%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA027-2 : 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 12:02:16 PM UTC 2026
% Result : Unsatisfiable 0.08s 5.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 44 ( 18 unt; 0 def)
% Number of atoms : 82 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 40 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 51 ( 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),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_plus(c_0,V_y,T_a) = V_y
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [T_a,V_a,V_c,V_b] :
( c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [T_a,V_a,V_b,V_c] :
( c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,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(f9,axiom,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_LOrder_Ojoin__semilorder(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [T] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [T] :
( class_LOrder_Ojoin__semilorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [T] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
! [T_a] :
( ! [V_y] : c_plus(c_0,V_y,T_a) = V_y
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f19,plain,
! [X0,X1] :
( c_plus(c_0,X1,X0) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_plus(X1,X3,X0),X2,X0)
| ~ c_lessequals(X1,c_minus(X2,X3,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X1,c_minus(X3,X2,X0),X0)
| ~ c_lessequals(c_plus(X1,X2,X0),X3,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f22,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)],[f8]) ).
fof(f23,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)],[f22]) ).
fof(f24,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_LOrder_Ojoin__semilorder(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f25,plain,
! [X0] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0] :
( class_LOrder_Ojoin__semilorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
! [X0] :
( class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f28,plain,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f29,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[f28,f17]) ).
fof(f30,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(resolution,[status(thm)],[f25,f29]) ).
fof(f31,plain,
class_LOrder_Ojoin__semilorder(t_b),
inference(resolution,[status(thm)],[f26,f29]) ).
fof(f32,plain,
class_Orderings_Oorder(t_b),
inference(resolution,[status(thm)],[f31,f24]) ).
fof(f33,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(resolution,[status(thm)],[f27,f17]) ).
fof(f34,plain,
! [X0] : c_plus(c_0,X0,t_b) = X0,
inference(resolution,[status(thm)],[f19,f33]) ).
fof(f39,plain,
( c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(resolution,[status(thm)],[f20,f14]) ).
fof(f40,plain,
( c_lessequals(v_k(v_x),v_f(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(forward_demodulation,[status(thm)],[f34,f39]) ).
fof(f41,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(forward_subsumption_resolution,[status(thm)],[f40,f30]) ).
fof(f42,plain,
! [X0] :
( c_lessequals(X0,v_f(v_x),t_b)
| ~ c_lessequals(X0,v_k(v_x),t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[status(thm)],[f41,f23]) ).
fof(f43,plain,
! [X0] :
( c_lessequals(X0,v_f(v_x),t_b)
| ~ c_lessequals(X0,v_k(v_x),t_b) ),
inference(forward_subsumption_resolution,[status(thm)],[f42,f32]) ).
fof(f44,plain,
c_lessequals(v_g(v_x),v_f(v_x),t_b),
inference(resolution,[status(thm)],[f43,f15]) ).
fof(f47,plain,
! [X0,X1] :
( c_lessequals(c_0,c_minus(X1,X0,t_b),t_b)
| ~ c_lessequals(X0,X1,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(paramodulation,[status(thm)],[f34,f21]) ).
fof(f48,plain,
! [X0,X1] :
( c_lessequals(c_0,c_minus(X1,X0,t_b),t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(forward_subsumption_resolution,[status(thm)],[f47,f30]) ).
fof(f51,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(resolution,[status(thm)],[f48,f44]) ).
fof(f53,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f51,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA027-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n002.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Mon Sep 21 13:27:38 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.37 % Drodi V4.1.1
% 0.08/5.39 % Refutation found
% 0.08/5.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.41 % Elapsed time: 0.040680 seconds
% 0.13/5.41 % CPU time: 0.119900 seconds
% 0.13/5.41 % Total memory used: 31.806 MB
% 0.13/5.41 % Net memory used: 31.462 MB
%------------------------------------------------------------------------------