%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT268-10 : TPTP v9.0.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n014.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 07:05:57 AM UTC 2025
% Result : Unsatisfiable 0.63s 0.79s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 12 RR)
% Number of literals : 18 ( 17 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 10 con; 0-4 aty)
% Number of variables : 18 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) != true,
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c1,axiom,
c_in(v_x,v_S,t_a) = true,
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c2,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
cnf(c3,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
cnf(c4,axiom,
ifeq(X,X,Y,Z) = Y,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c5,axiom,
c_lessequals(v_S,v_A,tc_set(t_a)) = true,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c6,plain,
c_lessequals(v_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)) = true,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,axiom,
c_Tarski_Oglb(X,Y,Z) = c_Tarski_Olub(X,c_Tarski_Odual(Y,Z),Z),
file('theBenchmark.p',cls_Tarski_Oglb__dual__lub_0) ).
cnf(c8,axiom,
c_Tarski_Opotype_Opset(c_Tarski_Odual(X,Y),Y,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(X,Y,tc_Product__Type_Ounit),
file('theBenchmark.p',cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) ).
cnf(c9,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
file('theBenchmark.p',cls_Tarski_Odual_Acl_A_58_APartialOrder_0) ).
cnf(c10,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
file('theBenchmark.p',cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) ).
cnf(c11,axiom,
ifeq(c_in(c_Pair(X,Y,Z,Z),c_Tarski_Opotype_Oorder(c_Tarski_Odual(W,Z),Z,tc_Product__Type_Ounit),tc_prod(Z,Z)),true,c_in(c_Pair(Y,X,Z,Z),c_Tarski_Opotype_Oorder(W,Z,tc_Product__Type_Ounit),tc_prod(Z,Z)),true) = true,
file('theBenchmark.p',cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0) ).
cnf(c12,axiom,
ifeq(c_lessequals(X,c_Tarski_Opotype_Opset(Y,Z,tc_Product__Type_Ounit),tc_set(Z)),true,ifeq(c_in(Y,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(Z,tc_Product__Type_Ounit)),true,ifeq(c_in(Y,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(Z,tc_Product__Type_Ounit)),true,ifeq(c_in(W,X,Z),true,c_in(c_Pair(W,c_Tarski_Olub(X,Y,Z),Z,Z),c_Tarski_Opotype_Oorder(Y,Z,tc_Product__Type_Ounit),tc_prod(Z,Z)),true),true),true),true) = true,
file('theBenchmark.p',cls_Tarski_OCL_Olub__upper_0) ).
cnf(c13,plain,
ifeq(c_lessequals(X,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(Y,X,t_a),true,c_in(c_Pair(Y,c_Tarski_Olub(X,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) = true,
inference(equational,[status(thm)],[c4,c8,c9,c10,c12]) ).
cnf(c14,plain,
c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) = true,
inference(equational,[status(thm)],[c1,c4,c6,c13]) ).
cnf(c15,plain,
c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) = true,
inference(equational,[status(thm)],[c4,c11,c14]) ).
cnf(g1,plain,
c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) = true,
inference(equational,[status(thm)],[c3,c7,c15]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT268-10 : TPTP v9.0.0. Released v7.5.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n014.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 12:04:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.63/0.79 % SZS status Unsatisfiable
% 0.63/0.79 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------