_Oreal)
| V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f214,axiom,
! [V_xa] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(V_xa),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f368,axiom,
! [V_w,V_z] :
( c_lessequals(V_z,V_w,tc_RealDef_Oreal)
| c_lessequals(V_w,V_z,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f378,axiom,
! [V_w] : c_lessequals(V_w,V_w,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f379,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f383,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f392,axiom,
! [T_a,V_a] :
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f400,axiom,
! [V_x,V_y] :
( ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f429,negated_conjecture,
! [V_xa] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_xa,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f509,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f911,plain,
! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f914,plain,
! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(X0),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f1200,plain,
! [X0,X1] :
( c_lessequals(X1,X0,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f368]) ).
fof(f1216,plain,
! [X0] : c_lessequals(X0,X0,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f378]) ).
fof(f1217,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)],[f379]) ).
fof(f1218,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)],[f1217]) ).
fof(f1224,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)],[f383]) ).
fof(f1237,plain,
! [T_a] :
( ! [V_a] : c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
inference(miniscoping,[status(thm)],[f392]) ).
fof(f1238,plain,
! [X0,X1] :
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Oidom(X0) ),
inference(cnf_transformation,[status(thm)],[f1237]) ).
fof(f1249,plain,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| X0 = X1
| c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f400]) ).
fof(f1283,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f1363,plain,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f509]) ).
fof(f1578,plain,
! [X0] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ),
inference(resolution,[status(thm)],[f1249,f1283]) ).
fof(f1581,plain,
! [X0] : c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f1238,f1363]) ).
fof(f1600,plain,
! [X0] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ),
inference(backward_demodulation,[status(thm)],[f1581,f1578]) ).
fof(f1601,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal) ),
inference(backward_demodulation,[status(thm)],[f1581,f1283]) ).
fof(f1628,plain,
! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f911,f1224]) ).
fof(f1668,plain,
! [X0] :
( X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1601,f911]) ).
fof(f1672,plain,
! [X0] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1668,f1200]) ).
fof(f1688,definition,
( sQ5_spl
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1690,plain,
( sQ5_spl
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f1688]) ).
fof(f1727,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f1600,f1216]) ).
fof(f1728,definition,
( sQ7_spl
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1729,plain,
( ~ sQ7_spl
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f1728]) ).
fof(f1730,plain,
( sQ7_spl
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f1728]) ).
fof(f1736,plain,
( ~ sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f1727,f1728,f1688]) ).
fof(f1740,plain,
! [X0] :
( ~ sQ7_spl
| X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(backward_demodulation,[status(thm)],[f1729,f1668]) ).
fof(f1741,plain,
! [X0] :
( ~ sQ7_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(backward_demodulation,[status(thm)],[f1729,f1601]) ).
fof(f1744,plain,
! [X0] :
( ~ sQ7_spl
| X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(forward_subsumption_resolution,[status(thm)],[f1740,f1628]) ).
fof(f1745,plain,
! [X0] :
( ~ sQ7_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(forward_subsumption_resolution,[status(thm)],[f1741,f1224]) ).
fof(f1746,plain,
! [X0,X1] :
( ~ sQ7_spl
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f1744,f1744]) ).
fof(f1753,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1746,f1745]) ).
fof(f1759,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| ~ c_HOL_Oord__class_Oless(X0,X1,X2) ),
inference(paramodulation,[status(thm)],[f1746,f1753]) ).
fof(f1925,plain,
! [X0] :
( sQ5_spl
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1218,f1690]) ).
fof(f2038,plain,
! [X0] :
( sQ5_spl
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1628,f1925]) ).
fof(f2041,plain,
! [X0] :
( sQ5_spl
| X0 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(forward_subsumption_resolution,[status(thm)],[f2038,f1672]) ).
fof(f2044,plain,
( sQ7_spl
| sQ5_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1730,f2041]) ).
fof(f2054,plain,
( sQ7_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f2044]) ).
fof(f2150,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f914,f1759]) ).
fof(f2151,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f2150]) ).
fof(f2152,plain,
$false,
inference(sat_refutation,[status(thm)],[f1736,f2054,f2151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG340-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Mon Sep 21 13:16:21 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.09/0.34 % Drodi V4.1.1
% 0.09/0.37 % Refutation found
% 0.09/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.40 % Elapsed time: 0.084212 seconds
% 0.09/0.40 % CPU time: 0.243523 seconds
% 0.09/0.40 % Total memory used: 123.345 MB
% 0.09/0.40 % Net memory used: 122.657 MB
%------------------------------------------------------------------------------