%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA019-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 12:02:14 PM UTC 2026
% Result : Unsatisfiable 0.09s 1.84s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 55 ( 17 unt; 0 def)
% Number of atoms : 101 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 97 ( 51 ~; 46 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
v_f(c_0) = c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
c_less(c_0,v_x,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [V_U] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(V_U)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(V_U)),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [V_U] :
( ~ c_less(c_0,V_U,t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U)),t_a),c_times(V_U,c_HOL_Oabs(v_h(v_xa(V_U)),t_a),t_a),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_x] :
( V_x = c_Suc(c_minus(V_x,c_1,tc_nat))
| ~ c_less(c_0,V_x,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V_n] :
( V_n = c_0
| c_less(c_0,V_n,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [T_a] :
( c_HOL_Oabs(c_0,T_a) = c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [T_a,V_a] :
( c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [T_a,V_x,V_y] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,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(f12,axiom,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_LOrder_Ojoin__semilorder(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [T] :
( class_LOrder_Ojoin__semilorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,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(f15,axiom,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,plain,
v_f(c_0) = c_0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f17,plain,
c_less(c_0,v_x,t_a),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
! [X0] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(X0)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(X0)),t_a),t_a),t_a),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
! [X0] :
( ~ c_less(c_0,X0,t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(X0)),t_a),c_times(X0,c_HOL_Oabs(v_h(v_xa(X0)),t_a),t_a),t_a) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f20,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [X0] :
( X0 = c_Suc(c_minus(X0,c_1,tc_nat))
| ~ c_less(c_0,X0,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0] :
( X0 = c_0
| c_less(c_0,X0,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f23,plain,
! [X0] :
( c_HOL_Oabs(c_0,X0) = c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f24,plain,
! [T_a] :
( ! [V_a] : c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f25,plain,
! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( c_lessequals(X1,X2,X0)
| ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f27,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)],[f11]) ).
fof(f28,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_LOrder_Ojoin__semilorder(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
! [X0] :
( class_LOrder_Ojoin__semilorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f30,plain,
! [X0] :
( class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f31,plain,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f32,plain,
class_LOrder_Ojoin__semilorder(t_a),
inference(resolution,[status(thm)],[f29,f20]) ).
fof(f33,plain,
class_Orderings_Oorder(t_a),
inference(resolution,[status(thm)],[f32,f28]) ).
fof(f34,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs(c_0,X0) = c_0 ),
inference(resolution,[status(thm)],[f23,f31]) ).
fof(f35,plain,
c_HOL_Oabs(c_0,t_a) = c_0,
inference(resolution,[status(thm)],[f34,f20]) ).
fof(f36,plain,
! [X0] :
( X0 = c_0
| X0 = c_Suc(c_minus(X0,c_1,tc_nat)) ),
inference(resolution,[status(thm)],[f21,f22]) ).
fof(f37,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_HOL_Oabs(X0,X1),X1) ),
inference(resolution,[status(thm)],[f25,f31]) ).
fof(f38,plain,
! [X0,X1] :
( c_lessequals(X0,X1,t_a)
| ~ c_less(X0,X1,t_a) ),
inference(resolution,[status(thm)],[f26,f33]) ).
fof(f40,plain,
! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,t_a),t_a),
inference(resolution,[status(thm)],[f37,f20]) ).
fof(f42,plain,
! [X0] :
( X0 = c_0
| c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X0,c_1,tc_nat))),t_a),c_times(v_x,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a) ),
inference(paramodulation,[status(thm)],[f36,f18]) ).
fof(f44,plain,
! [X0] :
( X0 = c_0
| X0 = c_0
| c_lessequals(c_HOL_Oabs(v_f(X0),t_a),c_times(v_x,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a) ),
inference(paramodulation,[status(thm)],[f36,f42]) ).
fof(f45,plain,
! [X0] :
( X0 = c_0
| c_lessequals(c_HOL_Oabs(v_f(X0),t_a),c_times(v_x,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a) ),
inference(duplicate_literals_removal,[status(thm)],[f44]) ).
fof(f49,plain,
( ~ c_less(c_0,v_x,t_a)
| v_xa(v_x) = c_0 ),
inference(resolution,[status(thm)],[f45,f19]) ).
fof(f51,plain,
v_xa(v_x) = c_0,
inference(forward_subsumption_resolution,[status(thm)],[f49,f17]) ).
fof(f54,plain,
( ~ c_less(c_0,v_x,t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a) ),
inference(paramodulation,[status(thm)],[f51,f19]) ).
fof(f64,plain,
( ~ c_less(c_0,v_x,t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(c_0),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a) ),
inference(forward_demodulation,[status(thm)],[f51,f54]) ).
fof(f65,plain,
( ~ c_less(c_0,v_x,t_a)
| ~ c_lessequals(c_HOL_Oabs(c_0,t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a) ),
inference(forward_demodulation,[status(thm)],[f16,f64]) ).
fof(f66,plain,
( ~ c_less(c_0,v_x,t_a)
| ~ c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a) ),
inference(forward_demodulation,[status(thm)],[f35,f65]) ).
fof(f67,plain,
~ c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(forward_subsumption_resolution,[status(thm)],[f66,f17]) ).
fof(f72,plain,
( ~ c_lessequals(c_0,v_x,t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
inference(resolution,[status(thm)],[f67,f27]) ).
fof(f74,plain,
( ~ c_lessequals(c_0,v_x,t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
inference(forward_subsumption_resolution,[status(thm)],[f72,f40]) ).
fof(f75,plain,
( ~ c_less(c_0,v_x,t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
inference(resolution,[status(thm)],[f74,f38]) ).
fof(f76,plain,
~ class_Ring__and__Field_Opordered__cancel__semiring(t_a),
inference(forward_subsumption_resolution,[status(thm)],[f75,f17]) ).
fof(f77,plain,
~ class_Ring__and__Field_Oordered__idom(t_a),
inference(resolution,[status(thm)],[f76,f30]) ).
fof(f78,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f77,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA019-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/1.81 % Computer : n012.cluster.edu
% 0.09/1.81 % Model : x86_64 x86_64
% 0.09/1.81 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/1.81 % Memory : 8046.5625MB
% 0.09/1.81 % OS : Linux 6.8.0-71-generic
% 0.09/1.81 % CPULimit : 300
% 0.09/1.81 % WCLimit : 300
% 0.09/1.81 % DateTime : Mon Sep 21 13:23:54 UTC 2026
% 0.09/1.81 % CPUTime :
% 0.09/1.82 % Drodi V4.1.1
% 0.09/1.84 % Refutation found
% 0.09/1.84 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/1.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/1.89 % Elapsed time: 0.073531 seconds
% 0.09/1.89 % CPU time: 0.057851 seconds
% 0.09/1.89 % Total memory used: 3.247 MB
% 0.09/1.89 % Net memory used: 3.245 MB
%------------------------------------------------------------------------------