%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU382+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:45 AM UTC 2025
% Result : Theorem 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU382+1 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:57:35 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 tff(inclusion_order_type, type, (
% 0.21/0.49 inclusion_order: $i > $i)).
% 0.21/0.49 tff(powerset_type, type, (
% 0.21/0.49 powerset: $i > $i)).
% 0.21/0.49 tff(tptp_fun_A_20_type, type, (
% 0.21/0.49 tptp_fun_A_20: $i)).
% 0.21/0.49 tff(the_InternalRel_type, type, (
% 0.21/0.49 the_InternalRel: $i > $i)).
% 0.21/0.49 tff(boole_POSet_type, type, (
% 0.21/0.49 boole_POSet: $i > $i)).
% 0.21/0.49 tff(the_carrier_type, type, (
% 0.21/0.49 the_carrier: $i > $i)).
% 0.21/0.49 tff(rel_str_of_type, type, (
% 0.21/0.49 rel_str_of: ( $i * $i ) > $i)).
% 0.21/0.49 tff(incl_POSet_type, type, (
% 0.21/0.49 incl_POSet: $i > $i)).
% 0.21/0.49 tff(rel_str_type, type, (
% 0.21/0.49 rel_str: $i > $o)).
% 0.21/0.49 tff(strict_rel_str_type, type, (
% 0.21/0.49 strict_rel_str: $i > $o)).
% 0.21/0.49 tff(complemented_relstr_type, type, (
% 0.21/0.49 complemented_relstr: $i > $o)).
% 0.21/0.49 tff(distributive_relstr_type, type, (
% 0.21/0.49 distributive_relstr: $i > $o)).
% 0.21/0.49 tff(join_complete_relstr_type, type, (
% 0.21/0.49 join_complete_relstr: $i > $o)).
% 0.21/0.49 tff(up_complete_relstr_type, type, (
% 0.21/0.49 up_complete_relstr: $i > $o)).
% 0.21/0.49 tff(bounded_relstr_type, type, (
% 0.21/0.49 bounded_relstr: $i > $o)).
% 0.21/0.49 tff(upper_bounded_relstr_type, type, (
% 0.21/0.49 upper_bounded_relstr: $i > $o)).
% 0.21/0.49 tff(lower_bounded_relstr_type, type, (
% 0.21/0.49 lower_bounded_relstr: $i > $o)).
% 0.21/0.49 tff(complete_relstr_type, type, (
% 0.21/0.49 complete_relstr: $i > $o)).
% 0.21/0.49 tff(with_infima_relstr_type, type, (
% 0.21/0.49 with_infima_relstr: $i > $o)).
% 0.21/0.49 tff(with_suprema_relstr_type, type, (
% 0.21/0.49 with_suprema_relstr: $i > $o)).
% 0.21/0.49 tff(antisymmetric_relstr_type, type, (
% 0.21/0.49 antisymmetric_relstr: $i > $o)).
% 0.21/0.49 tff(transitive_relstr_type, type, (
% 0.21/0.49 transitive_relstr: $i > $o)).
% 0.21/0.49 tff(reflexive_relstr_type, type, (
% 0.21/0.49 reflexive_relstr: $i > $o)).
% 0.21/0.49 tff(empty_carrier_type, type, (
% 0.21/0.49 empty_carrier: $i > $o)).
% 0.21/0.49 tff(relation_of2_type, type, (
% 0.21/0.49 relation_of2: ( $i * $i * $i ) > $o)).
% 0.21/0.49 tff(relation_of2_as_subset_type, type, (
% 0.21/0.49 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 0.21/0.49 tff(1,plain,
% 0.21/0.49 ((~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))) <=> (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(2,axiom,(~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t4_waybel_7')).
% 0.21/0.49 tff(3,plain,
% 0.21/0.49 (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.21/0.49 tff(4,plain,
% 0.21/0.49 (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.21/0.49 tff(5,plain,
% 0.21/0.49 (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.49 tff(6,plain,
% 0.21/0.49 (~![A: $i] : (the_carrier(boole_POSet(A)) = powerset(A))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.49 tff(7,plain,(
% 0.21/0.49 ~(the_carrier(boole_POSet(A!20)) = powerset(A!20))),
% 0.21/0.49 inference(skolemize,[status(sab)],[6])).
% 0.21/0.49 tff(8,plain,
% 0.21/0.49 (((~(the_carrier(boole_POSet(A!20)) = powerset(A!20))) | (~(the_InternalRel(boole_POSet(A!20)) = inclusion_order(powerset(A!20))))) | (the_carrier(boole_POSet(A!20)) = powerset(A!20))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(9,plain,
% 0.21/0.49 ((~(the_carrier(boole_POSet(A!20)) = powerset(A!20))) | (~(the_InternalRel(boole_POSet(A!20)) = inclusion_order(powerset(A!20))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.49 tff(10,plain,
% 0.21/0.49 (^[A: $i] : refl((incl_POSet(A) = rel_str_of(A, inclusion_order(A))) <=> (incl_POSet(A) = rel_str_of(A, inclusion_order(A))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(11,plain,
% 0.21/0.49 (![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A))) <=> ![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.49 tff(12,plain,
% 0.21/0.49 (![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A))) <=> ![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(13,axiom,(![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_yellow_1')).
% 0.21/0.49 tff(14,plain,
% 0.21/0.49 (![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.49 tff(15,plain,(
% 0.21/0.49 ![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[14])).
% 0.21/0.49 tff(16,plain,
% 0.21/0.49 (![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.21/0.49 tff(17,plain,
% 0.21/0.49 ((~![A: $i] : (incl_POSet(A) = rel_str_of(A, inclusion_order(A)))) | (incl_POSet(powerset(A!20)) = rel_str_of(powerset(A!20), inclusion_order(powerset(A!20))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(18,plain,
% 0.21/0.49 (incl_POSet(powerset(A!20)) = rel_str_of(powerset(A!20), inclusion_order(powerset(A!20)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.21/0.49 tff(19,plain,
% 0.21/0.49 (^[A: $i] : refl((boole_POSet(A) = incl_POSet(powerset(A))) <=> (boole_POSet(A) = incl_POSet(powerset(A))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(20,plain,
% 0.21/0.49 (![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A))) <=> ![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.49 tff(21,plain,
% 0.21/0.49 (![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A))) <=> ![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(22,axiom,(![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t4_yellow_1')).
% 0.21/0.49 tff(23,plain,
% 0.21/0.49 (![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.49 tff(24,plain,(
% 0.21/0.49 ![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[23])).
% 0.21/0.49 tff(25,plain,
% 0.21/0.49 (![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.21/0.49 tff(26,plain,
% 0.21/0.49 ((~![A: $i] : (boole_POSet(A) = incl_POSet(powerset(A)))) | (boole_POSet(A!20) = incl_POSet(powerset(A!20)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(27,plain,
% 0.21/0.49 (boole_POSet(A!20) = incl_POSet(powerset(A!20))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.21/0.49 tff(28,plain,
% 0.21/0.49 (^[A: $i] : refl((~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A))))) <=> (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(29,plain,
% 0.21/0.49 (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A))))) <=> ![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.49 tff(30,plain,
% 0.21/0.49 (^[A: $i] : rewrite((strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A))) <=> (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(31,plain,
% 0.21/0.49 (![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A))) <=> ![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.49 tff(32,plain,
% 0.21/0.49 (![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A))) <=> ![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(33,axiom,(![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_yellow_1')).
% 0.21/0.49 tff(34,plain,
% 0.21/0.49 (![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.49 tff(35,plain,(
% 0.21/0.49 ![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[34])).
% 0.21/0.49 tff(36,plain,
% 0.21/0.49 (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.21/0.49 tff(37,plain,
% 0.21/0.49 (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.21/0.49 tff(38,plain,
% 0.21/0.49 ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!20))) | (~rel_str(boole_POSet(A!20)))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(39,plain,
% 0.21/0.49 (~((~strict_rel_str(boole_POSet(A!20))) | (~rel_str(boole_POSet(A!20))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.21/0.49 tff(40,plain,
% 0.21/0.49 (((~strict_rel_str(boole_POSet(A!20))) | (~rel_str(boole_POSet(A!20)))) | rel_str(boole_POSet(A!20))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(41,plain,
% 0.21/0.49 (rel_str(boole_POSet(A!20))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.21/0.49 tff(42,plain,
% 0.21/0.49 (^[A: $i] : refl((~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))))) <=> (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(43,plain,
% 0.21/0.49 (![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))))) <=> ![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.49 tff(44,plain,
% 0.21/0.49 (^[A: $i] : rewrite(((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & distributive_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A))) <=> (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(45,plain,
% 0.21/0.49 (![A: $i] : ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & distributive_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A))) <=> ![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.49 tff(46,plain,
% 0.21/0.49 (![A: $i] : ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & distributive_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A))) <=> ![A: $i] : ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & distributive_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(47,plain,
% 0.21/0.49 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)))), (((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)))), (((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A))))), ((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)))), ((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A))))), (((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)))), (((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A))))), ((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)))), ((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A))))), (((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))), (((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))))), ((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)))), ((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A))))), (((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)))), (((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A))))), ((((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)))), ((((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A))))), (((((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)))), (((((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A))))), ((((((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)))), ((((((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A))))), (((((((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & distributive_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A))) & distributive_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A))) & distributive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & distributive_relstr(boole_POSet(A)))), (((((((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & distributive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & distributive_relstr(boole_POSet(A))))), ((((((((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & distributive_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & distributive_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & distributive_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & distributive_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)))), ((((((((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & distributive_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & distributive_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(48,plain,
% 0.21/0.49 (![A: $i] : (((((((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & distributive_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) <=> ![A: $i] : ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & distributive_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.49 tff(49,axiom,(![A: $i] : (((((((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & distributive_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc9_waybel_1')).
% 0.21/0.49 tff(50,plain,
% 0.21/0.49 (![A: $i] : ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & distributive_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.49 tff(51,plain,
% 0.21/0.49 (![A: $i] : ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & distributive_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.49 tff(52,plain,(
% 0.21/0.49 ![A: $i] : ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & distributive_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[51])).
% 0.21/0.49 tff(53,plain,
% 0.21/0.49 (![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.21/0.49 tff(54,plain,
% 0.21/0.49 (![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.21/0.49 tff(55,plain,
% 0.21/0.49 ((~![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A)))))) | (~(empty_carrier(boole_POSet(A!20)) | (~strict_rel_str(boole_POSet(A!20))) | (~reflexive_relstr(boole_POSet(A!20))) | (~transitive_relstr(boole_POSet(A!20))) | (~antisymmetric_relstr(boole_POSet(A!20))) | (~with_suprema_relstr(boole_POSet(A!20))) | (~with_infima_relstr(boole_POSet(A!20))) | (~complete_relstr(boole_POSet(A!20))) | (~lower_bounded_relstr(boole_POSet(A!20))) | (~upper_bounded_relstr(boole_POSet(A!20))) | (~bounded_relstr(boole_POSet(A!20))) | (~up_complete_relstr(boole_POSet(A!20))) | (~join_complete_relstr(boole_POSet(A!20))) | (~distributive_relstr(boole_POSet(A!20))) | (~complemented_relstr(boole_POSet(A!20)))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(56,plain,
% 0.21/0.49 (~(empty_carrier(boole_POSet(A!20)) | (~strict_rel_str(boole_POSet(A!20))) | (~reflexive_relstr(boole_POSet(A!20))) | (~transitive_relstr(boole_POSet(A!20))) | (~antisymmetric_relstr(boole_POSet(A!20))) | (~with_suprema_relstr(boole_POSet(A!20))) | (~with_infima_relstr(boole_POSet(A!20))) | (~complete_relstr(boole_POSet(A!20))) | (~lower_bounded_relstr(boole_POSet(A!20))) | (~upper_bounded_relstr(boole_POSet(A!20))) | (~bounded_relstr(boole_POSet(A!20))) | (~up_complete_relstr(boole_POSet(A!20))) | (~join_complete_relstr(boole_POSet(A!20))) | (~distributive_relstr(boole_POSet(A!20))) | (~complemented_relstr(boole_POSet(A!20))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.21/0.49 tff(57,plain,
% 0.21/0.49 ((empty_carrier(boole_POSet(A!20)) | (~strict_rel_str(boole_POSet(A!20))) | (~reflexive_relstr(boole_POSet(A!20))) | (~transitive_relstr(boole_POSet(A!20))) | (~antisymmetric_relstr(boole_POSet(A!20))) | (~with_suprema_relstr(boole_POSet(A!20))) | (~with_infima_relstr(boole_POSet(A!20))) | (~complete_relstr(boole_POSet(A!20))) | (~lower_bounded_relstr(boole_POSet(A!20))) | (~upper_bounded_relstr(boole_POSet(A!20))) | (~bounded_relstr(boole_POSet(A!20))) | (~up_complete_relstr(boole_POSet(A!20))) | (~join_complete_relstr(boole_POSet(A!20))) | (~distributive_relstr(boole_POSet(A!20))) | (~complemented_relstr(boole_POSet(A!20)))) | strict_rel_str(boole_POSet(A!20))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(58,plain,
% 0.21/0.49 (strict_rel_str(boole_POSet(A!20))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.21/0.49 tff(59,plain,
% 0.21/0.49 (^[A: $i] : refl(((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A))) <=> ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(60,plain,
% 0.21/0.49 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A))) <=> ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[59])).
% 0.21/0.49 tff(61,plain,
% 0.21/0.49 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A))) <=> ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(62,plain,
% 0.21/0.49 (^[A: $i] : trans(monotonicity(rewrite((strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A)))) <=> ((~strict_rel_str(A)) | (A = rel_str_of(the_carrier(A), the_InternalRel(A))))), ((rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A))))) <=> (rel_str(A) => ((~strict_rel_str(A)) | (A = rel_str_of(the_carrier(A), the_InternalRel(A))))))), rewrite((rel_str(A) => ((~strict_rel_str(A)) | (A = rel_str_of(the_carrier(A), the_InternalRel(A))))) <=> ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))), ((rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A))))) <=> ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(63,plain,
% 0.21/0.49 (![A: $i] : (rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A))))) <=> ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.49 tff(64,axiom,(![A: $i] : (rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v1_orders_2')).
% 0.21/0.49 tff(65,plain,
% 0.21/0.49 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.49 tff(66,plain,
% 0.21/0.49 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.21/0.49 tff(67,plain,(
% 0.21/0.49 ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[66])).
% 0.21/0.49 tff(68,plain,
% 0.21/0.49 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.21/0.49 tff(69,plain,
% 0.21/0.49 (((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((boole_POSet(A!20) = rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20)))) | (~strict_rel_str(boole_POSet(A!20))) | (~rel_str(boole_POSet(A!20))))) <=> ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | (boole_POSet(A!20) = rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20)))) | (~strict_rel_str(boole_POSet(A!20))) | (~rel_str(boole_POSet(A!20))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(70,plain,
% 0.21/0.49 ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((boole_POSet(A!20) = rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20)))) | (~strict_rel_str(boole_POSet(A!20))) | (~rel_str(boole_POSet(A!20))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(71,plain,
% 0.21/0.49 ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | (boole_POSet(A!20) = rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20)))) | (~strict_rel_str(boole_POSet(A!20))) | (~rel_str(boole_POSet(A!20)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.49 tff(72,plain,
% 0.21/0.49 ((boole_POSet(A!20) = rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20)))) | (~strict_rel_str(boole_POSet(A!20))) | (~rel_str(boole_POSet(A!20)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[71, 68])).
% 0.21/0.50 tff(73,plain,
% 0.21/0.50 (boole_POSet(A!20) = rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[72, 58, 41])).
% 0.21/0.50 tff(74,plain,
% 0.21/0.50 (rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20))) = boole_POSet(A!20)),
% 0.21/0.50 inference(symmetry,[status(thm)],[73])).
% 0.21/0.50 tff(75,plain,
% 0.21/0.50 (rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20))) = rel_str_of(powerset(A!20), inclusion_order(powerset(A!20)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[74, 27, 18])).
% 0.21/0.50 tff(76,plain,
% 0.21/0.50 (^[A: $i, B: $i, C: $i] : refl((relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(77,plain,
% 0.21/0.50 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.50 tff(78,plain,
% 0.21/0.50 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(79,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 0.21/0.50 tff(80,plain,
% 0.21/0.50 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.21/0.50 tff(81,plain,(
% 0.21/0.50 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.21/0.50 inference(skolemize,[status(sab)],[80])).
% 0.21/0.50 tff(82,plain,
% 0.21/0.50 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.21/0.50 tff(83,plain,
% 0.21/0.50 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20))) <=> relation_of2(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(84,plain,
% 0.21/0.50 (relation_of2_as_subset(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20))) <=> relation_of2(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.21/0.50 tff(85,plain,
% 0.21/0.50 (^[A: $i] : refl(((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(86,plain,
% 0.21/0.50 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[85])).
% 0.21/0.50 tff(87,plain,
% 0.21/0.50 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(88,plain,
% 0.21/0.50 (^[A: $i] : rewrite((rel_str(A) => relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(89,plain,
% 0.21/0.50 (![A: $i] : (rel_str(A) => relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[88])).
% 0.21/0.50 tff(90,axiom,(![A: $i] : (rel_str(A) => relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u1_orders_2')).
% 0.21/0.50 tff(91,plain,
% 0.21/0.50 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.50 tff(92,plain,
% 0.21/0.50 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.21/0.50 tff(93,plain,(
% 0.21/0.50 ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[92])).
% 0.21/0.50 tff(94,plain,
% 0.21/0.50 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.21/0.50 tff(95,plain,
% 0.21/0.50 (((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | ((~rel_str(boole_POSet(A!20))) | relation_of2_as_subset(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20))))) <=> ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | (~rel_str(boole_POSet(A!20))) | relation_of2_as_subset(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(96,plain,
% 0.21/0.50 ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | ((~rel_str(boole_POSet(A!20))) | relation_of2_as_subset(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(97,plain,
% 0.21/0.50 ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | (~rel_str(boole_POSet(A!20))) | relation_of2_as_subset(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.50 tff(98,plain,
% 0.21/0.50 ((~rel_str(boole_POSet(A!20))) | relation_of2_as_subset(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[97, 94])).
% 0.21/0.50 tff(99,plain,
% 0.21/0.50 (relation_of2_as_subset(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[98, 41])).
% 0.21/0.50 tff(100,plain,
% 0.21/0.50 ((~(relation_of2_as_subset(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20))) <=> relation_of2(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20))))) | (~relation_of2_as_subset(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)))) | relation_of2(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(101,plain,
% 0.21/0.50 ((~(relation_of2_as_subset(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20))) <=> relation_of2(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20))))) | relation_of2(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.21/0.50 tff(102,plain,
% 0.21/0.50 (relation_of2(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[101, 84])).
% 0.21/0.50 tff(103,plain,
% 0.21/0.50 (^[A: $i, B: $i] : refl(((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(104,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[103])).
% 0.21/0.50 tff(105,plain,
% 0.21/0.50 (^[A: $i, B: $i] : rewrite(((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(106,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[105])).
% 0.21/0.50 tff(107,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[106, 104])).
% 0.21/0.50 tff(108,plain,
% 0.21/0.50 (^[A: $i, B: $i] : rewrite(((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(109,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[108])).
% 0.21/0.50 tff(110,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(111,plain,
% 0.21/0.50 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i, D: $i] : rewrite(((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D))) <=> ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))), (![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D))) <=> ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))), ((relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D)))) <=> (relation_of2(B, A, A) => ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))))), rewrite((relation_of2(B, A, A) => ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))), ((relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D)))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(112,plain,
% 0.21/0.50 (![A: $i, B: $i] : (relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[111])).
% 0.21/0.50 tff(113,axiom,(![A: $i, B: $i] : (relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','free_g1_orders_2')).
% 0.21/0.50 tff(114,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.21/0.50 tff(115,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.21/0.50 tff(116,plain,(
% 0.21/0.50 ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[115])).
% 0.21/0.50 tff(117,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.21/0.50 tff(118,plain,
% 0.21/0.50 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[117, 107])).
% 0.21/0.50 tff(119,plain,
% 0.21/0.50 (((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~relation_of2(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!20)) = C)) | (~(the_InternalRel(boole_POSet(A!20)) = D))))))) <=> ((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~relation_of2(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!20)) = C)) | (~(the_InternalRel(boole_POSet(A!20)) = D))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(120,plain,
% 0.21/0.50 ((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~relation_of2(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!20)) = C)) | (~(the_InternalRel(boole_POSet(A!20)) = D))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(121,plain,
% 0.21/0.50 ((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~relation_of2(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!20)) = C)) | (~(the_InternalRel(boole_POSet(A!20)) = D)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.50 tff(122,plain,
% 0.21/0.50 ((~relation_of2(the_InternalRel(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)), the_carrier(boole_POSet(A!20)))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!20)) = C)) | (~(the_InternalRel(boole_POSet(A!20)) = D)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[121, 118])).
% 0.21/0.50 tff(123,plain,
% 0.21/0.50 (![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!20)) = C)) | (~(the_InternalRel(boole_POSet(A!20)) = D)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[122, 102])).
% 0.21/0.50 tff(124,plain,
% 0.21/0.50 (((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!20)) = C)) | (~(the_InternalRel(boole_POSet(A!20)) = D)))))) | ((~(rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20))) = rel_str_of(powerset(A!20), inclusion_order(powerset(A!20))))) | (~((~(the_carrier(boole_POSet(A!20)) = powerset(A!20))) | (~(the_InternalRel(boole_POSet(A!20)) = inclusion_order(powerset(A!20)))))))) <=> ((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!20)) = C)) | (~(the_InternalRel(boole_POSet(A!20)) = D)))))) | (~(rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20))) = rel_str_of(powerset(A!20), inclusion_order(powerset(A!20))))) | (~((~(the_carrier(boole_POSet(A!20)) = powerset(A!20))) | (~(the_InternalRel(boole_POSet(A!20)) = inclusion_order(powerset(A!20)))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(125,plain,
% 0.21/0.50 ((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!20)) = C)) | (~(the_InternalRel(boole_POSet(A!20)) = D)))))) | ((~(rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20))) = rel_str_of(powerset(A!20), inclusion_order(powerset(A!20))))) | (~((~(the_carrier(boole_POSet(A!20)) = powerset(A!20))) | (~(the_InternalRel(boole_POSet(A!20)) = inclusion_order(powerset(A!20)))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(126,plain,
% 0.21/0.50 ((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!20)) = C)) | (~(the_InternalRel(boole_POSet(A!20)) = D)))))) | (~(rel_str_of(the_carrier(boole_POSet(A!20)), the_InternalRel(boole_POSet(A!20))) = rel_str_of(powerset(A!20), inclusion_order(powerset(A!20))))) | (~((~(the_carrier(boole_POSet(A!20)) = powerset(A!20))) | (~(the_InternalRel(boole_POSet(A!20)) = inclusion_order(powerset(A!20))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.50 tff(127,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[126, 123, 75, 9])).
% 0.21/0.50 % SZS output end Proof
% 0.21/0.51 % E exiting
%------------------------------------------------------------------------------