%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU360+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 0.20s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU360+1 : TPTP v9.0.0. Released v3.3.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 06:52:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(in_type, type, (
% 0.20/0.38 in: ( $i * $i ) > $o)).
% 0.20/0.38 tff(the_carrier_type, type, (
% 0.20/0.38 the_carrier: $i > $i)).
% 0.20/0.38 tff(tptp_fun_A_13_type, type, (
% 0.20/0.38 tptp_fun_A_13: $i)).
% 0.20/0.38 tff(tptp_fun_D_10_type, type, (
% 0.20/0.38 tptp_fun_D_10: ( $i * $i * $i ) > $i)).
% 0.20/0.38 tff(empty_set_type, type, (
% 0.20/0.38 empty_set: $i)).
% 0.20/0.38 tff(tptp_fun_B_0_type, type, (
% 0.20/0.38 tptp_fun_B_0: $i > $i)).
% 0.20/0.38 tff(related_type, type, (
% 0.20/0.38 related: ( $i * $i * $i ) > $o)).
% 0.20/0.38 tff(relstr_set_smaller_type, type, (
% 0.20/0.38 relstr_set_smaller: ( $i * $i * $i ) > $o)).
% 0.20/0.38 tff(element_type, type, (
% 0.20/0.38 element: ( $i * $i ) > $o)).
% 0.20/0.38 tff(ex_sup_of_relstr_set_type, type, (
% 0.20/0.38 ex_sup_of_relstr_set: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_C_9_type, type, (
% 0.20/0.38 tptp_fun_C_9: ( $i * $i ) > $i)).
% 0.20/0.38 tff(rel_str_type, type, (
% 0.20/0.38 rel_str: $i > $o)).
% 0.20/0.38 tff(lower_bounded_relstr_type, type, (
% 0.20/0.38 lower_bounded_relstr: $i > $o)).
% 0.20/0.38 tff(antisymmetric_relstr_type, type, (
% 0.20/0.38 antisymmetric_relstr: $i > $o)).
% 0.20/0.38 tff(empty_carrier_type, type, (
% 0.20/0.38 empty_carrier: $i > $o)).
% 0.20/0.38 tff(ex_inf_of_relstr_set_type, type, (
% 0.20/0.38 ex_inf_of_relstr_set: ( $i * $i ) > $o)).
% 0.20/0.38 tff(relstr_element_smaller_type, type, (
% 0.20/0.38 relstr_element_smaller: ( $i * $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_D_12_type, type, (
% 0.20/0.38 tptp_fun_D_12: ( $i * $i * $i ) > $i)).
% 0.20/0.38 tff(tptp_fun_C_11_type, type, (
% 0.20/0.38 tptp_fun_C_11: ( $i * $i ) > $i)).
% 0.20/0.38 tff(tptp_fun_D_1_type, type, (
% 0.20/0.38 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.20/0.38 tff(empty_type, type, (
% 0.20/0.38 empty: $i > $o)).
% 0.20/0.38 tff(one_sorted_str_type, type, (
% 0.20/0.38 one_sorted_str: $i > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 ((~![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)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 ((~![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)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(3,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')).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (~![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))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (~![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))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (~![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))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (~![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))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.38 tff(8,plain,(
% 0.20/0.38 ~((~((~empty_carrier(A!13)) & antisymmetric_relstr(A!13) & lower_bounded_relstr(A!13) & rel_str(A!13))) | (ex_sup_of_relstr_set(A!13, empty_set) & ex_inf_of_relstr_set(A!13, the_carrier(A!13))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[7])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 ((~empty_carrier(A!13)) & antisymmetric_relstr(A!13) & lower_bounded_relstr(A!13) & rel_str(A!13)),
% 0.20/0.38 inference(or_elim,[status(thm)],[8])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (rel_str(A!13)),
% 0.20/0.39 inference(and_elim,[status(thm)],[9])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (antisymmetric_relstr(A!13)),
% 0.20/0.39 inference(and_elim,[status(thm)],[9])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (^[A: $i] : refl(((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (^[A: $i] : rewrite(((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[15, 13])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (^[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] : trans(monotonicity(rewrite(((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_9(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_9(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D))))) <=> ((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))), rewrite((ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))) <=> (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))), ((((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_9(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_9(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))) <=> (((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D))))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))), rewrite((((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D))))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))) <=> (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))))))), ((((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_9(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_9(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))) <=> (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))))))))), (![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_9(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_9(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))) <=> ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))))), (((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_9(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_9(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))))) <=> (((~antisymmetric_relstr(A)) | (~rel_str(A))) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))))))))), rewrite((((~antisymmetric_relstr(A)) | (~rel_str(A))) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))))), (((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_9(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_9(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_9(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_9(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (^[A: $i] : rewrite(((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_9(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_9(B, A)) & ![D: $i] : (related(A, tptp_fun_C_9(B, A), D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))))) <=> ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_9(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_9(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_9(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_9(B, A)) & ![D: $i] : (related(A, tptp_fun_C_9(B, A), D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A))))))))) <=> ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_9(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_9(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)))))) <=> ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D))))) <=> (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D))))))), (![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D))))) <=> ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D))))))), (((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D)))))) <=> ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)))))))), rewrite(((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D)))))) <=> ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D))))))), (((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D)))))) <=> ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D)))))) <=> ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.39 tff(24,axiom,(![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t15_yellow_0')).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.39 tff(27,plain,(
% 0.20/0.39 ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_9(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_9(B, A)) & ![D: $i] : (related(A, tptp_fun_C_9(B, A), D) | (~element(D, the_carrier(A))) | (~relstr_set_smaller(A, B, D))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[26])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_9(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_9(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[29, 16])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))))) | ((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))) | (~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, D)) | related(A!13, tptp_fun_C_9(B, A!13), D))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))))) | (~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))) | (~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, D)) | related(A!13, tptp_fun_C_9(B, A!13), D))))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))) | (~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, D)) | related(A!13, tptp_fun_C_9(B, A!13), D)))))))))) <=> ((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))) | (~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, D)) | related(A!13, tptp_fun_C_9(B, A!13), D))))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (^[B: $i] : rewrite((~((~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_C_9(B, A!13), D) | (~relstr_set_smaller(A!13, B, D)))))))) | (~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))))) <=> (~((~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))) | (~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, D)) | related(A!13, tptp_fun_C_9(B, A!13), D))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (![B: $i] : (~((~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_C_9(B, A!13), D) | (~relstr_set_smaller(A!13, B, D)))))))) | (~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))))) <=> ![B: $i] : (~((~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))) | (~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, D)) | related(A!13, tptp_fun_C_9(B, A!13), D)))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_C_9(B, A!13), D) | (~relstr_set_smaller(A!13, B, D)))))))) | (~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13))))))))))) <=> ((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))) | (~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, D)) | related(A!13, tptp_fun_C_9(B, A!13), D))))))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[34])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_C_9(B, A!13), D) | (~relstr_set_smaller(A!13, B, D)))))))) | (~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13))))))))))) <=> ((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))) | (~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, D)) | related(A!13, tptp_fun_C_9(B, A!13), D))))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[35, 32])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))))) | ((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_C_9(B, A!13), D) | (~relstr_set_smaller(A!13, B, D)))))))) | (~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))))) | ((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))) | (~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, D)) | related(A!13, tptp_fun_C_9(B, A!13), D)))))))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[36])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))))) | ((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_C_9(B, A!13), D) | (~relstr_set_smaller(A!13, B, D)))))))) | (~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))))) | (~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))) | (~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, D)) | related(A!13, tptp_fun_C_9(B, A!13), D))))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[37, 31])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))))) | ((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_C_9(B, A!13), D) | (~relstr_set_smaller(A!13, B, D)))))))) | (~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_9(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_9(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_9(B, A), D) | (~relstr_set_smaller(A, B, D)))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_10(C, B, A)) | (~element(tptp_fun_D_10(C, B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_D_10(C, B, A)))))))))))) | (~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))) | (~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, D)) | related(A!13, tptp_fun_C_9(B, A!13), D)))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (![B: $i] : (~((~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))) | (~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, D)) | related(A!13, tptp_fun_C_9(B, A!13), D)))))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[40, 30, 11, 10])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 ((~![B: $i] : (~((~(ex_sup_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, C)) | (~(related(A!13, C, tptp_fun_D_10(C, B, A!13)) | (~element(tptp_fun_D_10(C, B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_D_10(C, B, A!13)))))))) | (~((~ex_sup_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_9(B, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, tptp_fun_C_9(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_set_smaller(A!13, B, D)) | related(A!13, tptp_fun_C_9(B, A!13), D)))))))))) | (~((~(ex_sup_of_relstr_set(A!13, empty_set) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13)))))))) | (~((~ex_sup_of_relstr_set(A!13, empty_set)) | (~((~element(tptp_fun_C_9(empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_C_9(empty_set, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, D)) | related(A!13, tptp_fun_C_9(empty_set, A!13), D)))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (~((~(ex_sup_of_relstr_set(A!13, empty_set) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13)))))))) | (~((~ex_sup_of_relstr_set(A!13, empty_set)) | (~((~element(tptp_fun_C_9(empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_C_9(empty_set, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, D)) | related(A!13, tptp_fun_C_9(empty_set, A!13), D))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (((~(ex_sup_of_relstr_set(A!13, empty_set) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13)))))))) | (~((~ex_sup_of_relstr_set(A!13, empty_set)) | (~((~element(tptp_fun_C_9(empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_C_9(empty_set, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, D)) | related(A!13, tptp_fun_C_9(empty_set, A!13), D)))))))) | (ex_sup_of_relstr_set(A!13, empty_set) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13)))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (ex_sup_of_relstr_set(A!13, empty_set) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.20/0.41 tff(46,assumption,((~((~ex_inf_of_relstr_set(A!13, the_carrier(A!13))) | (~((~element(tptp_fun_C_11(the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_C_11(the_carrier(A!13), A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), D)) | related(A!13, D, tptp_fun_C_11(the_carrier(A!13), A!13)))))))) | (~(ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13))))))))), introduced(assumption)).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (^[A: $i] : refl(((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (^[A: $i] : rewrite(((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[50, 48])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (^[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] : trans(monotonicity(rewrite(((~ex_inf_of_relstr_set(A, B)) | (element(tptp_fun_C_11(B, A), the_carrier(A)) & relstr_element_smaller(A, B, tptp_fun_C_11(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A))))) <=> ((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))), rewrite((ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))) <=> (ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))), ((((~ex_inf_of_relstr_set(A, B)) | (element(tptp_fun_C_11(B, A), the_carrier(A)) & relstr_element_smaller(A, B, tptp_fun_C_11(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A))))) & (ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))) <=> (((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A))))))) & (ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))), rewrite((((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A))))))) & (ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))) <=> (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))))))), ((((~ex_inf_of_relstr_set(A, B)) | (element(tptp_fun_C_11(B, A), the_carrier(A)) & relstr_element_smaller(A, B, tptp_fun_C_11(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A))))) & (ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))) <=> (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))))))))), (![B: $i] : (((~ex_inf_of_relstr_set(A, B)) | (element(tptp_fun_C_11(B, A), the_carrier(A)) & relstr_element_smaller(A, B, tptp_fun_C_11(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A))))) & (ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))) <=> ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))))), (((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_inf_of_relstr_set(A, B)) | (element(tptp_fun_C_11(B, A), the_carrier(A)) & relstr_element_smaller(A, B, tptp_fun_C_11(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A))))) & (ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))))) <=> (((~antisymmetric_relstr(A)) | (~rel_str(A))) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))))))))), rewrite((((~antisymmetric_relstr(A)) | (~rel_str(A))) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))))), (((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_inf_of_relstr_set(A, B)) | (element(tptp_fun_C_11(B, A), the_carrier(A)) & relstr_element_smaller(A, B, tptp_fun_C_11(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A))))) & (ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_inf_of_relstr_set(A, B)) | (element(tptp_fun_C_11(B, A), the_carrier(A)) & relstr_element_smaller(A, B, tptp_fun_C_11(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A))))) & (ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (^[A: $i] : rewrite(((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_inf_of_relstr_set(A, B)) | (element(tptp_fun_C_11(B, A), the_carrier(A)) & relstr_element_smaller(A, B, tptp_fun_C_11(B, A)) & ![D: $i] : (related(A, D, tptp_fun_C_11(B, A)) | (~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D))))) & (ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))))) <=> ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_inf_of_relstr_set(A, B)) | (element(tptp_fun_C_11(B, A), the_carrier(A)) & relstr_element_smaller(A, B, tptp_fun_C_11(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A))))) & (ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_inf_of_relstr_set(A, B)) | (element(tptp_fun_C_11(B, A), the_carrier(A)) & relstr_element_smaller(A, B, tptp_fun_C_11(B, A)) & ![D: $i] : (related(A, D, tptp_fun_C_11(B, A)) | (~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D))))) & (ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A))))))))) <=> ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_inf_of_relstr_set(A, B)) | (element(tptp_fun_C_11(B, A), the_carrier(A)) & relstr_element_smaller(A, B, tptp_fun_C_11(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A))))) & (ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_inf_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_element_smaller(A, B, C) & ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)))))) <=> ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_inf_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_element_smaller(A, B, C) & ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((ex_inf_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_element_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_element_smaller(A, B, D) => related(A, D, C))))) <=> (ex_inf_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_element_smaller(A, B, C) & ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D))))))), (![B: $i] : (ex_inf_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_element_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_element_smaller(A, B, D) => related(A, D, C))))) <=> ![B: $i] : (ex_inf_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_element_smaller(A, B, C) & ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D))))))), (((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_inf_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_element_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_element_smaller(A, B, D) => related(A, D, C)))))) <=> ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_inf_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_element_smaller(A, B, C) & ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)))))))), rewrite(((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_inf_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_element_smaller(A, B, C) & ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)))))) <=> ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_inf_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_element_smaller(A, B, C) & ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D))))))), (((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_inf_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_element_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_element_smaller(A, B, D) => related(A, D, C)))))) <=> ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_inf_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_element_smaller(A, B, C) & ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_inf_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_element_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_element_smaller(A, B, D) => related(A, D, C)))))) <=> ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_inf_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_element_smaller(A, B, C) & ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.42 tff(59,axiom,(![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_inf_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_element_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_element_smaller(A, B, D) => related(A, D, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t16_yellow_0')).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_inf_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_element_smaller(A, B, C) & ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_inf_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_element_smaller(A, B, C) & ![D: $i] : (related(A, D, C) | (~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.20/0.42 tff(62,plain,(
% 0.20/0.42 ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_inf_of_relstr_set(A, B)) | (element(tptp_fun_C_11(B, A), the_carrier(A)) & relstr_element_smaller(A, B, tptp_fun_C_11(B, A)) & ![D: $i] : (related(A, D, tptp_fun_C_11(B, A)) | (~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D))))) & (ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[61])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (((~ex_inf_of_relstr_set(A, B)) | (element(tptp_fun_C_11(B, A), the_carrier(A)) & relstr_element_smaller(A, B, tptp_fun_C_11(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A))))) & (ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[64, 51])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))))) | ((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))))) | (~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13)))))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(67,plain,
% 0.21/0.42 (((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13))))))))))) <=> ((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13)))))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(68,plain,
% 0.21/0.42 (^[B: $i] : rewrite((~((~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13)))))))) | (~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))))) <=> (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13)))))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(69,plain,
% 0.21/0.42 (![B: $i] : (~((~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13)))))))) | (~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))))) <=> ![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13))))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[68])).
% 0.21/0.42 tff(70,plain,
% 0.21/0.42 (((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13)))))))) | (~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13))))))))))) <=> ((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13)))))))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[69])).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 (((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13)))))))) | (~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13))))))))))) <=> ((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13)))))))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[70, 67])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))))) | ((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13)))))))) | (~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))))) | ((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13))))))))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[71])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))))) | ((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13)))))))) | (~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))))) | (~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13)))))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[72, 66])).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))))) | ((~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13)))))))) | (~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (~((~((~ex_inf_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_11(B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_C_11(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (~relstr_element_smaller(A, B, D)) | related(A, D, tptp_fun_C_11(B, A)))))))) | (~(ex_inf_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_element_smaller(A, B, C)) | (~(related(A, tptp_fun_D_12(C, B, A), C) | (~element(tptp_fun_D_12(C, B, A), the_carrier(A))) | (~relstr_element_smaller(A, B, tptp_fun_D_12(C, B, A)))))))))))) | (~rel_str(A!13)) | (~antisymmetric_relstr(A!13)) | ![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13))))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13))))))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[75, 65, 11, 10])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 (((~![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13))))))))))) | (~((~((~ex_inf_of_relstr_set(A!13, the_carrier(A!13))) | (~((~element(tptp_fun_C_11(the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_C_11(the_carrier(A!13), A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), D)) | related(A!13, D, tptp_fun_C_11(the_carrier(A!13), A!13)))))))) | (~(ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13))))))))))) <=> ((~![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13))))))))))) | (~((~((~ex_inf_of_relstr_set(A!13, the_carrier(A!13))) | (~((~element(tptp_fun_C_11(the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_C_11(the_carrier(A!13), A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), D)) | related(A!13, D, tptp_fun_C_11(the_carrier(A!13), A!13)))))))) | (~(ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13)))))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 ((~((~(ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, the_carrier(A!13))) | (~((~element(tptp_fun_C_11(the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_C_11(the_carrier(A!13), A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), D)) | related(A!13, D, tptp_fun_C_11(the_carrier(A!13), A!13)))))))))) <=> (~((~((~ex_inf_of_relstr_set(A!13, the_carrier(A!13))) | (~((~element(tptp_fun_C_11(the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_C_11(the_carrier(A!13), A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), D)) | related(A!13, D, tptp_fun_C_11(the_carrier(A!13), A!13)))))))) | (~(ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13))))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 (((~![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13))))))))))) | (~((~(ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, the_carrier(A!13))) | (~((~element(tptp_fun_C_11(the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_C_11(the_carrier(A!13), A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), D)) | related(A!13, D, tptp_fun_C_11(the_carrier(A!13), A!13))))))))))) <=> ((~![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13))))))))))) | (~((~((~ex_inf_of_relstr_set(A!13, the_carrier(A!13))) | (~((~element(tptp_fun_C_11(the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_C_11(the_carrier(A!13), A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), D)) | related(A!13, D, tptp_fun_C_11(the_carrier(A!13), A!13)))))))) | (~(ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13)))))))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[78])).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (((~![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13))))))))))) | (~((~(ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, the_carrier(A!13))) | (~((~element(tptp_fun_C_11(the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_C_11(the_carrier(A!13), A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), D)) | related(A!13, D, tptp_fun_C_11(the_carrier(A!13), A!13))))))))))) <=> ((~![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13))))))))))) | (~((~((~ex_inf_of_relstr_set(A!13, the_carrier(A!13))) | (~((~element(tptp_fun_C_11(the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_C_11(the_carrier(A!13), A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), D)) | related(A!13, D, tptp_fun_C_11(the_carrier(A!13), A!13)))))))) | (~(ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13)))))))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[79, 77])).
% 0.21/0.44 tff(81,plain,
% 0.21/0.44 ((~![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13))))))))))) | (~((~(ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, the_carrier(A!13))) | (~((~element(tptp_fun_C_11(the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_C_11(the_carrier(A!13), A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), D)) | related(A!13, D, tptp_fun_C_11(the_carrier(A!13), A!13))))))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(82,plain,
% 0.21/0.44 ((~![B: $i] : (~((~(ex_inf_of_relstr_set(A!13, B) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, C)) | (~(related(A!13, tptp_fun_D_12(C, B, A!13), C) | (~element(tptp_fun_D_12(C, B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_D_12(C, B, A!13)))))))) | (~((~ex_inf_of_relstr_set(A!13, B)) | (~((~element(tptp_fun_C_11(B, A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, tptp_fun_C_11(B, A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, B, D)) | related(A!13, D, tptp_fun_C_11(B, A!13))))))))))) | (~((~((~ex_inf_of_relstr_set(A!13, the_carrier(A!13))) | (~((~element(tptp_fun_C_11(the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_C_11(the_carrier(A!13), A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), D)) | related(A!13, D, tptp_fun_C_11(the_carrier(A!13), A!13)))))))) | (~(ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13))))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.21/0.44 tff(83,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[82, 76, 46])).
% 0.21/0.44 tff(84,plain,(~((~((~ex_inf_of_relstr_set(A!13, the_carrier(A!13))) | (~((~element(tptp_fun_C_11(the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_C_11(the_carrier(A!13), A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), D)) | related(A!13, D, tptp_fun_C_11(the_carrier(A!13), A!13)))))))) | (~(ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13)))))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(85,plain,
% 0.21/0.44 (((~((~ex_inf_of_relstr_set(A!13, the_carrier(A!13))) | (~((~element(tptp_fun_C_11(the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_C_11(the_carrier(A!13), A!13))) | (~![D: $i] : ((~element(D, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), D)) | related(A!13, D, tptp_fun_C_11(the_carrier(A!13), A!13)))))))) | (~(ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13))))))))) | (ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13)))))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(86,plain,
% 0.21/0.44 (ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.21/0.44 tff(87,assumption,(![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13))))))), introduced(assumption)).
% 0.21/0.44 tff(88,assumption,(~(related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_B_0(A!13)) | (~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))))), introduced(assumption)).
% 0.21/0.44 tff(89,plain,
% 0.21/0.44 ((related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_B_0(A!13)) | (~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)))) | element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(90,plain,
% 0.21/0.44 (element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.21/0.44 tff(91,plain,
% 0.21/0.44 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(92,plain,
% 0.21/0.44 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[91])).
% 0.21/0.44 tff(93,plain,
% 0.21/0.44 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(94,plain,
% 0.21/0.44 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[93])).
% 0.21/0.44 tff(95,plain,
% 0.21/0.44 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[94, 92])).
% 0.21/0.44 tff(96,plain,
% 0.21/0.44 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))) & (relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(97,plain,
% 0.21/0.44 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))) & (relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.44 tff(98,plain,
% 0.21/0.44 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(99,plain,
% 0.21/0.44 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, C: $i] : trans(monotonicity(rewrite((relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D)))) <=> (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))), ((element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D))))) <=> (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))), rewrite((element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) <=> ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))))), ((element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D))))) <=> ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))))))), (![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D))))) <=> ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))), ((rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D)))))) <=> (rel_str(A) => ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))))))), rewrite((rel_str(A) => ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))), ((rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D)))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 (![A: $i] : (rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[99])).
% 0.21/0.45 tff(101,axiom,(![A: $i] : (rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_lattice3')).
% 0.21/0.45 tff(102,plain,
% 0.21/0.45 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.45 tff(103,plain,
% 0.21/0.45 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.21/0.45 tff(104,plain,(
% 0.21/0.45 ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))) & (relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[103])).
% 0.21/0.45 tff(105,plain,
% 0.21/0.45 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.21/0.45 tff(106,plain,
% 0.21/0.45 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[105, 95])).
% 0.21/0.45 tff(107,plain,
% 0.21/0.45 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | (~rel_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13))))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(108,plain,
% 0.21/0.45 (((~rel_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : (related(A!13, C, D) | (~in(D, B)) | (~element(D, the_carrier(A!13)))))) | (~(relstr_element_smaller(A!13, B, C) | (~(related(A!13, C, tptp_fun_D_1(C, B, A!13)) | (~in(tptp_fun_D_1(C, B, A!13), B)) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))))))))))) <=> ((~rel_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13))))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(109,plain,
% 0.21/0.45 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : (related(A!13, C, D) | (~in(D, B)) | (~element(D, the_carrier(A!13)))))) | (~(relstr_element_smaller(A!13, B, C) | (~(related(A!13, C, tptp_fun_D_1(C, B, A!13)) | (~in(tptp_fun_D_1(C, B, A!13), B)) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[108])).
% 0.21/0.45 tff(110,plain,
% 0.21/0.45 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : (related(A!13, C, D) | (~in(D, B)) | (~element(D, the_carrier(A!13)))))) | (~(relstr_element_smaller(A!13, B, C) | (~(related(A!13, C, tptp_fun_D_1(C, B, A!13)) | (~in(tptp_fun_D_1(C, B, A!13), B)) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | (~rel_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13))))))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[109, 107])).
% 0.21/0.45 tff(111,plain,
% 0.21/0.45 ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : (related(A!13, C, D) | (~in(D, B)) | (~element(D, the_carrier(A!13)))))) | (~(relstr_element_smaller(A!13, B, C) | (~(related(A!13, C, tptp_fun_D_1(C, B, A!13)) | (~in(tptp_fun_D_1(C, B, A!13), B)) | (~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13)))))))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(112,plain,
% 0.21/0.45 ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_1(C, B, A)) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | (~rel_str(A!13)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.45 tff(113,plain,
% 0.21/0.45 (![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[112, 106, 10])).
% 0.21/0.45 tff(114,plain,
% 0.21/0.45 (((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))) | ((~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13)))))))))) <=> ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))) | (~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13)))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(115,plain,
% 0.21/0.45 (((~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))) | ![D: $i] : ((~in(D, the_carrier(A!13))) | (~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13))))))))) <=> ((~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13)))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(116,plain,
% 0.21/0.46 (((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))) | ((~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))) | ![D: $i] : ((~in(D, the_carrier(A!13))) | (~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13)))))))))) <=> ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))) | ((~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13))))))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[115])).
% 0.21/0.46 tff(117,plain,
% 0.21/0.46 (((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))) | ((~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))) | ![D: $i] : ((~in(D, the_carrier(A!13))) | (~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13)))))))))) <=> ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))) | (~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13)))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[116, 114])).
% 0.21/0.46 tff(118,plain,
% 0.21/0.46 ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))) | ((~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))) | ![D: $i] : ((~in(D, the_carrier(A!13))) | (~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13)))))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(119,plain,
% 0.21/0.46 ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))) | (~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.46 tff(120,plain,
% 0.21/0.46 (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13)))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[119, 113, 90])).
% 0.21/0.46 tff(121,plain,
% 0.21/0.46 (((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_D_1(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13), A!13))))))) | ((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(122,plain,
% 0.21/0.46 ((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.21/0.46 tff(123,plain,
% 0.21/0.46 ((related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_B_0(A!13)) | (~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)))) | relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(124,plain,
% 0.21/0.46 (relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[123, 88])).
% 0.21/0.46 tff(125,plain,
% 0.21/0.46 ((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D)))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(126,plain,
% 0.21/0.46 ((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D)))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.21/0.47 tff(127,plain,
% 0.21/0.47 (![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[126, 122])).
% 0.21/0.47 tff(128,plain,
% 0.21/0.47 ((related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_B_0(A!13)) | (~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)))) | (~related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_B_0(A!13)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(129,plain,
% 0.21/0.47 (~related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_B_0(A!13))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[128, 88])).
% 0.21/0.47 tff(130,plain,
% 0.21/0.47 (^[A: $i] : refl((one_sorted_str(A) | (~rel_str(A))) <=> (one_sorted_str(A) | (~rel_str(A))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(131,plain,
% 0.21/0.47 (![A: $i] : (one_sorted_str(A) | (~rel_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.47 tff(132,plain,
% 0.21/0.47 (![A: $i] : (one_sorted_str(A) | (~rel_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(133,plain,
% 0.21/0.47 (^[A: $i] : rewrite((rel_str(A) => one_sorted_str(A)) <=> (one_sorted_str(A) | (~rel_str(A))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(134,plain,
% 0.21/0.47 (![A: $i] : (rel_str(A) => one_sorted_str(A)) <=> ![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[133])).
% 0.21/0.47 tff(135,axiom,(![A: $i] : (rel_str(A) => one_sorted_str(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_orders_2')).
% 0.21/0.47 tff(136,plain,
% 0.21/0.47 (![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.21/0.47 tff(137,plain,
% 0.21/0.47 (![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.21/0.47 tff(138,plain,(
% 0.21/0.47 ![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[137])).
% 0.21/0.47 tff(139,plain,
% 0.21/0.47 (![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.21/0.47 tff(140,plain,
% 0.21/0.47 (((~![A: $i] : (one_sorted_str(A) | (~rel_str(A)))) | (one_sorted_str(A!13) | (~rel_str(A!13)))) <=> ((~![A: $i] : (one_sorted_str(A) | (~rel_str(A)))) | one_sorted_str(A!13) | (~rel_str(A!13)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(141,plain,
% 0.21/0.47 ((~![A: $i] : (one_sorted_str(A) | (~rel_str(A)))) | (one_sorted_str(A!13) | (~rel_str(A!13)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(142,plain,
% 0.21/0.47 ((~![A: $i] : (one_sorted_str(A) | (~rel_str(A)))) | one_sorted_str(A!13) | (~rel_str(A!13))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.21/0.47 tff(143,plain,
% 0.21/0.47 (one_sorted_str(A!13)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[142, 139, 10])).
% 0.21/0.47 tff(144,plain,
% 0.21/0.47 (~empty_carrier(A!13)),
% 0.21/0.47 inference(and_elim,[status(thm)],[9])).
% 0.21/0.47 tff(145,plain,
% 0.21/0.47 (^[A: $i] : refl(((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A))) <=> ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(146,plain,
% 0.21/0.47 (![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A))) <=> ![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[145])).
% 0.21/0.47 tff(147,plain,
% 0.21/0.47 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & one_sorted_str(A)) <=> (~(empty_carrier(A) | (~one_sorted_str(A))))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (~(~(empty_carrier(A) | (~one_sorted_str(A))))))), rewrite((~(~(empty_carrier(A) | (~one_sorted_str(A))))) <=> (empty_carrier(A) | (~one_sorted_str(A)))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (empty_carrier(A) | (~one_sorted_str(A))))), (((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ((~empty(the_carrier(A))) | (empty_carrier(A) | (~one_sorted_str(A)))))), rewrite(((~empty(the_carrier(A))) | (empty_carrier(A) | (~one_sorted_str(A)))) <=> ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))), (((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(148,plain,
% 0.21/0.47 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[147])).
% 0.21/0.47 tff(149,plain,
% 0.21/0.47 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(150,plain,
% 0.21/0.47 (^[A: $i] : rewrite((((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A)))) <=> ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(151,plain,
% 0.21/0.47 (![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A)))) <=> ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[150])).
% 0.21/0.47 tff(152,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.21/0.47 tff(153,plain,
% 0.21/0.47 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.21/0.47 tff(154,plain,
% 0.21/0.47 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.21/0.47 tff(155,plain,(
% 0.21/0.47 ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[154])).
% 0.21/0.47 tff(156,plain,
% 0.21/0.47 (![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[155, 148])).
% 0.21/0.47 tff(157,plain,
% 0.21/0.47 (![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[156, 146])).
% 0.21/0.47 tff(158,plain,
% 0.21/0.47 (((~![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))) | (empty_carrier(A!13) | (~empty(the_carrier(A!13))) | (~one_sorted_str(A!13)))) <=> ((~![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))) | empty_carrier(A!13) | (~empty(the_carrier(A!13))) | (~one_sorted_str(A!13)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(159,plain,
% 0.21/0.47 (((~empty(the_carrier(A!13))) | empty_carrier(A!13) | (~one_sorted_str(A!13))) <=> (empty_carrier(A!13) | (~empty(the_carrier(A!13))) | (~one_sorted_str(A!13)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(160,plain,
% 0.21/0.47 (((~![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))) | ((~empty(the_carrier(A!13))) | empty_carrier(A!13) | (~one_sorted_str(A!13)))) <=> ((~![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))) | (empty_carrier(A!13) | (~empty(the_carrier(A!13))) | (~one_sorted_str(A!13))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[159])).
% 0.21/0.47 tff(161,plain,
% 0.21/0.47 (((~![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))) | ((~empty(the_carrier(A!13))) | empty_carrier(A!13) | (~one_sorted_str(A!13)))) <=> ((~![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))) | empty_carrier(A!13) | (~empty(the_carrier(A!13))) | (~one_sorted_str(A!13)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[160, 158])).
% 0.21/0.47 tff(162,plain,
% 0.21/0.47 ((~![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))) | ((~empty(the_carrier(A!13))) | empty_carrier(A!13) | (~one_sorted_str(A!13)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(163,plain,
% 0.21/0.47 ((~![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))) | empty_carrier(A!13) | (~empty(the_carrier(A!13))) | (~one_sorted_str(A!13))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.21/0.47 tff(164,plain,
% 0.21/0.47 (~empty(the_carrier(A!13))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[163, 157, 144, 143])).
% 0.21/0.47 tff(165,plain,
% 0.21/0.47 (^[A: $i] : refl(((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B)))))))) <=> ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(166,plain,
% 0.21/0.47 (![A: $i] : ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B)))))))) <=> ![A: $i] : ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[165])).
% 0.21/0.47 tff(167,plain,
% 0.21/0.47 (^[A: $i] : rewrite(((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B)))))))) <=> ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(168,plain,
% 0.21/0.47 (![A: $i] : ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B)))))))) <=> ![A: $i] : ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[167])).
% 0.21/0.47 tff(169,plain,
% 0.21/0.47 (![A: $i] : ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B)))))))) <=> ![A: $i] : ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[168, 166])).
% 0.21/0.47 tff(170,plain,
% 0.21/0.47 (^[A: $i] : rewrite(((~rel_str(A)) | (((~lower_bounded_relstr(A)) | (element(tptp_fun_B_0(A), the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A)))) & (lower_bounded_relstr(A) | ![B: $i] : (~(element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B)))))) <=> ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(171,plain,
% 0.21/0.47 (![A: $i] : ((~rel_str(A)) | (((~lower_bounded_relstr(A)) | (element(tptp_fun_B_0(A), the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A)))) & (lower_bounded_relstr(A) | ![B: $i] : (~(element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B)))))) <=> ![A: $i] : ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[170])).
% 0.21/0.47 tff(172,plain,
% 0.21/0.47 (![A: $i] : ((~rel_str(A)) | (lower_bounded_relstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B)))) <=> ![A: $i] : ((~rel_str(A)) | (lower_bounded_relstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(173,plain,
% 0.21/0.47 (^[A: $i] : trans(monotonicity(rewrite((lower_bounded_relstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B))) <=> (lower_bounded_relstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B)))), ((rel_str(A) => (lower_bounded_relstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B)))) <=> (rel_str(A) => (lower_bounded_relstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B)))))), rewrite((rel_str(A) => (lower_bounded_relstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B)))) <=> ((~rel_str(A)) | (lower_bounded_relstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B))))), ((rel_str(A) => (lower_bounded_relstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B)))) <=> ((~rel_str(A)) | (lower_bounded_relstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(174,plain,
% 0.21/0.47 (![A: $i] : (rel_str(A) => (lower_bounded_relstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B)))) <=> ![A: $i] : ((~rel_str(A)) | (lower_bounded_relstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[173])).
% 0.21/0.47 tff(175,axiom,(![A: $i] : (rel_str(A) => (lower_bounded_relstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_yellow_0')).
% 0.21/0.47 tff(176,plain,
% 0.21/0.47 (![A: $i] : ((~rel_str(A)) | (lower_bounded_relstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.21/0.47 tff(177,plain,
% 0.21/0.47 (![A: $i] : ((~rel_str(A)) | (lower_bounded_relstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.21/0.47 tff(178,plain,(
% 0.21/0.47 ![A: $i] : ((~rel_str(A)) | (((~lower_bounded_relstr(A)) | (element(tptp_fun_B_0(A), the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A)))) & (lower_bounded_relstr(A) | ![B: $i] : (~(element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B))))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[177])).
% 0.21/0.47 tff(179,plain,
% 0.21/0.47 (![A: $i] : ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[178, 171])).
% 0.21/0.47 tff(180,plain,
% 0.21/0.47 (![A: $i] : ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[179, 169])).
% 0.21/0.47 tff(181,plain,
% 0.21/0.47 (((~![A: $i] : ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B))))))))) | ((~rel_str(A!13)) | (~((~(lower_bounded_relstr(A!13) | ![B: $i] : ((~element(B, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), B))))) | (~((~lower_bounded_relstr(A!13)) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B))))))))) | (~rel_str(A!13)) | (~((~(lower_bounded_relstr(A!13) | ![B: $i] : ((~element(B, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), B))))) | (~((~lower_bounded_relstr(A!13)) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(182,plain,
% 0.21/0.47 (((~rel_str(A!13)) | (~((~((~lower_bounded_relstr(A!13)) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))))))) | (~(lower_bounded_relstr(A!13) | ![B: $i] : ((~element(B, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), B)))))))) <=> ((~rel_str(A!13)) | (~((~(lower_bounded_relstr(A!13) | ![B: $i] : ((~element(B, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), B))))) | (~((~lower_bounded_relstr(A!13)) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(183,plain,
% 0.21/0.47 (((~![A: $i] : ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B))))))))) | ((~rel_str(A!13)) | (~((~((~lower_bounded_relstr(A!13)) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))))))) | (~(lower_bounded_relstr(A!13) | ![B: $i] : ((~element(B, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), B))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B))))))))) | ((~rel_str(A!13)) | (~((~(lower_bounded_relstr(A!13) | ![B: $i] : ((~element(B, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), B))))) | (~((~lower_bounded_relstr(A!13)) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)))))))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[182])).
% 0.21/0.47 tff(184,plain,
% 0.21/0.47 (((~![A: $i] : ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B))))))))) | ((~rel_str(A!13)) | (~((~((~lower_bounded_relstr(A!13)) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))))))) | (~(lower_bounded_relstr(A!13) | ![B: $i] : ((~element(B, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), B))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B))))))))) | (~rel_str(A!13)) | (~((~(lower_bounded_relstr(A!13) | ![B: $i] : ((~element(B, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), B))))) | (~((~lower_bounded_relstr(A!13)) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[183, 181])).
% 0.21/0.47 tff(185,plain,
% 0.21/0.47 ((~![A: $i] : ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B))))))))) | ((~rel_str(A!13)) | (~((~((~lower_bounded_relstr(A!13)) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))))))) | (~(lower_bounded_relstr(A!13) | ![B: $i] : ((~element(B, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), B))))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(186,plain,
% 0.21/0.47 ((~![A: $i] : ((~rel_str(A)) | (~((~((~lower_bounded_relstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), tptp_fun_B_0(A))))))) | (~(lower_bounded_relstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~relstr_element_smaller(A, the_carrier(A), B))))))))) | (~rel_str(A!13)) | (~((~(lower_bounded_relstr(A!13) | ![B: $i] : ((~element(B, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), B))))) | (~((~lower_bounded_relstr(A!13)) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.21/0.47 tff(187,plain,
% 0.21/0.47 (~((~(lower_bounded_relstr(A!13) | ![B: $i] : ((~element(B, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), B))))) | (~((~lower_bounded_relstr(A!13)) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[186, 180, 10])).
% 0.21/0.47 tff(188,plain,
% 0.21/0.47 (((~(lower_bounded_relstr(A!13) | ![B: $i] : ((~element(B, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), B))))) | (~((~lower_bounded_relstr(A!13)) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)))))))) | ((~lower_bounded_relstr(A!13)) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(189,plain,
% 0.21/0.47 ((~lower_bounded_relstr(A!13)) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[188, 187])).
% 0.21/0.48 tff(190,plain,
% 0.21/0.48 (lower_bounded_relstr(A!13)),
% 0.21/0.48 inference(and_elim,[status(thm)],[9])).
% 0.21/0.48 tff(191,plain,
% 0.21/0.48 ((~((~lower_bounded_relstr(A!13)) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))))))) | (~lower_bounded_relstr(A!13)) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(192,plain,
% 0.21/0.48 ((~((~lower_bounded_relstr(A!13)) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))))))) | (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.21/0.48 tff(193,plain,
% 0.21/0.48 (~((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[192, 189])).
% 0.21/0.48 tff(194,plain,
% 0.21/0.48 (((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)))) | element(tptp_fun_B_0(A!13), the_carrier(A!13))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(195,plain,
% 0.21/0.48 (element(tptp_fun_B_0(A!13), the_carrier(A!13))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.21/0.48 tff(196,plain,
% 0.21/0.48 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(197,plain,
% 0.21/0.48 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[196])).
% 0.21/0.48 tff(198,plain,
% 0.21/0.48 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(199,plain,
% 0.21/0.48 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(200,plain,
% 0.21/0.48 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[199])).
% 0.21/0.48 tff(201,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 0.21/0.48 tff(202,plain,
% 0.21/0.48 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.21/0.48 tff(203,plain,
% 0.21/0.48 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.21/0.48 tff(204,plain,(
% 0.21/0.48 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[203])).
% 0.21/0.48 tff(205,plain,
% 0.21/0.48 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[204, 197])).
% 0.21/0.48 tff(206,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | empty(the_carrier(A!13)) | in(tptp_fun_B_0(A!13), the_carrier(A!13)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | empty(the_carrier(A!13)) | in(tptp_fun_B_0(A!13), the_carrier(A!13)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(207,plain,
% 0.21/0.48 ((empty(the_carrier(A!13)) | in(tptp_fun_B_0(A!13), the_carrier(A!13)) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13)))) <=> ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | empty(the_carrier(A!13)) | in(tptp_fun_B_0(A!13), the_carrier(A!13)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(208,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(A!13)) | in(tptp_fun_B_0(A!13), the_carrier(A!13)) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | empty(the_carrier(A!13)) | in(tptp_fun_B_0(A!13), the_carrier(A!13))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[207])).
% 0.21/0.48 tff(209,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(A!13)) | in(tptp_fun_B_0(A!13), the_carrier(A!13)) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | empty(the_carrier(A!13)) | in(tptp_fun_B_0(A!13), the_carrier(A!13)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[208, 206])).
% 0.21/0.48 tff(210,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(A!13)) | in(tptp_fun_B_0(A!13), the_carrier(A!13)) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(211,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | empty(the_carrier(A!13)) | in(tptp_fun_B_0(A!13), the_carrier(A!13))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.21/0.48 tff(212,plain,
% 0.21/0.48 (in(tptp_fun_B_0(A!13), the_carrier(A!13))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[211, 205, 195, 164])).
% 0.21/0.48 tff(213,plain,
% 0.21/0.48 (((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~in(tptp_fun_B_0(A!13), the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_B_0(A!13)))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D))) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~in(tptp_fun_B_0(A!13), the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_B_0(A!13)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(214,plain,
% 0.21/0.48 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~in(tptp_fun_B_0(A!13), the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_B_0(A!13)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(215,plain,
% 0.21/0.48 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D))) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~in(tptp_fun_B_0(A!13), the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_B_0(A!13))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.21/0.48 tff(216,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[215, 195, 212, 129, 127])).
% 0.21/0.48 tff(217,plain,(related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_B_0(A!13)) | (~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(218,plain,
% 0.21/0.48 (((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)))) | relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(219,plain,
% 0.21/0.48 (relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[218, 193])).
% 0.21/0.48 tff(220,plain,
% 0.21/0.48 (((~![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13))))))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | (~(related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_B_0(A!13)) | (~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13))))))) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | (~(related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_B_0(A!13)) | (~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(221,plain,
% 0.21/0.48 ((~![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13))))))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | (~(related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_B_0(A!13)) | (~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(222,plain,
% 0.21/0.48 ((~![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13))))))) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | (~(related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_B_0(A!13)) | (~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.21/0.48 tff(223,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[222, 195, 219, 217, 87])).
% 0.21/0.48 tff(224,plain,(~![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(225,plain,
% 0.21/0.48 ((~(ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13)))))))) | ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13))))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(226,plain,
% 0.21/0.48 ((~(ex_inf_of_relstr_set(A!13, the_carrier(A!13)) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13)))))))) | ex_inf_of_relstr_set(A!13, the_carrier(A!13))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[225, 224])).
% 0.21/0.48 tff(227,plain,
% 0.21/0.48 (ex_inf_of_relstr_set(A!13, the_carrier(A!13))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[226, 86])).
% 0.21/0.48 tff(228,plain,
% 0.21/0.48 ((~(~((~ex_sup_of_relstr_set(A!13, empty_set)) | (~ex_inf_of_relstr_set(A!13, the_carrier(A!13)))))) <=> ((~ex_sup_of_relstr_set(A!13, empty_set)) | (~ex_inf_of_relstr_set(A!13, the_carrier(A!13))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(229,plain,
% 0.21/0.48 ((ex_sup_of_relstr_set(A!13, empty_set) & ex_inf_of_relstr_set(A!13, the_carrier(A!13))) <=> (~((~ex_sup_of_relstr_set(A!13, empty_set)) | (~ex_inf_of_relstr_set(A!13, the_carrier(A!13)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(230,plain,
% 0.21/0.48 ((~(ex_sup_of_relstr_set(A!13, empty_set) & ex_inf_of_relstr_set(A!13, the_carrier(A!13)))) <=> (~(~((~ex_sup_of_relstr_set(A!13, empty_set)) | (~ex_inf_of_relstr_set(A!13, the_carrier(A!13))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[229])).
% 0.21/0.48 tff(231,plain,
% 0.21/0.48 ((~(ex_sup_of_relstr_set(A!13, empty_set) & ex_inf_of_relstr_set(A!13, the_carrier(A!13)))) <=> ((~ex_sup_of_relstr_set(A!13, empty_set)) | (~ex_inf_of_relstr_set(A!13, the_carrier(A!13))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[230, 228])).
% 0.21/0.48 tff(232,plain,
% 0.21/0.48 (~(ex_sup_of_relstr_set(A!13, empty_set) & ex_inf_of_relstr_set(A!13, the_carrier(A!13)))),
% 0.21/0.48 inference(or_elim,[status(thm)],[8])).
% 0.21/0.48 tff(233,plain,
% 0.21/0.48 ((~ex_sup_of_relstr_set(A!13, empty_set)) | (~ex_inf_of_relstr_set(A!13, the_carrier(A!13)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.21/0.48 tff(234,plain,
% 0.21/0.48 (~ex_sup_of_relstr_set(A!13, empty_set)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[233, 227])).
% 0.21/0.48 tff(235,plain,
% 0.21/0.48 ((~(ex_sup_of_relstr_set(A!13, empty_set) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13)))))))) | ex_sup_of_relstr_set(A!13, empty_set) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13))))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(236,plain,
% 0.21/0.48 ((~(ex_sup_of_relstr_set(A!13, empty_set) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13)))))))) | ![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[235, 234])).
% 0.21/0.48 tff(237,plain,
% 0.21/0.48 (![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[236, 45])).
% 0.21/0.48 tff(238,plain,
% 0.21/0.48 (^[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)))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(239,plain,
% 0.21/0.48 (![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))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[238])).
% 0.21/0.48 tff(240,plain,
% 0.21/0.48 (^[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)))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(241,plain,
% 0.21/0.48 (![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))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[240])).
% 0.21/0.48 tff(242,plain,
% 0.21/0.48 (![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))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[241, 239])).
% 0.21/0.49 tff(243,plain,
% 0.21/0.49 (^[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)))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(244,plain,
% 0.21/0.49 (![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))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[243])).
% 0.21/0.49 tff(245,plain,
% 0.21/0.49 (![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))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(246,plain,
% 0.21/0.49 (^[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))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(247,plain,
% 0.21/0.49 (![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))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[246])).
% 0.21/0.49 tff(248,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')).
% 0.21/0.49 tff(249,plain,
% 0.21/0.49 (![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))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.21/0.49 tff(250,plain,
% 0.21/0.49 (![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))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[249, 245])).
% 0.21/0.49 tff(251,plain,(
% 0.21/0.49 ![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))))),
% 0.21/0.49 inference(skolemize,[status(sab)],[250])).
% 0.21/0.49 tff(252,plain,
% 0.21/0.49 (![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))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[251, 244])).
% 0.21/0.49 tff(253,plain,
% 0.21/0.49 (![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))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[252, 242])).
% 0.21/0.49 tff(254,plain,
% 0.21/0.49 (((~![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!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | (~((~relstr_set_smaller(A!13, empty_set, B)) | (~relstr_element_smaller(A!13, 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!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | (~((~relstr_set_smaller(A!13, empty_set, B)) | (~relstr_element_smaller(A!13, empty_set, B))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(255,plain,
% 0.21/0.49 ((~![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!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | (~((~relstr_set_smaller(A!13, empty_set, B)) | (~relstr_element_smaller(A!13, empty_set, B))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(256,plain,
% 0.21/0.49 ((~![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!13)) | ![B: $i] : ((~element(B, the_carrier(A!13))) | (~((~relstr_set_smaller(A!13, empty_set, B)) | (~relstr_element_smaller(A!13, empty_set, B)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.21/0.49 tff(257,plain,
% 0.21/0.49 (![B: $i] : ((~element(B, the_carrier(A!13))) | (~((~relstr_set_smaller(A!13, empty_set, B)) | (~relstr_element_smaller(A!13, empty_set, B)))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[256, 10, 253])).
% 0.21/0.49 tff(258,plain,
% 0.21/0.49 (((~![B: $i] : ((~element(B, the_carrier(A!13))) | (~((~relstr_set_smaller(A!13, empty_set, B)) | (~relstr_element_smaller(A!13, empty_set, B)))))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~((~relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))) | (~relstr_element_smaller(A!13, empty_set, tptp_fun_B_0(A!13))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!13))) | (~((~relstr_set_smaller(A!13, empty_set, B)) | (~relstr_element_smaller(A!13, empty_set, B)))))) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~((~relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))) | (~relstr_element_smaller(A!13, empty_set, tptp_fun_B_0(A!13))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(259,plain,
% 0.21/0.49 ((~![B: $i] : ((~element(B, the_carrier(A!13))) | (~((~relstr_set_smaller(A!13, empty_set, B)) | (~relstr_element_smaller(A!13, empty_set, B)))))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~((~relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))) | (~relstr_element_smaller(A!13, empty_set, tptp_fun_B_0(A!13))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(260,plain,
% 0.21/0.49 ((~![B: $i] : ((~element(B, the_carrier(A!13))) | (~((~relstr_set_smaller(A!13, empty_set, B)) | (~relstr_element_smaller(A!13, empty_set, B)))))) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~((~relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))) | (~relstr_element_smaller(A!13, empty_set, tptp_fun_B_0(A!13)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.21/0.49 tff(261,plain,
% 0.21/0.49 (~((~relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))) | (~relstr_element_smaller(A!13, empty_set, tptp_fun_B_0(A!13))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[260, 257, 195])).
% 0.21/0.49 tff(262,plain,
% 0.21/0.49 (((~relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))) | (~relstr_element_smaller(A!13, empty_set, tptp_fun_B_0(A!13)))) | relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(263,plain,
% 0.21/0.49 (relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[262, 261])).
% 0.21/0.49 tff(264,plain,
% 0.21/0.49 (((~![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13))))))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))) | (~((~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13))))))) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))) | (~((~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(265,plain,
% 0.21/0.49 (((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))) | (~(related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)) | (~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)))))) <=> ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))) | (~((~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(266,plain,
% 0.21/0.49 (((~![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13))))))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))) | (~(related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)) | (~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13))))))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))) | (~((~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[265])).
% 0.21/0.49 tff(267,plain,
% 0.21/0.49 (((~![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13))))))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))) | (~(related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)) | (~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13))))))) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))) | (~((~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[266, 264])).
% 0.21/0.49 tff(268,plain,
% 0.21/0.49 ((~![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13))))))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))) | (~(related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)) | (~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(269,plain,
% 0.21/0.49 ((~![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, C)) | (~(related(A!13, C, tptp_fun_D_10(C, empty_set, A!13)) | (~element(tptp_fun_D_10(C, empty_set, A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(C, empty_set, A!13))))))) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))) | (~((~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.21/0.49 tff(270,plain,
% 0.21/0.49 (~((~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[269, 195, 263, 237])).
% 0.21/0.49 tff(271,plain,
% 0.21/0.49 (((~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)))) | (~related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(272,plain,
% 0.21/0.49 (~related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[271, 270])).
% 0.21/0.49 tff(273,plain,
% 0.21/0.49 (((~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)) | (~relstr_set_smaller(A!13, empty_set, tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)))) | element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(274,plain,
% 0.21/0.49 (element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[273, 270])).
% 0.21/0.49 tff(275,plain,
% 0.21/0.49 (((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13)))))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)))))))))) <=> ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13)))))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)))))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(276,plain,
% 0.21/0.50 (((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | ![D: $i] : ((~in(D, the_carrier(A!13))) | (~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))))))))) <=> ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13)))))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)))))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(277,plain,
% 0.21/0.50 (((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | ![D: $i] : ((~in(D, the_carrier(A!13))) | (~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)))))))))) <=> ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13)))))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))))))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[276])).
% 0.21/0.50 tff(278,plain,
% 0.21/0.50 (((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | ![D: $i] : ((~in(D, the_carrier(A!13))) | (~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)))))))))) <=> ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13)))))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)))))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[277, 275])).
% 0.21/0.50 tff(279,plain,
% 0.21/0.50 ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))) | ((~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | ![D: $i] : ((~in(D, the_carrier(A!13))) | (~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)))))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(280,plain,
% 0.21/0.50 ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!13))) | related(A!13, C, D)))) | (~(relstr_element_smaller(A!13, B, C) | (~((~element(tptp_fun_D_1(C, B, A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(C, B, A!13), B)) | related(A!13, C, tptp_fun_D_1(C, B, A!13)))))))))) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13)))))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.21/0.50 tff(281,plain,
% 0.21/0.50 (~((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13)))))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[280, 195, 113])).
% 0.21/0.50 tff(282,plain,
% 0.21/0.50 (((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13)))))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13)) | (~((~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13))))))) | ((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13)))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(283,plain,
% 0.21/0.50 ((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[282, 281])).
% 0.21/0.50 tff(284,plain,
% 0.21/0.50 ((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13)))))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(285,plain,
% 0.21/0.50 ((~((~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13)))))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[284, 219])).
% 0.21/0.50 tff(286,plain,
% 0.21/0.50 (![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[285, 283])).
% 0.21/0.50 tff(287,plain,
% 0.21/0.50 (((~![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13))))) | ((~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)) | (~in(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13))))) | (~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)) | (~in(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(288,plain,
% 0.21/0.50 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13))))) | ((~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)) | (~in(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(289,plain,
% 0.21/0.50 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D) | (~in(D, the_carrier(A!13))))) | (~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)) | (~in(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.21/0.50 tff(290,plain,
% 0.21/0.50 (~in(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[289, 286, 274, 272])).
% 0.21/0.50 tff(291,plain,
% 0.21/0.50 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(A!13)) | (~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | in(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(the_carrier(A!13)) | (~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | in(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(292,plain,
% 0.21/0.50 ((empty(the_carrier(A!13)) | in(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13)) | (~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13)))) <=> (empty(the_carrier(A!13)) | (~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | in(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(293,plain,
% 0.21/0.50 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(A!13)) | in(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13)) | (~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(A!13)) | (~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | in(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[292])).
% 0.21/0.50 tff(294,plain,
% 0.21/0.50 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(A!13)) | in(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13)) | (~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(the_carrier(A!13)) | (~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | in(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[293, 291])).
% 0.21/0.50 tff(295,plain,
% 0.21/0.50 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(A!13)) | in(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13)) | (~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(296,plain,
% 0.21/0.50 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(the_carrier(A!13)) | (~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))) | in(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.21/0.50 tff(297,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[296, 205, 164, 274, 290])).
% 0.21/0.50 % SZS output end Proof
% 0.21/0.50 % E exiting
%------------------------------------------------------------------------------