TSTP Solution File: SEU360+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU360+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 : Tue Sep 20 07:29:07 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU360+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n025.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 : Sat Sep 3 12:45:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(in_type, type, (
% 0.19/0.39 in: ( $i * $i ) > $o)).
% 0.19/0.39 tff(the_carrier_type, type, (
% 0.19/0.39 the_carrier: $i > $i)).
% 0.19/0.39 tff(tptp_fun_A_13_type, type, (
% 0.19/0.39 tptp_fun_A_13: $i)).
% 0.19/0.39 tff(tptp_fun_D_10_type, type, (
% 0.19/0.39 tptp_fun_D_10: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(empty_set_type, type, (
% 0.19/0.39 empty_set: $i)).
% 0.19/0.39 tff(tptp_fun_B_0_type, type, (
% 0.19/0.39 tptp_fun_B_0: $i > $i)).
% 0.19/0.39 tff(element_type, type, (
% 0.19/0.39 element: ( $i * $i ) > $o)).
% 0.19/0.39 tff(relstr_set_smaller_type, type, (
% 0.19/0.39 relstr_set_smaller: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(related_type, type, (
% 0.19/0.39 related: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(ex_sup_of_relstr_set_type, type, (
% 0.19/0.39 ex_sup_of_relstr_set: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_C_9_type, type, (
% 0.19/0.39 tptp_fun_C_9: ( $i * $i ) > $i)).
% 0.19/0.39 tff(rel_str_type, type, (
% 0.19/0.39 rel_str: $i > $o)).
% 0.19/0.39 tff(lower_bounded_relstr_type, type, (
% 0.19/0.39 lower_bounded_relstr: $i > $o)).
% 0.19/0.39 tff(antisymmetric_relstr_type, type, (
% 0.19/0.39 antisymmetric_relstr: $i > $o)).
% 0.19/0.39 tff(empty_carrier_type, type, (
% 0.19/0.39 empty_carrier: $i > $o)).
% 0.19/0.39 tff(ex_inf_of_relstr_set_type, type, (
% 0.19/0.39 ex_inf_of_relstr_set: ( $i * $i ) > $o)).
% 0.19/0.39 tff(relstr_element_smaller_type, type, (
% 0.19/0.39 relstr_element_smaller: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_D_12_type, type, (
% 0.19/0.39 tptp_fun_D_12: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_C_11_type, type, (
% 0.19/0.39 tptp_fun_C_11: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_D_1_type, type, (
% 0.19/0.39 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(empty_type, type, (
% 0.19/0.39 empty: $i > $o)).
% 0.19/0.39 tff(one_sorted_str_type, type, (
% 0.19/0.39 one_sorted_str: $i > $o)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 ((~![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)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 ((~![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)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 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/sandbox2/benchmark/theBenchmark.p','t42_yellow_0')).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (~![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))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (~![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))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (~![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))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (~![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))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (~![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))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (~![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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (~![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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.19/0.40 tff(11,plain,(
% 0.19/0.40 ~((~((~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))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[10])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 ((~empty_carrier(A!13)) & antisymmetric_relstr(A!13) & lower_bounded_relstr(A!13) & rel_str(A!13)),
% 0.19/0.40 inference(or_elim,[status(thm)],[11])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (rel_str(A!13)),
% 0.19/0.40 inference(and_elim,[status(thm)],[12])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (antisymmetric_relstr(A!13)),
% 0.19/0.40 inference(and_elim,[status(thm)],[12])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (^[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))))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (![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))))))))))) <=> ![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)))))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (^[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))))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (![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))))))))))) <=> ![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)))))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![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))))))))))) <=> ![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)))))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[18, 16])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (^[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)))))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (![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)))))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (^[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))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (![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)))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (^[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))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.40 tff(27,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/sandbox2/benchmark/theBenchmark.p','t15_yellow_0')).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.40 tff(30,plain,(
% 0.19/0.40 ![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)))))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[29])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (![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)))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (![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)))))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (![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)))))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[32, 19])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (((~![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)) | (~((~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)))))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 ((~![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)))))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 ((~![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))))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (![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))))))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[36, 33, 14, 13])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (((~![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))))))))))) | (~((~(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)))))))))) <=> ((~![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))))))))))) | (~((~(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))))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 ((~((~((~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))) | related(A!13, tptp_fun_C_9(empty_set, A!13), D) | (~relstr_set_smaller(A!13, empty_set, 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) | ![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)))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (((~![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))))))))))) | (~((~((~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))) | related(A!13, tptp_fun_C_9(empty_set, A!13), D) | (~relstr_set_smaller(A!13, empty_set, 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))))))))))) <=> ((~![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))))))))))) | (~((~(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))))))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[39])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (((~![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))))))))))) | (~((~((~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))) | related(A!13, tptp_fun_C_9(empty_set, A!13), D) | (~relstr_set_smaller(A!13, empty_set, 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))))))))))) <=> ((~![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))))))))))) | (~((~(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))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[40, 38])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 ((~![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))))))))))) | (~((~((~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))) | related(A!13, tptp_fun_C_9(empty_set, A!13), D) | (~relstr_set_smaller(A!13, empty_set, 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))))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 ((~![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))))))))))) | (~((~(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)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 (~((~(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))))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[43, 37])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 (((~(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)))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (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))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.19/0.42 tff(47,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)).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (^[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))))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (![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))))))))))) <=> ![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)))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 (^[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))))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 (![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))))))))))) <=> ![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)))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 (![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))))))))))) <=> ![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)))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[51, 49])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (^[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)))))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (![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))))))))) <=> ![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)))))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 (^[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))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 (![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)))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 (![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))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 (^[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))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 (![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))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.43 tff(60,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/sandbox2/benchmark/theBenchmark.p','t16_yellow_0')).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (![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))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 (![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))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.19/0.43 tff(63,plain,(
% 0.19/0.43 ![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)))))))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[62])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 (![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)))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 (![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)))))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 (![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)))))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[65, 52])).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 (((~![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)) | (~((~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)))))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 ((~![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)))))))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 ((~![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))))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 (![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))))))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[69, 66, 14, 13])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.44 ((~![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))))))))))) | (~((~((~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: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13))))))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[71, 70, 47])).
% 0.19/0.44 tff(73,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,[]))).
% 0.19/0.44 tff(74,plain,
% 0.19/0.44 (((~((~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)))))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 (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))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.44 tff(76,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)).
% 0.19/0.44 tff(77,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)).
% 0.19/0.44 tff(78,plain,
% 0.19/0.44 ((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))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 (element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.19/0.44 tff(80,plain,
% 0.19/0.44 (^[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))))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 (![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)))))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 (^[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))))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(83,plain,
% 0.19/0.44 (![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)))))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 (![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)))))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[83, 81])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 (^[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))))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 (![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)))))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.44 tff(87,plain,
% 0.19/0.44 (![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)))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(88,plain,
% 0.19/0.44 (^[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)))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(89,plain,
% 0.19/0.44 (![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)))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.44 tff(90,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/sandbox2/benchmark/theBenchmark.p','d8_lattice3')).
% 0.19/0.44 tff(91,plain,
% 0.19/0.44 (![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)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.44 tff(92,plain,
% 0.19/0.44 (![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)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.19/0.44 tff(93,plain,(
% 0.19/0.44 ![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)))))))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[92])).
% 0.19/0.44 tff(94,plain,
% 0.19/0.44 (![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)))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.19/0.44 tff(95,plain,
% 0.19/0.44 (![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)))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[94, 84])).
% 0.19/0.44 tff(96,plain,
% 0.19/0.44 (((~![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)))))))))))) | ((~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) | (~(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) | (~(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)))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(97,plain,
% 0.19/0.44 (((~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) | (~(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)))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(98,plain,
% 0.19/0.44 (((~![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)))))))))))) | ((~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) | (~(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))))))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[97])).
% 0.19/0.45 tff(99,plain,
% 0.19/0.45 (((~![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) | (~(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)))))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[98, 96])).
% 0.19/0.45 tff(100,plain,
% 0.19/0.45 ((~![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)))))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(101,plain,
% 0.19/0.45 ((~![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) | (~(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))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.45 tff(102,plain,
% 0.19/0.45 (![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) | (~(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))))))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[101, 95, 13])).
% 0.19/0.45 tff(103,plain,
% 0.19/0.45 (((~![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) | (~(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))))))))))) | ((~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)) | (~(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)) | (~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))) | (~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))))))))))) <=> ((~![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) | (~(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))))))))))) | (~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)) | (~(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)) | (~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))) | (~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))))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(104,plain,
% 0.19/0.45 (((~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)) | (~(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)) | (~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))) | (~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)))))))))) <=> ((~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)) | (~(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)) | (~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))) | (~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))))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(105,plain,
% 0.19/0.45 (((~![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) | (~(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))))))))))) | ((~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)) | (~(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)) | (~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))) | (~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))))))))))) <=> ((~![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) | (~(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))))))))))) | ((~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)) | (~(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)) | (~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))) | (~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)))))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[104])).
% 0.19/0.45 tff(106,plain,
% 0.19/0.45 (((~![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) | (~(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))))))))))) | ((~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)) | (~(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)) | (~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))) | (~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))))))))))) <=> ((~![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) | (~(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))))))))))) | (~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)) | (~(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)) | (~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))) | (~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))))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[105, 103])).
% 0.19/0.46 tff(107,plain,
% 0.19/0.46 ((~![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) | (~(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))))))))))) | ((~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)) | (~(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)) | (~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))) | (~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))))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(108,plain,
% 0.19/0.46 ((~![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) | (~(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))))))))))) | (~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)) | (~(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)) | (~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))) | (~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)))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.46 tff(109,plain,
% 0.19/0.46 (~((~((~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)) | (~(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)) | (~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))) | (~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))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[108, 102, 79])).
% 0.19/0.46 tff(110,plain,
% 0.19/0.46 (((~((~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)) | (~(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)) | (~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))) | (~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)))))))) | ((~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)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(111,plain,
% 0.19/0.46 ((~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))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.19/0.46 tff(112,plain,
% 0.19/0.46 ((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))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(113,plain,
% 0.19/0.46 (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))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[112, 77])).
% 0.19/0.46 tff(114,plain,
% 0.19/0.46 ((~((~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))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(115,plain,
% 0.19/0.46 ((~((~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))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.19/0.46 tff(116,plain,
% 0.19/0.46 (![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))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[115, 111])).
% 0.19/0.46 tff(117,plain,
% 0.19/0.46 ((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)))) | (~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)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(118,plain,
% 0.19/0.46 (~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))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[117, 77])).
% 0.19/0.46 tff(119,plain,
% 0.19/0.46 (^[A: $i] : refl((one_sorted_str(A) | (~rel_str(A))) <=> (one_sorted_str(A) | (~rel_str(A))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(120,plain,
% 0.19/0.46 (![A: $i] : (one_sorted_str(A) | (~rel_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[119])).
% 0.19/0.46 tff(121,plain,
% 0.19/0.46 (![A: $i] : (one_sorted_str(A) | (~rel_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(122,plain,
% 0.19/0.46 (^[A: $i] : rewrite((rel_str(A) => one_sorted_str(A)) <=> (one_sorted_str(A) | (~rel_str(A))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(123,plain,
% 0.19/0.46 (![A: $i] : (rel_str(A) => one_sorted_str(A)) <=> ![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[122])).
% 0.19/0.46 tff(124,axiom,(![A: $i] : (rel_str(A) => one_sorted_str(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_orders_2')).
% 0.19/0.46 tff(125,plain,
% 0.19/0.46 (![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.46 tff(126,plain,
% 0.19/0.46 (![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.19/0.46 tff(127,plain,(
% 0.19/0.46 ![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[126])).
% 0.19/0.46 tff(128,plain,
% 0.19/0.46 (![A: $i] : (one_sorted_str(A) | (~rel_str(A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.19/0.46 tff(129,plain,
% 0.19/0.46 (((~![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)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(130,plain,
% 0.19/0.46 ((~![A: $i] : (one_sorted_str(A) | (~rel_str(A)))) | (one_sorted_str(A!13) | (~rel_str(A!13)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(131,plain,
% 0.19/0.46 ((~![A: $i] : (one_sorted_str(A) | (~rel_str(A)))) | one_sorted_str(A!13) | (~rel_str(A!13))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.19/0.46 tff(132,plain,
% 0.19/0.46 (one_sorted_str(A!13)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[131, 128, 13])).
% 0.19/0.46 tff(133,plain,
% 0.19/0.46 (~empty_carrier(A!13)),
% 0.19/0.46 inference(and_elim,[status(thm)],[12])).
% 0.19/0.46 tff(134,plain,
% 0.19/0.46 (^[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))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(135,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[134])).
% 0.19/0.46 tff(136,plain,
% 0.19/0.46 (^[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)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(137,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[136])).
% 0.19/0.46 tff(138,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(139,plain,
% 0.19/0.46 (^[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)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(140,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[139])).
% 0.19/0.46 tff(141,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.19/0.46 tff(142,plain,
% 0.19/0.46 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.19/0.46 tff(143,plain,
% 0.19/0.46 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.19/0.46 tff(144,plain,(
% 0.19/0.46 ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[143])).
% 0.19/0.46 tff(145,plain,
% 0.19/0.46 (![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[144, 137])).
% 0.19/0.46 tff(146,plain,
% 0.19/0.46 (![A: $i] : ((~empty(the_carrier(A))) | empty_carrier(A) | (~one_sorted_str(A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[145, 135])).
% 0.19/0.46 tff(147,plain,
% 0.19/0.46 (((~![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)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(148,plain,
% 0.19/0.46 (((~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)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(149,plain,
% 0.19/0.46 (((~![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))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[148])).
% 0.19/0.46 tff(150,plain,
% 0.19/0.46 (((~![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)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[149, 147])).
% 0.19/0.46 tff(151,plain,
% 0.19/0.46 ((~![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)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(152,plain,
% 0.19/0.46 ((~![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))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.19/0.46 tff(153,plain,
% 0.19/0.46 (~empty(the_carrier(A!13))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[152, 146, 133, 132])).
% 0.19/0.46 tff(154,plain,
% 0.19/0.46 (^[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)))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(155,plain,
% 0.19/0.46 (![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))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[154])).
% 0.19/0.46 tff(156,plain,
% 0.19/0.46 (^[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)))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(157,plain,
% 0.19/0.46 (![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))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[156])).
% 0.19/0.46 tff(158,plain,
% 0.19/0.46 (![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))))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[157, 155])).
% 0.19/0.47 tff(159,plain,
% 0.19/0.47 (^[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)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(160,plain,
% 0.19/0.47 (![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))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[159])).
% 0.19/0.47 tff(161,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(162,plain,
% 0.19/0.47 (^[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))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(163,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[162])).
% 0.19/0.47 tff(164,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/sandbox2/benchmark/theBenchmark.p','d4_yellow_0')).
% 0.19/0.47 tff(165,plain,
% 0.19/0.47 (![A: $i] : ((~rel_str(A)) | (lower_bounded_relstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.19/0.47 tff(166,plain,
% 0.19/0.47 (![A: $i] : ((~rel_str(A)) | (lower_bounded_relstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & relstr_element_smaller(A, the_carrier(A), B))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[165, 161])).
% 0.19/0.47 tff(167,plain,(
% 0.19/0.47 ![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))))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[166])).
% 0.19/0.47 tff(168,plain,
% 0.19/0.47 (![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))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[167, 160])).
% 0.19/0.47 tff(169,plain,
% 0.19/0.47 (![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))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[168, 158])).
% 0.19/0.47 tff(170,plain,
% 0.19/0.47 (((~![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)) | (~((~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))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(171,plain,
% 0.19/0.47 ((~![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))))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(172,plain,
% 0.19/0.47 ((~![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)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.19/0.47 tff(173,plain,
% 0.19/0.47 (~((~((~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))))))) | (~(lower_bounded_relstr(A!13) | ![B: $i] : ((~element(B, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), B))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[172, 169, 13])).
% 0.19/0.47 tff(174,plain,
% 0.19/0.47 (((~((~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))))))) | (~(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))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(175,plain,
% 0.19/0.47 ((~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)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.19/0.47 tff(176,plain,
% 0.19/0.47 (lower_bounded_relstr(A!13)),
% 0.19/0.47 inference(and_elim,[status(thm)],[12])).
% 0.19/0.47 tff(177,plain,
% 0.19/0.47 ((~((~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))))))) | (~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)))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(178,plain,
% 0.19/0.47 ((~((~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))))))) | (~((~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)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.19/0.47 tff(179,plain,
% 0.19/0.47 (~((~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))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[178, 175])).
% 0.19/0.47 tff(180,plain,
% 0.19/0.47 (((~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))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(181,plain,
% 0.19/0.47 (element(tptp_fun_B_0(A!13), the_carrier(A!13))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.19/0.47 tff(182,plain,
% 0.19/0.47 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(183,plain,
% 0.19/0.47 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[182])).
% 0.19/0.47 tff(184,plain,
% 0.19/0.47 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(185,plain,
% 0.19/0.47 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(186,plain,
% 0.19/0.47 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[185])).
% 0.19/0.47 tff(187,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_subset')).
% 0.19/0.47 tff(188,plain,
% 0.19/0.47 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.47 tff(189,plain,
% 0.19/0.47 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[188, 184])).
% 0.19/0.47 tff(190,plain,(
% 0.19/0.47 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[189])).
% 0.19/0.47 tff(191,plain,
% 0.19/0.47 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[190, 183])).
% 0.19/0.47 tff(192,plain,
% 0.19/0.47 (((~![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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(193,plain,
% 0.19/0.47 ((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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(194,plain,
% 0.19/0.47 (((~![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))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[193])).
% 0.19/0.47 tff(195,plain,
% 0.19/0.47 (((~![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)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[194, 192])).
% 0.19/0.47 tff(196,plain,
% 0.19/0.47 ((~![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))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(197,plain,
% 0.19/0.47 ((~![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))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.19/0.47 tff(198,plain,
% 0.19/0.47 (in(tptp_fun_B_0(A!13), the_carrier(A!13))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[197, 191, 181, 153])).
% 0.19/0.47 tff(199,plain,
% 0.19/0.47 (((~![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))) | ((~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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(200,plain,
% 0.19/0.47 ((~![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))) | ((~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)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(201,plain,
% 0.19/0.47 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), D))) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~in(tptp_fun_B_0(A!13), the_carrier(A!13))) | related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_B_0(A!13))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.19/0.47 tff(202,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[201, 181, 198, 118, 116])).
% 0.19/0.48 tff(203,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,[]))).
% 0.19/0.48 tff(204,plain,
% 0.19/0.48 (((~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))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(205,plain,
% 0.19/0.48 (relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[204, 179])).
% 0.19/0.48 tff(206,plain,
% 0.19/0.48 (((~![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))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(207,plain,
% 0.19/0.48 ((~![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))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(208,plain,
% 0.19/0.48 ((~![C: $i] : ((~element(C, the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), C)) | (~(related(A!13, tptp_fun_D_12(C, the_carrier(A!13), A!13), C) | (~element(tptp_fun_D_12(C, the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(C, the_carrier(A!13), A!13))))))) | (~element(tptp_fun_B_0(A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(A!13))) | (~(related(A!13, tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), tptp_fun_B_0(A!13)) | (~element(tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_D_12(tptp_fun_B_0(A!13), the_carrier(A!13), A!13)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.19/0.48 tff(209,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[208, 181, 205, 203, 76])).
% 0.19/0.48 tff(210,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,[]))).
% 0.19/0.48 tff(211,plain,
% 0.19/0.48 ((~(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))))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(212,plain,
% 0.19/0.48 ((~(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))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.19/0.48 tff(213,plain,
% 0.19/0.48 (ex_inf_of_relstr_set(A!13, the_carrier(A!13))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[212, 75])).
% 0.19/0.48 tff(214,plain,
% 0.19/0.48 ((~(~((~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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(215,plain,
% 0.19/0.48 ((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)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(216,plain,
% 0.19/0.48 ((~(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))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[215])).
% 0.19/0.48 tff(217,plain,
% 0.19/0.48 ((~(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))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[216, 214])).
% 0.19/0.48 tff(218,plain,
% 0.19/0.48 (~(ex_sup_of_relstr_set(A!13, empty_set) & ex_inf_of_relstr_set(A!13, the_carrier(A!13)))),
% 0.19/0.48 inference(or_elim,[status(thm)],[11])).
% 0.19/0.48 tff(219,plain,
% 0.19/0.48 ((~ex_sup_of_relstr_set(A!13, empty_set)) | (~ex_inf_of_relstr_set(A!13, the_carrier(A!13)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.19/0.48 tff(220,plain,
% 0.19/0.48 (~ex_sup_of_relstr_set(A!13, empty_set)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[219, 213])).
% 0.19/0.48 tff(221,plain,
% 0.19/0.48 ((~(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))))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(222,plain,
% 0.19/0.48 ((~(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))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.19/0.48 tff(223,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[222, 46])).
% 0.19/0.48 tff(224,plain,
% 0.19/0.48 (^[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)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(225,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[224])).
% 0.19/0.48 tff(226,plain,
% 0.19/0.48 (^[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)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(227,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[226])).
% 0.19/0.48 tff(228,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[227, 225])).
% 0.19/0.48 tff(229,plain,
% 0.19/0.48 (^[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)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(230,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[229])).
% 0.19/0.48 tff(231,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(232,plain,
% 0.19/0.48 (^[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))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(233,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[232])).
% 0.19/0.48 tff(234,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/sandbox2/benchmark/theBenchmark.p','t6_yellow_0')).
% 0.19/0.48 tff(235,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.19/0.48 tff(236,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[235, 231])).
% 0.19/0.48 tff(237,plain,(
% 0.19/0.48 ![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))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[236])).
% 0.19/0.48 tff(238,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[237, 230])).
% 0.19/0.48 tff(239,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[238, 228])).
% 0.19/0.48 tff(240,plain,
% 0.19/0.48 (((~![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))))))) | ((~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))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(241,plain,
% 0.19/0.48 ((~![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))))))) | ((~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))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(242,plain,
% 0.19/0.48 ((~![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))))))) | (~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)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.19/0.48 tff(243,plain,
% 0.19/0.48 (![B: $i] : ((~element(B, the_carrier(A!13))) | (~((~relstr_set_smaller(A!13, empty_set, B)) | (~relstr_element_smaller(A!13, empty_set, B)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[242, 13, 239])).
% 0.19/0.48 tff(244,plain,
% 0.19/0.48 (((~![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))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(245,plain,
% 0.19/0.48 ((~![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))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(246,plain,
% 0.19/0.48 ((~![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)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.19/0.48 tff(247,plain,
% 0.19/0.48 (~((~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))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[246, 243, 181])).
% 0.19/0.48 tff(248,plain,
% 0.19/0.48 (((~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))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(249,plain,
% 0.19/0.48 (relstr_set_smaller(A!13, empty_set, tptp_fun_B_0(A!13))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[248, 247])).
% 0.19/0.48 tff(250,plain,
% 0.19/0.48 (((~![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))))))) | ((~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))) | (~(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))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(251,plain,
% 0.19/0.48 ((~![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))))))) | ((~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))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(252,plain,
% 0.19/0.48 ((~![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))))))) | (~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)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.19/0.48 tff(253,plain,
% 0.19/0.48 (~(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))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[252, 181, 249, 223])).
% 0.19/0.48 tff(254,plain,
% 0.19/0.48 ((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_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(255,plain,
% 0.19/0.48 (element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[254, 253])).
% 0.19/0.48 tff(256,plain,
% 0.19/0.48 ((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)))) | (~related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(257,plain,
% 0.19/0.48 (~related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[256, 253])).
% 0.19/0.48 tff(258,plain,
% 0.19/0.48 (((~![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) | (~(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))))))))))) | ((~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))) | (~in(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)) | (~(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)) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(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) | (~(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))))))))))) | (~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))) | (~in(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)) | (~(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)) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(259,plain,
% 0.19/0.49 (((~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)) | (~(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)) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(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))) | (~in(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)) | (~(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)) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(260,plain,
% 0.19/0.49 (((~![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) | (~(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))))))))))) | ((~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)) | (~(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)) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(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) | (~(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))))))))))) | ((~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))) | (~in(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)) | (~(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)) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13)))))))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[259])).
% 0.19/0.49 tff(261,plain,
% 0.19/0.49 (((~![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) | (~(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))))))))))) | ((~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)) | (~(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)) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(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) | (~(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))))))))))) | (~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))) | (~in(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)) | (~(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)) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[260, 258])).
% 0.19/0.49 tff(262,plain,
% 0.19/0.49 ((~![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) | (~(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))))))))))) | ((~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)) | (~(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)) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(263,plain,
% 0.19/0.49 ((~![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) | (~(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))))))))))) | (~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))) | (~in(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)) | (~(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)) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13)))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.19/0.49 tff(264,plain,
% 0.19/0.49 (~((~((~relstr_element_smaller(A!13, the_carrier(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_B_0(A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(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)) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~element(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[263, 181, 102])).
% 0.19/0.49 tff(265,plain,
% 0.19/0.49 (((~((~relstr_element_smaller(A!13, the_carrier(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_B_0(A!13), D)))) | (~(relstr_element_smaller(A!13, the_carrier(A!13), tptp_fun_B_0(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)) | (~in(tptp_fun_D_1(tptp_fun_B_0(A!13), the_carrier(A!13), A!13), the_carrier(A!13))) | (~element(tptp_fun_D_1(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_B_0(A!13))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(266,plain,
% 0.19/0.49 ((~relstr_element_smaller(A!13, the_carrier(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_B_0(A!13), D))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[265, 264])).
% 0.19/0.49 tff(267,plain,
% 0.19/0.49 ((~((~relstr_element_smaller(A!13, the_carrier(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_B_0(A!13), D)))) | (~relstr_element_smaller(A!13, the_carrier(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_B_0(A!13), D))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(268,plain,
% 0.19/0.49 ((~((~relstr_element_smaller(A!13, the_carrier(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_B_0(A!13), D)))) | ![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[267, 205])).
% 0.19/0.49 tff(269,plain,
% 0.19/0.49 (![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[268, 266])).
% 0.19/0.49 tff(270,plain,
% 0.19/0.49 (((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D))) | ((~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))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D))) | (~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))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(271,plain,
% 0.19/0.49 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D))) | ((~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))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(272,plain,
% 0.19/0.49 ((~![D: $i] : ((~element(D, the_carrier(A!13))) | (~in(D, the_carrier(A!13))) | related(A!13, tptp_fun_B_0(A!13), D))) | (~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))) | related(A!13, tptp_fun_B_0(A!13), tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.19/0.49 tff(273,plain,
% 0.19/0.49 (~in(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[272, 269, 257, 255])).
% 0.19/0.49 tff(274,plain,
% 0.19/0.49 (((~![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)) | 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))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(275,plain,
% 0.19/0.49 ((~![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))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(276,plain,
% 0.19/0.49 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(the_carrier(A!13)) | in(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13)) | (~element(tptp_fun_D_10(tptp_fun_B_0(A!13), empty_set, A!13), the_carrier(A!13)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.19/0.49 tff(277,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[276, 191, 153, 255, 273])).
% 0.19/0.49 % SZS output end Proof
%------------------------------------------------------------------------------