%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA039-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 12:02:18 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.37s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 11 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 90 ( 49 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 54 ( 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [V_U] : c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [T_a,V_a] :
( c_lessequals(V_a,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(f5,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(f6,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [T_a,V_a,V_b,V_c] :
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [T] :
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [X0] : c_lessequals(c_HOL_Oabs(v_h(X0),t_a),c_times(v_c,c_HOL_Oabs(v_f(X0),t_a),t_a),t_a),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f13,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [T_a] :
( ! [V_a] : c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f15,plain,
! [X0,X1] :
( c_lessequals(X1,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,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)],[f5]) ).
fof(f17,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)],[f16]) ).
fof(f18,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)],[f6]) ).
fof(f19,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)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_times(X1,X3,X0),c_times(X2,X3,X0),X0)
| ~ c_lessequals(c_0,X3,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f21,plain,
! [X0] :
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f22,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f23,plain,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f24,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[status(thm)],[f23,f13]) ).
fof(f25,plain,
! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,t_a),t_a),
inference(resolution,[status(thm)],[f24,f17]) ).
fof(f26,plain,
! [X0] : c_lessequals(X0,c_HOL_Oabs(X0,t_a),t_a),
inference(resolution,[status(thm)],[f24,f15]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_lessequals(X3,X1,X2)
| ~ c_lessequals(X3,X0,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(resolution,[status(thm)],[f19,f22]) ).
fof(f28,plain,
! [X0,X1,X2] :
( c_lessequals(X2,X1,t_a)
| ~ c_lessequals(X2,X0,t_a)
| ~ c_lessequals(X0,X1,t_a) ),
inference(resolution,[status(thm)],[f27,f13]) ).
fof(f29,plain,
! [X0] :
( ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),X0,t_a)
| ~ c_lessequals(X0,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a) ),
inference(resolution,[status(thm)],[f28,f12]) ).
fof(f30,plain,
! [X0] :
( ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a)
| ~ c_lessequals(X0,c_HOL_Oabs(v_c,t_a),t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a)
| ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a) ),
inference(resolution,[status(thm)],[f29,f20]) ).
fof(f32,plain,
! [X0] :
( ~ c_lessequals(X0,c_HOL_Oabs(v_c,t_a),t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a)
| ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a) ),
inference(forward_subsumption_resolution,[status(thm)],[f30,f25]) ).
fof(f33,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| ~ c_lessequals(X0,c_HOL_Oabs(v_c,t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a) ),
inference(resolution,[status(thm)],[f32,f21]) ).
fof(f34,plain,
! [X0] :
( ~ c_lessequals(X0,c_HOL_Oabs(v_c,t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a) ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f13]) ).
fof(f38,plain,
~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a),
inference(resolution,[status(thm)],[f34,f11]) ).
fof(f40,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f38,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA039-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n026.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 13:28:38 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.37 % Refutation found
% 0.10/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.041475 seconds
% 0.12/0.41 % CPU time: 0.077120 seconds
% 0.12/0.41 % Total memory used: 7.097 MB
% 0.12/0.41 % Net memory used: 7.054 MB
%------------------------------------------------------------------------------