TSTP Solution File: REL002+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : REL002+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 02:59:50 EDT 2022
% Result : Theorem 2.12s 1.61s
% Output : Proof 2.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL002+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Sep 2 19:30:47 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 2.12/1.61 % SZS status Theorem
% 2.12/1.61 % SZS output start Proof
% 2.12/1.61 tff(top_type, type, (
% 2.12/1.61 top: $i)).
% 2.12/1.61 tff(join_type, type, (
% 2.12/1.61 join: ( $i * $i ) > $i)).
% 2.12/1.61 tff(tptp_fun_X0_0_type, type, (
% 2.12/1.61 tptp_fun_X0_0: $i)).
% 2.12/1.61 tff(complement_type, type, (
% 2.12/1.61 complement: $i > $i)).
% 2.12/1.61 tff(meet_type, type, (
% 2.12/1.61 meet: ( $i * $i ) > $i)).
% 2.12/1.61 tff(zero_type, type, (
% 2.12/1.61 zero: $i)).
% 2.12/1.61 tff(1,plain,
% 2.12/1.61 (^[X0: $i] : refl((top = join(X0, complement(X0))) <=> (top = join(X0, complement(X0))))),
% 2.12/1.61 inference(bind,[status(th)],[])).
% 2.12/1.61 tff(2,plain,
% 2.12/1.61 (![X0: $i] : (top = join(X0, complement(X0))) <=> ![X0: $i] : (top = join(X0, complement(X0)))),
% 2.12/1.61 inference(quant_intro,[status(thm)],[1])).
% 2.12/1.61 tff(3,plain,
% 2.12/1.61 (![X0: $i] : (top = join(X0, complement(X0))) <=> ![X0: $i] : (top = join(X0, complement(X0)))),
% 2.12/1.61 inference(rewrite,[status(thm)],[])).
% 2.12/1.61 tff(4,axiom,(![X0: $i] : (top = join(X0, complement(X0)))), file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax','def_top')).
% 2.12/1.61 tff(5,plain,
% 2.12/1.61 (![X0: $i] : (top = join(X0, complement(X0)))),
% 2.12/1.61 inference(modus_ponens,[status(thm)],[4, 3])).
% 2.12/1.61 tff(6,plain,(
% 2.12/1.61 ![X0: $i] : (top = join(X0, complement(X0)))),
% 2.12/1.61 inference(skolemize,[status(sab)],[5])).
% 2.12/1.61 tff(7,plain,
% 2.12/1.61 (![X0: $i] : (top = join(X0, complement(X0)))),
% 2.12/1.61 inference(modus_ponens,[status(thm)],[6, 2])).
% 2.12/1.61 tff(8,plain,
% 2.12/1.61 ((~![X0: $i] : (top = join(X0, complement(X0)))) | (top = join(join(complement(join(complement(top), complement(top))), join(complement(top), top)), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.12/1.61 inference(quant_inst,[status(thm)],[])).
% 2.12/1.61 tff(9,plain,
% 2.12/1.61 (top = join(join(complement(join(complement(top), complement(top))), join(complement(top), top)), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))),
% 2.12/1.61 inference(unit_resolution,[status(thm)],[8, 7])).
% 2.12/1.61 tff(10,plain,
% 2.12/1.61 (join(join(complement(join(complement(top), complement(top))), join(complement(top), top)), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))) = top),
% 2.12/1.61 inference(symmetry,[status(thm)],[9])).
% 2.12/1.61 tff(11,plain,
% 2.12/1.61 (^[X0: $i, X1: $i, X2: $i] : refl((join(X0, join(X1, X2)) = join(join(X0, X1), X2)) <=> (join(X0, join(X1, X2)) = join(join(X0, X1), X2)))),
% 2.12/1.61 inference(bind,[status(th)],[])).
% 2.12/1.61 tff(12,plain,
% 2.12/1.61 (![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2)) <=> ![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 2.12/1.61 inference(quant_intro,[status(thm)],[11])).
% 2.12/1.61 tff(13,plain,
% 2.12/1.61 (![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2)) <=> ![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 2.12/1.61 inference(rewrite,[status(thm)],[])).
% 2.12/1.61 tff(14,axiom,(![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))), file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax','maddux2_join_associativity')).
% 2.12/1.61 tff(15,plain,
% 2.12/1.61 (![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 2.12/1.61 inference(modus_ponens,[status(thm)],[14, 13])).
% 2.12/1.61 tff(16,plain,(
% 2.12/1.61 ![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 2.12/1.61 inference(skolemize,[status(sab)],[15])).
% 2.12/1.61 tff(17,plain,
% 2.12/1.61 (![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 2.12/1.61 inference(modus_ponens,[status(thm)],[16, 12])).
% 2.12/1.61 tff(18,plain,
% 2.12/1.61 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.12/1.61 inference(quant_inst,[status(thm)],[])).
% 2.12/1.61 tff(19,plain,
% 2.12/1.61 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.12/1.61 inference(unit_resolution,[status(thm)],[18, 17])).
% 2.12/1.61 tff(20,plain,
% 2.12/1.61 (^[X0: $i, X1: $i] : refl((X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1)))) <=> (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1)))))),
% 2.12/1.61 inference(bind,[status(th)],[])).
% 2.12/1.61 tff(21,plain,
% 2.12/1.61 (![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1)))) <=> ![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))),
% 2.12/1.61 inference(quant_intro,[status(thm)],[20])).
% 2.12/1.61 tff(22,plain,
% 2.12/1.61 (![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1)))) <=> ![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))),
% 2.12/1.61 inference(rewrite,[status(thm)],[])).
% 2.12/1.61 tff(23,axiom,(![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))), file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax','maddux3_a_kind_of_de_Morgan')).
% 2.12/1.61 tff(24,plain,
% 2.12/1.61 (![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))),
% 2.12/1.61 inference(modus_ponens,[status(thm)],[23, 22])).
% 2.12/1.61 tff(25,plain,(
% 2.12/1.61 ![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))),
% 2.12/1.61 inference(skolemize,[status(sab)],[24])).
% 2.12/1.61 tff(26,plain,
% 2.12/1.61 (![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))),
% 2.12/1.61 inference(modus_ponens,[status(thm)],[25, 21])).
% 2.12/1.61 tff(27,plain,
% 2.12/1.61 ((~![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))) | (top = join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.61 inference(quant_inst,[status(thm)],[])).
% 2.12/1.61 tff(28,plain,
% 2.12/1.61 (top = join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))),
% 2.12/1.61 inference(unit_resolution,[status(thm)],[27, 26])).
% 2.12/1.61 tff(29,plain,
% 2.12/1.61 (join(complement(top), top) = join(complement(top), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.61 inference(monotonicity,[status(thm)],[28])).
% 2.12/1.61 tff(30,plain,
% 2.12/1.61 (join(complement(top), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(complement(top), top)),
% 2.12/1.61 inference(symmetry,[status(thm)],[29])).
% 2.12/1.61 tff(31,plain,
% 2.12/1.61 (^[X0: $i, X1: $i] : refl((join(X0, X1) = join(X1, X0)) <=> (join(X0, X1) = join(X1, X0)))),
% 2.12/1.61 inference(bind,[status(th)],[])).
% 2.12/1.61 tff(32,plain,
% 2.12/1.61 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0)) <=> ![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 2.12/1.61 inference(quant_intro,[status(thm)],[31])).
% 2.12/1.61 tff(33,plain,
% 2.12/1.61 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0)) <=> ![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 2.12/1.61 inference(rewrite,[status(thm)],[])).
% 2.12/1.61 tff(34,axiom,(![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))), file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax','maddux1_join_commutativity')).
% 2.12/1.61 tff(35,plain,
% 2.12/1.61 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 2.12/1.61 inference(modus_ponens,[status(thm)],[34, 33])).
% 2.12/1.61 tff(36,plain,(
% 2.12/1.61 ![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 2.12/1.61 inference(skolemize,[status(sab)],[35])).
% 2.12/1.61 tff(37,plain,
% 2.12/1.61 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 2.12/1.61 inference(modus_ponens,[status(thm)],[36, 32])).
% 2.12/1.61 tff(38,plain,
% 2.12/1.61 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(top), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top)))),
% 2.12/1.61 inference(quant_inst,[status(thm)],[])).
% 2.12/1.61 tff(39,plain,
% 2.12/1.61 (join(complement(top), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top))),
% 2.12/1.61 inference(unit_resolution,[status(thm)],[38, 37])).
% 2.12/1.61 tff(40,plain,
% 2.12/1.61 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top)) = join(complement(top), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.61 inference(symmetry,[status(thm)],[39])).
% 2.12/1.61 tff(41,plain,
% 2.12/1.61 (join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))) = top),
% 2.12/1.61 inference(symmetry,[status(thm)],[28])).
% 2.12/1.61 tff(42,plain,
% 2.12/1.61 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top)) = join(top, complement(top))),
% 2.12/1.61 inference(monotonicity,[status(thm)],[41])).
% 2.12/1.61 tff(43,plain,
% 2.12/1.61 (join(top, complement(top)) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top))),
% 2.12/1.61 inference(symmetry,[status(thm)],[42])).
% 2.12/1.61 tff(44,plain,
% 2.12/1.61 ((~![X0: $i] : (top = join(X0, complement(X0)))) | (top = join(top, complement(top)))),
% 2.12/1.61 inference(quant_inst,[status(thm)],[])).
% 2.12/1.61 tff(45,plain,
% 2.12/1.61 (top = join(top, complement(top))),
% 2.12/1.61 inference(unit_resolution,[status(thm)],[44, 7])).
% 2.12/1.61 tff(46,plain,
% 2.12/1.61 (join(top, complement(top)) = top),
% 2.12/1.61 inference(symmetry,[status(thm)],[45])).
% 2.12/1.61 tff(47,plain,
% 2.12/1.61 (join(complement(top), top) = top),
% 2.12/1.61 inference(transitivity,[status(thm)],[29, 39, 42, 46])).
% 2.12/1.61 tff(48,plain,
% 2.12/1.61 (complement(join(complement(top), top)) = complement(top)),
% 2.12/1.61 inference(monotonicity,[status(thm)],[47])).
% 2.12/1.61 tff(49,plain,
% 2.12/1.61 (complement(top) = complement(join(complement(top), top))),
% 2.12/1.61 inference(symmetry,[status(thm)],[48])).
% 2.12/1.61 tff(50,plain,
% 2.12/1.61 (complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = complement(top)),
% 2.12/1.61 inference(monotonicity,[status(thm)],[41])).
% 2.12/1.61 tff(51,plain,
% 2.12/1.61 (complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = complement(join(complement(top), top))),
% 2.12/1.61 inference(transitivity,[status(thm)],[50, 49])).
% 2.12/1.61 tff(52,plain,
% 2.12/1.61 (complement(top) = complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.61 inference(symmetry,[status(thm)],[50])).
% 2.12/1.61 tff(53,plain,
% 2.12/1.61 (join(complement(top), complement(top)) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.12/1.61 inference(monotonicity,[status(thm)],[52, 52])).
% 2.12/1.61 tff(54,plain,
% 2.12/1.61 (complement(join(complement(top), complement(top))) = complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.12/1.61 inference(monotonicity,[status(thm)],[53])).
% 2.12/1.61 tff(55,plain,
% 2.12/1.61 (complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = complement(join(complement(top), complement(top)))),
% 2.12/1.61 inference(symmetry,[status(thm)],[54])).
% 2.12/1.61 tff(56,plain,
% 2.12/1.61 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))),
% 2.12/1.61 inference(monotonicity,[status(thm)],[55, 51])).
% 2.12/1.61 tff(57,plain,
% 2.12/1.61 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(top), top)),
% 2.12/1.61 inference(transitivity,[status(thm)],[56, 41, 45, 43, 40, 30])).
% 2.12/1.61 tff(58,plain,
% 2.12/1.61 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = join(complement(join(complement(top), complement(top))), join(complement(top), top))),
% 2.12/1.61 inference(monotonicity,[status(thm)],[55, 57])).
% 2.12/1.61 tff(59,plain,
% 2.12/1.61 (join(complement(join(complement(top), complement(top))), join(complement(top), top)) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.12/1.61 inference(symmetry,[status(thm)],[58])).
% 2.12/1.61 tff(60,plain,
% 2.12/1.61 (join(complement(join(complement(top), complement(top))), join(complement(top), top)) = join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.12/1.61 inference(transitivity,[status(thm)],[59, 19])).
% 2.12/1.61 tff(61,plain,
% 2.12/1.61 (join(join(complement(join(complement(top), complement(top))), join(complement(top), top)), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))) = join(join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))),
% 2.12/1.61 inference(monotonicity,[status(thm)],[60])).
% 2.12/1.61 tff(62,plain,
% 2.12/1.61 (join(join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))) = join(join(complement(join(complement(top), complement(top))), join(complement(top), top)), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))),
% 2.12/1.61 inference(symmetry,[status(thm)],[61])).
% 2.12/1.61 tff(63,plain,
% 2.12/1.61 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.12/1.61 inference(quant_inst,[status(thm)],[])).
% 2.12/1.61 tff(64,plain,
% 2.12/1.61 (join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))),
% 2.12/1.61 inference(unit_resolution,[status(thm)],[63, 17])).
% 2.12/1.61 tff(65,plain,
% 2.12/1.61 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))),
% 2.12/1.61 inference(quant_inst,[status(thm)],[])).
% 2.12/1.61 tff(66,plain,
% 2.12/1.61 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.12/1.61 inference(unit_resolution,[status(thm)],[65, 17])).
% 2.12/1.61 tff(67,plain,
% 2.12/1.61 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(complement(top), complement(top))), join(complement(join(complement(top), top)), complement(top))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top)))),
% 2.12/1.61 inference(quant_inst,[status(thm)],[])).
% 2.12/1.61 tff(68,plain,
% 2.12/1.61 (join(complement(join(complement(top), complement(top))), join(complement(join(complement(top), top)), complement(top))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top))),
% 2.12/1.61 inference(unit_resolution,[status(thm)],[67, 17])).
% 2.12/1.61 tff(69,plain,
% 2.12/1.61 (complement(join(complement(top), top)) = complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.61 inference(transitivity,[status(thm)],[48, 52])).
% 2.12/1.61 tff(70,plain,
% 2.12/1.61 (join(complement(join(complement(top), top)), complement(top)) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.12/1.61 inference(monotonicity,[status(thm)],[69, 52])).
% 2.12/1.61 tff(71,plain,
% 2.12/1.61 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(join(complement(top), top)), complement(top))),
% 2.12/1.61 inference(symmetry,[status(thm)],[70])).
% 2.12/1.61 tff(72,plain,
% 2.12/1.61 ((~![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))) | (join(complement(top), complement(top)) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.12/1.61 inference(quant_inst,[status(thm)],[])).
% 2.12/1.61 tff(73,plain,
% 2.12/1.61 (join(complement(top), complement(top)) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))),
% 2.12/1.61 inference(unit_resolution,[status(thm)],[72, 26])).
% 2.12/1.61 tff(74,plain,
% 2.12/1.61 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))) = join(complement(top), complement(top))),
% 2.12/1.61 inference(symmetry,[status(thm)],[73])).
% 2.12/1.61 tff(75,plain,
% 2.12/1.61 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))) = join(complement(join(complement(top), top)), complement(top))),
% 2.12/1.61 inference(transitivity,[status(thm)],[74, 53, 71])).
% 2.12/1.61 tff(76,plain,
% 2.12/1.61 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(complement(join(complement(top), complement(top))), join(complement(join(complement(top), top)), complement(top)))),
% 2.12/1.61 inference(monotonicity,[status(thm)],[55, 75])).
% 2.12/1.61 tff(77,plain,
% 2.12/1.62 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(complement(top), top)),
% 2.12/1.62 inference(transitivity,[status(thm)],[76, 68, 40, 30])).
% 2.12/1.62 tff(78,plain,
% 2.12/1.62 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = join(complement(join(complement(top), complement(top))), join(complement(top), top))),
% 2.12/1.62 inference(monotonicity,[status(thm)],[55, 77])).
% 2.12/1.62 tff(79,plain,
% 2.12/1.62 (join(complement(join(complement(top), complement(top))), join(complement(top), top)) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))),
% 2.12/1.62 inference(symmetry,[status(thm)],[78])).
% 2.12/1.62 tff(80,plain,
% 2.12/1.62 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(complement(top), top)),
% 2.12/1.62 inference(monotonicity,[status(thm)],[50, 41])).
% 2.12/1.62 tff(81,plain,
% 2.12/1.62 (join(complement(top), top) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.62 inference(symmetry,[status(thm)],[80])).
% 2.12/1.62 tff(82,plain,
% 2.12/1.62 (join(complement(join(complement(top), complement(top))), join(complement(top), top)) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.12/1.62 inference(monotonicity,[status(thm)],[54, 81])).
% 2.12/1.62 tff(83,plain,
% 2.12/1.62 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(join(complement(top), complement(top))), join(complement(top), top))),
% 2.12/1.62 inference(symmetry,[status(thm)],[82])).
% 2.12/1.62 tff(84,plain,
% 2.12/1.62 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.12/1.62 inference(quant_inst,[status(thm)],[])).
% 2.12/1.62 tff(85,plain,
% 2.12/1.62 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.62 inference(unit_resolution,[status(thm)],[84, 17])).
% 2.12/1.62 tff(86,plain,
% 2.12/1.62 (join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.12/1.62 inference(symmetry,[status(thm)],[85])).
% 2.12/1.62 tff(87,plain,
% 2.12/1.62 ((~![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))) | (X0!0 = join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))))),
% 2.12/1.62 inference(quant_inst,[status(thm)],[])).
% 2.12/1.62 tff(88,plain,
% 2.12/1.62 (X0!0 = join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))),
% 2.12/1.62 inference(unit_resolution,[status(thm)],[87, 26])).
% 2.12/1.62 tff(89,plain,
% 2.12/1.62 (join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))) = X0!0),
% 2.12/1.62 inference(symmetry,[status(thm)],[88])).
% 2.12/1.62 tff(90,plain,
% 2.12/1.62 (complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))) = complement(X0!0)),
% 2.12/1.62 inference(monotonicity,[status(thm)],[89])).
% 2.12/1.62 tff(91,plain,
% 2.12/1.62 (complement(X0!0) = complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))))),
% 2.12/1.62 inference(symmetry,[status(thm)],[90])).
% 2.12/1.62 tff(92,plain,
% 2.12/1.62 (join(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))), complement(X0!0)) = join(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))), complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))))),
% 2.12/1.62 inference(monotonicity,[status(thm)],[91])).
% 2.12/1.62 tff(93,plain,
% 2.12/1.62 (join(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))), complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))))) = join(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))), complement(X0!0))),
% 2.12/1.62 inference(symmetry,[status(thm)],[92])).
% 2.12/1.62 tff(94,plain,
% 2.12/1.62 ((~![X0: $i] : (top = join(X0, complement(X0)))) | (top = join(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))), complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))))))),
% 2.12/1.62 inference(quant_inst,[status(thm)],[])).
% 2.12/1.62 tff(95,plain,
% 2.12/1.62 (top = join(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))), complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))))),
% 2.12/1.62 inference(unit_resolution,[status(thm)],[94, 7])).
% 2.12/1.62 tff(96,plain,
% 2.12/1.62 (join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))) = join(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))), complement(X0!0))),
% 2.12/1.62 inference(transitivity,[status(thm)],[41, 95, 93])).
% 2.12/1.62 tff(97,plain,
% 2.12/1.62 (join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))), complement(X0!0)))),
% 2.12/1.62 inference(monotonicity,[status(thm)],[56, 96])).
% 2.12/1.62 tff(98,plain,
% 2.12/1.62 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))), complement(X0!0))) = join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.62 inference(symmetry,[status(thm)],[97])).
% 2.12/1.62 tff(99,plain,
% 2.12/1.62 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))), complement(X0!0))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(X0!0)))),
% 2.12/1.62 inference(quant_inst,[status(thm)],[])).
% 2.12/1.62 tff(100,plain,
% 2.12/1.62 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))), complement(X0!0))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(X0!0))),
% 2.12/1.62 inference(unit_resolution,[status(thm)],[99, 17])).
% 2.12/1.62 tff(101,plain,
% 2.12/1.62 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(X0!0)) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))), complement(X0!0)))),
% 2.12/1.62 inference(symmetry,[status(thm)],[100])).
% 2.12/1.62 tff(102,plain,
% 2.12/1.62 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))) = join(top, X0!0)),
% 2.12/1.62 inference(monotonicity,[status(thm)],[41, 89])).
% 2.12/1.62 tff(103,plain,
% 2.12/1.62 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(X0!0)) = join(join(top, X0!0), complement(X0!0))),
% 2.12/1.62 inference(monotonicity,[status(thm)],[102])).
% 2.12/1.62 tff(104,plain,
% 2.12/1.62 (join(join(top, X0!0), complement(X0!0)) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(X0!0))),
% 2.12/1.62 inference(symmetry,[status(thm)],[103])).
% 2.12/1.62 tff(105,plain,
% 2.12/1.62 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(X0!0), join(top, X0!0)) = join(join(top, X0!0), complement(X0!0)))),
% 2.12/1.62 inference(quant_inst,[status(thm)],[])).
% 2.12/1.62 tff(106,plain,
% 2.12/1.62 (join(complement(X0!0), join(top, X0!0)) = join(join(top, X0!0), complement(X0!0))),
% 2.12/1.62 inference(unit_resolution,[status(thm)],[105, 37])).
% 2.12/1.62 tff(107,plain,
% 2.12/1.62 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(X0!0, X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))),
% 2.12/1.62 inference(quant_inst,[status(thm)],[])).
% 2.12/1.62 tff(108,plain,
% 2.12/1.62 (join(join(X0!0, X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))),
% 2.12/1.62 inference(unit_resolution,[status(thm)],[107, 17])).
% 2.12/1.62 tff(109,plain,
% 2.12/1.62 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(join(X0!0, X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(X0!0, X0!0)))),
% 2.12/1.62 inference(quant_inst,[status(thm)],[])).
% 2.12/1.62 tff(110,plain,
% 2.12/1.62 (join(join(X0!0, X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(X0!0, X0!0))),
% 2.12/1.62 inference(unit_resolution,[status(thm)],[109, 37])).
% 2.12/1.62 tff(111,plain,
% 2.12/1.62 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(X0!0, X0!0)) = join(join(X0!0, X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.62 inference(symmetry,[status(thm)],[110])).
% 2.12/1.62 tff(112,plain,
% 2.12/1.62 (join(complement(top), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = top),
% 2.12/1.62 inference(transitivity,[status(thm)],[39, 42, 46])).
% 2.12/1.62 tff(113,plain,
% 2.12/1.62 (join(join(complement(top), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(top)) = join(top, complement(top))),
% 2.12/1.62 inference(monotonicity,[status(thm)],[112])).
% 2.12/1.62 tff(114,plain,
% 2.12/1.62 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top)), complement(top)) = join(join(complement(top), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(top))),
% 2.12/1.62 inference(monotonicity,[status(thm)],[40])).
% 2.12/1.62 tff(115,plain,
% 2.12/1.62 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(top), complement(top))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top)), complement(top)))),
% 2.12/1.62 inference(quant_inst,[status(thm)],[])).
% 2.12/1.62 tff(116,plain,
% 2.12/1.62 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(top), complement(top))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top)), complement(top))),
% 2.12/1.62 inference(unit_resolution,[status(thm)],[115, 17])).
% 2.12/1.62 tff(117,plain,
% 2.12/1.62 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(top), complement(top)))),
% 2.12/1.62 inference(monotonicity,[status(thm)],[74])).
% 2.12/1.62 tff(118,plain,
% 2.12/1.62 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))),
% 2.12/1.62 inference(transitivity,[status(thm)],[117, 116, 114, 113, 46, 28])).
% 2.12/1.62 tff(119,plain,
% 2.12/1.62 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))), join(X0!0, X0!0)) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(X0!0, X0!0))),
% 2.12/1.62 inference(monotonicity,[status(thm)],[118])).
% 2.12/1.62 tff(120,plain,
% 2.12/1.62 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))), join(X0!0, X0!0)))),
% 2.12/1.62 inference(quant_inst,[status(thm)],[])).
% 2.12/1.62 tff(121,plain,
% 2.12/1.62 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))), join(X0!0, X0!0))),
% 2.12/1.62 inference(unit_resolution,[status(thm)],[120, 17])).
% 2.12/1.62 tff(122,plain,
% 2.12/1.62 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0))) = join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.12/1.62 inference(quant_inst,[status(thm)],[])).
% 2.12/1.62 tff(123,plain,
% 2.12/1.62 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0))) = join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.62 inference(unit_resolution,[status(thm)],[122, 37])).
% 2.12/1.62 tff(124,plain,
% 2.12/1.62 (join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)))),
% 2.12/1.62 inference(symmetry,[status(thm)],[123])).
% 2.12/1.62 tff(125,plain,
% 2.12/1.62 (join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.12/1.62 inference(symmetry,[status(thm)],[56])).
% 2.12/1.62 tff(126,plain,
% 2.12/1.62 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.62 inference(monotonicity,[status(thm)],[125])).
% 2.12/1.62 tff(127,plain,
% 2.12/1.62 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))),
% 2.12/1.62 inference(transitivity,[status(thm)],[126, 86, 83, 79, 66, 64, 62, 10, 28])).
% 2.12/1.62 tff(128,plain,
% 2.12/1.62 (join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.62 inference(monotonicity,[status(thm)],[127])).
% 2.12/1.62 tff(129,plain,
% 2.12/1.62 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.12/1.62 inference(quant_inst,[status(thm)],[])).
% 2.12/1.62 tff(130,plain,
% 2.12/1.62 (join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.62 inference(unit_resolution,[status(thm)],[129, 17])).
% 2.12/1.62 tff(131,plain,
% 2.12/1.62 (join(join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.12/1.63 inference(symmetry,[status(thm)],[130])).
% 2.12/1.63 tff(132,plain,
% 2.12/1.63 ((~![X0: $i] : (top = join(X0, complement(X0)))) | (top = join(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))), complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))))),
% 2.12/1.63 inference(quant_inst,[status(thm)],[])).
% 2.12/1.63 tff(133,plain,
% 2.12/1.63 (top = join(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))), complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))),
% 2.12/1.63 inference(unit_resolution,[status(thm)],[132, 7])).
% 2.12/1.63 tff(134,plain,
% 2.12/1.63 (join(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))), complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))) = top),
% 2.12/1.63 inference(symmetry,[status(thm)],[133])).
% 2.12/1.63 tff(135,plain,
% 2.12/1.63 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))) = join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), complement(join(top, X0!0))))),
% 2.12/1.63 inference(quant_inst,[status(thm)],[])).
% 2.12/1.63 tff(136,plain,
% 2.12/1.63 (join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))) = join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), complement(join(top, X0!0)))),
% 2.12/1.63 inference(unit_resolution,[status(thm)],[135, 37])).
% 2.12/1.63 tff(137,plain,
% 2.12/1.63 (join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), complement(join(top, X0!0))) = join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))),
% 2.12/1.63 inference(symmetry,[status(thm)],[136])).
% 2.12/1.63 tff(138,plain,
% 2.12/1.63 ((~![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))) | (join(top, X0!0) = join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))),
% 2.12/1.63 inference(quant_inst,[status(thm)],[])).
% 2.12/1.63 tff(139,plain,
% 2.12/1.63 (join(top, X0!0) = join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))),
% 2.12/1.63 inference(unit_resolution,[status(thm)],[138, 26])).
% 2.12/1.63 tff(140,plain,
% 2.12/1.63 (complement(join(top, X0!0)) = complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))),
% 2.12/1.63 inference(monotonicity,[status(thm)],[139])).
% 2.12/1.63 tff(141,plain,
% 2.12/1.63 (complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))) = complement(join(top, X0!0))),
% 2.12/1.63 inference(symmetry,[status(thm)],[140])).
% 2.12/1.63 tff(142,plain,
% 2.12/1.63 (join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))) = join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), complement(join(top, X0!0)))),
% 2.12/1.63 inference(monotonicity,[status(thm)],[141])).
% 2.12/1.63 tff(143,plain,
% 2.12/1.63 (join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))) = join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))),
% 2.12/1.63 inference(transitivity,[status(thm)],[142, 137])).
% 2.12/1.63 tff(144,plain,
% 2.12/1.63 (join(join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))), complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))) = join(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))), complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))),
% 2.12/1.63 inference(monotonicity,[status(thm)],[143])).
% 2.12/1.63 tff(145,plain,
% 2.12/1.63 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))), complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))) = join(join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))), complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))))),
% 2.12/1.63 inference(quant_inst,[status(thm)],[])).
% 2.12/1.63 tff(146,plain,
% 2.12/1.63 (join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))), complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))) = join(join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))), complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))),
% 2.12/1.63 inference(unit_resolution,[status(thm)],[145, 17])).
% 2.12/1.63 tff(147,plain,
% 2.12/1.63 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top)) = top),
% 2.12/1.63 inference(transitivity,[status(thm)],[42, 46])).
% 2.12/1.63 tff(148,plain,
% 2.12/1.63 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top)), X0!0) = join(top, X0!0)),
% 2.12/1.63 inference(monotonicity,[status(thm)],[147])).
% 2.12/1.63 tff(149,plain,
% 2.12/1.63 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(top), X0!0)) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top)), X0!0))),
% 2.12/1.63 inference(quant_inst,[status(thm)],[])).
% 2.12/1.63 tff(150,plain,
% 2.12/1.63 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(top), X0!0)) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top)), X0!0)),
% 2.12/1.63 inference(unit_resolution,[status(thm)],[149, 17])).
% 2.12/1.63 tff(151,plain,
% 2.12/1.63 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))), join(complement(top), X0!0)) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(top), X0!0))),
% 2.12/1.63 inference(monotonicity,[status(thm)],[118])).
% 2.12/1.63 tff(152,plain,
% 2.12/1.63 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))), join(complement(top), X0!0)))),
% 2.12/1.63 inference(quant_inst,[status(thm)],[])).
% 2.12/1.63 tff(153,plain,
% 2.12/1.63 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))), join(complement(top), X0!0))),
% 2.12/1.63 inference(unit_resolution,[status(thm)],[152, 17])).
% 2.12/1.63 tff(154,plain,
% 2.12/1.63 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))) = join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.12/1.63 inference(quant_inst,[status(thm)],[])).
% 2.12/1.63 tff(155,plain,
% 2.12/1.63 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))) = join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.63 inference(unit_resolution,[status(thm)],[154, 37])).
% 2.12/1.63 tff(156,plain,
% 2.12/1.63 (join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))),
% 2.12/1.63 inference(symmetry,[status(thm)],[155])).
% 2.12/1.63 tff(157,plain,
% 2.12/1.63 (join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.63 inference(monotonicity,[status(thm)],[127])).
% 2.12/1.63 tff(158,plain,
% 2.12/1.63 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.12/1.63 inference(quant_inst,[status(thm)],[])).
% 2.12/1.63 tff(159,plain,
% 2.12/1.63 (join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.63 inference(unit_resolution,[status(thm)],[158, 17])).
% 2.12/1.63 tff(160,plain,
% 2.12/1.63 (join(join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.12/1.63 inference(symmetry,[status(thm)],[159])).
% 2.12/1.63 tff(161,plain,
% 2.12/1.63 ((~![X0: $i] : (top = join(X0, complement(X0)))) | (top = join(join(top, X0!0), complement(join(top, X0!0))))),
% 2.12/1.63 inference(quant_inst,[status(thm)],[])).
% 2.12/1.63 tff(162,plain,
% 2.12/1.63 (top = join(join(top, X0!0), complement(join(top, X0!0)))),
% 2.12/1.63 inference(unit_resolution,[status(thm)],[161, 7])).
% 2.12/1.63 tff(163,plain,
% 2.12/1.63 (join(join(top, X0!0), complement(join(top, X0!0))) = top),
% 2.12/1.63 inference(symmetry,[status(thm)],[162])).
% 2.12/1.63 tff(164,plain,
% 2.12/1.63 (join(join(top, X0!0), complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))) = join(join(top, X0!0), complement(join(top, X0!0)))),
% 2.12/1.63 inference(monotonicity,[status(thm)],[141])).
% 2.12/1.63 tff(165,plain,
% 2.12/1.63 (join(join(top, X0!0), complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))) = join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))),
% 2.12/1.63 inference(transitivity,[status(thm)],[164, 163, 28])).
% 2.12/1.63 tff(166,plain,
% 2.12/1.63 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))), join(complement(top), X0!0)) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))),
% 2.12/1.63 inference(symmetry,[status(thm)],[153])).
% 2.12/1.63 tff(167,plain,
% 2.12/1.63 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(top), X0!0)) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))), join(complement(top), X0!0))),
% 2.12/1.63 inference(symmetry,[status(thm)],[151])).
% 2.12/1.63 tff(168,plain,
% 2.12/1.63 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top)), X0!0) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(top), X0!0))),
% 2.12/1.63 inference(symmetry,[status(thm)],[150])).
% 2.12/1.63 tff(169,plain,
% 2.12/1.63 (join(top, X0!0) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top)), X0!0)),
% 2.12/1.63 inference(symmetry,[status(thm)],[148])).
% 2.12/1.63 tff(170,plain,
% 2.12/1.63 (join(top, X0!0) = join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.63 inference(transitivity,[status(thm)],[169, 168, 167, 166, 155])).
% 2.12/1.64 tff(171,plain,
% 2.12/1.64 (join(join(top, X0!0), join(join(top, X0!0), complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))))) = join(join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.64 inference(monotonicity,[status(thm)],[170, 165])).
% 2.12/1.64 tff(172,plain,
% 2.12/1.64 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(top, X0!0), join(join(top, X0!0), complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))))) = join(join(join(top, X0!0), join(top, X0!0)), complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))))),
% 2.12/1.64 inference(quant_inst,[status(thm)],[])).
% 2.12/1.64 tff(173,plain,
% 2.12/1.64 (join(join(top, X0!0), join(join(top, X0!0), complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))))) = join(join(join(top, X0!0), join(top, X0!0)), complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))))),
% 2.12/1.64 inference(unit_resolution,[status(thm)],[172, 17])).
% 2.12/1.64 tff(174,plain,
% 2.12/1.64 (join(join(join(top, X0!0), join(top, X0!0)), complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))) = join(join(top, X0!0), join(join(top, X0!0), complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))))),
% 2.12/1.64 inference(symmetry,[status(thm)],[173])).
% 2.12/1.64 tff(175,plain,
% 2.12/1.64 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), X0!0) = join(top, X0!0)),
% 2.12/1.64 inference(monotonicity,[status(thm)],[41])).
% 2.12/1.64 tff(176,plain,
% 2.12/1.64 (join(top, X0!0) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), X0!0)),
% 2.12/1.64 inference(symmetry,[status(thm)],[175])).
% 2.12/1.64 tff(177,plain,
% 2.12/1.64 (join(join(top, X0!0), join(top, X0!0)) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), X0!0), join(top, X0!0))),
% 2.12/1.64 inference(monotonicity,[status(thm)],[176])).
% 2.12/1.64 tff(178,plain,
% 2.12/1.64 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), X0!0), join(top, X0!0)) = join(join(top, X0!0), join(top, X0!0))),
% 2.12/1.64 inference(symmetry,[status(thm)],[177])).
% 2.12/1.64 tff(179,plain,
% 2.12/1.64 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(X0!0, join(top, X0!0))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), X0!0), join(top, X0!0)))),
% 2.12/1.64 inference(quant_inst,[status(thm)],[])).
% 2.12/1.64 tff(180,plain,
% 2.12/1.64 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(X0!0, join(top, X0!0))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), X0!0), join(top, X0!0))),
% 2.12/1.64 inference(unit_resolution,[status(thm)],[179, 17])).
% 2.12/1.64 tff(181,plain,
% 2.12/1.64 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))),
% 2.12/1.64 inference(quant_inst,[status(thm)],[])).
% 2.12/1.64 tff(182,plain,
% 2.12/1.64 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.12/1.64 inference(unit_resolution,[status(thm)],[181, 17])).
% 2.12/1.64 tff(183,plain,
% 2.12/1.64 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))),
% 2.12/1.64 inference(symmetry,[status(thm)],[182])).
% 2.12/1.64 tff(184,plain,
% 2.12/1.64 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.12/1.64 inference(transitivity,[status(thm)],[74, 53])).
% 2.12/1.64 tff(185,plain,
% 2.12/1.64 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0))) = join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))),
% 2.12/1.64 inference(transitivity,[status(thm)],[121, 119, 111, 108])).
% 2.12/1.64 tff(186,plain,
% 2.12/1.64 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.12/1.64 inference(monotonicity,[status(thm)],[185, 184])).
% 2.12/1.64 tff(187,plain,
% 2.12/1.64 (join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.12/1.64 inference(symmetry,[status(thm)],[186])).
% 2.12/1.64 tff(188,plain,
% 2.12/1.64 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = join(join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.12/1.64 inference(quant_inst,[status(thm)],[])).
% 2.12/1.64 tff(189,plain,
% 2.12/1.64 (join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = join(join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.12/1.64 inference(unit_resolution,[status(thm)],[188, 17])).
% 2.12/1.64 tff(190,plain,
% 2.12/1.64 (join(join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.12/1.64 inference(symmetry,[status(thm)],[189])).
% 2.12/1.64 tff(191,plain,
% 2.12/1.64 (join(join(X0!0, X0!0), top) = join(join(X0!0, X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.64 inference(monotonicity,[status(thm)],[28])).
% 2.12/1.64 tff(192,plain,
% 2.12/1.64 (join(join(X0!0, X0!0), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top))) = join(join(X0!0, X0!0), top)),
% 2.12/1.64 inference(monotonicity,[status(thm)],[147])).
% 2.12/1.64 tff(193,plain,
% 2.12/1.64 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(X0!0, X0!0), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top))) = join(join(join(X0!0, X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(top)))),
% 2.12/1.64 inference(quant_inst,[status(thm)],[])).
% 2.12/1.64 tff(194,plain,
% 2.12/1.64 (join(join(X0!0, X0!0), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top))) = join(join(join(X0!0, X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(top))),
% 2.12/1.64 inference(unit_resolution,[status(thm)],[193, 17])).
% 2.12/1.64 tff(195,plain,
% 2.12/1.64 (join(join(join(X0!0, X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(top)) = join(join(X0!0, X0!0), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top)))),
% 2.12/1.64 inference(symmetry,[status(thm)],[194])).
% 2.12/1.64 tff(196,plain,
% 2.12/1.64 (join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))) = join(join(X0!0, X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.64 inference(symmetry,[status(thm)],[108])).
% 2.12/1.64 tff(197,plain,
% 2.12/1.64 (join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(join(join(X0!0, X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(top))),
% 2.12/1.64 inference(monotonicity,[status(thm)],[196, 50])).
% 2.12/1.64 tff(198,plain,
% 2.12/1.64 (join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(join(X0!0, X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.64 inference(transitivity,[status(thm)],[197, 195, 192, 191])).
% 2.12/1.64 tff(199,plain,
% 2.12/1.64 (join(join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(join(join(X0!0, X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(top))),
% 2.12/1.64 inference(monotonicity,[status(thm)],[198, 50])).
% 2.12/1.64 tff(200,plain,
% 2.12/1.64 (join(join(join(X0!0, X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(top)) = join(join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.12/1.64 inference(symmetry,[status(thm)],[199])).
% 2.12/1.64 tff(201,plain,
% 2.12/1.64 (join(join(X0!0, X0!0), top) = join(join(X0!0, X0!0), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top)))),
% 2.12/1.64 inference(symmetry,[status(thm)],[192])).
% 2.12/1.64 tff(202,plain,
% 2.12/1.64 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(X0!0, join(X0!0, top)) = join(join(X0!0, X0!0), top))),
% 2.12/1.64 inference(quant_inst,[status(thm)],[])).
% 2.12/1.64 tff(203,plain,
% 2.12/1.64 (join(X0!0, join(X0!0, top)) = join(join(X0!0, X0!0), top)),
% 2.12/1.64 inference(unit_resolution,[status(thm)],[202, 17])).
% 2.12/1.64 tff(204,plain,
% 2.12/1.64 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(X0!0, top) = join(top, X0!0))),
% 2.12/1.64 inference(quant_inst,[status(thm)],[])).
% 2.12/1.64 tff(205,plain,
% 2.12/1.64 (join(X0!0, top) = join(top, X0!0)),
% 2.12/1.64 inference(unit_resolution,[status(thm)],[204, 37])).
% 2.12/1.64 tff(206,plain,
% 2.12/1.64 (join(top, X0!0) = join(X0!0, top)),
% 2.12/1.64 inference(symmetry,[status(thm)],[205])).
% 2.12/1.64 tff(207,plain,
% 2.12/1.64 (join(X0!0, join(top, X0!0)) = join(X0!0, join(X0!0, top))),
% 2.12/1.64 inference(monotonicity,[status(thm)],[206])).
% 2.12/1.64 tff(208,plain,
% 2.12/1.64 (join(X0!0, join(top, X0!0)) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))),
% 2.12/1.64 inference(transitivity,[status(thm)],[207, 203, 201, 194, 200, 190, 187, 183])).
% 2.12/1.64 tff(209,plain,
% 2.12/1.64 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(X0!0, join(top, X0!0))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.12/1.64 inference(monotonicity,[status(thm)],[208])).
% 2.12/1.64 tff(210,plain,
% 2.12/1.64 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(X0!0, join(top, X0!0)))),
% 2.12/1.64 inference(symmetry,[status(thm)],[209])).
% 2.12/1.64 tff(211,plain,
% 2.12/1.64 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.12/1.64 inference(quant_inst,[status(thm)],[])).
% 2.12/1.64 tff(212,plain,
% 2.12/1.64 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))),
% 2.12/1.64 inference(unit_resolution,[status(thm)],[211, 17])).
% 2.12/1.64 tff(213,plain,
% 2.12/1.64 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.12/1.64 inference(symmetry,[status(thm)],[212])).
% 2.12/1.64 tff(214,plain,
% 2.12/1.64 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))),
% 2.12/1.64 inference(monotonicity,[status(thm)],[127])).
% 2.12/1.64 tff(215,plain,
% 2.12/1.64 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))),
% 2.12/1.65 inference(symmetry,[status(thm)],[214])).
% 2.12/1.65 tff(216,plain,
% 2.12/1.65 (join(join(X0!0, X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(X0!0, X0!0), top)),
% 2.12/1.65 inference(symmetry,[status(thm)],[191])).
% 2.12/1.65 tff(217,plain,
% 2.12/1.65 (join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))) = join(join(top, X0!0), join(top, X0!0))),
% 2.12/1.65 inference(transitivity,[status(thm)],[196, 216, 201, 194, 200, 190, 187, 183, 215, 213, 210, 180, 178])).
% 2.12/1.65 tff(218,plain,
% 2.12/1.65 (join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(top, X0!0))) = join(join(join(top, X0!0), join(top, X0!0)), complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))))),
% 2.12/1.65 inference(monotonicity,[status(thm)],[217, 140])).
% 2.12/1.65 tff(219,plain,
% 2.12/1.65 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))) = join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(top, X0!0))))),
% 2.12/1.65 inference(quant_inst,[status(thm)],[])).
% 2.12/1.65 tff(220,plain,
% 2.12/1.65 (join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))) = join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(top, X0!0)))),
% 2.12/1.65 inference(unit_resolution,[status(thm)],[219, 37])).
% 2.12/1.65 tff(221,plain,
% 2.12/1.65 (join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))) = join(top, X0!0)),
% 2.12/1.65 inference(transitivity,[status(thm)],[220, 218, 174, 171, 160, 157, 156, 153, 151, 150, 148])).
% 2.12/1.65 tff(222,plain,
% 2.12/1.65 (complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))) = complement(join(top, X0!0))),
% 2.12/1.65 inference(monotonicity,[status(thm)],[221])).
% 2.12/1.65 tff(223,plain,
% 2.12/1.65 (complement(join(top, X0!0)) = complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))),
% 2.12/1.65 inference(symmetry,[status(thm)],[222])).
% 2.12/1.65 tff(224,plain,
% 2.12/1.65 (complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))) = complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))),
% 2.12/1.65 inference(transitivity,[status(thm)],[141, 223])).
% 2.12/1.65 tff(225,plain,
% 2.12/1.65 (join(complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))), complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))) = join(complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))), complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))),
% 2.12/1.65 inference(monotonicity,[status(thm)],[224])).
% 2.12/1.65 tff(226,plain,
% 2.12/1.65 (join(complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))), complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))) = join(complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))), complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))),
% 2.12/1.65 inference(symmetry,[status(thm)],[225])).
% 2.12/1.65 tff(227,plain,
% 2.12/1.65 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))) = join(complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))), complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))))),
% 2.12/1.65 inference(quant_inst,[status(thm)],[])).
% 2.12/1.65 tff(228,plain,
% 2.12/1.65 (join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))) = join(complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))), complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))),
% 2.12/1.65 inference(unit_resolution,[status(thm)],[227, 37])).
% 2.12/1.65 tff(229,plain,
% 2.12/1.65 (join(top, X0!0) = join(complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))), complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))))),
% 2.12/1.65 inference(transitivity,[status(thm)],[139, 228, 226])).
% 2.12/1.65 tff(230,plain,
% 2.12/1.65 (join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), join(top, X0!0)) = join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))), complement(join(complement(join(top, X0!0)), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))), complement(join(complement(join(top, X0!0)), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))))),
% 2.12/1.65 inference(monotonicity,[status(thm)],[229])).
% 2.12/1.65 tff(231,plain,
% 2.12/1.65 (join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), join(top, X0!0)) = join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))),
% 2.12/1.65 inference(transitivity,[status(thm)],[230, 146, 144, 134, 28])).
% 2.12/1.65 tff(232,plain,
% 2.12/1.65 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))), join(X0!0, X0!0)) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)))),
% 2.12/1.65 inference(symmetry,[status(thm)],[121])).
% 2.12/1.65 tff(233,plain,
% 2.12/1.65 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(X0!0, X0!0)) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))), join(X0!0, X0!0))),
% 2.12/1.65 inference(symmetry,[status(thm)],[119])).
% 2.12/1.65 tff(234,plain,
% 2.12/1.65 (join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))) = join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.65 inference(transitivity,[status(thm)],[196, 110, 233, 232, 123])).
% 2.12/1.65 tff(235,plain,
% 2.12/1.65 (join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), join(top, X0!0))) = join(join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(X0!0, X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.12/1.65 inference(monotonicity,[status(thm)],[234, 231])).
% 2.12/1.65 tff(236,plain,
% 2.12/1.65 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), join(top, X0!0))) = join(join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))), join(top, X0!0)))),
% 2.12/1.65 inference(quant_inst,[status(thm)],[])).
% 2.12/1.65 tff(237,plain,
% 2.12/1.65 (join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), join(top, X0!0))) = join(join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))), join(top, X0!0))),
% 2.12/1.65 inference(unit_resolution,[status(thm)],[236, 17])).
% 2.12/1.65 tff(238,plain,
% 2.12/1.65 (join(join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))), join(top, X0!0)) = join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), join(complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))), join(top, X0!0)))),
% 2.12/1.65 inference(symmetry,[status(thm)],[237])).
% 2.12/1.65 tff(239,plain,
% 2.12/1.65 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(top), complement(top))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.12/1.65 inference(symmetry,[status(thm)],[117])).
% 2.12/1.65 tff(240,plain,
% 2.12/1.65 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top)), complement(top)) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(top), complement(top)))),
% 2.12/1.65 inference(symmetry,[status(thm)],[116])).
% 2.12/1.65 tff(241,plain,
% 2.12/1.65 (join(join(complement(top), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(top)) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(top)), complement(top))),
% 2.12/1.65 inference(symmetry,[status(thm)],[114])).
% 2.12/1.65 tff(242,plain,
% 2.12/1.65 (join(top, complement(top)) = join(join(complement(top), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(top))),
% 2.12/1.65 inference(symmetry,[status(thm)],[113])).
% 2.12/1.65 tff(243,plain,
% 2.12/1.65 (top = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.12/1.65 inference(transitivity,[status(thm)],[45, 242, 241, 240, 239])).
% 2.12/1.65 tff(244,plain,
% 2.12/1.65 (join(X0!0, top) = join(X0!0, join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))),
% 2.12/1.65 inference(monotonicity,[status(thm)],[243])).
% 2.12/1.65 tff(245,plain,
% 2.12/1.65 (join(X0!0, join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = join(X0!0, top)),
% 2.22/1.65 inference(symmetry,[status(thm)],[244])).
% 2.22/1.65 tff(246,plain,
% 2.22/1.65 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(X0!0, join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = join(join(X0!0, join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))),
% 2.22/1.65 inference(quant_inst,[status(thm)],[])).
% 2.22/1.65 tff(247,plain,
% 2.22/1.65 (join(X0!0, join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = join(join(X0!0, join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.22/1.65 inference(unit_resolution,[status(thm)],[246, 17])).
% 2.22/1.65 tff(248,plain,
% 2.22/1.65 (join(join(X0!0, join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(X0!0, join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))),
% 2.22/1.65 inference(symmetry,[status(thm)],[247])).
% 2.22/1.65 tff(249,plain,
% 2.22/1.65 (join(X0!0, join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(X0!0, top)),
% 2.22/1.65 inference(monotonicity,[status(thm)],[41])).
% 2.22/1.65 tff(250,plain,
% 2.22/1.65 (join(X0!0, join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(top, X0!0)),
% 2.22/1.65 inference(transitivity,[status(thm)],[249, 205])).
% 2.22/1.65 tff(251,plain,
% 2.22/1.65 (join(join(X0!0, join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(join(top, X0!0), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.22/1.65 inference(monotonicity,[status(thm)],[250, 184])).
% 2.22/1.65 tff(252,plain,
% 2.22/1.65 (join(join(top, X0!0), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = join(join(X0!0, join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.22/1.65 inference(symmetry,[status(thm)],[251])).
% 2.22/1.65 tff(253,plain,
% 2.22/1.65 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(top), complement(top))),
% 2.22/1.65 inference(symmetry,[status(thm)],[53])).
% 2.22/1.65 tff(254,plain,
% 2.22/1.65 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))),
% 2.22/1.65 inference(transitivity,[status(thm)],[253, 73])).
% 2.22/1.65 tff(255,plain,
% 2.22/1.65 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(top), X0!0)))),
% 2.22/1.65 inference(quant_inst,[status(thm)],[])).
% 2.22/1.65 tff(256,plain,
% 2.22/1.65 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(top), X0!0))),
% 2.22/1.65 inference(unit_resolution,[status(thm)],[255, 17])).
% 2.22/1.65 tff(257,plain,
% 2.22/1.65 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(top), X0!0)) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0)))),
% 2.22/1.65 inference(symmetry,[status(thm)],[256])).
% 2.22/1.65 tff(258,plain,
% 2.22/1.65 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(top, complement(top))),
% 2.22/1.65 inference(monotonicity,[status(thm)],[41, 50])).
% 2.22/1.65 tff(259,plain,
% 2.22/1.65 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))),
% 2.22/1.65 inference(transitivity,[status(thm)],[258, 46, 28])).
% 2.22/1.65 tff(260,plain,
% 2.22/1.65 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(top), X0!0)) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(top), X0!0))),
% 2.22/1.65 inference(monotonicity,[status(thm)],[259])).
% 2.22/1.65 tff(261,plain,
% 2.22/1.65 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(top), X0!0)) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(top), X0!0))),
% 2.22/1.66 inference(symmetry,[status(thm)],[260])).
% 2.22/1.66 tff(262,plain,
% 2.22/1.66 (join(top, X0!0) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0)))),
% 2.22/1.66 inference(transitivity,[status(thm)],[169, 168, 261, 257])).
% 2.22/1.66 tff(263,plain,
% 2.22/1.66 (join(join(top, X0!0), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.22/1.66 inference(monotonicity,[status(thm)],[262, 254])).
% 2.22/1.66 tff(264,plain,
% 2.22/1.66 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(join(top, X0!0), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.22/1.66 inference(symmetry,[status(thm)],[263])).
% 2.22/1.66 tff(265,plain,
% 2.22/1.66 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))),
% 2.22/1.66 inference(quant_inst,[status(thm)],[])).
% 2.22/1.66 tff(266,plain,
% 2.22/1.66 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.22/1.66 inference(unit_resolution,[status(thm)],[265, 17])).
% 2.22/1.66 tff(267,plain,
% 2.22/1.66 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = join(top, X0!0)),
% 2.22/1.66 inference(transitivity,[status(thm)],[266, 264, 252, 248, 245, 205])).
% 2.22/1.66 tff(268,plain,
% 2.22/1.66 ((~![X0: $i] : (top = join(X0, complement(X0)))) | (top = join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))))),
% 2.22/1.66 inference(quant_inst,[status(thm)],[])).
% 2.22/1.66 tff(269,plain,
% 2.22/1.66 (top = join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))),
% 2.22/1.66 inference(unit_resolution,[status(thm)],[268, 7])).
% 2.22/1.66 tff(270,plain,
% 2.22/1.66 (join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))) = join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))),
% 2.22/1.66 inference(transitivity,[status(thm)],[41, 269])).
% 2.22/1.66 tff(271,plain,
% 2.22/1.66 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))) = join(join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))), join(top, X0!0))),
% 2.22/1.66 inference(monotonicity,[status(thm)],[270, 267])).
% 2.22/1.66 tff(272,plain,
% 2.22/1.66 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.22/1.66 inference(quant_inst,[status(thm)],[])).
% 2.22/1.66 tff(273,plain,
% 2.22/1.66 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))),
% 2.22/1.66 inference(unit_resolution,[status(thm)],[272, 17])).
% 2.22/1.66 tff(274,plain,
% 2.22/1.66 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.22/1.66 inference(symmetry,[status(thm)],[273])).
% 2.22/1.66 tff(275,plain,
% 2.22/1.66 (join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.22/1.66 inference(symmetry,[status(thm)],[126])).
% 2.22/1.66 tff(276,plain,
% 2.22/1.66 (join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))),
% 2.22/1.66 inference(symmetry,[status(thm)],[66])).
% 2.22/1.66 tff(277,plain,
% 2.22/1.66 (join(join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))) = join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.22/1.66 inference(symmetry,[status(thm)],[64])).
% 2.22/1.66 tff(278,plain,
% 2.22/1.66 (join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.22/1.66 inference(transitivity,[status(thm)],[41, 9, 61, 277, 276, 78, 82, 85, 275])).
% 2.22/1.66 tff(279,plain,
% 2.22/1.66 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))),
% 2.22/1.66 inference(monotonicity,[status(thm)],[278])).
% 2.22/1.66 tff(280,plain,
% 2.22/1.66 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))),
% 2.22/1.66 inference(symmetry,[status(thm)],[266])).
% 2.22/1.66 tff(281,plain,
% 2.22/1.66 (join(top, X0!0) = join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))),
% 2.22/1.66 inference(transitivity,[status(thm)],[206, 244, 247, 251, 263, 280, 279, 274, 271, 238, 235, 131, 128, 124, 121, 119, 111, 108])).
% 2.22/1.66 tff(282,plain,
% 2.22/1.66 (join(complement(X0!0), join(top, X0!0)) = join(complement(X0!0), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))),
% 2.22/1.66 inference(monotonicity,[status(thm)],[281])).
% 2.22/1.66 tff(283,plain,
% 2.22/1.66 (join(complement(X0!0), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))) = join(complement(X0!0), join(top, X0!0))),
% 2.22/1.66 inference(symmetry,[status(thm)],[282])).
% 2.22/1.66 tff(284,plain,
% 2.22/1.66 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(X0!0), complement(join(top, X0!0))) = join(complement(join(top, X0!0)), complement(X0!0)))),
% 2.22/1.66 inference(quant_inst,[status(thm)],[])).
% 2.22/1.66 tff(285,plain,
% 2.22/1.66 (join(complement(X0!0), complement(join(top, X0!0))) = join(complement(join(top, X0!0)), complement(X0!0))),
% 2.22/1.66 inference(unit_resolution,[status(thm)],[284, 37])).
% 2.22/1.66 tff(286,plain,
% 2.22/1.66 (join(complement(join(top, X0!0)), complement(X0!0)) = join(complement(X0!0), complement(join(top, X0!0)))),
% 2.22/1.66 inference(symmetry,[status(thm)],[285])).
% 2.22/1.66 tff(287,plain,
% 2.22/1.66 (complement(join(complement(join(top, X0!0)), complement(X0!0))) = complement(join(complement(X0!0), complement(join(top, X0!0))))),
% 2.22/1.66 inference(monotonicity,[status(thm)],[286])).
% 2.22/1.66 tff(288,plain,
% 2.22/1.66 (^[X0: $i] : refl((zero = meet(X0, complement(X0))) <=> (zero = meet(X0, complement(X0))))),
% 2.22/1.66 inference(bind,[status(th)],[])).
% 2.22/1.66 tff(289,plain,
% 2.22/1.66 (![X0: $i] : (zero = meet(X0, complement(X0))) <=> ![X0: $i] : (zero = meet(X0, complement(X0)))),
% 2.22/1.66 inference(quant_intro,[status(thm)],[288])).
% 2.22/1.66 tff(290,plain,
% 2.22/1.66 (![X0: $i] : (zero = meet(X0, complement(X0))) <=> ![X0: $i] : (zero = meet(X0, complement(X0)))),
% 2.22/1.66 inference(rewrite,[status(thm)],[])).
% 2.22/1.66 tff(291,axiom,(![X0: $i] : (zero = meet(X0, complement(X0)))), file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax','def_zero')).
% 2.22/1.66 tff(292,plain,
% 2.22/1.66 (![X0: $i] : (zero = meet(X0, complement(X0)))),
% 2.22/1.66 inference(modus_ponens,[status(thm)],[291, 290])).
% 2.22/1.66 tff(293,plain,(
% 2.22/1.66 ![X0: $i] : (zero = meet(X0, complement(X0)))),
% 2.22/1.66 inference(skolemize,[status(sab)],[292])).
% 2.22/1.66 tff(294,plain,
% 2.22/1.66 (![X0: $i] : (zero = meet(X0, complement(X0)))),
% 2.22/1.66 inference(modus_ponens,[status(thm)],[293, 289])).
% 2.22/1.66 tff(295,plain,
% 2.22/1.66 ((~![X0: $i] : (zero = meet(X0, complement(X0)))) | (zero = meet(join(complement(top), top), complement(join(complement(top), top))))),
% 2.22/1.66 inference(quant_inst,[status(thm)],[])).
% 2.22/1.66 tff(296,plain,
% 2.22/1.66 (zero = meet(join(complement(top), top), complement(join(complement(top), top)))),
% 2.22/1.66 inference(unit_resolution,[status(thm)],[295, 294])).
% 2.22/1.66 tff(297,plain,
% 2.22/1.66 ((~![X0: $i] : (zero = meet(X0, complement(X0)))) | (zero = meet(join(top, X0!0), complement(join(top, X0!0))))),
% 2.22/1.66 inference(quant_inst,[status(thm)],[])).
% 2.22/1.66 tff(298,plain,
% 2.22/1.66 (zero = meet(join(top, X0!0), complement(join(top, X0!0)))),
% 2.22/1.66 inference(unit_resolution,[status(thm)],[297, 294])).
% 2.22/1.66 tff(299,plain,
% 2.22/1.66 (meet(join(top, X0!0), complement(join(top, X0!0))) = zero),
% 2.22/1.66 inference(symmetry,[status(thm)],[298])).
% 2.22/1.66 tff(300,plain,
% 2.22/1.66 (^[X0: $i, X1: $i] : refl((meet(X0, X1) = complement(join(complement(X0), complement(X1)))) <=> (meet(X0, X1) = complement(join(complement(X0), complement(X1)))))),
% 2.22/1.66 inference(bind,[status(th)],[])).
% 2.22/1.66 tff(301,plain,
% 2.22/1.66 (![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1)))) <=> ![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))),
% 2.22/1.66 inference(quant_intro,[status(thm)],[300])).
% 2.22/1.66 tff(302,plain,
% 2.22/1.66 (![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1)))) <=> ![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))),
% 2.22/1.66 inference(rewrite,[status(thm)],[])).
% 2.22/1.66 tff(303,axiom,(![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))), file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax','maddux4_definiton_of_meet')).
% 2.22/1.66 tff(304,plain,
% 2.22/1.66 (![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))),
% 2.22/1.66 inference(modus_ponens,[status(thm)],[303, 302])).
% 2.22/1.66 tff(305,plain,(
% 2.22/1.66 ![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))),
% 2.22/1.66 inference(skolemize,[status(sab)],[304])).
% 2.22/1.66 tff(306,plain,
% 2.22/1.66 (![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))),
% 2.22/1.66 inference(modus_ponens,[status(thm)],[305, 301])).
% 2.22/1.66 tff(307,plain,
% 2.22/1.66 ((~![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))) | (meet(join(top, X0!0), complement(join(top, X0!0))) = complement(join(complement(join(top, X0!0)), complement(complement(join(top, X0!0))))))),
% 2.22/1.66 inference(quant_inst,[status(thm)],[])).
% 2.22/1.66 tff(308,plain,
% 2.22/1.66 (meet(join(top, X0!0), complement(join(top, X0!0))) = complement(join(complement(join(top, X0!0)), complement(complement(join(top, X0!0)))))),
% 2.22/1.66 inference(unit_resolution,[status(thm)],[307, 306])).
% 2.22/1.66 tff(309,plain,
% 2.22/1.66 (complement(join(complement(join(top, X0!0)), complement(complement(join(top, X0!0))))) = meet(join(top, X0!0), complement(join(top, X0!0)))),
% 2.22/1.66 inference(symmetry,[status(thm)],[308])).
% 2.22/1.66 tff(310,plain,
% 2.22/1.66 (complement(join(complement(join(top, X0!0)), complement(complement(join(top, X0!0))))) = meet(join(complement(top), top), complement(join(complement(top), top)))),
% 2.22/1.66 inference(transitivity,[status(thm)],[309, 299, 296])).
% 2.22/1.66 tff(311,plain,
% 2.22/1.66 (join(complement(join(complement(join(top, X0!0)), complement(complement(join(top, X0!0))))), complement(join(complement(join(top, X0!0)), complement(X0!0)))) = join(meet(join(complement(top), top), complement(join(complement(top), top))), complement(join(complement(X0!0), complement(join(top, X0!0)))))),
% 2.22/1.66 inference(monotonicity,[status(thm)],[310, 287])).
% 2.22/1.66 tff(312,plain,
% 2.22/1.66 (join(meet(join(complement(top), top), complement(join(complement(top), top))), complement(join(complement(X0!0), complement(join(top, X0!0))))) = join(complement(join(complement(join(top, X0!0)), complement(complement(join(top, X0!0))))), complement(join(complement(join(top, X0!0)), complement(X0!0))))),
% 2.22/1.66 inference(symmetry,[status(thm)],[311])).
% 2.22/1.66 tff(313,plain,
% 2.22/1.66 (join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0))) = join(complement(X0!0), complement(join(top, X0!0)))),
% 2.22/1.66 inference(monotonicity,[status(thm)],[90])).
% 2.22/1.66 tff(314,plain,
% 2.22/1.66 (join(complement(X0!0), complement(join(top, X0!0))) = join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0)))),
% 2.22/1.66 inference(symmetry,[status(thm)],[313])).
% 2.22/1.66 tff(315,plain,
% 2.22/1.66 (complement(join(complement(X0!0), complement(join(top, X0!0)))) = complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0))))),
% 2.22/1.66 inference(monotonicity,[status(thm)],[314])).
% 2.22/1.66 tff(316,plain,
% 2.22/1.66 ((~![X0: $i] : (top = join(X0, complement(X0)))) | (top = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))))),
% 2.22/1.66 inference(quant_inst,[status(thm)],[])).
% 2.22/1.66 tff(317,plain,
% 2.22/1.66 (top = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.22/1.66 inference(unit_resolution,[status(thm)],[316, 7])).
% 2.22/1.66 tff(318,plain,
% 2.22/1.66 (complement(top) = complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))))),
% 2.22/1.66 inference(monotonicity,[status(thm)],[317])).
% 2.22/1.66 tff(319,plain,
% 2.22/1.66 (complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))) = complement(top)),
% 2.22/1.66 inference(symmetry,[status(thm)],[318])).
% 2.22/1.66 tff(320,plain,
% 2.22/1.66 ((~![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))) | (meet(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))))),
% 2.22/1.66 inference(quant_inst,[status(thm)],[])).
% 2.22/1.66 tff(321,plain,
% 2.22/1.66 (meet(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))))),
% 2.22/1.66 inference(unit_resolution,[status(thm)],[320, 306])).
% 2.22/1.66 tff(322,plain,
% 2.22/1.66 ((~![X0: $i] : (zero = meet(X0, complement(X0)))) | (zero = meet(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.22/1.66 inference(quant_inst,[status(thm)],[])).
% 2.22/1.66 tff(323,plain,
% 2.22/1.66 (zero = meet(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.22/1.66 inference(unit_resolution,[status(thm)],[322, 294])).
% 2.22/1.66 tff(324,plain,
% 2.22/1.66 (meet(join(complement(top), top), complement(join(complement(top), top))) = zero),
% 2.22/1.66 inference(symmetry,[status(thm)],[296])).
% 2.22/1.66 tff(325,plain,
% 2.22/1.66 (meet(join(complement(top), top), complement(join(complement(top), top))) = complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.22/1.66 inference(transitivity,[status(thm)],[324, 323, 321, 319, 52])).
% 2.22/1.66 tff(326,plain,
% 2.22/1.66 (join(meet(join(complement(top), top), complement(join(complement(top), top))), meet(join(complement(top), top), complement(join(complement(top), top)))) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.22/1.66 inference(monotonicity,[status(thm)],[325, 325])).
% 2.22/1.66 tff(327,plain,
% 2.22/1.66 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(meet(join(complement(top), top), complement(join(complement(top), top))), meet(join(complement(top), top), complement(join(complement(top), top))))),
% 2.22/1.67 inference(symmetry,[status(thm)],[326])).
% 2.22/1.67 tff(328,plain,
% 2.22/1.67 ((~![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))) | (join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))))),
% 2.22/1.67 inference(quant_inst,[status(thm)],[])).
% 2.22/1.67 tff(329,plain,
% 2.22/1.67 (join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.22/1.67 inference(unit_resolution,[status(thm)],[328, 26])).
% 2.22/1.67 tff(330,plain,
% 2.22/1.67 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))) = join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))),
% 2.22/1.67 inference(symmetry,[status(thm)],[329])).
% 2.22/1.67 tff(331,plain,
% 2.22/1.67 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))) = join(complement(join(complement(top), top)), complement(join(complement(top), complement(top)))))),
% 2.22/1.67 inference(quant_inst,[status(thm)],[])).
% 2.22/1.67 tff(332,plain,
% 2.22/1.67 (join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))) = join(complement(join(complement(top), top)), complement(join(complement(top), complement(top))))),
% 2.22/1.67 inference(unit_resolution,[status(thm)],[331, 37])).
% 2.22/1.67 tff(333,plain,
% 2.22/1.67 (join(complement(join(complement(top), top)), complement(join(complement(top), complement(top)))) = join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))),
% 2.22/1.67 inference(symmetry,[status(thm)],[332])).
% 2.22/1.67 tff(334,plain,
% 2.22/1.67 (join(complement(top), complement(join(complement(top), complement(top)))) = join(complement(join(complement(top), top)), complement(join(complement(top), complement(top))))),
% 2.22/1.67 inference(monotonicity,[status(thm)],[49])).
% 2.22/1.67 tff(335,plain,
% 2.22/1.67 (complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = complement(join(complement(top), complement(top)))),
% 2.22/1.67 inference(monotonicity,[status(thm)],[74])).
% 2.22/1.67 tff(336,plain,
% 2.22/1.67 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = join(complement(top), complement(join(complement(top), complement(top))))),
% 2.22/1.67 inference(monotonicity,[status(thm)],[50, 335])).
% 2.22/1.67 tff(337,plain,
% 2.22/1.67 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))) = top),
% 2.22/1.67 inference(transitivity,[status(thm)],[336, 334, 333, 41])).
% 2.22/1.67 tff(338,plain,
% 2.22/1.67 (complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))) = complement(top)),
% 2.22/1.67 inference(monotonicity,[status(thm)],[337])).
% 2.22/1.67 tff(339,plain,
% 2.22/1.67 (complement(top) = complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.22/1.67 inference(symmetry,[status(thm)],[338])).
% 2.22/1.67 tff(340,plain,
% 2.22/1.67 (complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.22/1.67 inference(transitivity,[status(thm)],[50, 339])).
% 2.22/1.67 tff(341,plain,
% 2.22/1.67 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.22/1.67 inference(monotonicity,[status(thm)],[340])).
% 2.22/1.67 tff(342,plain,
% 2.22/1.67 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))) = join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))),
% 2.22/1.67 inference(transitivity,[status(thm)],[341, 330])).
% 2.22/1.67 tff(343,plain,
% 2.22/1.67 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))) = join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.22/1.67 inference(monotonicity,[status(thm)],[125, 342])).
% 2.22/1.67 tff(344,plain,
% 2.22/1.67 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))))),
% 2.22/1.67 inference(quant_inst,[status(thm)],[])).
% 2.22/1.67 tff(345,plain,
% 2.22/1.67 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.22/1.67 inference(unit_resolution,[status(thm)],[344, 17])).
% 2.22/1.67 tff(346,plain,
% 2.22/1.67 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))))),
% 2.22/1.67 inference(symmetry,[status(thm)],[345])).
% 2.22/1.67 tff(347,plain,
% 2.22/1.67 (join(top, complement(top)) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.22/1.67 inference(symmetry,[status(thm)],[258])).
% 2.22/1.67 tff(348,plain,
% 2.22/1.67 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = top),
% 2.22/1.67 inference(symmetry,[status(thm)],[317])).
% 2.22/1.67 tff(349,plain,
% 2.22/1.67 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = join(complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.22/1.67 inference(quant_inst,[status(thm)],[])).
% 2.22/1.67 tff(350,plain,
% 2.22/1.67 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = join(complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.22/1.67 inference(unit_resolution,[status(thm)],[349, 37])).
% 2.22/1.67 tff(351,plain,
% 2.22/1.67 (join(complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.22/1.67 inference(symmetry,[status(thm)],[350])).
% 2.22/1.67 tff(352,plain,
% 2.22/1.67 (join(complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), meet(join(complement(top), top), complement(join(complement(top), top)))) = join(complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.22/1.67 inference(monotonicity,[status(thm)],[325])).
% 2.22/1.67 tff(353,plain,
% 2.22/1.67 (join(complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), meet(join(complement(top), top), complement(join(complement(top), top)))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.22/1.67 inference(transitivity,[status(thm)],[352, 351, 348, 45, 347])).
% 2.22/1.67 tff(354,plain,
% 2.22/1.67 (join(join(complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), meet(join(complement(top), top), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.22/1.67 inference(monotonicity,[status(thm)],[353])).
% 2.22/1.67 tff(355,plain,
% 2.22/1.67 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(meet(join(complement(top), top), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))) = join(join(complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), meet(join(complement(top), top), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))))),
% 2.22/1.67 inference(quant_inst,[status(thm)],[])).
% 2.22/1.67 tff(356,plain,
% 2.22/1.67 (join(complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(meet(join(complement(top), top), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))) = join(join(complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), meet(join(complement(top), top), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.22/1.67 inference(unit_resolution,[status(thm)],[355, 17])).
% 2.22/1.67 tff(357,plain,
% 2.22/1.67 (meet(join(complement(top), top), complement(join(complement(top), top))) = complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.22/1.67 inference(transitivity,[status(thm)],[324, 323, 321, 319, 339])).
% 2.22/1.67 tff(358,plain,
% 2.22/1.67 (join(meet(join(complement(top), top), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.22/1.67 inference(monotonicity,[status(thm)],[357])).
% 2.22/1.67 tff(359,plain,
% 2.22/1.67 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))) = join(meet(join(complement(top), top), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.22/1.67 inference(symmetry,[status(thm)],[358])).
% 2.22/1.67 tff(360,plain,
% 2.22/1.67 (join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))) = join(meet(join(complement(top), top), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.22/1.67 inference(transitivity,[status(thm)],[329, 359])).
% 2.22/1.67 tff(361,plain,
% 2.22/1.67 (join(complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(meet(join(complement(top), top), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))))),
% 2.22/1.67 inference(monotonicity,[status(thm)],[360])).
% 2.22/1.67 tff(362,plain,
% 2.22/1.67 (complement(meet(join(complement(top), top), complement(join(complement(top), top)))) = complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.22/1.67 inference(monotonicity,[status(thm)],[325])).
% 2.22/1.67 tff(363,plain,
% 2.22/1.67 (join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.22/1.67 inference(monotonicity,[status(thm)],[362])).
% 2.22/1.67 tff(364,plain,
% 2.22/1.67 (join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = top),
% 2.22/1.67 inference(transitivity,[status(thm)],[363, 361, 356, 354, 346, 343, 86, 83, 79, 66, 64, 62, 10])).
% 2.22/1.67 tff(365,plain,
% 2.22/1.67 (complement(join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = complement(top)),
% 2.22/1.67 inference(monotonicity,[status(thm)],[364])).
% 2.22/1.67 tff(366,plain,
% 2.22/1.67 (complement(top) = complement(join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.22/1.67 inference(symmetry,[status(thm)],[365])).
% 2.22/1.67 tff(367,plain,
% 2.22/1.67 (complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = complement(join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.22/1.67 inference(transitivity,[status(thm)],[50, 366])).
% 2.22/1.67 tff(368,plain,
% 2.22/1.67 (join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.22/1.67 inference(monotonicity,[status(thm)],[362])).
% 2.22/1.67 tff(369,plain,
% 2.22/1.67 (join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = top),
% 2.22/1.67 inference(transitivity,[status(thm)],[368, 351, 348])).
% 2.22/1.67 tff(370,plain,
% 2.22/1.67 (complement(join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = complement(top)),
% 2.22/1.67 inference(monotonicity,[status(thm)],[369])).
% 2.22/1.67 tff(371,plain,
% 2.22/1.67 (complement(top) = complement(join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.22/1.67 inference(symmetry,[status(thm)],[370])).
% 2.22/1.67 tff(372,plain,
% 2.22/1.67 (complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = complement(join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.22/1.67 inference(transitivity,[status(thm)],[50, 371])).
% 2.22/1.67 tff(373,plain,
% 2.22/1.67 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.22/1.68 inference(monotonicity,[status(thm)],[372, 367])).
% 2.22/1.68 tff(374,plain,
% 2.22/1.68 (join(complement(join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.22/1.68 inference(symmetry,[status(thm)],[373])).
% 2.22/1.68 tff(375,plain,
% 2.22/1.68 ((~![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))) | (meet(join(complement(top), top), complement(join(complement(top), top))) = join(complement(join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))))),
% 2.22/1.68 inference(quant_inst,[status(thm)],[])).
% 2.22/1.68 tff(376,plain,
% 2.22/1.68 (meet(join(complement(top), top), complement(join(complement(top), top))) = join(complement(join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(meet(join(complement(top), top), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[375, 26])).
% 2.22/1.68 tff(377,plain,
% 2.22/1.68 (meet(join(complement(top), top), complement(join(complement(top), top))) = join(meet(join(complement(top), top), complement(join(complement(top), top))), meet(join(complement(top), top), complement(join(complement(top), top))))),
% 2.22/1.68 inference(transitivity,[status(thm)],[376, 374, 327])).
% 2.22/1.68 tff(378,plain,
% 2.22/1.68 (join(meet(join(complement(top), top), complement(join(complement(top), top))), complement(join(complement(X0!0), complement(join(top, X0!0))))) = join(join(meet(join(complement(top), top), complement(join(complement(top), top))), meet(join(complement(top), top), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0)))))),
% 2.22/1.68 inference(monotonicity,[status(thm)],[377, 315])).
% 2.22/1.68 tff(379,plain,
% 2.22/1.68 (join(join(meet(join(complement(top), top), complement(join(complement(top), top))), meet(join(complement(top), top), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0))))) = join(meet(join(complement(top), top), complement(join(complement(top), top))), complement(join(complement(X0!0), complement(join(top, X0!0)))))),
% 2.22/1.68 inference(symmetry,[status(thm)],[378])).
% 2.22/1.68 tff(380,plain,
% 2.22/1.68 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(meet(join(complement(top), top), complement(join(complement(top), top))), join(meet(join(complement(top), top), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0)))))) = join(join(meet(join(complement(top), top), complement(join(complement(top), top))), meet(join(complement(top), top), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0))))))),
% 2.22/1.68 inference(quant_inst,[status(thm)],[])).
% 2.22/1.68 tff(381,plain,
% 2.22/1.68 (join(meet(join(complement(top), top), complement(join(complement(top), top))), join(meet(join(complement(top), top), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0)))))) = join(join(meet(join(complement(top), top), complement(join(complement(top), top))), meet(join(complement(top), top), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0)))))),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[380, 17])).
% 2.22/1.68 tff(382,plain,
% 2.22/1.68 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(meet(join(complement(top), top), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0))))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0)))), meet(join(complement(top), top), complement(join(complement(top), top)))))),
% 2.22/1.68 inference(quant_inst,[status(thm)],[])).
% 2.22/1.68 tff(383,plain,
% 2.22/1.68 (join(meet(join(complement(top), top), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0))))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0)))), meet(join(complement(top), top), complement(join(complement(top), top))))),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[382, 37])).
% 2.22/1.68 tff(384,plain,
% 2.22/1.68 (join(complement(X0!0), join(top, X0!0)) = top),
% 2.22/1.68 inference(transitivity,[status(thm)],[106, 104, 101, 98, 86, 83, 79, 66, 64, 62, 10])).
% 2.22/1.68 tff(385,plain,
% 2.22/1.68 (complement(join(complement(X0!0), join(top, X0!0))) = complement(top)),
% 2.22/1.68 inference(monotonicity,[status(thm)],[384])).
% 2.22/1.68 tff(386,plain,
% 2.22/1.68 (complement(top) = complement(join(complement(X0!0), join(top, X0!0)))),
% 2.22/1.68 inference(symmetry,[status(thm)],[385])).
% 2.22/1.68 tff(387,plain,
% 2.22/1.68 (meet(join(complement(top), top), complement(join(complement(top), top))) = complement(join(complement(X0!0), join(top, X0!0)))),
% 2.22/1.68 inference(transitivity,[status(thm)],[324, 323, 321, 319, 386])).
% 2.22/1.68 tff(388,plain,
% 2.22/1.68 (join(meet(join(complement(top), top), complement(join(complement(top), top))), join(meet(join(complement(top), top), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0)))))) = join(complement(join(complement(X0!0), join(top, X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0)))), meet(join(complement(top), top), complement(join(complement(top), top)))))),
% 2.22/1.68 inference(monotonicity,[status(thm)],[387, 383])).
% 2.22/1.68 tff(389,plain,
% 2.22/1.68 (join(complement(join(complement(X0!0), join(top, X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0)))), meet(join(complement(top), top), complement(join(complement(top), top))))) = join(meet(join(complement(top), top), complement(join(complement(top), top))), join(meet(join(complement(top), top), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0))))))),
% 2.22/1.68 inference(symmetry,[status(thm)],[388])).
% 2.22/1.68 tff(390,plain,
% 2.22/1.68 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(complement(X0!0), join(top, X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0)))), meet(join(complement(top), top), complement(join(complement(top), top))))) = join(join(complement(join(complement(X0!0), join(top, X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0))))), meet(join(complement(top), top), complement(join(complement(top), top)))))),
% 2.22/1.68 inference(quant_inst,[status(thm)],[])).
% 2.22/1.68 tff(391,plain,
% 2.22/1.68 (join(complement(join(complement(X0!0), join(top, X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0)))), meet(join(complement(top), top), complement(join(complement(top), top))))) = join(join(complement(join(complement(X0!0), join(top, X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0))))), meet(join(complement(top), top), complement(join(complement(top), top))))),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[390, 17])).
% 2.22/1.68 tff(392,plain,
% 2.22/1.68 (join(join(complement(join(complement(X0!0), join(top, X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0))))), meet(join(complement(top), top), complement(join(complement(top), top)))) = join(complement(join(complement(X0!0), join(top, X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0)))), meet(join(complement(top), top), complement(join(complement(top), top)))))),
% 2.22/1.68 inference(symmetry,[status(thm)],[391])).
% 2.22/1.68 tff(393,plain,
% 2.22/1.68 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))) = join(complement(join(complement(X0!0), join(top, X0!0))), complement(join(complement(X0!0), complement(join(top, X0!0))))))),
% 2.22/1.68 inference(quant_inst,[status(thm)],[])).
% 2.22/1.68 tff(394,plain,
% 2.22/1.68 (join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0)))) = join(complement(join(complement(X0!0), join(top, X0!0))), complement(join(complement(X0!0), complement(join(top, X0!0)))))),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[393, 37])).
% 2.22/1.68 tff(395,plain,
% 2.22/1.68 (join(complement(join(complement(X0!0), join(top, X0!0))), complement(join(complement(X0!0), complement(join(top, X0!0))))) = join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))),
% 2.22/1.68 inference(symmetry,[status(thm)],[394])).
% 2.22/1.68 tff(396,plain,
% 2.22/1.68 (complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0)))) = complement(join(complement(X0!0), complement(join(top, X0!0))))),
% 2.25/1.68 inference(symmetry,[status(thm)],[315])).
% 2.25/1.68 tff(397,plain,
% 2.25/1.68 (join(complement(join(complement(X0!0), join(top, X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0))))) = join(complement(join(complement(X0!0), join(top, X0!0))), complement(join(complement(X0!0), complement(join(top, X0!0)))))),
% 2.25/1.68 inference(monotonicity,[status(thm)],[396])).
% 2.25/1.68 tff(398,plain,
% 2.25/1.68 (join(complement(join(complement(X0!0), join(top, X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0))))) = X0!0),
% 2.25/1.68 inference(transitivity,[status(thm)],[397, 395, 89])).
% 2.25/1.68 tff(399,plain,
% 2.25/1.68 (join(join(complement(join(complement(X0!0), join(top, X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0))))), meet(join(complement(top), top), complement(join(complement(top), top)))) = join(X0!0, complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.25/1.68 inference(monotonicity,[status(thm)],[398, 325])).
% 2.25/1.68 tff(400,plain,
% 2.25/1.68 (join(X0!0, complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(join(complement(join(complement(X0!0), join(top, X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(join(top, X0!0)))), complement(join(complement(X0!0), join(top, X0!0))))), complement(join(top, X0!0))))), meet(join(complement(top), top), complement(join(complement(top), top))))),
% 2.25/1.68 inference(symmetry,[status(thm)],[399])).
% 2.25/1.68 tff(401,plain,
% 2.25/1.68 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), X0!0) = join(X0!0, complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.25/1.68 inference(quant_inst,[status(thm)],[])).
% 2.25/1.68 tff(402,plain,
% 2.25/1.68 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), X0!0) = join(X0!0, complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.25/1.68 inference(unit_resolution,[status(thm)],[401, 37])).
% 2.25/1.68 tff(403,plain,
% 2.25/1.68 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), X0!0) = join(complement(top), X0!0)),
% 2.25/1.68 inference(monotonicity,[status(thm)],[50])).
% 2.25/1.68 tff(404,plain,
% 2.25/1.68 (join(complement(top), X0!0) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), X0!0)),
% 2.25/1.68 inference(symmetry,[status(thm)],[403])).
% 2.25/1.68 tff(405,plain,
% 2.25/1.68 ((~![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))) | (join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))))),
% 2.25/1.68 inference(quant_inst,[status(thm)],[])).
% 2.25/1.68 tff(406,plain,
% 2.25/1.68 (join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.25/1.68 inference(unit_resolution,[status(thm)],[405, 26])).
% 2.25/1.68 tff(407,plain,
% 2.25/1.68 (join(complement(join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.25/1.68 inference(symmetry,[status(thm)],[406])).
% 2.25/1.68 tff(408,plain,
% 2.25/1.68 (join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.25/1.68 inference(transitivity,[status(thm)],[41, 45, 347])).
% 2.25/1.68 tff(409,plain,
% 2.25/1.68 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.25/1.68 inference(monotonicity,[status(thm)],[408])).
% 2.25/1.68 tff(410,plain,
% 2.25/1.68 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))))),
% 2.25/1.68 inference(quant_inst,[status(thm)],[])).
% 2.25/1.68 tff(411,plain,
% 2.25/1.68 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.25/1.68 inference(unit_resolution,[status(thm)],[410, 37])).
% 2.25/1.68 tff(412,plain,
% 2.25/1.68 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.25/1.68 inference(quant_inst,[status(thm)],[])).
% 2.25/1.68 tff(413,plain,
% 2.25/1.68 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.25/1.68 inference(unit_resolution,[status(thm)],[412, 37])).
% 2.25/1.68 tff(414,plain,
% 2.25/1.68 (join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.25/1.68 inference(symmetry,[status(thm)],[413])).
% 2.25/1.68 tff(415,plain,
% 2.25/1.68 (complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))),
% 2.25/1.68 inference(monotonicity,[status(thm)],[414])).
% 2.25/1.68 tff(416,plain,
% 2.25/1.68 (join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.25/1.68 inference(monotonicity,[status(thm)],[415])).
% 2.25/1.68 tff(417,plain,
% 2.25/1.68 (join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = top),
% 2.25/1.68 inference(transitivity,[status(thm)],[416, 411, 409, 346, 343, 86, 83, 79, 66, 64, 62, 10])).
% 2.25/1.68 tff(418,plain,
% 2.25/1.68 (complement(join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = complement(top)),
% 2.25/1.68 inference(monotonicity,[status(thm)],[417])).
% 2.25/1.68 tff(419,plain,
% 2.25/1.68 (complement(join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.25/1.69 inference(transitivity,[status(thm)],[418, 52])).
% 2.25/1.69 tff(420,plain,
% 2.25/1.69 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.25/1.69 inference(quant_inst,[status(thm)],[])).
% 2.25/1.69 tff(421,plain,
% 2.25/1.69 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))))) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.25/1.69 inference(unit_resolution,[status(thm)],[420, 37])).
% 2.25/1.69 tff(422,plain,
% 2.25/1.69 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))))),
% 2.25/1.69 inference(symmetry,[status(thm)],[421])).
% 2.25/1.69 tff(423,plain,
% 2.25/1.69 (join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.25/1.69 inference(monotonicity,[status(thm)],[415])).
% 2.25/1.69 tff(424,plain,
% 2.25/1.69 (join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = top),
% 2.25/1.69 inference(transitivity,[status(thm)],[423, 422, 341, 330, 41])).
% 2.25/1.69 tff(425,plain,
% 2.25/1.69 (complement(join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = complement(top)),
% 2.25/1.69 inference(monotonicity,[status(thm)],[424])).
% 2.25/1.69 tff(426,plain,
% 2.25/1.69 (complement(join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.25/1.69 inference(transitivity,[status(thm)],[425, 52])).
% 2.25/1.69 tff(427,plain,
% 2.25/1.69 (join(complement(join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.25/1.69 inference(monotonicity,[status(thm)],[426, 419])).
% 2.25/1.69 tff(428,plain,
% 2.25/1.69 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))),
% 2.25/1.69 inference(symmetry,[status(thm)],[427])).
% 2.25/1.69 tff(429,plain,
% 2.25/1.69 (meet(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = zero),
% 2.25/1.69 inference(symmetry,[status(thm)],[323])).
% 2.25/1.69 tff(430,plain,
% 2.25/1.69 (complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))) = meet(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.25/1.69 inference(symmetry,[status(thm)],[321])).
% 2.25/1.69 tff(431,plain,
% 2.25/1.69 (complement(top) = join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.25/1.69 inference(transitivity,[status(thm)],[318, 430, 429, 296, 376, 374, 428, 407])).
% 2.25/1.69 tff(432,plain,
% 2.25/1.69 (join(complement(top), X0!0) = join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), X0!0)),
% 2.25/1.69 inference(monotonicity,[status(thm)],[431])).
% 2.25/1.69 tff(433,plain,
% 2.25/1.69 (join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), X0!0) = join(complement(top), X0!0)),
% 2.25/1.69 inference(symmetry,[status(thm)],[432])).
% 2.25/1.69 tff(434,plain,
% 2.25/1.69 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), X0!0)) = join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), X0!0))),
% 2.25/1.69 inference(quant_inst,[status(thm)],[])).
% 2.25/1.69 tff(435,plain,
% 2.25/1.69 (join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), X0!0)) = join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), X0!0)),
% 2.25/1.69 inference(unit_resolution,[status(thm)],[434, 17])).
% 2.25/1.69 tff(436,plain,
% 2.25/1.69 (join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), X0!0)) = join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))),
% 2.25/1.69 inference(monotonicity,[status(thm)],[403])).
% 2.25/1.69 tff(437,plain,
% 2.25/1.69 (join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)) = join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), X0!0))),
% 2.25/1.69 inference(symmetry,[status(thm)],[436])).
% 2.25/1.69 tff(438,plain,
% 2.25/1.69 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))) = join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.25/1.69 inference(transitivity,[status(thm)],[74, 53, 428, 407])).
% 2.25/1.69 tff(439,plain,
% 2.25/1.69 (join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)) = join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(top), X0!0))),
% 2.25/1.69 inference(monotonicity,[status(thm)],[438])).
% 2.25/1.69 tff(440,plain,
% 2.25/1.69 (join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(top), X0!0)) = join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))),
% 2.25/1.69 inference(symmetry,[status(thm)],[439])).
% 2.25/1.69 tff(441,plain,
% 2.25/1.69 (join(meet(join(complement(top), top), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.25/1.69 inference(monotonicity,[status(thm)],[325])).
% 2.25/1.69 tff(442,plain,
% 2.25/1.69 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(meet(join(complement(top), top), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.25/1.69 inference(symmetry,[status(thm)],[441])).
% 2.25/1.69 tff(443,plain,
% 2.25/1.69 (join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(meet(join(complement(top), top), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.25/1.69 inference(transitivity,[status(thm)],[414, 442])).
% 2.25/1.69 tff(444,plain,
% 2.25/1.69 (join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(top), X0!0)) = join(join(meet(join(complement(top), top), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))), join(complement(top), X0!0))),
% 2.25/1.69 inference(monotonicity,[status(thm)],[443])).
% 2.25/1.69 tff(445,plain,
% 2.25/1.69 (join(join(meet(join(complement(top), top), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))), join(complement(top), X0!0)) = join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), join(complement(top), X0!0))),
% 2.25/1.69 inference(symmetry,[status(thm)],[444])).
% 2.25/1.69 tff(446,plain,
% 2.25/1.69 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(meet(join(complement(top), top), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))) = join(join(meet(join(complement(top), top), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))), join(complement(top), X0!0)))),
% 2.25/1.69 inference(quant_inst,[status(thm)],[])).
% 2.25/1.69 tff(447,plain,
% 2.25/1.69 (join(meet(join(complement(top), top), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))) = join(join(meet(join(complement(top), top), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))), join(complement(top), X0!0))),
% 2.25/1.69 inference(unit_resolution,[status(thm)],[446, 17])).
% 2.25/1.69 tff(448,plain,
% 2.25/1.69 (join(meet(join(complement(top), top), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))),
% 2.25/1.69 inference(monotonicity,[status(thm)],[325])).
% 2.25/1.69 tff(449,plain,
% 2.25/1.69 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))) = join(meet(join(complement(top), top), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))),
% 2.25/1.69 inference(symmetry,[status(thm)],[448])).
% 2.25/1.69 tff(450,plain,
% 2.25/1.69 (join(complement(join(complement(top), complement(top))), join(complement(top), top)) = top),
% 2.25/1.69 inference(transitivity,[status(thm)],[79, 66, 64, 62, 10])).
% 2.25/1.69 tff(451,plain,
% 2.25/1.69 (complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))) = complement(top)),
% 2.25/1.69 inference(monotonicity,[status(thm)],[450])).
% 2.25/1.69 tff(452,plain,
% 2.25/1.69 (complement(top) = complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))),
% 2.25/1.69 inference(symmetry,[status(thm)],[451])).
% 2.25/1.69 tff(453,plain,
% 2.25/1.69 (complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))),
% 2.25/1.69 inference(transitivity,[status(thm)],[50, 452])).
% 2.25/1.69 tff(454,plain,
% 2.25/1.69 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))) = join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))),
% 2.25/1.69 inference(monotonicity,[status(thm)],[453])).
% 2.25/1.69 tff(455,plain,
% 2.25/1.69 (join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))),
% 2.25/1.69 inference(symmetry,[status(thm)],[454])).
% 2.25/1.69 tff(456,plain,
% 2.25/1.69 (join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))) = join(complement(join(complement(join(top, X0!0)), complement(complement(join(top, X0!0))))), complement(join(complement(join(top, X0!0)), complement(X0!0))))),
% 2.25/1.69 inference(transitivity,[status(thm)],[455, 449, 447, 445, 440, 437, 435, 433, 404, 402, 400, 392, 389, 381, 379, 312])).
% 2.25/1.69 tff(457,plain,
% 2.25/1.69 (complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))) = complement(join(complement(join(complement(join(top, X0!0)), complement(complement(join(top, X0!0))))), complement(join(complement(join(top, X0!0)), complement(X0!0)))))),
% 2.25/1.69 inference(monotonicity,[status(thm)],[456])).
% 2.25/1.69 tff(458,plain,
% 2.25/1.69 (complement(join(complement(join(complement(join(top, X0!0)), complement(complement(join(top, X0!0))))), complement(join(complement(join(top, X0!0)), complement(X0!0))))) = complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))),
% 2.25/1.69 inference(symmetry,[status(thm)],[457])).
% 2.25/1.69 tff(459,plain,
% 2.25/1.69 ((~![X0: $i] : (zero = meet(X0, complement(X0)))) | (zero = meet(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))))),
% 2.25/1.69 inference(quant_inst,[status(thm)],[])).
% 2.25/1.69 tff(460,plain,
% 2.25/1.69 (zero = meet(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))),
% 2.25/1.69 inference(unit_resolution,[status(thm)],[459, 294])).
% 2.25/1.69 tff(461,plain,
% 2.25/1.69 (meet(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))) = zero),
% 2.25/1.70 inference(symmetry,[status(thm)],[460])).
% 2.25/1.70 tff(462,plain,
% 2.25/1.70 ((~![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))) | (meet(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))) = complement(join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))))))),
% 2.25/1.70 inference(quant_inst,[status(thm)],[])).
% 2.25/1.70 tff(463,plain,
% 2.25/1.70 (meet(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))) = complement(join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))))),
% 2.25/1.70 inference(unit_resolution,[status(thm)],[462, 306])).
% 2.25/1.70 tff(464,plain,
% 2.25/1.70 (complement(join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))))) = meet(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))),
% 2.25/1.70 inference(symmetry,[status(thm)],[463])).
% 2.25/1.70 tff(465,plain,
% 2.25/1.70 (complement(join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))))) = complement(join(complement(join(top, X0!0)), complement(complement(join(top, X0!0)))))),
% 2.25/1.70 inference(transitivity,[status(thm)],[464, 461, 298, 308])).
% 2.25/1.70 tff(466,plain,
% 2.25/1.70 (join(complement(join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))))), complement(join(complement(join(top, X0!0)), complement(X0!0)))) = join(complement(join(complement(join(top, X0!0)), complement(complement(join(top, X0!0))))), complement(join(complement(join(top, X0!0)), complement(X0!0))))),
% 2.25/1.70 inference(monotonicity,[status(thm)],[465])).
% 2.25/1.70 tff(467,plain,
% 2.25/1.70 (join(complement(join(complement(join(top, X0!0)), complement(complement(join(top, X0!0))))), complement(join(complement(join(top, X0!0)), complement(X0!0)))) = join(complement(join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))))), complement(join(complement(join(top, X0!0)), complement(X0!0))))),
% 2.25/1.70 inference(symmetry,[status(thm)],[466])).
% 2.25/1.70 tff(468,plain,
% 2.25/1.70 (complement(join(complement(join(complement(join(top, X0!0)), complement(complement(join(top, X0!0))))), complement(join(complement(join(top, X0!0)), complement(X0!0))))) = complement(join(complement(join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))))), complement(join(complement(join(top, X0!0)), complement(X0!0)))))),
% 2.25/1.70 inference(monotonicity,[status(thm)],[467])).
% 2.25/1.70 tff(469,plain,
% 2.25/1.70 (complement(join(complement(join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))))), complement(join(complement(join(top, X0!0)), complement(X0!0))))) = complement(join(complement(join(complement(join(top, X0!0)), complement(complement(join(top, X0!0))))), complement(join(complement(join(top, X0!0)), complement(X0!0)))))),
% 2.25/1.70 inference(symmetry,[status(thm)],[468])).
% 2.25/1.70 tff(470,plain,
% 2.25/1.70 ((~![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))) | (meet(join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))), join(complement(join(top, X0!0)), complement(X0!0))) = complement(join(complement(join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))))), complement(join(complement(join(top, X0!0)), complement(X0!0))))))),
% 2.25/1.70 inference(quant_inst,[status(thm)],[])).
% 2.25/1.70 tff(471,plain,
% 2.25/1.70 (meet(join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))), join(complement(join(top, X0!0)), complement(X0!0))) = complement(join(complement(join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))))), complement(join(complement(join(top, X0!0)), complement(X0!0)))))),
% 2.25/1.70 inference(unit_resolution,[status(thm)],[470, 306])).
% 2.25/1.70 tff(472,plain,
% 2.25/1.70 ((~![X0: $i] : (top = join(X0, complement(X0)))) | (top = join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))))),
% 2.25/1.70 inference(quant_inst,[status(thm)],[])).
% 2.25/1.70 tff(473,plain,
% 2.25/1.70 (top = join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))))),
% 2.25/1.70 inference(unit_resolution,[status(thm)],[472, 7])).
% 2.25/1.70 tff(474,plain,
% 2.25/1.70 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))) = top),
% 2.25/1.70 inference(symmetry,[status(thm)],[473])).
% 2.25/1.70 tff(475,plain,
% 2.25/1.70 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))) = join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))),
% 2.25/1.70 inference(transitivity,[status(thm)],[474, 28])).
% 2.25/1.70 tff(476,plain,
% 2.25/1.70 (meet(join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))), join(complement(join(top, X0!0)), complement(X0!0))) = meet(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(top, X0!0)), complement(X0!0)))),
% 2.25/1.70 inference(monotonicity,[status(thm)],[475])).
% 2.25/1.70 tff(477,plain,
% 2.25/1.70 (meet(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(top, X0!0)), complement(X0!0))) = meet(join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))), join(complement(join(top, X0!0)), complement(X0!0)))),
% 2.25/1.70 inference(symmetry,[status(thm)],[476])).
% 2.25/1.70 tff(478,plain,
% 2.25/1.70 (join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))) = join(join(top, X0!0), complement(X0!0))),
% 2.25/1.70 inference(transitivity,[status(thm)],[41, 9, 61, 277, 276, 78, 82, 85, 97, 100, 103])).
% 2.25/1.70 tff(479,plain,
% 2.25/1.70 (meet(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(top, X0!0)), complement(X0!0))) = meet(join(join(top, X0!0), complement(X0!0)), join(complement(join(top, X0!0)), complement(X0!0)))),
% 2.25/1.70 inference(monotonicity,[status(thm)],[478])).
% 2.25/1.70 tff(480,plain,
% 2.25/1.70 (meet(join(join(top, X0!0), complement(X0!0)), join(complement(join(top, X0!0)), complement(X0!0))) = meet(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(top, X0!0)), complement(X0!0)))),
% 2.25/1.70 inference(symmetry,[status(thm)],[479])).
% 2.25/1.70 tff(481,plain,
% 2.25/1.70 ((~![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))) | (meet(join(join(top, X0!0), complement(X0!0)), join(complement(join(top, X0!0)), complement(X0!0))) = complement(join(complement(join(join(top, X0!0), complement(X0!0))), complement(join(complement(join(top, X0!0)), complement(X0!0))))))),
% 2.25/1.70 inference(quant_inst,[status(thm)],[])).
% 2.25/1.70 tff(482,plain,
% 2.25/1.70 (meet(join(join(top, X0!0), complement(X0!0)), join(complement(join(top, X0!0)), complement(X0!0))) = complement(join(complement(join(join(top, X0!0), complement(X0!0))), complement(join(complement(join(top, X0!0)), complement(X0!0)))))),
% 2.25/1.70 inference(unit_resolution,[status(thm)],[481, 306])).
% 2.25/1.70 tff(483,plain,
% 2.25/1.70 (complement(join(complement(join(join(top, X0!0), complement(X0!0))), complement(join(complement(join(top, X0!0)), complement(X0!0))))) = meet(join(join(top, X0!0), complement(X0!0)), join(complement(join(top, X0!0)), complement(X0!0)))),
% 2.25/1.70 inference(symmetry,[status(thm)],[482])).
% 2.25/1.70 tff(484,plain,
% 2.25/1.70 (join(join(top, X0!0), complement(X0!0)) = join(complement(X0!0), join(top, X0!0))),
% 2.25/1.70 inference(symmetry,[status(thm)],[106])).
% 2.25/1.70 tff(485,plain,
% 2.25/1.70 (complement(join(join(top, X0!0), complement(X0!0))) = complement(join(complement(X0!0), join(top, X0!0)))),
% 2.25/1.70 inference(monotonicity,[status(thm)],[484])).
% 2.25/1.70 tff(486,plain,
% 2.25/1.70 (join(complement(join(join(top, X0!0), complement(X0!0))), complement(join(complement(join(top, X0!0)), complement(X0!0)))) = join(complement(join(complement(X0!0), join(top, X0!0))), complement(join(complement(X0!0), complement(join(top, X0!0)))))),
% 2.25/1.70 inference(monotonicity,[status(thm)],[485, 287])).
% 2.25/1.70 tff(487,plain,
% 2.25/1.70 (join(complement(join(join(top, X0!0), complement(X0!0))), complement(join(complement(join(top, X0!0)), complement(X0!0)))) = X0!0),
% 2.25/1.70 inference(transitivity,[status(thm)],[486, 395, 89])).
% 2.25/1.70 tff(488,plain,
% 2.25/1.70 (complement(join(complement(join(join(top, X0!0), complement(X0!0))), complement(join(complement(join(top, X0!0)), complement(X0!0))))) = complement(X0!0)),
% 2.25/1.70 inference(monotonicity,[status(thm)],[487])).
% 2.25/1.70 tff(489,plain,
% 2.25/1.70 (complement(X0!0) = complement(join(complement(join(join(top, X0!0), complement(X0!0))), complement(join(complement(join(top, X0!0)), complement(X0!0)))))),
% 2.25/1.70 inference(symmetry,[status(thm)],[488])).
% 2.25/1.70 tff(490,plain,
% 2.25/1.70 (complement(X0!0) = complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))),
% 2.25/1.70 inference(transitivity,[status(thm)],[489, 483, 480, 477, 471, 469, 458])).
% 2.25/1.70 tff(491,plain,
% 2.25/1.70 (join(complement(X0!0), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))),
% 2.25/1.70 inference(monotonicity,[status(thm)],[490])).
% 2.25/1.70 tff(492,plain,
% 2.25/1.70 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))) = join(complement(X0!0), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))),
% 2.25/1.70 inference(symmetry,[status(thm)],[491])).
% 2.25/1.70 tff(493,plain,
% 2.25/1.70 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))),
% 2.25/1.70 inference(quant_inst,[status(thm)],[])).
% 2.25/1.70 tff(494,plain,
% 2.25/1.70 (join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))),
% 2.25/1.70 inference(unit_resolution,[status(thm)],[493, 37])).
% 2.25/1.70 tff(495,plain,
% 2.25/1.70 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(top), X0!0)) = join(join(complement(top), X0!0), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))))),
% 2.25/1.70 inference(quant_inst,[status(thm)],[])).
% 2.25/1.70 tff(496,plain,
% 2.25/1.70 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(top), X0!0)) = join(join(complement(top), X0!0), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))))),
% 2.25/1.70 inference(unit_resolution,[status(thm)],[495, 37])).
% 2.25/1.70 tff(497,plain,
% 2.25/1.70 (join(complement(join(complement(top), top)), X0!0) = join(complement(top), X0!0)),
% 2.25/1.70 inference(monotonicity,[status(thm)],[48])).
% 2.25/1.70 tff(498,plain,
% 2.25/1.70 (join(complement(top), X0!0) = join(complement(join(complement(top), top)), X0!0)),
% 2.25/1.70 inference(symmetry,[status(thm)],[497])).
% 2.25/1.70 tff(499,plain,
% 2.25/1.70 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(top), X0!0)) = join(complement(join(complement(top), complement(top))), join(complement(join(complement(top), top)), X0!0))),
% 2.25/1.70 inference(monotonicity,[status(thm)],[55, 498])).
% 2.25/1.70 tff(500,plain,
% 2.25/1.70 (join(complement(join(complement(top), complement(top))), join(complement(join(complement(top), top)), X0!0)) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(top), X0!0))),
% 2.25/1.71 inference(symmetry,[status(thm)],[499])).
% 2.25/1.71 tff(501,plain,
% 2.25/1.71 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(complement(top), complement(top))), join(complement(join(complement(top), top)), X0!0)) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), X0!0))),
% 2.25/1.71 inference(quant_inst,[status(thm)],[])).
% 2.25/1.71 tff(502,plain,
% 2.25/1.71 (join(complement(join(complement(top), complement(top))), join(complement(join(complement(top), top)), X0!0)) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), X0!0)),
% 2.25/1.71 inference(unit_resolution,[status(thm)],[501, 17])).
% 2.25/1.71 tff(503,plain,
% 2.25/1.71 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), X0!0) = join(complement(join(complement(top), complement(top))), join(complement(join(complement(top), top)), X0!0))),
% 2.25/1.71 inference(symmetry,[status(thm)],[502])).
% 2.25/1.71 tff(504,plain,
% 2.25/1.71 (join(top, X0!0) = join(join(complement(top), X0!0), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))))),
% 2.25/1.71 inference(transitivity,[status(thm)],[176, 503, 500, 496])).
% 2.25/1.71 tff(505,plain,
% 2.25/1.71 (join(join(top, X0!0), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))) = join(join(join(complement(top), X0!0), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))),
% 2.25/1.71 inference(monotonicity,[status(thm)],[504])).
% 2.25/1.71 tff(506,plain,
% 2.25/1.71 (join(join(join(complement(top), X0!0), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))) = join(join(top, X0!0), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))),
% 2.25/1.71 inference(symmetry,[status(thm)],[505])).
% 2.25/1.71 tff(507,plain,
% 2.25/1.71 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(top), X0!0)) = join(join(complement(top), X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.25/1.71 inference(quant_inst,[status(thm)],[])).
% 2.25/1.71 tff(508,plain,
% 2.25/1.71 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(top), X0!0)) = join(join(complement(top), X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.25/1.71 inference(unit_resolution,[status(thm)],[507, 37])).
% 2.25/1.71 tff(509,plain,
% 2.25/1.71 (join(join(complement(top), X0!0), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(top), X0!0))),
% 2.25/1.71 inference(symmetry,[status(thm)],[496])).
% 2.25/1.71 tff(510,plain,
% 2.25/1.71 (join(join(complement(top), X0!0), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))) = join(join(complement(top), X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.25/1.71 inference(transitivity,[status(thm)],[509, 499, 502, 175, 169, 168, 508])).
% 2.25/1.71 tff(511,plain,
% 2.25/1.71 (join(join(join(complement(top), X0!0), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))) = join(join(join(complement(top), X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))),
% 2.25/1.71 inference(monotonicity,[status(thm)],[510])).
% 2.25/1.71 tff(512,plain,
% 2.25/1.71 (join(join(join(complement(top), X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))) = join(join(join(complement(top), X0!0), complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))))), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))),
% 2.25/1.71 inference(symmetry,[status(thm)],[511])).
% 2.25/1.71 tff(513,plain,
% 2.25/1.71 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(complement(top), X0!0), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))) = join(join(join(complement(top), X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))),
% 2.25/1.71 inference(quant_inst,[status(thm)],[])).
% 2.25/1.71 tff(514,plain,
% 2.25/1.71 (join(join(complement(top), X0!0), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))) = join(join(join(complement(top), X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))),
% 2.25/1.71 inference(unit_resolution,[status(thm)],[513, 17])).
% 2.25/1.71 tff(515,plain,
% 2.25/1.71 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.25/1.71 inference(quant_inst,[status(thm)],[])).
% 2.25/1.71 tff(516,plain,
% 2.25/1.71 (join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))) = join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))),
% 2.25/1.71 inference(unit_resolution,[status(thm)],[515, 17])).
% 2.25/1.71 tff(517,plain,
% 2.25/1.71 (join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))) = join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))))),
% 2.25/1.71 inference(symmetry,[status(thm)],[516])).
% 2.25/1.71 tff(518,plain,
% 2.25/1.71 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))) = join(join(complement(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))))),
% 2.25/1.71 inference(monotonicity,[status(thm)],[125])).
% 2.25/1.71 tff(519,plain,
% 2.25/1.71 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))) = join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))),
% 2.25/1.71 inference(transitivity,[status(thm)],[518, 517, 76, 68, 42, 46, 28])).
% 2.25/1.71 tff(520,plain,
% 2.25/1.71 (join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))) = join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))),
% 2.25/1.71 inference(monotonicity,[status(thm)],[519])).
% 2.25/1.71 tff(521,plain,
% 2.25/1.71 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))),
% 2.25/1.71 inference(quant_inst,[status(thm)],[])).
% 2.25/1.71 tff(522,plain,
% 2.25/1.71 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))) = join(join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))),
% 2.25/1.71 inference(unit_resolution,[status(thm)],[521, 17])).
% 2.25/1.71 tff(523,plain,
% 2.25/1.71 (join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))) = join(top, X0!0)),
% 2.25/1.71 inference(transitivity,[status(thm)],[522, 520, 153, 151, 150, 148])).
% 2.25/1.71 tff(524,plain,
% 2.25/1.71 (join(join(complement(top), X0!0), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))) = join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), X0!0), join(top, X0!0))),
% 2.25/1.71 inference(monotonicity,[status(thm)],[404, 523])).
% 2.25/1.71 tff(525,plain,
% 2.25/1.71 (join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), X0!0), join(top, X0!0)) = join(join(complement(top), X0!0), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))),
% 2.25/1.71 inference(symmetry,[status(thm)],[524])).
% 2.25/1.71 tff(526,plain,
% 2.25/1.71 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(X0!0, join(top, X0!0))) = join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), X0!0), join(top, X0!0)))),
% 2.25/1.71 inference(quant_inst,[status(thm)],[])).
% 2.25/1.71 tff(527,plain,
% 2.25/1.71 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(X0!0, join(top, X0!0))) = join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), X0!0), join(top, X0!0))),
% 2.25/1.71 inference(unit_resolution,[status(thm)],[526, 17])).
% 2.25/1.71 tff(528,plain,
% 2.25/1.71 (join(X0!0, join(top, X0!0)) = join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))),
% 2.25/1.71 inference(transitivity,[status(thm)],[207, 203, 191, 108])).
% 2.25/1.71 tff(529,plain,
% 2.25/1.71 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(X0!0, join(top, X0!0))) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))),
% 2.25/1.71 inference(monotonicity,[status(thm)],[528])).
% 2.25/1.71 tff(530,plain,
% 2.25/1.71 (join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(X0!0, join(top, X0!0)))),
% 2.25/1.71 inference(symmetry,[status(thm)],[529])).
% 2.25/1.71 tff(531,plain,
% 2.25/1.71 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top)))))),
% 2.25/1.71 inference(quant_inst,[status(thm)],[])).
% 2.25/1.71 tff(532,plain,
% 2.25/1.71 (join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))) = join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))))),
% 2.25/1.71 inference(unit_resolution,[status(thm)],[531, 37])).
% 2.25/1.71 tff(533,plain,
% 2.25/1.71 (join(join(join(X0!0, X0!0), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(top)) = join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.25/1.71 inference(symmetry,[status(thm)],[197])).
% 2.25/1.71 tff(534,plain,
% 2.25/1.71 (join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))) = join(join(top, X0!0), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))),
% 2.25/1.71 inference(transitivity,[status(thm)],[196, 216, 201, 194, 533, 532, 530, 527, 525, 514, 512, 506])).
% 2.25/1.71 tff(535,plain,
% 2.25/1.71 (join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))) = join(join(join(top, X0!0), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))),
% 2.25/1.72 inference(monotonicity,[status(thm)],[534])).
% 2.25/1.72 tff(536,plain,
% 2.25/1.72 (join(join(join(top, X0!0), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))) = join(join(join(join(X0!0, X0!0), complement(join(complement(top), complement(top)))), complement(join(complement(top), top))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))),
% 2.25/1.72 inference(symmetry,[status(thm)],[535])).
% 2.25/1.72 tff(537,plain,
% 2.25/1.72 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(top, X0!0), join(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))) = join(join(join(top, X0!0), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))))),
% 2.25/1.72 inference(quant_inst,[status(thm)],[])).
% 2.25/1.72 tff(538,plain,
% 2.25/1.72 (join(join(top, X0!0), join(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))) = join(join(join(top, X0!0), join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))),
% 2.25/1.72 inference(unit_resolution,[status(thm)],[537, 17])).
% 2.25/1.72 tff(539,plain,
% 2.25/1.72 ((~![X0: $i] : (top = join(X0, complement(X0)))) | (top = join(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))))),
% 2.25/1.72 inference(quant_inst,[status(thm)],[])).
% 2.25/1.72 tff(540,plain,
% 2.25/1.72 (top = join(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))),
% 2.25/1.72 inference(unit_resolution,[status(thm)],[539, 7])).
% 2.25/1.72 tff(541,plain,
% 2.25/1.72 (join(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))) = top),
% 2.25/1.72 inference(symmetry,[status(thm)],[540])).
% 2.25/1.72 tff(542,plain,
% 2.25/1.72 (join(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))) = join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))),
% 2.25/1.72 inference(transitivity,[status(thm)],[541, 28])).
% 2.25/1.72 tff(543,plain,
% 2.25/1.72 (join(join(top, X0!0), join(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)))))) = join(join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))))),
% 2.25/1.72 inference(monotonicity,[status(thm)],[170, 542])).
% 2.25/1.72 tff(544,plain,
% 2.25/1.72 (join(join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(top, X0!0), join(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))), complement(join(complement(join(complement(join(complement(top), complement(top))), join(complement(top), top))), join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0))))))),
% 2.25/1.72 inference(symmetry,[status(thm)],[543])).
% 2.25/1.72 tff(545,plain,
% 2.25/1.72 (join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))) = join(join(join(complement(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))), complement(join(complement(join(complement(top), complement(top))), join(complement(top), top)))), join(complement(top), X0!0)), join(join(complement(join(complement(top), complement(top))), complement(join(complement(top), top))), join(complement(join(complement(top), complement(top))), complement(join(complement(top), top)))))),
% 2.25/1.72 inference(symmetry,[status(thm)],[157])).
% 2.25/1.72 tff(546,plain,
% 2.25/1.72 (join(X0!0, top) = top),
% 2.25/1.72 inference(transitivity,[status(thm)],[205, 169, 168, 167, 166, 155, 545, 159, 544, 538, 536, 494, 492, 283, 106, 104, 101, 98, 86, 83, 79, 66, 64, 62, 10])).
% 2.25/1.72 tff(547,plain,
% 2.25/1.72 ((~![X0: $i] : (join(X0, top) = top)) <=> (~![X0: $i] : (join(X0, top) = top))),
% 2.25/1.72 inference(rewrite,[status(thm)],[])).
% 2.25/1.72 tff(548,axiom,(~![X0: $i] : (join(X0, top) = top)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 2.25/1.72 tff(549,plain,
% 2.25/1.72 (~![X0: $i] : (join(X0, top) = top)),
% 2.25/1.72 inference(modus_ponens,[status(thm)],[548, 547])).
% 2.25/1.72 tff(550,plain,
% 2.25/1.72 (~![X0: $i] : (join(X0, top) = top)),
% 2.25/1.72 inference(modus_ponens,[status(thm)],[549, 547])).
% 2.25/1.72 tff(551,plain,
% 2.25/1.72 (~![X0: $i] : (join(X0, top) = top)),
% 2.25/1.72 inference(modus_ponens,[status(thm)],[550, 547])).
% 2.25/1.72 tff(552,plain,
% 2.25/1.72 (~![X0: $i] : (join(X0, top) = top)),
% 2.25/1.72 inference(modus_ponens,[status(thm)],[551, 547])).
% 2.25/1.72 tff(553,plain,
% 2.25/1.72 (~![X0: $i] : (join(X0, top) = top)),
% 2.25/1.72 inference(modus_ponens,[status(thm)],[552, 547])).
% 2.25/1.72 tff(554,plain,
% 2.25/1.72 (~![X0: $i] : (join(X0, top) = top)),
% 2.25/1.72 inference(modus_ponens,[status(thm)],[553, 547])).
% 2.25/1.72 tff(555,plain,
% 2.25/1.72 (~![X0: $i] : (join(X0, top) = top)),
% 2.25/1.72 inference(modus_ponens,[status(thm)],[554, 547])).
% 2.25/1.72 tff(556,plain,(
% 2.25/1.72 ~(join(X0!0, top) = top)),
% 2.25/1.72 inference(skolemize,[status(sab)],[555])).
% 2.25/1.72 tff(557,plain,
% 2.25/1.72 ($false),
% 2.25/1.72 inference(unit_resolution,[status(thm)],[556, 546])).
% 2.25/1.72 % SZS output end Proof
%------------------------------------------------------------------------------