%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA023-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 12:02:15 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 64 ( 64 unt; 4 def)
% Number of atoms : 64 ( 63 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 8 con; 0-4 aty)
% Number of variables : 60 ( 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq2(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [T_a,V_y] : ifeq2(class_OrderedGroup_Ocomm__monoid__add(T_a),true,c_plus(c_0,V_y,T_a),V_y) = V_y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [T_a,V_a,V_c,V_b] : ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true,c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [T_a,V_a,V_b,V_c] : ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a),true,ifeq(c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a),true,c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [T_a,V_x,V_y,V_z] : ifeq(class_Orderings_Oorder(T_a),true,ifeq(c_lessequals(V_x,V_y,T_a),true,ifeq(c_lessequals(V_y,V_z,T_a),true,c_lessequals(V_x,V_z,T_a),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [T] : ifeq(class_Orderings_Olinorder(T),true,class_Orderings_Oorder(T),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [T] : ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Ocomm__monoid__add(T),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [T] : ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Orderings_Olinorder(T),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [T] : ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Opordered__ab__group__add(T),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0,X1,X2] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [X0,X1] : ifeq2(class_OrderedGroup_Ocomm__monoid__add(X0),true,c_plus(c_0,X1,X0),X1) = X1,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0,X1,X2,X3] : ifeq(class_OrderedGroup_Opordered__ab__group__add(X0),true,ifeq(c_lessequals(X1,c_minus(X2,X3,X0),X0),true,c_lessequals(c_plus(X1,X3,X0),X2,X0),true),true) = true,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [X0,X1,X2,X3] : ifeq(class_OrderedGroup_Opordered__ab__group__add(X0),true,ifeq(c_lessequals(c_plus(X1,X2,X0),X3,X0),true,c_lessequals(X1,c_minus(X3,X2,X0),X0),true),true) = true,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
! [X0,X1,X2,X3] : ifeq(class_Orderings_Oorder(X0),true,ifeq(c_lessequals(X1,X2,X0),true,ifeq(c_lessequals(X2,X3,X0),true,c_lessequals(X1,X3,X0),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f22,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
! [X0] : ifeq(class_Orderings_Olinorder(X0),true,class_Orderings_Oorder(X0),true) = true,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f25,plain,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Ocomm__monoid__add(X0),true) = true,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f26,plain,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Orderings_Olinorder(X0),true) = true,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f27,plain,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Opordered__ab__group__add(X0),true) = true,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f28,plain,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f29,definition,
sF2_fnc = v_f(v_x),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f30,definition,
sF3_fnc = v_g(v_x),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f31,definition,
sF1_fnc = c_minus(sF2_fnc,sF3_fnc,t_b),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f32,definition,
sF0_fnc = c_lessequals(c_0,sF1_fnc,t_b),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f33,plain,
sF0_fnc != true,
inference(definition_folding,[],[f23,f32,f31,f30,f29]) ).
fof(f34,plain,
c_lessequals(c_0,c_minus(v_k(v_x),sF3_fnc,t_b),t_b) = true,
inference(forward_demodulation,[status(thm)],[f30,f21]) ).
fof(f35,plain,
c_lessequals(v_k(v_x),sF2_fnc,t_b) = true,
inference(forward_demodulation,[status(thm)],[f29,f22]) ).
fof(f36,plain,
ifeq(true,true,class_OrderedGroup_Ocomm__monoid__add(t_b),true) = true,
inference(paramodulation,[status(thm)],[f28,f25]) ).
fof(f37,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b) = true,
inference(forward_demodulation,[status(thm)],[f16,f36]) ).
fof(f40,plain,
ifeq(true,true,class_Orderings_Olinorder(t_b),true) = true,
inference(paramodulation,[status(thm)],[f28,f26]) ).
fof(f41,plain,
class_Orderings_Olinorder(t_b) = true,
inference(forward_demodulation,[status(thm)],[f16,f40]) ).
fof(f43,plain,
ifeq(true,true,class_Orderings_Oorder(t_b),true) = true,
inference(paramodulation,[status(thm)],[f41,f24]) ).
fof(f45,plain,
class_Orderings_Oorder(t_b) = true,
inference(forward_demodulation,[status(thm)],[f16,f43]) ).
fof(f48,plain,
ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) = true,
inference(paramodulation,[status(thm)],[f28,f27]) ).
fof(f49,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b) = true,
inference(forward_demodulation,[status(thm)],[f16,f48]) ).
fof(f52,plain,
! [X0] : ifeq2(true,true,c_plus(c_0,X0,t_b),X0) = X0,
inference(paramodulation,[status(thm)],[f37,f17]) ).
fof(f53,plain,
! [X0] : c_plus(c_0,X0,t_b) = X0,
inference(forward_demodulation,[status(thm)],[f15,f52]) ).
fof(f57,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,sF3_fnc,t_b),v_k(v_x),t_b),true),true) = true,
inference(paramodulation,[status(thm)],[f34,f18]) ).
fof(f61,plain,
ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,sF3_fnc,t_b),v_k(v_x),t_b),true),true) = true,
inference(forward_demodulation,[status(thm)],[f49,f57]) ).
fof(f62,plain,
ifeq(true,true,c_lessequals(c_plus(c_0,sF3_fnc,t_b),v_k(v_x),t_b),true) = true,
inference(forward_demodulation,[status(thm)],[f16,f61]) ).
fof(f63,plain,
c_lessequals(c_plus(c_0,sF3_fnc,t_b),v_k(v_x),t_b) = true,
inference(forward_demodulation,[status(thm)],[f16,f62]) ).
fof(f64,plain,
c_lessequals(sF3_fnc,v_k(v_x),t_b) = true,
inference(forward_demodulation,[status(thm)],[f53,f63]) ).
fof(f90,plain,
! [X0,X1] : ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X0,X1,t_b),true,c_lessequals(c_0,c_minus(X1,X0,t_b),t_b),true),true) = true,
inference(paramodulation,[status(thm)],[f53,f19]) ).
fof(f94,plain,
! [X0,X1] : ifeq(true,true,ifeq(c_lessequals(X0,X1,t_b),true,c_lessequals(c_0,c_minus(X1,X0,t_b),t_b),true),true) = true,
inference(forward_demodulation,[status(thm)],[f49,f90]) ).
fof(f95,plain,
! [X0,X1] : ifeq(c_lessequals(X0,X1,t_b),true,c_lessequals(c_0,c_minus(X1,X0,t_b),t_b),true) = true,
inference(forward_demodulation,[status(thm)],[f16,f94]) ).
fof(f107,plain,
ifeq(c_lessequals(sF3_fnc,sF2_fnc,t_b),true,c_lessequals(c_0,sF1_fnc,t_b),true) = true,
inference(paramodulation,[status(thm)],[f31,f95]) ).
fof(f112,plain,
ifeq(c_lessequals(sF3_fnc,sF2_fnc,t_b),true,sF0_fnc,true) = true,
inference(forward_demodulation,[status(thm)],[f32,f107]) ).
fof(f219,plain,
! [X0] : ifeq(class_Orderings_Oorder(t_b),true,ifeq(true,true,ifeq(c_lessequals(v_k(v_x),X0,t_b),true,c_lessequals(sF3_fnc,X0,t_b),true),true),true) = true,
inference(paramodulation,[status(thm)],[f64,f20]) ).
fof(f244,plain,
! [X0] : ifeq(true,true,ifeq(true,true,ifeq(c_lessequals(v_k(v_x),X0,t_b),true,c_lessequals(sF3_fnc,X0,t_b),true),true),true) = true,
inference(forward_demodulation,[status(thm)],[f45,f219]) ).
fof(f245,plain,
! [X0] : ifeq(true,true,ifeq(c_lessequals(v_k(v_x),X0,t_b),true,c_lessequals(sF3_fnc,X0,t_b),true),true) = true,
inference(forward_demodulation,[status(thm)],[f16,f244]) ).
fof(f246,plain,
! [X0] : ifeq(c_lessequals(v_k(v_x),X0,t_b),true,c_lessequals(sF3_fnc,X0,t_b),true) = true,
inference(forward_demodulation,[status(thm)],[f16,f245]) ).
fof(f321,plain,
ifeq(true,true,c_lessequals(sF3_fnc,sF2_fnc,t_b),true) = true,
inference(paramodulation,[status(thm)],[f35,f246]) ).
fof(f324,plain,
c_lessequals(sF3_fnc,sF2_fnc,t_b) = true,
inference(forward_demodulation,[status(thm)],[f16,f321]) ).
fof(f328,plain,
ifeq(true,true,sF0_fnc,true) = true,
inference(backward_demodulation,[status(thm)],[f324,f112]) ).
fof(f336,plain,
sF0_fnc = true,
inference(forward_demodulation,[status(thm)],[f16,f328]) ).
fof(f337,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f336,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA023-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 13:19:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.035735 seconds
% 0.13/0.40 % CPU time: 0.052308 seconds
% 0.13/0.40 % Total memory used: 2.892 MB
% 0.13/0.40 % Net memory used: 2.868 MB
%------------------------------------------------------------------------------