TSTP Solution File: REL046+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : REL046+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 03:00:22 EDT 2022
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : REL046+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 20:49:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(tptp_fun_X2_0_type, type, (
% 0.19/0.42 tptp_fun_X2_0: $i)).
% 0.19/0.42 tff(join_type, type, (
% 0.19/0.42 join: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_X0_2_type, type, (
% 0.19/0.42 tptp_fun_X0_2: $i)).
% 0.19/0.42 tff(complement_type, type, (
% 0.19/0.42 complement: $i > $i)).
% 0.19/0.42 tff(tptp_fun_X1_1_type, type, (
% 0.19/0.42 tptp_fun_X1_1: $i)).
% 0.19/0.42 tff(meet_type, type, (
% 0.19/0.42 meet: ( $i * $i ) > $i)).
% 0.19/0.42 tff(1,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(4,axiom,(![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax','maddux3_a_kind_of_de_Morgan')).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.42 tff(6,plain,(
% 0.19/0.42 ![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[5])).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 (![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 ((~![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))) | (X2!0 = join(complement(join(complement(X2!0), complement(join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))))), complement(join(complement(X2!0), join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 (X2!0 = join(complement(join(complement(X2!0), complement(join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))))), complement(join(complement(X2!0), join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (join(complement(join(complement(X2!0), complement(join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))))), complement(join(complement(X2!0), join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))))) = X2!0),
% 0.19/0.42 inference(symmetry,[status(thm)],[9])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 (^[X0: $i, X1: $i] : refl((join(X0, X1) = join(X1, X0)) <=> (join(X0, X1) = join(X1, X0)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0)) <=> ![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0)) <=> ![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(14,axiom,(![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))), file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax','maddux1_join_commutativity')).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.42 tff(16,plain,(
% 0.19/0.42 ![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 0.19/0.43 inference(skolemize,[status(sab)],[15])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(X1!1), complement(X2!0)) = join(complement(X2!0), complement(X1!1)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 (join(complement(X1!1), complement(X2!0)) = join(complement(X2!0), complement(X1!1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (join(complement(X2!0), complement(X1!1)) = join(complement(X1!1), complement(X2!0))),
% 0.19/0.43 inference(symmetry,[status(thm)],[19])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 ((~![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))) | (X1!1 = join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 (X1!1 = join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[21, 7])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 (join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))) = X1!1),
% 0.19/0.43 inference(symmetry,[status(thm)],[22])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 (complement(join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))) = complement(X1!1)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[23])).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 (join(complement(X2!0), complement(join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))))) = join(complement(X2!0), complement(X1!1))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[24])).
% 0.19/0.43 tff(26,plain,
% 0.19/0.43 (join(complement(X2!0), complement(join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))))) = join(complement(X1!1), complement(X2!0))),
% 0.19/0.43 inference(transitivity,[status(thm)],[25, 20])).
% 0.19/0.43 tff(27,plain,
% 0.19/0.43 (complement(join(complement(X2!0), complement(join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))))) = complement(join(complement(X1!1), complement(X2!0)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[26])).
% 0.19/0.43 tff(28,plain,
% 0.19/0.43 (complement(join(complement(X1!1), complement(X2!0))) = complement(join(complement(X2!0), complement(join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))))))),
% 0.19/0.43 inference(symmetry,[status(thm)],[27])).
% 0.19/0.43 tff(29,plain,
% 0.19/0.43 (^[X0: $i, X1: $i] : refl((meet(X0, X1) = complement(join(complement(X0), complement(X1)))) <=> (meet(X0, X1) = complement(join(complement(X0), complement(X1)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(32,axiom,(![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax','maddux4_definiton_of_meet')).
% 0.19/0.43 tff(33,plain,
% 0.19/0.43 (![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.43 tff(34,plain,(
% 0.19/0.43 ![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[33])).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 (![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 ((~![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))) | (meet(X1!1, X2!0) = complement(join(complement(X1!1), complement(X2!0))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(37,plain,
% 0.19/0.43 (meet(X1!1, X2!0) = complement(join(complement(X1!1), complement(X2!0)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.43 tff(38,plain,
% 0.19/0.43 ((~![X0: $i, X1: $i, X2: $i] : ((~(join(X0, meet(X1, X2)) = meet(X1, X2))) | ((join(X0, X1) = X1) & (join(X0, X2) = X2)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~(join(X0, meet(X1, X2)) = meet(X1, X2))) | ((join(X0, X1) = X1) & (join(X0, X2) = X2))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(39,plain,
% 0.19/0.43 ((~![X0: $i, X1: $i, X2: $i] : ((join(X0, meet(X1, X2)) = meet(X1, X2)) => ((join(X0, X1) = X1) & (join(X0, X2) = X2)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~(join(X0, meet(X1, X2)) = meet(X1, X2))) | ((join(X0, X1) = X1) & (join(X0, X2) = X2))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(40,axiom,(~![X0: $i, X1: $i, X2: $i] : ((join(X0, meet(X1, X2)) = meet(X1, X2)) => ((join(X0, X1) = X1) & (join(X0, X2) = X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 (~![X0: $i, X1: $i, X2: $i] : ((~(join(X0, meet(X1, X2)) = meet(X1, X2))) | ((join(X0, X1) = X1) & (join(X0, X2) = X2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.43 tff(42,plain,
% 0.19/0.43 (~![X0: $i, X1: $i, X2: $i] : ((~(join(X0, meet(X1, X2)) = meet(X1, X2))) | ((join(X0, X1) = X1) & (join(X0, X2) = X2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 (~![X0: $i, X1: $i, X2: $i] : ((~(join(X0, meet(X1, X2)) = meet(X1, X2))) | ((join(X0, X1) = X1) & (join(X0, X2) = X2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 (~![X0: $i, X1: $i, X2: $i] : ((~(join(X0, meet(X1, X2)) = meet(X1, X2))) | ((join(X0, X1) = X1) & (join(X0, X2) = X2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[43, 38])).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 (~![X0: $i, X1: $i, X2: $i] : ((~(join(X0, meet(X1, X2)) = meet(X1, X2))) | ((join(X0, X1) = X1) & (join(X0, X2) = X2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[44, 38])).
% 0.19/0.43 tff(46,plain,
% 0.19/0.43 (~![X0: $i, X1: $i, X2: $i] : ((~(join(X0, meet(X1, X2)) = meet(X1, X2))) | ((join(X0, X1) = X1) & (join(X0, X2) = X2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 (~![X0: $i, X1: $i, X2: $i] : ((~(join(X0, meet(X1, X2)) = meet(X1, X2))) | ((join(X0, X1) = X1) & (join(X0, X2) = X2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[46, 38])).
% 0.19/0.43 tff(48,plain,(
% 0.19/0.43 ~((~(join(X0!2, meet(X1!1, X2!0)) = meet(X1!1, X2!0))) | ((join(X0!2, X1!1) = X1!1) & (join(X0!2, X2!0) = X2!0)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[47])).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 (join(X0!2, meet(X1!1, X2!0)) = meet(X1!1, X2!0)),
% 0.19/0.43 inference(or_elim,[status(thm)],[48])).
% 0.19/0.43 tff(50,plain,
% 0.19/0.43 (join(X0!2, meet(X1!1, X2!0)) = complement(join(complement(X2!0), complement(join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[49, 37, 28])).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 (join(join(X0!2, meet(X1!1, X2!0)), complement(join(complement(X2!0), join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))))) = join(complement(join(complement(X2!0), complement(join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))))), complement(join(complement(X2!0), join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[50])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 (^[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)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(55,axiom,(![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))), file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax','maddux2_join_associativity')).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 (![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.43 tff(57,plain,(
% 0.19/0.43 ![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 0.19/0.43 inference(skolemize,[status(sab)],[56])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 (![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(X0!2, join(meet(X1!1, X2!0), complement(join(complement(X2!0), join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))))))) = join(join(X0!2, meet(X1!1, X2!0)), complement(join(complement(X2!0), join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (join(X0!2, join(meet(X1!1, X2!0), complement(join(complement(X2!0), join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))))))) = join(join(X0!2, meet(X1!1, X2!0)), complement(join(complement(X2!0), join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (meet(X1!1, X2!0) = complement(join(complement(X2!0), complement(join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[37, 28])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 (join(meet(X1!1, X2!0), complement(join(complement(X2!0), join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))))) = join(complement(join(complement(X2!0), complement(join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))))), complement(join(complement(X2!0), join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[61])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 (join(complement(join(complement(X2!0), complement(join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))))), complement(join(complement(X2!0), join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))))) = join(meet(X1!1, X2!0), complement(join(complement(X2!0), join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))))))),
% 0.19/0.43 inference(symmetry,[status(thm)],[62])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 (X2!0 = join(meet(X1!1, X2!0), complement(join(complement(X2!0), join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[9, 63])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 (join(X0!2, X2!0) = join(X0!2, join(meet(X1!1, X2!0), complement(join(complement(X2!0), join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[64])).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 (join(X0!2, X2!0) = X2!0),
% 0.19/0.43 inference(transitivity,[status(thm)],[65, 60, 51, 10])).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 (join(X0!2, meet(X1!1, X2!0)) = complement(join(complement(X1!1), complement(X2!0)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[49, 37])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 (join(join(X0!2, meet(X1!1, X2!0)), complement(join(complement(X1!1), X2!0))) = join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[67])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(X0!2, join(meet(X1!1, X2!0), complement(join(complement(X1!1), X2!0)))) = join(join(X0!2, meet(X1!1, X2!0)), complement(join(complement(X1!1), X2!0))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(70,plain,
% 0.19/0.44 (join(X0!2, join(meet(X1!1, X2!0), complement(join(complement(X1!1), X2!0)))) = join(join(X0!2, meet(X1!1, X2!0)), complement(join(complement(X1!1), X2!0)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[69, 58])).
% 0.19/0.44 tff(71,plain,
% 0.19/0.44 (join(meet(X1!1, X2!0), complement(join(complement(X1!1), X2!0))) = join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 (join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))) = join(meet(X1!1, X2!0), complement(join(complement(X1!1), X2!0)))),
% 0.19/0.44 inference(symmetry,[status(thm)],[71])).
% 0.19/0.44 tff(73,plain,
% 0.19/0.44 (X1!1 = join(meet(X1!1, X2!0), complement(join(complement(X1!1), X2!0)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[22, 72])).
% 0.19/0.44 tff(74,plain,
% 0.19/0.44 (join(X0!2, X1!1) = join(X0!2, join(meet(X1!1, X2!0), complement(join(complement(X1!1), X2!0))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[73])).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 (join(X0!2, X1!1) = X1!1),
% 0.19/0.44 inference(transitivity,[status(thm)],[74, 70, 68, 23])).
% 0.19/0.44 tff(76,plain,
% 0.19/0.44 ((~(~((~(join(X0!2, X1!1) = X1!1)) | (~(join(X0!2, X2!0) = X2!0))))) <=> ((~(join(X0!2, X1!1) = X1!1)) | (~(join(X0!2, X2!0) = X2!0)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(77,plain,
% 0.19/0.44 (((join(X0!2, X1!1) = X1!1) & (join(X0!2, X2!0) = X2!0)) <=> (~((~(join(X0!2, X1!1) = X1!1)) | (~(join(X0!2, X2!0) = X2!0))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(78,plain,
% 0.19/0.44 ((~((join(X0!2, X1!1) = X1!1) & (join(X0!2, X2!0) = X2!0))) <=> (~(~((~(join(X0!2, X1!1) = X1!1)) | (~(join(X0!2, X2!0) = X2!0)))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[77])).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 ((~((join(X0!2, X1!1) = X1!1) & (join(X0!2, X2!0) = X2!0))) <=> ((~(join(X0!2, X1!1) = X1!1)) | (~(join(X0!2, X2!0) = X2!0)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[78, 76])).
% 0.19/0.44 tff(80,plain,
% 0.19/0.44 (~((join(X0!2, X1!1) = X1!1) & (join(X0!2, X2!0) = X2!0))),
% 0.19/0.44 inference(or_elim,[status(thm)],[48])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 ((~(join(X0!2, X1!1) = X1!1)) | (~(join(X0!2, X2!0) = X2!0))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 (~(join(X0!2, X2!0) = X2!0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[81, 75])).
% 0.19/0.44 tff(83,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[82, 66])).
% 0.19/0.44 % SZS output end Proof
%------------------------------------------------------------------------------