%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA024-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:02:15 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 36 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [T_a,V_a,V_b] :
( V_a = c_plus(c_minus(V_a,V_b,T_a),V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [T_a,V_a,V_b,V_c] :
( c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [V_U] : c_lessequals(v_k(V_U),v_f(V_U),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [T] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [T] :
( class_OrderedGroup_Opordered__ab__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_a = c_plus(c_minus(V_a,V_b,T_a),V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f9,plain,
! [X0,X1,X2] :
( X1 = c_plus(c_minus(X1,X2,X0),X2,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X1,c_minus(X3,X2,X0),X0)
| ~ c_lessequals(c_plus(X1,X2,X0),X3,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0] : c_lessequals(v_k(X0),v_f(X0),t_b),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [X0] :
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f15,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f16,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(resolution,[status(thm)],[f14,f15]) ).
fof(f17,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(resolution,[status(thm)],[f13,f16]) ).
fof(f18,plain,
! [X0,X1] : X0 = c_plus(c_minus(X0,X1,t_b),X1,t_b),
inference(resolution,[status(thm)],[f9,f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( c_lessequals(c_minus(X0,X2,t_b),c_minus(X1,X2,t_b),t_b)
| ~ c_lessequals(X0,X1,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(paramodulation,[status(thm)],[f18,f10]) ).
fof(f20,plain,
! [X0,X1,X2] :
( c_lessequals(c_minus(X0,X2,t_b),c_minus(X1,X2,t_b),t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(forward_subsumption_resolution,[status(thm)],[f19,f16]) ).
fof(f21,plain,
! [X0,X1] : c_lessequals(c_minus(v_k(X0),X1,t_b),c_minus(v_f(X0),X1,t_b),t_b),
inference(resolution,[status(thm)],[f20,f11]) ).
fof(f23,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f12,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA024-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n026.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 21 13:27:07 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.043405 seconds
% 0.13/0.40 % CPU time: 0.131361 seconds
% 0.13/0.40 % Total memory used: 38.559 MB
% 0.13/0.40 % Net memory used: 38.055 MB
%------------------------------------------------------------------------------