%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA018-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 0.14s 5.61s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 43 ( 20 unt; 0 def)
% Number of atoms : 80 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 77 ( 40 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 63 ( 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [V_U] : c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
c_less(c_0,v_ca,t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [V_U] : c_lessequals(c_HOL_Oabs(v_x(V_U),t_b),c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [T_a,V_a,V_b,V_c] :
( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Osemigroup__mult(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,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(f8,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(f9,axiom,
! [T_a,V_a,V_b,V_c] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,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(f10,axiom,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_LOrder_Ojoin__semilorder(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [T] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [T] :
( class_LOrder_Ojoin__semilorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [T] :
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0] : c_lessequals(c_HOL_Oabs(v_f(X0),t_b),c_times(v_c,c_HOL_Oabs(v_g(X0),t_b),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
c_less(c_0,v_ca,t_b),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [X0] : c_lessequals(c_HOL_Oabs(v_x(X0),t_b),c_times(v_ca,c_HOL_Oabs(v_f(X0),t_b),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f19,plain,
! [T_a] :
( ! [V_a,V_b,V_c] : c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Osemigroup__mult(T_a) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0)
| ~ class_OrderedGroup_Osemigroup__mult(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,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)],[f7]) ).
fof(f22,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)],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( c_lessequals(X1,X2,X0)
| ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_times(X3,X1,X0),c_times(X3,X2,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)],[f9]) ).
fof(f25,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_LOrder_Ojoin__semilorder(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0] :
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
! [X0] :
( class_LOrder_Ojoin__semilorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f28,plain,
! [X0] :
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f29,plain,
( c_lessequals(c_0,v_ca,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[status(thm)],[f23,f15]) ).
fof(f31,plain,
! [X0,X1] :
( c_lessequals(c_times(X0,c_HOL_Oabs(v_f(X1),t_b),t_b),c_times(X0,c_times(v_c,c_HOL_Oabs(v_g(X1),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,X0,t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(resolution,[status(thm)],[f24,f14]) ).
fof(f32,plain,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(resolution,[status(thm)],[f26,f18]) ).
fof(f33,plain,
! [X0,X1,X2] : c_times(c_times(X0,X1,t_b),X2,t_b) = c_times(X0,c_times(X1,X2,t_b),t_b),
inference(resolution,[status(thm)],[f20,f32]) ).
fof(f34,plain,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b),
inference(backward_demodulation,[status(thm)],[f33,f17]) ).
fof(f38,plain,
class_LOrder_Ojoin__semilorder(t_b),
inference(resolution,[status(thm)],[f27,f18]) ).
fof(f39,plain,
class_Orderings_Oorder(t_b),
inference(resolution,[status(thm)],[f38,f25]) ).
fof(f40,plain,
c_lessequals(c_0,v_ca,t_b),
inference(backward_subsumption_resolution,[status(thm)],[f29,f39]) ).
fof(f41,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(resolution,[status(thm)],[f28,f18]) ).
fof(f42,plain,
! [X0,X1] :
( c_lessequals(c_times(X0,c_HOL_Oabs(v_f(X1),t_b),t_b),c_times(X0,c_times(v_c,c_HOL_Oabs(v_g(X1),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,X0,t_b) ),
inference(backward_subsumption_resolution,[status(thm)],[f31,f41]) ).
fof(f57,plain,
! [X0] : c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(X0),t_b),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(X0),t_b),t_b),t_b),t_b),
inference(resolution,[status(thm)],[f42,f40]) ).
fof(f59,plain,
! [X0,X1] :
( c_lessequals(X0,c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(X1),t_b),t_b),t_b),t_b)
| ~ c_lessequals(X0,c_times(v_ca,c_HOL_Oabs(v_f(X1),t_b),t_b),t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[status(thm)],[f57,f22]) ).
fof(f61,plain,
! [X0,X1] :
( c_lessequals(X0,c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(X1),t_b),t_b),t_b),t_b)
| ~ c_lessequals(X0,c_times(v_ca,c_HOL_Oabs(v_f(X1),t_b),t_b),t_b) ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f39]) ).
fof(f68,plain,
! [X0] : c_lessequals(c_HOL_Oabs(v_x(X0),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(X0),t_b),t_b),t_b),t_b),
inference(resolution,[status(thm)],[f61,f16]) ).
fof(f70,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f34,f68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA018-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.58 % Computer : n002.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.58 % CPULimit : 300
% 0.10/5.58 % WCLimit : 300
% 0.10/5.58 % DateTime : Mon Sep 21 13:26:25 UTC 2026
% 0.10/5.58 % CPUTime :
% 0.10/5.59 % Drodi V4.1.1
% 0.14/5.61 % Refutation found
% 0.14/5.61 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.63 % Elapsed time: 0.041304 seconds
% 0.14/5.63 % CPU time: 0.123708 seconds
% 0.14/5.63 % Total memory used: 34.704 MB
% 0.14/5.63 % Net memory used: 34.318 MB
%------------------------------------------------------------------------------