%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU361+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:27:42 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU361+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:54:41 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(related_type, type, (
% 0.12/0.37 related: ( $i * $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_B_9_type, type, (
% 0.12/0.37 tptp_fun_B_9: $i)).
% 0.12/0.37 tff(join_on_relstr_type, type, (
% 0.12/0.37 join_on_relstr: ( $i * $i ) > $i)).
% 0.12/0.37 tff(empty_set_type, type, (
% 0.12/0.37 empty_set: $i)).
% 0.12/0.37 tff(tptp_fun_A_8_type, type, (
% 0.12/0.37 tptp_fun_A_8: $i)).
% 0.12/0.37 tff(bottom_of_relstr_type, type, (
% 0.12/0.37 bottom_of_relstr: $i > $i)).
% 0.12/0.37 tff(rel_str_type, type, (
% 0.12/0.37 rel_str: $i > $o)).
% 0.12/0.37 tff(element_type, type, (
% 0.12/0.37 element: ( $i * $i ) > $o)).
% 0.12/0.37 tff(the_carrier_type, type, (
% 0.12/0.37 the_carrier: $i > $i)).
% 0.12/0.37 tff(lower_bounded_relstr_type, type, (
% 0.12/0.37 lower_bounded_relstr: $i > $o)).
% 0.12/0.37 tff(antisymmetric_relstr_type, type, (
% 0.12/0.37 antisymmetric_relstr: $i > $o)).
% 0.12/0.37 tff(empty_carrier_type, type, (
% 0.12/0.37 empty_carrier: $i > $o)).
% 0.12/0.37 tff(relstr_set_smaller_type, type, (
% 0.12/0.37 relstr_set_smaller: ( $i * $i * $i ) > $o)).
% 0.12/0.37 tff(ex_sup_of_relstr_set_type, type, (
% 0.12/0.37 ex_sup_of_relstr_set: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_D_7_type, type, (
% 0.12/0.37 tptp_fun_D_7: ( $i * $i * $i ) > $i)).
% 0.12/0.37 tff(ex_inf_of_relstr_set_type, type, (
% 0.12/0.37 ex_inf_of_relstr_set: ( $i * $i ) > $o)).
% 0.12/0.37 tff(relstr_element_smaller_type, type, (
% 0.12/0.37 relstr_element_smaller: ( $i * $i * $i ) > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 ((((~empty_carrier(A!8)) & antisymmetric_relstr(A!8) & lower_bounded_relstr(A!8) & rel_str(A!8)) & (~((~element(B!9, the_carrier(A!8))) | related(A!8, bottom_of_relstr(A!8), B!9)))) <=> ((~empty_carrier(A!8)) & antisymmetric_relstr(A!8) & lower_bounded_relstr(A!8) & rel_str(A!8) & (~((~element(B!9, the_carrier(A!8))) | related(A!8, bottom_of_relstr(A!8), B!9))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 ((~![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | related(A, bottom_of_relstr(A), B)))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | related(A, bottom_of_relstr(A), B))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 ((~![A: $i] : (((((~empty_carrier(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => related(A, bottom_of_relstr(A), B)))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | related(A, bottom_of_relstr(A), B))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,axiom,(~![A: $i] : (((((~empty_carrier(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => related(A, bottom_of_relstr(A), B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t44_yellow_0')).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (~![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | related(A, bottom_of_relstr(A), B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | related(A, bottom_of_relstr(A), B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | related(A, bottom_of_relstr(A), B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (~![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | related(A, bottom_of_relstr(A), B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 ((~empty_carrier(A!8)) & antisymmetric_relstr(A!8) & lower_bounded_relstr(A!8) & rel_str(A!8) & (~((~element(B!9, the_carrier(A!8))) | related(A!8, bottom_of_relstr(A!8), B!9)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (rel_str(A!8)),
% 0.12/0.37 inference(and_elim,[status(thm)],[9])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (^[A: $i] : refl(((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set))) <=> ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set))) <=> ![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set))) <=> ![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (^[A: $i] : rewrite((rel_str(A) => (bottom_of_relstr(A) = join_on_relstr(A, empty_set))) <=> ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![A: $i] : (rel_str(A) => (bottom_of_relstr(A) = join_on_relstr(A, empty_set))) <=> ![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.38 tff(16,axiom,(![A: $i] : (rel_str(A) => (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d11_yellow_0')).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.12/0.38 tff(19,plain,(
% 0.12/0.38 ![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[18])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (((~![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))) | ((~rel_str(A!8)) | (bottom_of_relstr(A!8) = join_on_relstr(A!8, empty_set)))) <=> ((~![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))) | (~rel_str(A!8)) | (bottom_of_relstr(A!8) = join_on_relstr(A!8, empty_set)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 ((~![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))) | ((~rel_str(A!8)) | (bottom_of_relstr(A!8) = join_on_relstr(A!8, empty_set)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 ((~![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))) | (~rel_str(A!8)) | (bottom_of_relstr(A!8) = join_on_relstr(A!8, empty_set))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (bottom_of_relstr(A!8) = join_on_relstr(A!8, empty_set)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (join_on_relstr(A!8, empty_set) = bottom_of_relstr(A!8)),
% 0.12/0.38 inference(symmetry,[status(thm)],[24])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (related(A!8, join_on_relstr(A!8, empty_set), B!9) <=> related(A!8, bottom_of_relstr(A!8), B!9)),
% 0.12/0.38 inference(monotonicity,[status(thm)],[25])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (related(A!8, bottom_of_relstr(A!8), B!9) <=> related(A!8, join_on_relstr(A!8, empty_set), B!9)),
% 0.12/0.38 inference(symmetry,[status(thm)],[26])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 ((~related(A!8, bottom_of_relstr(A!8), B!9)) <=> (~related(A!8, join_on_relstr(A!8, empty_set), B!9))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (~((~element(B!9, the_carrier(A!8))) | related(A!8, bottom_of_relstr(A!8), B!9))),
% 0.12/0.38 inference(and_elim,[status(thm)],[9])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (~related(A!8, bottom_of_relstr(A!8), B!9)),
% 0.12/0.38 inference(or_elim,[status(thm)],[29])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (~related(A!8, join_on_relstr(A!8, empty_set), B!9)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[30, 28])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (element(join_on_relstr(A!8, empty_set), the_carrier(A!8)) <=> element(bottom_of_relstr(A!8), the_carrier(A!8))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[25])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (element(bottom_of_relstr(A!8), the_carrier(A!8)) <=> element(join_on_relstr(A!8, empty_set), the_carrier(A!8))),
% 0.12/0.38 inference(symmetry,[status(thm)],[32])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (^[A: $i] : refl(((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A))) <=> ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (^[A: $i] : rewrite((rel_str(A) => element(bottom_of_relstr(A), the_carrier(A))) <=> ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (![A: $i] : (rel_str(A) => element(bottom_of_relstr(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[37])).
% 0.12/0.38 tff(39,axiom,(![A: $i] : (rel_str(A) => element(bottom_of_relstr(A), the_carrier(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k3_yellow_0')).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.12/0.38 tff(42,plain,(
% 0.12/0.38 ![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[41])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (((~![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))) | ((~rel_str(A!8)) | element(bottom_of_relstr(A!8), the_carrier(A!8)))) <=> ((~![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))) | (~rel_str(A!8)) | element(bottom_of_relstr(A!8), the_carrier(A!8)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 ((~![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))) | ((~rel_str(A!8)) | element(bottom_of_relstr(A!8), the_carrier(A!8)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 ((~![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))) | (~rel_str(A!8)) | element(bottom_of_relstr(A!8), the_carrier(A!8))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (element(bottom_of_relstr(A!8), the_carrier(A!8))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[46, 43, 10])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (element(join_on_relstr(A!8, empty_set), the_carrier(A!8))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[47, 33])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (antisymmetric_relstr(A!8)),
% 0.12/0.38 inference(and_elim,[status(thm)],[9])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite(((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))), (![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))), (((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))))))))), rewrite(((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))), (((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[50])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (^[A: $i] : refl(((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[52])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (^[A: $i] : rewrite(((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[54])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[55, 53])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((antisymmetric_relstr(A) & rel_str(A)) <=> (~((~antisymmetric_relstr(A)) | (~rel_str(A))))), ((~(antisymmetric_relstr(A) & rel_str(A))) <=> (~(~((~antisymmetric_relstr(A)) | (~rel_str(A))))))), rewrite((~(~((~antisymmetric_relstr(A)) | (~rel_str(A))))) <=> ((~antisymmetric_relstr(A)) | (~rel_str(A)))), ((~(antisymmetric_relstr(A) & rel_str(A))) <=> ((~antisymmetric_relstr(A)) | (~rel_str(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) | (~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A)))))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))), (![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) | (~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A)))))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))), (((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) | (~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))))))) <=> (((~antisymmetric_relstr(A)) | (~rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))))), rewrite((((~antisymmetric_relstr(A)) | (~rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))), (((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) | (~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(58,plain,
% 0.20/0.38 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) | (~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.38 tff(59,plain,
% 0.20/0.38 (^[A: $i] : rewrite(((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))) <=> ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) | (~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(60,plain,
% 0.20/0.39 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))) <=> ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) | (~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A)))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))) <=> ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite(((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))) <=> (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))), (![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))) <=> ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))), ((element(B, the_carrier(A)) => ![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))) <=> (element(B, the_carrier(A)) => ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))), ((element(B, the_carrier(A)) => ![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))), (((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))) <=> ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))))), rewrite(((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))) <=> ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))), (((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))) <=> ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))) <=> ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.39 tff(64,axiom,(![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t30_yellow_0')).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.20/0.39 tff(67,plain,(
% 0.20/0.39 ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[66])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) | (~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A)))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[69, 56])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[70, 51])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))) | ((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D))))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))) | (~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D))))))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) <=> ((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D))))))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 (^[B: $i] : rewrite(((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : (related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)) | (~element(D, the_carrier(A!8)))))))))))) <=> ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D))))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : (related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)) | (~element(D, the_carrier(A!8)))))))))))) <=> ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : (related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)) | (~element(D, the_carrier(A!8))))))))))))) <=> ((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D))))))))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[75])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : (related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)) | (~element(D, the_carrier(A!8))))))))))))) <=> ((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D))))))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[76, 73])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))) | ((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : (related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)) | (~element(D, the_carrier(A!8)))))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))) | ((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[77])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))) | ((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : (related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)) | (~element(D, the_carrier(A!8)))))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))) | (~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D))))))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[78, 72])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))) | ((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : (related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)) | (~element(D, the_carrier(A!8)))))))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))) | (~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[81, 71, 49, 10])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (((~![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) | ((~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) | (~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 (((~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, join_on_relstr(A!8, empty_set), D) | (~relstr_set_smaller(A!8, C, D))))))))))) <=> ((~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (((~![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) | ((~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, join_on_relstr(A!8, empty_set), D) | (~relstr_set_smaller(A!8, C, D)))))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) | ((~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[84])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (((~![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) | ((~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, join_on_relstr(A!8, empty_set), D) | (~relstr_set_smaller(A!8, C, D)))))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) | (~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[85, 83])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 ((~![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) | ((~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, join_on_relstr(A!8, empty_set), D) | (~relstr_set_smaller(A!8, C, D)))))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 ((~![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~((~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | related(A!8, B, tptp_fun_D_7(C, B, A!8)))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(B = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) | (~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 ((~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[88, 82])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[89, 48])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (((~![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) | (~((~(ex_sup_of_relstr_set(A!8, empty_set) | (~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~((~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) <=> ((~![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) | (~((~(ex_sup_of_relstr_set(A!8, empty_set) | (~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~((~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 ((~((~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, empty_set))))) | (~((~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, empty_set))) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))) <=> (~((~(ex_sup_of_relstr_set(A!8, empty_set) | (~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~((~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (((~![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) | (~((~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, empty_set))))) | (~((~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, empty_set))) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) <=> ((~![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) | (~((~(ex_sup_of_relstr_set(A!8, empty_set) | (~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~((~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (((~![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) | (~((~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, empty_set))))) | (~((~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, empty_set))) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) <=> ((~![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) | (~((~(ex_sup_of_relstr_set(A!8, empty_set) | (~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~((~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[93, 91])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 ((~![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) | (~((~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, empty_set))))) | (~((~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, empty_set))) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 ((~![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))) | (~((~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) | (~((~(ex_sup_of_relstr_set(A!8, empty_set) | (~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~((~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (~((~(ex_sup_of_relstr_set(A!8, empty_set) | (~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~((~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[96, 90])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (((~(ex_sup_of_relstr_set(A!8, empty_set) | (~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~((~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))) | ((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 ((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (lower_bounded_relstr(A!8)),
% 0.20/0.43 inference(and_elim,[status(thm)],[9])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (~empty_carrier(A!8)),
% 0.20/0.43 inference(and_elim,[status(thm)],[9])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (^[A: $i] : refl((empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A)))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A)))))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A)) <=> (~(empty_carrier(A) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~rel_str(A))))), ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) <=> (~(~(empty_carrier(A) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~rel_str(A))))))), rewrite((~(~(empty_carrier(A) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~rel_str(A))))) <=> (empty_carrier(A) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~rel_str(A)))), ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) <=> (empty_carrier(A) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~rel_str(A))))), rewrite((ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A))) <=> (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A)))))), (((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))) <=> ((empty_carrier(A) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~rel_str(A))) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A)))))))), rewrite(((empty_carrier(A) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~rel_str(A))) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A)))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))), (((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))) <=> (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) <=> ((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A))), (((((~empty_carrier(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) <=> (((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A)) & rel_str(A)))), rewrite((((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A)) & rel_str(A)) <=> ((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))), (((((~empty_carrier(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) <=> ((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A)))), ((((((~empty_carrier(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) => (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))) <=> (((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A)) => (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))))), rewrite((((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A)) => (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))) <=> ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A))))), ((((((~empty_carrier(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) => (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))) <=> ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 (![A: $i] : (((((~empty_carrier(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) => (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.43 tff(109,axiom,(![A: $i] : (((((~empty_carrier(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) => (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t42_yellow_0')).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 (![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 (![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.20/0.43 tff(112,plain,(
% 0.20/0.43 ![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[111])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[113, 103])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 (((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))) | (empty_carrier(A!8) | (~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | (~lower_bounded_relstr(A!8)) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~ex_inf_of_relstr_set(A!8, the_carrier(A!8))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))) | empty_carrier(A!8) | (~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | (~lower_bounded_relstr(A!8)) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~ex_inf_of_relstr_set(A!8, the_carrier(A!8))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))) | (empty_carrier(A!8) | (~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | (~lower_bounded_relstr(A!8)) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~ex_inf_of_relstr_set(A!8, the_carrier(A!8))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))) | empty_carrier(A!8) | (~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | (~lower_bounded_relstr(A!8)) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~ex_inf_of_relstr_set(A!8, the_carrier(A!8)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~ex_inf_of_relstr_set(A!8, the_carrier(A!8))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[117, 114, 101, 49, 100, 10])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 (((~ex_sup_of_relstr_set(A!8, empty_set)) | (~ex_inf_of_relstr_set(A!8, the_carrier(A!8)))) | ex_sup_of_relstr_set(A!8, empty_set)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 (ex_sup_of_relstr_set(A!8, empty_set)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 ((~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))) | (~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 ((~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[122, 99])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 (((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))) | ![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 (![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[126])).
% 0.20/0.43 tff(128,plain,
% 0.20/0.43 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.43 tff(130,plain,
% 0.20/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[129, 127])).
% 0.20/0.43 tff(131,plain,
% 0.20/0.43 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[131])).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(134,plain,
% 0.20/0.43 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, the_carrier(A)) => (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))) <=> ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))), (![B: $i] : (element(B, the_carrier(A)) => (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))), ((rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))) <=> (rel_str(A) => ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))))), rewrite((rel_str(A) => ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))), ((rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 (![A: $i] : (rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[134])).
% 0.20/0.44 tff(136,axiom,(![A: $i] : (rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t6_yellow_0')).
% 0.20/0.44 tff(137,plain,
% 0.20/0.44 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.20/0.44 tff(139,plain,(
% 0.20/0.44 ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[138])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[140, 130])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))) | ((~rel_str(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))) | (~rel_str(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))) | ((~rel_str(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(144,plain,
% 0.20/0.44 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))) | (~rel_str(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.44 tff(145,plain,
% 0.20/0.44 (![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[144, 10, 141])).
% 0.20/0.44 tff(146,plain,
% 0.20/0.44 (element(B!9, the_carrier(A!8))),
% 0.20/0.44 inference(or_elim,[status(thm)],[29])).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 (((~![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B)))))) | ((~element(B!9, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9)))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B)))))) | (~element(B!9, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 ((~![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B)))))) | ((~element(B!9, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 ((~![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B)))))) | (~element(B!9, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 (~((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[149, 146, 145])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 (((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9))) | relstr_set_smaller(A!8, empty_set, B!9)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 (relstr_set_smaller(A!8, empty_set, B!9)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 (((~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))) | ((~element(B!9, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, B!9)) | related(A!8, join_on_relstr(A!8, empty_set), B!9))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))) | (~element(B!9, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, B!9)) | related(A!8, join_on_relstr(A!8, empty_set), B!9))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 ((~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))) | ((~element(B!9, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, B!9)) | related(A!8, join_on_relstr(A!8, empty_set), B!9))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 ((~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))) | (~element(B!9, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, B!9)) | related(A!8, join_on_relstr(A!8, empty_set), B!9)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.44 tff(156,plain,
% 0.20/0.44 (related(A!8, join_on_relstr(A!8, empty_set), B!9)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[155, 146, 152, 125])).
% 0.20/0.44 tff(157,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[156, 31])).
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44 % E exiting
%------------------------------------------------------------------------------