%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SEU361+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n015.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 07:29:08 EDT 2022

% Result   : Theorem 0.20s 0.43s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU361+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n015.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat Sep  3 12:48:10 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.20/0.43  % SZS status Theorem
% 0.20/0.43  % SZS output start Proof
% 0.20/0.43  tff(related_type, type, (
% 0.20/0.43     related: ( $i * $i * $i ) > $o)).
% 0.20/0.43  tff(tptp_fun_B_9_type, type, (
% 0.20/0.43     tptp_fun_B_9: $i)).
% 0.20/0.43  tff(join_on_relstr_type, type, (
% 0.20/0.43     join_on_relstr: ( $i * $i ) > $i)).
% 0.20/0.43  tff(empty_set_type, type, (
% 0.20/0.43     empty_set: $i)).
% 0.20/0.43  tff(tptp_fun_A_8_type, type, (
% 0.20/0.43     tptp_fun_A_8: $i)).
% 0.20/0.43  tff(bottom_of_relstr_type, type, (
% 0.20/0.43     bottom_of_relstr: $i > $i)).
% 0.20/0.43  tff(rel_str_type, type, (
% 0.20/0.43     rel_str: $i > $o)).
% 0.20/0.43  tff(element_type, type, (
% 0.20/0.43     element: ( $i * $i ) > $o)).
% 0.20/0.43  tff(the_carrier_type, type, (
% 0.20/0.43     the_carrier: $i > $i)).
% 0.20/0.43  tff(lower_bounded_relstr_type, type, (
% 0.20/0.43     lower_bounded_relstr: $i > $o)).
% 0.20/0.43  tff(antisymmetric_relstr_type, type, (
% 0.20/0.43     antisymmetric_relstr: $i > $o)).
% 0.20/0.43  tff(empty_carrier_type, type, (
% 0.20/0.43     empty_carrier: $i > $o)).
% 0.20/0.43  tff(relstr_set_smaller_type, type, (
% 0.20/0.43     relstr_set_smaller: ( $i * $i * $i ) > $o)).
% 0.20/0.43  tff(ex_sup_of_relstr_set_type, type, (
% 0.20/0.43     ex_sup_of_relstr_set: ( $i * $i ) > $o)).
% 0.20/0.43  tff(tptp_fun_D_7_type, type, (
% 0.20/0.43     tptp_fun_D_7: ( $i * $i * $i ) > $i)).
% 0.20/0.43  tff(ex_inf_of_relstr_set_type, type, (
% 0.20/0.43     ex_inf_of_relstr_set: ( $i * $i ) > $o)).
% 0.20/0.43  tff(relstr_element_smaller_type, type, (
% 0.20/0.43     relstr_element_smaller: ( $i * $i * $i ) > $o)).
% 0.20/0.43  tff(1,plain,
% 0.20/0.43      ((((~empty_carrier(A!8)) & antisymmetric_relstr(A!8) & lower_bounded_relstr(A!8) & rel_str(A!8)) & (~((~element(B!9, the_carrier(A!8))) | related(A!8, bottom_of_relstr(A!8), B!9)))) <=> ((~empty_carrier(A!8)) & antisymmetric_relstr(A!8) & lower_bounded_relstr(A!8) & rel_str(A!8) & (~((~element(B!9, the_carrier(A!8))) | related(A!8, bottom_of_relstr(A!8), B!9))))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(2,plain,
% 0.20/0.43      ((~(~((~empty_carrier(A!8)) & antisymmetric_relstr(A!8) & lower_bounded_relstr(A!8) & rel_str(A!8)))) <=> ((~empty_carrier(A!8)) & antisymmetric_relstr(A!8) & lower_bounded_relstr(A!8) & rel_str(A!8))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(3,plain,
% 0.20/0.43      (((~(~((~empty_carrier(A!8)) & antisymmetric_relstr(A!8) & lower_bounded_relstr(A!8) & rel_str(A!8)))) & (~((~element(B!9, the_carrier(A!8))) | related(A!8, bottom_of_relstr(A!8), B!9)))) <=> (((~empty_carrier(A!8)) & antisymmetric_relstr(A!8) & lower_bounded_relstr(A!8) & rel_str(A!8)) & (~((~element(B!9, the_carrier(A!8))) | related(A!8, bottom_of_relstr(A!8), B!9))))),
% 0.20/0.43      inference(monotonicity,[status(thm)],[2])).
% 0.20/0.43  tff(4,plain,
% 0.20/0.43      (((~(~((~empty_carrier(A!8)) & antisymmetric_relstr(A!8) & lower_bounded_relstr(A!8) & rel_str(A!8)))) & (~((~element(B!9, the_carrier(A!8))) | related(A!8, bottom_of_relstr(A!8), B!9)))) <=> ((~empty_carrier(A!8)) & antisymmetric_relstr(A!8) & lower_bounded_relstr(A!8) & rel_str(A!8) & (~((~element(B!9, the_carrier(A!8))) | related(A!8, bottom_of_relstr(A!8), B!9))))),
% 0.20/0.43      inference(transitivity,[status(thm)],[3, 1])).
% 0.20/0.43  tff(5,plain,
% 0.20/0.43      ((~![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | related(A, bottom_of_relstr(A), B)))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | related(A, bottom_of_relstr(A), B))))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(6,plain,
% 0.20/0.43      ((~![A: $i] : (((((~empty_carrier(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => related(A, bottom_of_relstr(A), B)))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | related(A, bottom_of_relstr(A), B))))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(7,axiom,(~![A: $i] : (((((~empty_carrier(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => related(A, bottom_of_relstr(A), B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t44_yellow_0')).
% 0.20/0.43  tff(8,plain,
% 0.20/0.43      (~![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | related(A, bottom_of_relstr(A), B)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.44  tff(9,plain,
% 0.20/0.44      (~![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | related(A, bottom_of_relstr(A), B)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[8, 5])).
% 0.20/0.44  tff(10,plain,
% 0.20/0.44      (~![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | related(A, bottom_of_relstr(A), B)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.44  tff(11,plain,
% 0.20/0.44      (~![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | related(A, bottom_of_relstr(A), B)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[10, 5])).
% 0.20/0.44  tff(12,plain,
% 0.20/0.44      (~![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | related(A, bottom_of_relstr(A), B)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[11, 5])).
% 0.20/0.44  tff(13,plain,
% 0.20/0.44      (~![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | related(A, bottom_of_relstr(A), B)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[12, 5])).
% 0.20/0.44  tff(14,plain,
% 0.20/0.44      (~![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | related(A, bottom_of_relstr(A), B)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[13, 5])).
% 0.20/0.44  tff(15,plain,
% 0.20/0.44      ((~empty_carrier(A!8)) & antisymmetric_relstr(A!8) & lower_bounded_relstr(A!8) & rel_str(A!8) & (~((~element(B!9, the_carrier(A!8))) | related(A!8, bottom_of_relstr(A!8), B!9)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[14, 4])).
% 0.20/0.44  tff(16,plain,
% 0.20/0.44      (rel_str(A!8)),
% 0.20/0.44      inference(and_elim,[status(thm)],[15])).
% 0.20/0.44  tff(17,plain,
% 0.20/0.44      (^[A: $i] : refl(((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set))) <=> ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(18,plain,
% 0.20/0.44      (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set))) <=> ![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[17])).
% 0.20/0.44  tff(19,plain,
% 0.20/0.44      (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set))) <=> ![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(20,plain,
% 0.20/0.44      (^[A: $i] : rewrite((rel_str(A) => (bottom_of_relstr(A) = join_on_relstr(A, empty_set))) <=> ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(21,plain,
% 0.20/0.44      (![A: $i] : (rel_str(A) => (bottom_of_relstr(A) = join_on_relstr(A, empty_set))) <=> ![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[20])).
% 0.20/0.44  tff(22,axiom,(![A: $i] : (rel_str(A) => (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d11_yellow_0')).
% 0.20/0.44  tff(23,plain,
% 0.20/0.44      (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.44  tff(24,plain,
% 0.20/0.44      (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.44  tff(25,plain,(
% 0.20/0.44      ![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.44      inference(skolemize,[status(sab)],[24])).
% 0.20/0.44  tff(26,plain,
% 0.20/0.44      (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[25, 18])).
% 0.20/0.44  tff(27,plain,
% 0.20/0.44      (((~![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))) | ((~rel_str(A!8)) | (bottom_of_relstr(A!8) = join_on_relstr(A!8, empty_set)))) <=> ((~![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))) | (~rel_str(A!8)) | (bottom_of_relstr(A!8) = join_on_relstr(A!8, empty_set)))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(28,plain,
% 0.20/0.44      ((~![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))) | ((~rel_str(A!8)) | (bottom_of_relstr(A!8) = join_on_relstr(A!8, empty_set)))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(29,plain,
% 0.20/0.44      ((~![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))) | (~rel_str(A!8)) | (bottom_of_relstr(A!8) = join_on_relstr(A!8, empty_set))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.44  tff(30,plain,
% 0.20/0.44      (bottom_of_relstr(A!8) = join_on_relstr(A!8, empty_set)),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[29, 26, 16])).
% 0.20/0.44  tff(31,plain,
% 0.20/0.44      (join_on_relstr(A!8, empty_set) = bottom_of_relstr(A!8)),
% 0.20/0.44      inference(symmetry,[status(thm)],[30])).
% 0.20/0.44  tff(32,plain,
% 0.20/0.44      (related(A!8, join_on_relstr(A!8, empty_set), B!9) <=> related(A!8, bottom_of_relstr(A!8), B!9)),
% 0.20/0.44      inference(monotonicity,[status(thm)],[31])).
% 0.20/0.44  tff(33,plain,
% 0.20/0.44      (related(A!8, bottom_of_relstr(A!8), B!9) <=> related(A!8, join_on_relstr(A!8, empty_set), B!9)),
% 0.20/0.44      inference(symmetry,[status(thm)],[32])).
% 0.20/0.44  tff(34,plain,
% 0.20/0.44      ((~related(A!8, bottom_of_relstr(A!8), B!9)) <=> (~related(A!8, join_on_relstr(A!8, empty_set), B!9))),
% 0.20/0.44      inference(monotonicity,[status(thm)],[33])).
% 0.20/0.44  tff(35,plain,
% 0.20/0.44      (~((~element(B!9, the_carrier(A!8))) | related(A!8, bottom_of_relstr(A!8), B!9))),
% 0.20/0.44      inference(and_elim,[status(thm)],[15])).
% 0.20/0.44  tff(36,plain,
% 0.20/0.44      (~related(A!8, bottom_of_relstr(A!8), B!9)),
% 0.20/0.44      inference(or_elim,[status(thm)],[35])).
% 0.20/0.44  tff(37,plain,
% 0.20/0.44      (~related(A!8, join_on_relstr(A!8, empty_set), B!9)),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[36, 34])).
% 0.20/0.44  tff(38,plain,
% 0.20/0.44      (element(join_on_relstr(A!8, empty_set), the_carrier(A!8)) <=> element(bottom_of_relstr(A!8), the_carrier(A!8))),
% 0.20/0.44      inference(monotonicity,[status(thm)],[31])).
% 0.20/0.44  tff(39,plain,
% 0.20/0.44      (element(bottom_of_relstr(A!8), the_carrier(A!8)) <=> element(join_on_relstr(A!8, empty_set), the_carrier(A!8))),
% 0.20/0.44      inference(symmetry,[status(thm)],[38])).
% 0.20/0.44  tff(40,plain,
% 0.20/0.44      (^[A: $i] : refl(((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A))) <=> ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(41,plain,
% 0.20/0.44      (![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[40])).
% 0.20/0.44  tff(42,plain,
% 0.20/0.44      (![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(43,plain,
% 0.20/0.44      (^[A: $i] : rewrite((rel_str(A) => element(bottom_of_relstr(A), the_carrier(A))) <=> ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(44,plain,
% 0.20/0.44      (![A: $i] : (rel_str(A) => element(bottom_of_relstr(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[43])).
% 0.20/0.44  tff(45,axiom,(![A: $i] : (rel_str(A) => element(bottom_of_relstr(A), the_carrier(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_yellow_0')).
% 0.20/0.44  tff(46,plain,
% 0.20/0.44      (![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.44  tff(47,plain,
% 0.20/0.44      (![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.44  tff(48,plain,(
% 0.20/0.44      ![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))),
% 0.20/0.44      inference(skolemize,[status(sab)],[47])).
% 0.20/0.44  tff(49,plain,
% 0.20/0.44      (![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[48, 41])).
% 0.20/0.44  tff(50,plain,
% 0.20/0.44      (((~![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))) | ((~rel_str(A!8)) | element(bottom_of_relstr(A!8), the_carrier(A!8)))) <=> ((~![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))) | (~rel_str(A!8)) | element(bottom_of_relstr(A!8), the_carrier(A!8)))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(51,plain,
% 0.20/0.44      ((~![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))) | ((~rel_str(A!8)) | element(bottom_of_relstr(A!8), the_carrier(A!8)))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(52,plain,
% 0.20/0.44      ((~![A: $i] : ((~rel_str(A)) | element(bottom_of_relstr(A), the_carrier(A)))) | (~rel_str(A!8)) | element(bottom_of_relstr(A!8), the_carrier(A!8))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.44  tff(53,plain,
% 0.20/0.44      (element(bottom_of_relstr(A!8), the_carrier(A!8))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[52, 49, 16])).
% 0.20/0.44  tff(54,plain,
% 0.20/0.44      (element(join_on_relstr(A!8, empty_set), the_carrier(A!8))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[53, 39])).
% 0.20/0.44  tff(55,plain,
% 0.20/0.44      (antisymmetric_relstr(A!8)),
% 0.20/0.44      inference(and_elim,[status(thm)],[15])).
% 0.20/0.44  tff(56,plain,
% 0.20/0.44      (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite(((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))), (![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))), (((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))))))))), rewrite(((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))), (((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(57,plain,
% 0.20/0.44      (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[56])).
% 0.20/0.44  tff(58,plain,
% 0.20/0.44      (^[A: $i] : refl(((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(59,plain,
% 0.20/0.44      (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[58])).
% 0.20/0.44  tff(60,plain,
% 0.20/0.44      (^[A: $i] : rewrite(((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(61,plain,
% 0.20/0.44      (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[60])).
% 0.20/0.44  tff(62,plain,
% 0.20/0.44      (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))),
% 0.20/0.44      inference(transitivity,[status(thm)],[61, 59])).
% 0.20/0.44  tff(63,plain,
% 0.20/0.44      (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((antisymmetric_relstr(A) & rel_str(A)) <=> (~((~antisymmetric_relstr(A)) | (~rel_str(A))))), ((~(antisymmetric_relstr(A) & rel_str(A))) <=> (~(~((~antisymmetric_relstr(A)) | (~rel_str(A))))))), rewrite((~(~((~antisymmetric_relstr(A)) | (~rel_str(A))))) <=> ((~antisymmetric_relstr(A)) | (~rel_str(A)))), ((~(antisymmetric_relstr(A) & rel_str(A))) <=> ((~antisymmetric_relstr(A)) | (~rel_str(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) | (~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A)))))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))), (![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) | (~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A)))))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))), (((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) | (~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))))))) <=> (((~antisymmetric_relstr(A)) | (~rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))))), rewrite((((~antisymmetric_relstr(A)) | (~rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))), (((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) | (~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))))),
% 0.20/0.45      inference(bind,[status(th)],[])).
% 0.20/0.45  tff(64,plain,
% 0.20/0.45      (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) | (~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))),
% 0.20/0.45      inference(quant_intro,[status(thm)],[63])).
% 0.20/0.45  tff(65,plain,
% 0.20/0.45      (^[A: $i] : rewrite(((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))) <=> ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) | (~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))))))))),
% 0.20/0.45      inference(bind,[status(th)],[])).
% 0.20/0.45  tff(66,plain,
% 0.20/0.45      (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))) <=> ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) | (~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A)))))))))),
% 0.20/0.45      inference(quant_intro,[status(thm)],[65])).
% 0.20/0.45  tff(67,plain,
% 0.20/0.45      (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))) <=> ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))),
% 0.20/0.45      inference(rewrite,[status(thm)],[])).
% 0.20/0.45  tff(68,plain,
% 0.20/0.45      (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite(((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))) <=> (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))), (![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))) <=> ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))), ((element(B, the_carrier(A)) => ![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))) <=> (element(B, the_carrier(A)) => ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))), ((element(B, the_carrier(A)) => ![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))), (((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))) <=> ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))))), rewrite(((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))) <=> ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))), (((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))) <=> ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))))),
% 0.20/0.45      inference(bind,[status(th)],[])).
% 0.20/0.45  tff(69,plain,
% 0.20/0.45      (![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)))))) <=> ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))),
% 0.20/0.45      inference(quant_intro,[status(thm)],[68])).
% 0.20/0.45  tff(70,axiom,(![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : ((((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) => (relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D))))) & ((relstr_set_smaller(A, C, B) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, C, D) => related(A, B, D)))) => ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t30_yellow_0')).
% 0.20/0.45  tff(71,plain,
% 0.20/0.45      (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.45  tff(72,plain,
% 0.20/0.45      (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & ((~(relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[71, 67])).
% 0.20/0.45  tff(73,plain,(
% 0.20/0.45      ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A)))))) | ((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))))))),
% 0.20/0.45      inference(skolemize,[status(sab)],[72])).
% 0.20/0.45  tff(74,plain,
% 0.20/0.45      (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (((~((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C))) | (relstr_set_smaller(A, C, B) & ![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))) & (((B = join_on_relstr(A, C)) & ex_sup_of_relstr_set(A, C)) | (~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A)))))))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[73, 66])).
% 0.20/0.45  tff(75,plain,
% 0.20/0.45      (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[74, 64])).
% 0.20/0.45  tff(76,plain,
% 0.20/0.45      (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A))))))))) | (~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C))))))))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[75, 62])).
% 0.20/0.45  tff(77,plain,
% 0.20/0.45      (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[76, 57])).
% 0.20/0.45  tff(78,plain,
% 0.20/0.45      (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))) | ((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D))))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))) | (~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D))))))))))))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(79,plain,
% 0.20/0.46      (((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) <=> ((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D))))))))))))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(80,plain,
% 0.20/0.46      (^[B: $i] : rewrite(((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : (related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)) | (~element(D, the_carrier(A!8)))))))))))) <=> ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D))))))))))))),
% 0.20/0.46      inference(bind,[status(th)],[])).
% 0.20/0.46  tff(81,plain,
% 0.20/0.46      (![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : (related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)) | (~element(D, the_carrier(A!8)))))))))))) <=> ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))),
% 0.20/0.46      inference(quant_intro,[status(thm)],[80])).
% 0.20/0.46  tff(82,plain,
% 0.20/0.46      (((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : (related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)) | (~element(D, the_carrier(A!8))))))))))))) <=> ((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D))))))))))))),
% 0.20/0.46      inference(monotonicity,[status(thm)],[81])).
% 0.20/0.46  tff(83,plain,
% 0.20/0.46      (((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : (related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)) | (~element(D, the_carrier(A!8))))))))))))) <=> ((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D))))))))))))),
% 0.20/0.46      inference(transitivity,[status(thm)],[82, 79])).
% 0.20/0.46  tff(84,plain,
% 0.20/0.46      (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))) | ((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : (related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)) | (~element(D, the_carrier(A!8)))))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))) | ((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))))),
% 0.20/0.46      inference(monotonicity,[status(thm)],[83])).
% 0.20/0.46  tff(85,plain,
% 0.20/0.46      (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))) | ((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : (related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)) | (~element(D, the_carrier(A!8)))))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))) | (~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D))))))))))))),
% 0.20/0.46      inference(transitivity,[status(thm)],[84, 78])).
% 0.20/0.46  tff(86,plain,
% 0.20/0.46      ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))) | ((~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : (related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)) | (~element(D, the_carrier(A!8)))))))))))))),
% 0.20/0.47      inference(quant_inst,[status(thm)],[])).
% 0.20/0.47  tff(87,plain,
% 0.20/0.47      ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : (~((~((~relstr_set_smaller(A, C, B)) | (~(related(A, B, tptp_fun_D_7(C, B, A)) | (~relstr_set_smaller(A, C, tptp_fun_D_7(C, B, A))) | (~element(tptp_fun_D_7(C, B, A), the_carrier(A))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)))))) | (~((~(B = join_on_relstr(A, C))) | (~ex_sup_of_relstr_set(A, C)) | (~((~relstr_set_smaller(A, C, B)) | (~![D: $i] : (related(A, B, D) | (~relstr_set_smaller(A, C, D)) | (~element(D, the_carrier(A)))))))))))))) | (~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.47  tff(88,plain,
% 0.20/0.47      (![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[87, 77, 55, 16])).
% 0.20/0.47  tff(89,plain,
% 0.20/0.47      (((~![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) | ((~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) | (~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(90,plain,
% 0.20/0.47      (((~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, join_on_relstr(A!8, empty_set), D) | (~relstr_set_smaller(A!8, C, D))))))))))) <=> ((~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(91,plain,
% 0.20/0.47      (((~![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) | ((~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, join_on_relstr(A!8, empty_set), D) | (~relstr_set_smaller(A!8, C, D)))))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) | ((~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))))),
% 0.20/0.47      inference(monotonicity,[status(thm)],[90])).
% 0.20/0.47  tff(92,plain,
% 0.20/0.47      (((~![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) | ((~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, join_on_relstr(A!8, empty_set), D) | (~relstr_set_smaller(A!8, C, D)))))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) | (~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))))),
% 0.20/0.48      inference(transitivity,[status(thm)],[91, 89])).
% 0.20/0.48  tff(93,plain,
% 0.20/0.48      ((~![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) | ((~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, join_on_relstr(A!8, empty_set), D) | (~relstr_set_smaller(A!8, C, D)))))))))))),
% 0.20/0.48      inference(quant_inst,[status(thm)],[])).
% 0.20/0.48  tff(94,plain,
% 0.20/0.48      ((~![B: $i] : ((~element(B, the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, B)) | (~(related(A!8, B, tptp_fun_D_7(C, B, A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, B, A!8))) | (~element(tptp_fun_D_7(C, B, A!8), the_carrier(A!8))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)))))) | (~((~(B = join_on_relstr(A!8, C))) | (~ex_sup_of_relstr_set(A!8, C)) | (~((~relstr_set_smaller(A!8, C, B)) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | related(A!8, B, D) | (~relstr_set_smaller(A!8, C, D)))))))))))) | (~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))),
% 0.20/0.48      inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.48  tff(95,plain,
% 0.20/0.48      ((~element(join_on_relstr(A!8, empty_set), the_carrier(A!8))) | ![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))),
% 0.20/0.48      inference(unit_resolution,[status(thm)],[94, 88])).
% 0.20/0.48  tff(96,plain,
% 0.20/0.48      (![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))),
% 0.20/0.48      inference(unit_resolution,[status(thm)],[95, 54])).
% 0.20/0.48  tff(97,plain,
% 0.20/0.48      (((~![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) | (~((~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | ex_sup_of_relstr_set(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) <=> ((~![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) | (~((~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | ex_sup_of_relstr_set(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))))),
% 0.20/0.48      inference(rewrite,[status(thm)],[])).
% 0.20/0.48  tff(98,plain,
% 0.20/0.48      ((~((~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, empty_set))))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, empty_set))) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))) <=> (~((~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | ex_sup_of_relstr_set(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))),
% 0.20/0.49      inference(rewrite,[status(thm)],[])).
% 0.20/0.49  tff(99,plain,
% 0.20/0.49      (((~![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) | (~((~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, empty_set))))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, empty_set))) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) <=> ((~![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) | (~((~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | ex_sup_of_relstr_set(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))))),
% 0.20/0.49      inference(monotonicity,[status(thm)],[98])).
% 0.20/0.49  tff(100,plain,
% 0.20/0.49      (((~![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) | (~((~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, empty_set))))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, empty_set))) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) <=> ((~![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) | (~((~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | ex_sup_of_relstr_set(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))))),
% 0.20/0.49      inference(transitivity,[status(thm)],[99, 97])).
% 0.20/0.49  tff(101,plain,
% 0.20/0.49      ((~![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) | (~((~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, empty_set))))))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, empty_set))) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))),
% 0.20/0.49      inference(quant_inst,[status(thm)],[])).
% 0.20/0.49  tff(102,plain,
% 0.20/0.49      ((~![C: $i] : (~((~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, C, tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(C, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))))))) | (~((~ex_sup_of_relstr_set(A!8, C)) | (~(join_on_relstr(A!8, empty_set) = join_on_relstr(A!8, C))) | (~((~relstr_set_smaller(A!8, C, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, C, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))) | (~((~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | ex_sup_of_relstr_set(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.49  tff(103,plain,
% 0.20/0.49      (~((~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | ex_sup_of_relstr_set(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))))),
% 0.20/0.49      inference(unit_resolution,[status(thm)],[102, 96])).
% 0.20/0.49  tff(104,plain,
% 0.20/0.49      (((~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~(related(A!8, join_on_relstr(A!8, empty_set), tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8)) | (~relstr_set_smaller(A!8, empty_set, tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8))) | (~element(tptp_fun_D_7(empty_set, join_on_relstr(A!8, empty_set), A!8), the_carrier(A!8))))) | ex_sup_of_relstr_set(A!8, empty_set))) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))))) | ((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(105,plain,
% 0.20/0.50      ((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[104, 103])).
% 0.20/0.50  tff(106,plain,
% 0.20/0.50      (lower_bounded_relstr(A!8)),
% 0.20/0.50      inference(and_elim,[status(thm)],[15])).
% 0.20/0.50  tff(107,plain,
% 0.20/0.50      (~empty_carrier(A!8)),
% 0.20/0.50      inference(and_elim,[status(thm)],[15])).
% 0.20/0.50  tff(108,plain,
% 0.20/0.50      (^[A: $i] : refl((empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A)))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A)))))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(109,plain,
% 0.20/0.50      (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A)))))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[108])).
% 0.20/0.50  tff(110,plain,
% 0.20/0.50      (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A)) <=> (~(empty_carrier(A) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~rel_str(A))))), ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) <=> (~(~(empty_carrier(A) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~rel_str(A))))))), rewrite((~(~(empty_carrier(A) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~rel_str(A))))) <=> (empty_carrier(A) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~rel_str(A)))), ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) <=> (empty_carrier(A) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~rel_str(A))))), rewrite((ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A))) <=> (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A)))))), (((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))) <=> ((empty_carrier(A) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~rel_str(A))) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A)))))))), rewrite(((empty_carrier(A) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~rel_str(A))) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A)))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))), (((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))) <=> (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(111,plain,
% 0.20/0.50      (![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[110])).
% 0.20/0.50  tff(112,plain,
% 0.20/0.50      (![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A))))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(113,plain,
% 0.20/0.50      (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) <=> ((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A))), (((((~empty_carrier(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) <=> (((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A)) & rel_str(A)))), rewrite((((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A)) & rel_str(A)) <=> ((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))), (((((~empty_carrier(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) <=> ((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A)))), ((((((~empty_carrier(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) => (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))) <=> (((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A)) => (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))))), rewrite((((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A)) => (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))) <=> ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A))))), ((((((~empty_carrier(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) => (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))) <=> ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A))))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(114,plain,
% 0.20/0.50      (![A: $i] : (((((~empty_carrier(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) => (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A))))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[113])).
% 0.20/0.50  tff(115,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')).
% 0.20/0.50  tff(116,plain,
% 0.20/0.50      (![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.50  tff(117,plain,
% 0.20/0.50      (![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[116, 112])).
% 0.20/0.50  tff(118,plain,(
% 0.20/0.50      ![A: $i] : ((~((~empty_carrier(A)) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | (ex_sup_of_relstr_set(A, empty_set) & ex_inf_of_relstr_set(A, the_carrier(A))))),
% 0.20/0.50      inference(skolemize,[status(sab)],[117])).
% 0.20/0.50  tff(119,plain,
% 0.20/0.50      (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[118, 111])).
% 0.20/0.50  tff(120,plain,
% 0.20/0.50      (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[119, 109])).
% 0.20/0.50  tff(121,plain,
% 0.20/0.50      (((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))) | (empty_carrier(A!8) | (~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | (~lower_bounded_relstr(A!8)) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~ex_inf_of_relstr_set(A!8, the_carrier(A!8))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))) | empty_carrier(A!8) | (~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | (~lower_bounded_relstr(A!8)) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~ex_inf_of_relstr_set(A!8, the_carrier(A!8))))))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(122,plain,
% 0.20/0.50      ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))) | (empty_carrier(A!8) | (~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | (~lower_bounded_relstr(A!8)) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~ex_inf_of_relstr_set(A!8, the_carrier(A!8))))))),
% 0.20/0.50      inference(quant_inst,[status(thm)],[])).
% 0.20/0.50  tff(123,plain,
% 0.20/0.50      ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~antisymmetric_relstr(A)) | (~lower_bounded_relstr(A)) | (~((~ex_sup_of_relstr_set(A, empty_set)) | (~ex_inf_of_relstr_set(A, the_carrier(A))))))) | empty_carrier(A!8) | (~rel_str(A!8)) | (~antisymmetric_relstr(A!8)) | (~lower_bounded_relstr(A!8)) | (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~ex_inf_of_relstr_set(A!8, the_carrier(A!8)))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.50  tff(124,plain,
% 0.20/0.50      (~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~ex_inf_of_relstr_set(A!8, the_carrier(A!8))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[123, 120, 107, 55, 106, 16])).
% 0.20/0.50  tff(125,plain,
% 0.20/0.50      (((~ex_sup_of_relstr_set(A!8, empty_set)) | (~ex_inf_of_relstr_set(A!8, the_carrier(A!8)))) | ex_sup_of_relstr_set(A!8, empty_set)),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(126,plain,
% 0.20/0.50      (ex_sup_of_relstr_set(A!8, empty_set)),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[125, 124])).
% 0.20/0.50  tff(127,plain,
% 0.20/0.50      ((~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))) | (~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(128,plain,
% 0.20/0.50      ((~((~ex_sup_of_relstr_set(A!8, empty_set)) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))))) | (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[127, 126])).
% 0.20/0.50  tff(129,plain,
% 0.20/0.50      (~((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[128, 105])).
% 0.20/0.50  tff(130,plain,
% 0.20/0.50      (((~relstr_set_smaller(A!8, empty_set, join_on_relstr(A!8, empty_set))) | (~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D)))) | ![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(131,plain,
% 0.20/0.50      (![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[130, 129])).
% 0.20/0.50  tff(132,plain,
% 0.20/0.50      (^[A: $i] : refl(((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B)))))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(133,plain,
% 0.20/0.50      (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[132])).
% 0.20/0.50  tff(134,plain,
% 0.20/0.50      (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B)))))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(135,plain,
% 0.20/0.50      (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[134])).
% 0.20/0.50  tff(136,plain,
% 0.20/0.50      (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))),
% 0.20/0.50      inference(transitivity,[status(thm)],[135, 133])).
% 0.20/0.50  tff(137,plain,
% 0.20/0.50      (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B)))))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(138,plain,
% 0.20/0.50      (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[137])).
% 0.20/0.50  tff(139,plain,
% 0.20/0.50      (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(140,plain,
% 0.20/0.51      (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, the_carrier(A)) => (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))) <=> ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))), (![B: $i] : (element(B, the_carrier(A)) => (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))), ((rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))) <=> (rel_str(A) => ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))))), rewrite((rel_str(A) => ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))), ((rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(141,plain,
% 0.20/0.51      (![A: $i] : (rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[140])).
% 0.20/0.51  tff(142,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')).
% 0.20/0.51  tff(143,plain,
% 0.20/0.51      (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.51  tff(144,plain,
% 0.20/0.51      (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[143, 139])).
% 0.20/0.51  tff(145,plain,(
% 0.20/0.51      ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.20/0.51      inference(skolemize,[status(sab)],[144])).
% 0.20/0.51  tff(146,plain,
% 0.20/0.51      (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[145, 138])).
% 0.20/0.51  tff(147,plain,
% 0.20/0.51      (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[146, 136])).
% 0.20/0.51  tff(148,plain,
% 0.20/0.51      (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))) | ((~rel_str(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))) | (~rel_str(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B))))))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(149,plain,
% 0.20/0.51      ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))) | ((~rel_str(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B))))))),
% 0.20/0.51      inference(quant_inst,[status(thm)],[])).
% 0.20/0.51  tff(150,plain,
% 0.20/0.51      ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~relstr_set_smaller(A, empty_set, B)) | (~relstr_element_smaller(A, empty_set, B))))))) | (~rel_str(A!8)) | ![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B)))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.51  tff(151,plain,
% 0.20/0.51      (![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B)))))),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[150, 16, 147])).
% 0.20/0.51  tff(152,plain,
% 0.20/0.51      (element(B!9, the_carrier(A!8))),
% 0.20/0.51      inference(or_elim,[status(thm)],[35])).
% 0.20/0.51  tff(153,plain,
% 0.20/0.51      (((~![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B)))))) | ((~element(B!9, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9)))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B)))))) | (~element(B!9, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9)))))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(154,plain,
% 0.20/0.51      ((~![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B)))))) | ((~element(B!9, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9)))))),
% 0.20/0.51      inference(quant_inst,[status(thm)],[])).
% 0.20/0.51  tff(155,plain,
% 0.20/0.51      ((~![B: $i] : ((~element(B, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B)) | (~relstr_element_smaller(A!8, empty_set, B)))))) | (~element(B!9, the_carrier(A!8))) | (~((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.51  tff(156,plain,
% 0.20/0.51      (~((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9)))),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[155, 152, 151])).
% 0.20/0.51  tff(157,plain,
% 0.20/0.51      (((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9))) | relstr_set_smaller(A!8, empty_set, B!9)),
% 0.20/0.51      inference(tautology,[status(thm)],[])).
% 0.20/0.51  tff(158,plain,
% 0.20/0.51      (relstr_set_smaller(A!8, empty_set, B!9)),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[157, 156])).
% 0.20/0.51  tff(159,plain,
% 0.20/0.51      (((~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))) | ((~element(B!9, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, B!9)) | related(A!8, join_on_relstr(A!8, empty_set), B!9))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))) | (~element(B!9, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, B!9)) | related(A!8, join_on_relstr(A!8, empty_set), B!9))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(160,plain,
% 0.20/0.51      ((~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))) | ((~element(B!9, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, B!9)) | related(A!8, join_on_relstr(A!8, empty_set), B!9))),
% 0.20/0.51      inference(quant_inst,[status(thm)],[])).
% 0.20/0.51  tff(161,plain,
% 0.20/0.51      ((~![D: $i] : ((~element(D, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, D)) | related(A!8, join_on_relstr(A!8, empty_set), D))) | (~element(B!9, the_carrier(A!8))) | (~relstr_set_smaller(A!8, empty_set, B!9)) | related(A!8, join_on_relstr(A!8, empty_set), B!9)),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[160, 159])).
% 0.20/0.51  tff(162,plain,
% 0.20/0.51      (related(A!8, join_on_relstr(A!8, empty_set), B!9)),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[161, 152, 158, 131])).
% 0.20/0.51  tff(163,plain,
% 0.20/0.51      ($false),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[162, 37])).
% 0.20/0.51  % SZS output end Proof
%------------------------------------------------------------------------------