%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA009-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 12:02:12 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 12 unt; 0 def)
% Number of atoms : 37 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [T_a,V_a,V_b,V_c] :
( c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [T_a,V_a] :
( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [V_U] : c_lessequals(v_lb(V_U),v_f(V_U),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [T] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [T] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,plain,
! [T_a,V_a,V_b] :
( ! [V_c] : c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f9,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_plus(X1,X3,X0),c_plus(X2,X3,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [T_a] :
( ! [V_a] : c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1] :
( c_plus(X1,c_uminus(X1,X0),X0) = c_0
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0] : c_lessequals(v_lb(X0),v_f(X0),t_b),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0] :
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f17,plain,
! [X0,X1] :
( c_lessequals(c_plus(v_lb(X0),X1,t_b),c_plus(v_f(X0),X1,t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
inference(resolution,[status(thm)],[f9,f12]) ).
fof(f18,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(resolution,[status(thm)],[f14,f16]) ).
fof(f19,plain,
! [X0,X1] : c_lessequals(c_plus(v_lb(X0),X1,t_b),c_plus(v_f(X0),X1,t_b),t_b),
inference(backward_subsumption_resolution,[status(thm)],[f17,f18]) ).
fof(f34,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(resolution,[status(thm)],[f15,f16]) ).
fof(f35,plain,
! [X0] : c_plus(X0,c_uminus(X0,t_b),t_b) = c_0,
inference(resolution,[status(thm)],[f34,f11]) ).
fof(f84,plain,
! [X0] : c_lessequals(c_0,c_plus(v_f(X0),c_uminus(v_lb(X0),t_b),t_b),t_b),
inference(paramodulation,[status(thm)],[f35,f19]) ).
fof(f93,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f13,f84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA009-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n020.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 13:23:48 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 0.18/0.48 % Refutation found
% 0.18/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.51 % Elapsed time: 0.060583 seconds
% 0.18/0.51 % CPU time: 0.173344 seconds
% 0.18/0.51 % Total memory used: 37.309 MB
% 0.18/0.51 % Net memory used: 36.908 MB
%------------------------------------------------------------------------------