%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT268-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:44:40 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.43s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of clauses : 67 ( 67 unt; 0 nHn; 35 RR)
% Number of literals : 67 ( 66 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 10 con; 0-4 aty)
% Number of variables : 67 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(c2,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c3,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)) = 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(congruence,[status(thm)],[c2]) ).
cnf(c4,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c5,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(substitution,[status(thm)],[c4]) ).
cnf(c6,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)) = 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),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,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(substitution,[status(thm)],[c4]) ).
cnf(c8,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)) = 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(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
ifeq(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),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(substitution,[status(thm)],[c4]) ).
cnf(c10,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) = ifeq(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),true),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,axiom,
c_lessequals(v_S,v_A,tc_set(t_a)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c12,plain,
true = c_lessequals(v_S,v_A,tc_set(t_a)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
ifeq(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),true) = ifeq(c_lessequals(v_S,v_A,tc_set(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),true),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,axiom,
c_in(v_x,v_S,t_a) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c15,plain,
true = c_in(v_x,v_S,t_a),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,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) = ifeq(c_in(v_x,v_S,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)),true),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
ifeq(c_lessequals(v_S,v_A,tc_set(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),true) = ifeq(c_lessequals(v_S,v_A,tc_set(t_a)),true,ifeq(c_in(v_x,v_S,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)),true),true),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,axiom,
c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Oglb__dual__lub_0) ).
cnf(c19,plain,
c_Tarski_Oglb(X,v_cl,t_a) = c_Tarski_Olub(X,c_Tarski_Odual(v_cl,t_a),t_a),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
c_Pair(X2,c_Tarski_Oglb(X,v_cl,t_a),t_a,t_a) = c_Pair(X2,c_Tarski_Olub(X,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
c_in(c_Pair(X,c_Tarski_Oglb(X2,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)) = c_in(c_Pair(X,c_Tarski_Olub(X2,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(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Oglb(X2,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(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
ifeq(c_lessequals(X2,v_A,tc_set(t_a)),true,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Oglb(X2,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),true) = ifeq(c_lessequals(X2,v_A,tc_set(t_a)),true,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
ifeq(true,true,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),
inference(substitution,[status(thm)],[c4]) ).
cnf(c25,plain,
ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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) = ifeq(true,true,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
ifeq(c_lessequals(X2,v_A,tc_set(t_a)),true,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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_lessequals(X2,v_A,tc_set(t_a)),true,ifeq(true,true,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(congruence,[status(thm)],[c25]) ).
cnf(c27,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c28,plain,
true = c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
ifeq(true,true,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
ifeq(c_lessequals(X2,v_A,tc_set(t_a)),true,ifeq(true,true,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(X2,v_A,tc_set(t_a)),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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
ifeq(true,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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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_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_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(substitution,[status(thm)],[c4]) ).
cnf(c32,plain,
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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(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_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
ifeq(c_lessequals(X2,v_A,tc_set(t_a)),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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(X2,v_A,tc_set(t_a)),true,ifeq(true,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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(congruence,[status(thm)],[c32]) ).
cnf(c34,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c35,plain,
c_lessequals(X,v_A,tc_set(t_a)) = c_lessequals(X,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
ifeq(c_lessequals(X2,v_A,tc_set(t_a)),true,ifeq(true,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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(X2,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(true,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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(congruence,[status(thm)],[c35]) ).
cnf(c37,axiom,
c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl2,T_a2),T_a2,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl2,T_a2,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) ).
cnf(c38,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(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
c_lessequals(X,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)) = c_lessequals(X,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
ifeq(c_lessequals(X2,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(true,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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(X2,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(true,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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(congruence,[status(thm)],[c40]) ).
cnf(c42,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c43,plain,
true = c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
ifeq(true,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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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_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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
ifeq(c_lessequals(X2,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(true,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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(X2,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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(congruence,[status(thm)],[c44]) ).
cnf(c46,axiom,
ifeq(c_lessequals(V_S2,c_Tarski_Opotype_Opset(V_cl2,T_a2,tc_Product__Type_Ounit),tc_set(T_a2)),true,ifeq(c_in(V_cl2,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a2,tc_Product__Type_Ounit)),true,ifeq(c_in(V_cl2,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a2,tc_Product__Type_Ounit)),true,ifeq(c_in(V_x,V_S2,T_a2),true,c_in(c_Pair(V_x,c_Tarski_Olub(V_S2,V_cl2,T_a2),T_a2,T_a2),c_Tarski_Opotype_Oorder(V_cl2,T_a2,tc_Product__Type_Ounit),tc_prod(T_a2,T_a2)),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OCL_Olub__upper_0) ).
cnf(c47,plain,
ifeq(c_lessequals(X2,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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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) = true,
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
ifeq(c_lessequals(X2,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(true,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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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) = true,
inference(transitivity,[status(thm)],[c45,c47]) ).
cnf(c49,plain,
ifeq(c_lessequals(X2,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(true,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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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) = true,
inference(transitivity,[status(thm)],[c41,c48]) ).
cnf(c50,plain,
ifeq(c_lessequals(X2,v_A,tc_set(t_a)),true,ifeq(true,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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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) = true,
inference(transitivity,[status(thm)],[c36,c49]) ).
cnf(c51,plain,
ifeq(c_lessequals(X2,v_A,tc_set(t_a)),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,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(transitivity,[status(thm)],[c33,c50]) ).
cnf(c52,plain,
ifeq(c_lessequals(X2,v_A,tc_set(t_a)),true,ifeq(true,true,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(transitivity,[status(thm)],[c30,c51]) ).
cnf(c53,plain,
ifeq(c_lessequals(X2,v_A,tc_set(t_a)),true,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Olub(X2,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(transitivity,[status(thm)],[c26,c52]) ).
cnf(c54,plain,
ifeq(c_lessequals(X2,v_A,tc_set(t_a)),true,ifeq(c_in(X,X2,t_a),true,c_in(c_Pair(X,c_Tarski_Oglb(X2,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),true) = true,
inference(transitivity,[status(thm)],[c23,c53]) ).
cnf(c55,plain,
ifeq(c_lessequals(v_S,v_A,tc_set(t_a)),true,ifeq(c_in(v_x,v_S,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)),true),true) = true,
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
ifeq(c_lessequals(v_S,v_A,tc_set(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),true) = true,
inference(transitivity,[status(thm)],[c17,c55]) ).
cnf(c57,plain,
ifeq(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),true) = true,
inference(transitivity,[status(thm)],[c13,c56]) ).
cnf(c58,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) = true,
inference(transitivity,[status(thm)],[c10,c57]) ).
cnf(c59,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(transitivity,[status(thm)],[c8,c58]) ).
cnf(c60,plain,
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(symmetry,[status(thm)],[c59]) ).
cnf(c61,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) = 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),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,axiom,
ifeq(c_in(c_Pair(V_x2,V_y,T_a2,T_a2),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl2,T_a2),T_a2,tc_Product__Type_Ounit),tc_prod(T_a2,T_a2)),true,c_in(c_Pair(V_y,V_x2,T_a2,T_a2),c_Tarski_Opotype_Oorder(V_cl2,T_a2,tc_Product__Type_Ounit),tc_prod(T_a2,T_a2)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0) ).
cnf(c63,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(substitution,[status(thm)],[c62]) ).
cnf(c64,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(transitivity,[status(thm)],[c61,c63]) ).
cnf(c65,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)) = true,
inference(transitivity,[status(thm)],[c6,c64]) ).
cnf(c66,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(transitivity,[status(thm)],[c3,c65]) ).
cnf(c67,plain,
$false,
inference(resolution,[status(thm)],[c1,c66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT268-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 14:12:45 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.43 Command-line arguments: --no-flatten-goal
% 0.13/0.43
% 0.13/0.43 % SZS status Unsatisfiable
% 0.13/0.43
% 0.13/0.43 % SZS output start CNFRefutation
% See solution above
% 0.48/0.49
% 0.48/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------