%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA044-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 12:02:19 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 14 unt; 0 def)
% Number of atoms : 43 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 39 ( 21 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [V_U,V_V] : c_lessequals(c_0,v_l(V_U,V_V),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
! [V_U] : c_lessequals(c_0,v_h(V_U),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [T_a,V_b,V_a] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [T] :
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0,X1] : c_lessequals(c_0,v_l(X0,X1),t_b),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0] : c_lessequals(c_0,v_h(X0),t_b),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,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)],[f5]) ).
fof(f14,plain,
! [X0,X1,X2] :
( c_lessequals(c_0,c_times(X2,X1,X0),X0)
| ~ c_lessequals(c_0,X2,X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f15,plain,
! [X0] :
( class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f16,plain,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f19,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(resolution,[status(thm)],[f15,f12]) ).
fof(f20,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[f16,f12]) ).
fof(f24,plain,
! [X0,X1] :
( c_lessequals(c_0,c_times(X0,v_h(X1),t_b),t_b)
| ~ c_lessequals(c_0,X0,t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b) ),
inference(resolution,[status(thm)],[f14,f10]) ).
fof(f26,plain,
! [X0,X1] :
( c_lessequals(c_0,c_times(X0,v_h(X1),t_b),t_b)
| ~ c_lessequals(c_0,X0,t_b) ),
inference(forward_subsumption_resolution,[status(thm)],[f24,f19]) ).
fof(f41,plain,
! [X0,X1,X2] : c_lessequals(c_0,c_times(v_l(X0,X1),v_h(X2),t_b),t_b),
inference(resolution,[status(thm)],[f26,f9]) ).
fof(f52,plain,
! [X0,X1,X2] :
( c_HOL_Oabs(c_times(v_l(X0,X1),v_h(X2),t_b),t_b) = c_times(v_l(X0,X1),v_h(X2),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(resolution,[status(thm)],[f41,f13]) ).
fof(f54,plain,
! [X0,X1,X2] : c_HOL_Oabs(c_times(v_l(X0,X1),v_h(X2),t_b),t_b) = c_times(v_l(X0,X1),v_h(X2),t_b),
inference(forward_subsumption_resolution,[status(thm)],[f52,f20]) ).
fof(f131,plain,
c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),
inference(backward_demodulation,[status(thm)],[f54,f11]) ).
fof(f132,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA044-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 13:26:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.42 % Elapsed time: 0.047849 seconds
% 0.09/0.42 % CPU time: 0.144693 seconds
% 0.09/0.42 % Total memory used: 41.530 MB
% 0.09/0.42 % Net memory used: 41.012 MB
%------------------------------------------------------------------------------