%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : ANA023-10 : TPTP v9.0.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 15 06:11:24 AM UTC 2025
% Result : Unsatisfiable 0.94s 1.11s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 13 RR)
% Number of literals : 26 ( 25 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-4 aty)
% Number of variables : 28 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c1,axiom,
class_Ring__and__Field_Oordered__idom(t_b) = true,
file('theBenchmark.p',tfree_tcs) ).
cnf(c2,axiom,
ifeq2(X,X,Y,Z) = Y,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c3,axiom,
ifeq(X,X,Y,Z) = Y,
file('theBenchmark.p',ifeq_axiom_001) ).
cnf(c4,axiom,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c5,axiom,
ifeq(class_Orderings_Olinorder(X),true,class_Orderings_Oorder(X),true) = true,
file('theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
cnf(c6,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_Orderings_Olinorder(X),true) = true,
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
cnf(c7,plain,
class_Orderings_Olinorder(t_b) = true,
inference(equational,[status(thm)],[c1,c3,c6]) ).
cnf(c8,plain,
class_Orderings_Oorder(t_b) = true,
inference(equational,[status(thm)],[c3,c5,c7]) ).
cnf(c9,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_OrderedGroup_Ocomm__monoid__add(X),true) = true,
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
cnf(c10,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b) = true,
inference(equational,[status(thm)],[c1,c3,c9]) ).
cnf(c11,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_OrderedGroup_Opordered__ab__group__add(X),true) = true,
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
cnf(c12,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b) = true,
inference(equational,[status(thm)],[c1,c3,c11]) ).
cnf(c13,axiom,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(X),true,c_plus(c_0,Y,X),Y) = Y,
file('theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
cnf(c14,plain,
c_plus(c_0,X,t_b) = X,
inference(equational,[status(thm)],[c2,c10,c13]) ).
cnf(c15,axiom,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true,
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c16,axiom,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X),true,ifeq(c_lessequals(Y,c_minus(Z,W,X),X),true,c_lessequals(c_plus(Y,W,X),Z,X),true),true) = true,
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).
cnf(c17,plain,
c_lessequals(v_g(v_x),v_k(v_x),t_b) = true,
inference(equational,[status(thm)],[c3,c12,c14,c15,c16]) ).
cnf(c22,axiom,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X),true,ifeq(c_lessequals(c_plus(Y,Z,X),W,X),true,c_lessequals(Y,c_minus(W,Z,X),X),true),true) = true,
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
cnf(c23,plain,
ifeq(c_lessequals(X,Y,t_b),true,c_lessequals(c_0,c_minus(Y,X,t_b),t_b),true) = true,
inference(equational,[status(thm)],[c3,c12,c14,c22]) ).
cnf(c31,axiom,
ifeq(class_Orderings_Oorder(X),true,ifeq(c_lessequals(Y,Z,X),true,ifeq(c_lessequals(Z,W,X),true,c_lessequals(Y,W,X),true),true),true) = true,
file('theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
cnf(c34,plain,
ifeq(c_lessequals(X,v_k(v_x),t_b),true,c_lessequals(X,v_f(v_x),t_b),true) = true,
inference(equational,[status(thm)],[c3,c4,c8,c31]) ).
cnf(c35,plain,
c_lessequals(v_g(v_x),v_f(v_x),t_b) = true,
inference(equational,[status(thm)],[c3,c17,c34]) ).
cnf(c37,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = true,
inference(equational,[status(thm)],[c3,c23,c35]) ).
cnf(g1,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = true,
inference(equational,[status(thm)],[c37]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA023-10 : TPTP v9.0.0. Released v7.5.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 03:59:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.94/1.11 % SZS status Unsatisfiable
% 0.94/1.11 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------