%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA010-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 16 unt; 0 def)
% Number of atoms : 55 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 28 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 45 ( 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [T_a,V_y] :
( c_HOL_Oabs(V_y,T_a) = V_y
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [T_a,V_y,V_z,V_x] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [T_a,V_a,V_b] :
( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [V_U] : c_lessequals(c_0,v_f(V_U),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
! [V_U] : c_lessequals(v_f(V_U),c_times(v_c,v_g(V_U),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [V_U] : ~ c_lessequals(v_f(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0,X1] :
( c_HOL_Oabs(X1,X0) = X1
| ~ c_lessequals(c_0,X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [T_a,V_z,V_x] :
( c_lessequals(V_x,V_z,T_a)
| ! [V_y] :
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X3,X2,X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [T_a] :
( ! [V_a,V_b] : c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f14,plain,
! [X0,X1,X2] :
( c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0] : c_lessequals(c_0,v_f(X0),t_b),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f16,plain,
! [X0] : c_lessequals(v_f(X0),c_times(v_c,v_g(X0),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f17,plain,
! [X0] : ~ c_lessequals(v_f(v_x(X0)),c_times(X0,c_HOL_Oabs(v_g(v_x(X0)),t_b),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f18,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f19,plain,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f20,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f22,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[f19,f20]) ).
fof(f24,plain,
! [X0,X1] : c_HOL_Oabs(c_times(X0,X1,t_b),t_b) = c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(X1,t_b),t_b),
inference(resolution,[status(thm)],[f14,f20]) ).
fof(f27,plain,
! [X0] : ~ c_lessequals(v_f(v_x(c_HOL_Oabs(X0,t_b))),c_HOL_Oabs(c_times(X0,v_g(v_x(c_HOL_Oabs(X0,t_b))),t_b),t_b),t_b),
inference(paramodulation,[status(thm)],[f24,f17]) ).
fof(f68,plain,
class_Orderings_Oorder(t_b),
inference(resolution,[status(thm)],[f18,f22]) ).
fof(f69,plain,
! [X0,X1] :
( c_lessequals(X0,c_times(v_c,v_g(X1),t_b),t_b)
| ~ c_lessequals(X0,v_f(X1),t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[status(thm)],[f12,f16]) ).
fof(f71,plain,
! [X0,X1] :
( c_lessequals(X0,c_times(v_c,v_g(X1),t_b),t_b)
| ~ c_lessequals(X0,v_f(X1),t_b) ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f68]) ).
fof(f73,plain,
! [X0] : c_lessequals(c_0,c_times(v_c,v_g(X0),t_b),t_b),
inference(resolution,[status(thm)],[f71,f15]) ).
fof(f74,plain,
! [X0] :
( c_HOL_Oabs(c_times(v_c,v_g(X0),t_b),t_b) = c_times(v_c,v_g(X0),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(resolution,[status(thm)],[f73,f10]) ).
fof(f76,plain,
! [X0] : c_HOL_Oabs(c_times(v_c,v_g(X0),t_b),t_b) = c_times(v_c,v_g(X0),t_b),
inference(forward_subsumption_resolution,[status(thm)],[f74,f22]) ).
fof(f78,plain,
~ c_lessequals(v_f(v_x(c_HOL_Oabs(v_c,t_b))),c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b),
inference(paramodulation,[status(thm)],[f76,f27]) ).
fof(f87,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f78,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA010-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n017.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 13:18:42 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.051790 seconds
% 0.14/0.41 % CPU time: 0.147352 seconds
% 0.14/0.41 % Total memory used: 44.324 MB
% 0.14/0.41 % Net memory used: 43.829 MB
%------------------------------------------------------------------------------