TSTP Solution File: LAT268-10 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT268-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 : 600s
% DateTime : Sun Jul 17 06:01:52 EDT 2022
% Result : Unsatisfiable 0.19s 0.39s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 43
% Syntax : Number of clauses : 119 ( 62 unt; 0 nHn; 102 RR)
% Number of literals : 204 ( 203 equ; 86 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 10 con; 0-4 aty)
% Number of variables : 53 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq(A,A,B,C) = B ).
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(v_S,v_A,tc_set(t_a)) = true ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_x,v_S,t_a) = true ).
cnf(cls_conjecture_2,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 ).
cnf(cls_Tarski_OA_A_61_61_Apset_Acl_0,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) ).
cnf(cls_Tarski_OCL_Olub__upper_0,axiom,
ifeq(c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a)),true,ifeq(c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_x,V_S,T_a),true,c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)),true),true),true),true) = true ).
cnf(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,axiom,
ifeq(c_in(c_Pair(V_x,V_y,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,c_in(c_Pair(V_y,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) = true ).
cnf(cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0,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 ).
cnf(cls_Tarski_Odual_Acl_A_58_APartialOrder_0,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 ).
cnf(cls_Tarski_Oglb__dual__lub_0,axiom,
c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) ).
cnf(cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0,axiom,
c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit) ).
cnf(cls_Tarski_Or_A_61_61_Aorder_Acl_0,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) ).
cnf(refute_0_0,plain,
ifeq(c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,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) = true,
inference(subst,[],[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:[bind(T_a,$fot(t_a)),bind(V_cl,$fot(v_cl)),bind(V_x,$fot(v_x)),bind(V_y,$fot(c_Tarski_Oglb(v_S,v_cl,t_a)))]]) ).
cnf(refute_0_1,plain,
ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) = true,
inference(subst,[],[cls_Tarski_OCL_Olub__upper_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_cl,$fot(X_16)),bind(V_x,$fot(v_x))]]) ).
cnf(refute_0_2,plain,
( c_in(v_x,v_S,t_a) != true
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) != true
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true),true) ),[0,2,2,2,0],$fot(true)]]) ).
cnf(refute_0_3,plain,
( ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) != true
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) = true ),
inference(resolve,[$cnf( $equal(c_in(v_x,v_S,t_a),true) )],[cls_conjecture_1,refute_0_2]) ).
cnf(refute_0_4,plain,
ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(v_x,v_S,t_a),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true),true) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) = c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)))),bind(C,$fot(true))]]) ).
cnf(refute_0_6,plain,
ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) = ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),
introduced(tautology,[refl,[$fot(ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true))]]) ).
cnf(refute_0_7,plain,
( ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) != ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true)
| ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) != c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) = ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true)) ),[1,2],$fot(c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)))]]) ).
cnf(refute_0_8,plain,
( ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) != c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) = ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) ),
inference(resolve,[$cnf( $equal(ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) = ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) = ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true))]]) ).
cnf(refute_0_11,plain,
( ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) != ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true)
| ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) != ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true)
| ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) = ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true)) ),[1,2],$fot(ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true))]]) ).
cnf(refute_0_12,plain,
( ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) != ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true)
| ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) = ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) = ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),
inference(resolve,[$cnf( $equal(ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true)) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) = ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true))]]) ).
cnf(refute_0_15,plain,
( ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) != ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true)
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) != ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true)
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) = ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true),ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true)) ),[1,2],$fot(ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true))]]) ).
cnf(refute_0_16,plain,
( ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) != ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true)
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) = ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true),ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) = ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),
inference(resolve,[$cnf( $equal(ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true)) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
( ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) != ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true)
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) != true
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true),true) ),[0],$fot(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true))]]) ).
cnf(refute_0_19,plain,
( ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) != true
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true),ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X_16,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(X_16,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X_16,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X_16,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X_16,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true),true) )],[refute_0_4,refute_0_19]) ).
cnf(refute_0_21,plain,
ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) = true,
inference(subst,[],[refute_0_20:[bind(X_16,$fot(c_Tarski_Odual(v_cl,t_a)))]]) ).
cnf(refute_0_22,plain,
( 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
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(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,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),true),true) != true
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,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),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) ),[0,2,2,0],$fot(true)]]) ).
cnf(refute_0_23,plain,
( ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(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,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),true),true) != true
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,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),true),true) = true ),
inference(resolve,[$cnf( $equal(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true) )],[cls_Tarski_Odual_Acl_A_58_APartialOrder_0,refute_0_22]) ).
cnf(refute_0_24,plain,
ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) )],[refute_0_21,refute_0_23]) ).
cnf(refute_0_25,plain,
ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) = c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)))),bind(C,$fot(true))]]) ).
cnf(refute_0_26,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_27,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_28,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( c_Tarski_Oglb(V_S,V_cl,T_a) != c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a)
| c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) = c_Tarski_Oglb(V_S,V_cl,T_a) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(c_Tarski_Oglb(V_S,V_cl,T_a))),bind(Y,$fot(c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a)))]]) ).
cnf(refute_0_30,plain,
c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) = c_Tarski_Oglb(V_S,V_cl,T_a),
inference(resolve,[$cnf( $equal(c_Tarski_Oglb(V_S,V_cl,T_a),c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a)) )],[cls_Tarski_Oglb__dual__lub_0,refute_0_29]) ).
cnf(refute_0_31,plain,
c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a) = c_Tarski_Oglb(v_S,v_cl,t_a),
inference(subst,[],[refute_0_30:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_cl,$fot(v_cl))]]) ).
cnf(refute_0_32,plain,
c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a) = c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),
introduced(tautology,[refl,[$fot(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a))]]) ).
cnf(refute_0_33,plain,
( c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a) != c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a)
| c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a) != c_Tarski_Oglb(v_S,v_cl,t_a)
| c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a) = c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a) ),
introduced(tautology,[equality,[$cnf( $equal(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a)) ),[1,1],$fot(c_Tarski_Oglb(v_S,v_cl,t_a))]]) ).
cnf(refute_0_34,plain,
( c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a) != c_Tarski_Oglb(v_S,v_cl,t_a)
| c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a) = c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a) ),
inference(resolve,[$cnf( $equal(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a) = c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),
inference(resolve,[$cnf( $equal(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),c_Tarski_Oglb(v_S,v_cl,t_a)) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) = c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
introduced(tautology,[refl,[$fot(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)))]]) ).
cnf(refute_0_37,plain,
( c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a) != c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a)
| 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)) != 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))
| 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)) = c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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)) ),
introduced(tautology,[equality,[$cnf( $equal(c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))) ),[1,0],$fot(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a))]]) ).
cnf(refute_0_38,plain,
( c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a) != c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a)
| 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)) = c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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)) ),
inference(resolve,[$cnf( $equal(c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) = c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(resolve,[$cnf( $equal(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a)) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) = c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)))),bind(C,$fot(true))]]) ).
cnf(refute_0_41,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_42,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_28,refute_0_41]) ).
cnf(refute_0_43,plain,
( c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) != c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) != c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) = c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(subst,[],[refute_0_42:[bind(X,$fot(ifeq(true,true,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))),bind(Y,$fot(c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)))),bind(Z,$fot(c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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))))]]) ).
cnf(refute_0_44,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)) != c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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))
| ifeq(true,true,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) = c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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)) ),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) = c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(resolve,[$cnf( $equal(c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))) )],[refute_0_39,refute_0_44]) ).
cnf(refute_0_46,plain,
ifeq(true,true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) = ifeq(true,true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),
introduced(tautology,[refl,[$fot(ifeq(true,true,ifeq(true,true,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),true))]]) ).
cnf(refute_0_47,plain,
( ifeq(true,true,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) != c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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))
| ifeq(true,true,ifeq(true,true,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),true) != ifeq(true,true,ifeq(true,true,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),true)
| ifeq(true,true,ifeq(true,true,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),true) = ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),ifeq(true,true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true)) ),[1,2],$fot(c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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)))]]) ).
cnf(refute_0_48,plain,
( ifeq(true,true,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) != c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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))
| ifeq(true,true,ifeq(true,true,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),true) = ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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(resolve,[$cnf( $equal(ifeq(true,true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),ifeq(true,true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
ifeq(true,true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) = ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) = ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),
introduced(tautology,[refl,[$fot(ifeq(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,ifeq(true,true,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),true))]]) ).
cnf(refute_0_51,plain,
( 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
| ifeq(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,ifeq(true,true,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),true) != ifeq(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,ifeq(true,true,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),true)
| ifeq(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,ifeq(true,true,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),true) = ifeq(true,true,ifeq(true,true,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),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true)) ),[1,0],$fot(true)]]) ).
cnf(refute_0_52,plain,
( 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
| ifeq(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,ifeq(true,true,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),true) = ifeq(true,true,ifeq(true,true,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),true) ),
inference(resolve,[$cnf( $equal(ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) = ifeq(true,true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),
inference(resolve,[$cnf( $equal(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true) )],[cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0,refute_0_52]) ).
cnf(refute_0_54,plain,
( ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) != ifeq(true,true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true)
| ifeq(true,true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) != ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true)
| ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) = ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) ),
inference(subst,[],[refute_0_42:[bind(X,$fot(ifeq(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,ifeq(true,true,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),true))),bind(Y,$fot(ifeq(true,true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true))),bind(Z,$fot(ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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)))]]) ).
cnf(refute_0_55,plain,
( ifeq(true,true,ifeq(true,true,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),true) != ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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)
| ifeq(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,ifeq(true,true,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),true) = ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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(resolve,[$cnf( $equal(ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),ifeq(true,true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) = ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true)) )],[refute_0_49,refute_0_55]) ).
cnf(refute_0_57,plain,
( ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) != ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true)
| ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) != c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) = c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(subst,[],[refute_0_42:[bind(X,$fot(ifeq(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,ifeq(true,true,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),true))),bind(Y,$fot(ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true))),bind(Z,$fot(c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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))))]]) ).
cnf(refute_0_58,plain,
( ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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) != c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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))
| ifeq(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,ifeq(true,true,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),true) = c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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)) ),
inference(resolve,[$cnf( $equal(ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) = c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))) )],[refute_0_25,refute_0_58]) ).
cnf(refute_0_60,plain,
ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) = ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(true,true,ifeq(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,ifeq(true,true,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),true),true))]]) ).
cnf(refute_0_61,plain,
( ifeq(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,ifeq(true,true,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),true) != c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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))
| ifeq(true,true,ifeq(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,ifeq(true,true,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),true),true) != ifeq(true,true,ifeq(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,ifeq(true,true,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),true),true)
| ifeq(true,true,ifeq(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,ifeq(true,true,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),true),true) = ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true)) ),[1,2],$fot(c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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)))]]) ).
cnf(refute_0_62,plain,
( ifeq(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,ifeq(true,true,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),true) != c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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))
| ifeq(true,true,ifeq(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,ifeq(true,true,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),true),true) = ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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(resolve,[$cnf( $equal(ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) = ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),
inference(resolve,[$cnf( $equal(ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( v_A != c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)
| c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A ),
inference(subst,[],[refute_0_28:[bind(X,$fot(v_A)),bind(Y,$fot(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)))]]) ).
cnf(refute_0_65,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
inference(resolve,[$cnf( $equal(v_A,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)) )],[cls_Tarski_OA_A_61_61_Apset_Acl_0,refute_0_64]) ).
cnf(refute_0_66,plain,
c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
inference(subst,[],[cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0:[bind(T_a,$fot(t_a)),bind(V_cl,$fot(v_cl))]]) ).
cnf(refute_0_67,plain,
( c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit) != c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)
| c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) != v_A
| c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit) = v_A ),
inference(subst,[],[refute_0_42:[bind(X,$fot(c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit))),bind(Y,$fot(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit))),bind(Z,$fot(v_A))]]) ).
cnf(refute_0_68,plain,
( c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) != v_A
| c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit) = v_A ),
inference(resolve,[$cnf( $equal(c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit) = v_A,
inference(resolve,[$cnf( $equal(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),v_A) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)) = c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),
introduced(tautology,[refl,[$fot(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)))]]) ).
cnf(refute_0_71,plain,
( c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit) != v_A
| c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)) != c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)) = c_lessequals(v_S,v_A,tc_set(t_a)) ),
introduced(tautology,[equality,[$cnf( $equal(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a))) ),[1,1],$fot(v_A)]]) ).
cnf(refute_0_72,plain,
( c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit) != v_A
| c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)) = c_lessequals(v_S,v_A,tc_set(t_a)) ),
inference(resolve,[$cnf( $equal(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)) = c_lessequals(v_S,v_A,tc_set(t_a)),
inference(resolve,[$cnf( $equal(c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),v_A) )],[refute_0_69,refute_0_72]) ).
cnf(refute_0_74,plain,
( c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)) != c_lessequals(v_S,v_A,tc_set(t_a))
| c_lessequals(v_S,v_A,tc_set(t_a)) != true
| c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)) = true ),
inference(subst,[],[refute_0_42:[bind(X,$fot(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)))),bind(Y,$fot(c_lessequals(v_S,v_A,tc_set(t_a)))),bind(Z,$fot(true))]]) ).
cnf(refute_0_75,plain,
( c_lessequals(v_S,v_A,tc_set(t_a)) != true
| c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)) = true ),
inference(resolve,[$cnf( $equal(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),c_lessequals(v_S,v_A,tc_set(t_a))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)) = true,
inference(resolve,[$cnf( $equal(c_lessequals(v_S,v_A,tc_set(t_a)),true) )],[cls_conjecture_0,refute_0_75]) ).
cnf(refute_0_77,plain,
ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) = ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,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),true),true))]]) ).
cnf(refute_0_78,plain,
( c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)) != true
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,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),true),true) != ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,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),true),true)
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,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),true),true) = ifeq(true,true,ifeq(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,ifeq(true,true,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),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true)) ),[1,0],$fot(true)]]) ).
cnf(refute_0_79,plain,
( c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)) != true
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,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),true),true) = ifeq(true,true,ifeq(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,ifeq(true,true,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),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) = ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),
inference(resolve,[$cnf( $equal(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
( ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,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),true),true) != ifeq(true,true,ifeq(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,ifeq(true,true,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),true),true)
| ifeq(true,true,ifeq(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,ifeq(true,true,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),true),true) != ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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)
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,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),true),true) = ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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(subst,[],[refute_0_42:[bind(X,$fot(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,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),true),true))),bind(Y,$fot(ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true))),bind(Z,$fot(ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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)))]]) ).
cnf(refute_0_82,plain,
( ifeq(true,true,ifeq(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,ifeq(true,true,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),true),true) != ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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)
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,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),true),true) = ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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(resolve,[$cnf( $equal(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) = ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(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,ifeq(true,true,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),true),true),ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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)) )],[refute_0_63,refute_0_82]) ).
cnf(refute_0_84,plain,
( ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,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),true),true) != ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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)
| ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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) != c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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))
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,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),true),true) = c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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)) ),
inference(subst,[],[refute_0_42:[bind(X,$fot(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,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),true),true))),bind(Y,$fot(ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true))),bind(Z,$fot(c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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))))]]) ).
cnf(refute_0_85,plain,
( ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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) != c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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))
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,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),true),true) = c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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)) ),
inference(resolve,[$cnf( $equal(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) = c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))) )],[refute_0_25,refute_0_85]) ).
cnf(refute_0_87,plain,
( ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) != c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true) != true
| c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) ),[0],$fot(c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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)))]]) ).
cnf(refute_0_88,plain,
( ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,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),true),true) != true
| c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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(resolve,[$cnf( $equal(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) = true,
inference(resolve,[$cnf( $equal(ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true) )],[refute_0_24,refute_0_88]) ).
cnf(refute_0_90,plain,
( c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) != true
| ifeq(c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) != true
| ifeq(true,true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_91,plain,
( ifeq(c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,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,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,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) != true
| ifeq(true,true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,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) = true ),
inference(resolve,[$cnf( $equal(c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
ifeq(true,true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) )],[refute_0_0,refute_0_91]) ).
cnf(refute_0_93,plain,
( v_r != c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)
| c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r ),
inference(subst,[],[refute_0_28:[bind(X,$fot(v_r)),bind(Y,$fot(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)))]]) ).
cnf(refute_0_94,plain,
c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r,
inference(resolve,[$cnf( $equal(v_r,c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)) )],[cls_Tarski_Or_A_61_61_Aorder_Acl_0,refute_0_93]) ).
cnf(refute_0_95,plain,
c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) = c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
introduced(tautology,[refl,[$fot(c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,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)))]]) ).
cnf(refute_0_96,plain,
( c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) != v_r
| c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,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)) != c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,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))
| c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,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)) = 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)) ),
introduced(tautology,[equality,[$cnf( $equal(c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))) ),[1,1],$fot(v_r)]]) ).
cnf(refute_0_97,plain,
( c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) != v_r
| c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,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)) = 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)) ),
inference(resolve,[$cnf( $equal(c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) = c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[$cnf( $equal(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),v_r) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
ifeq(true,true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) = c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)))),bind(C,$fot(true))]]) ).
cnf(refute_0_100,plain,
( c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,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)) != 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))
| ifeq(true,true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,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) != c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,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))
| ifeq(true,true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,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) = 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)) ),
inference(subst,[],[refute_0_42:[bind(X,$fot(ifeq(true,true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true))),bind(Y,$fot(c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,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)))),bind(Z,$fot(c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))))]]) ).
cnf(refute_0_101,plain,
( c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) != c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ifeq(true,true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) = c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
ifeq(true,true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) = c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[$cnf( $equal(c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
( ifeq(true,true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) != c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ifeq(true,true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) != true
| c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true) ),[0],$fot(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)))]]) ).
cnf(refute_0_104,plain,
( ifeq(true,true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,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) != true
| 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(resolve,[$cnf( $equal(ifeq(true,true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,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),true) )],[refute_0_92,refute_0_104]) ).
cnf(refute_0_106,plain,
$false,
inference(resolve,[$cnf( $equal(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) )],[refute_0_105,cls_conjecture_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT268-10 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.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 : 600
% 0.12/0.34 % DateTime : Wed Jun 29 19:49:18 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.39
% 0.19/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.46
%------------------------------------------------------------------------------