TSTP Solution File: REL001+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : REL001+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 82.49s 53.55s
% Output : Proof 82.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : REL001+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 19:21:18 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 82.49/53.55 % SZS status Theorem
% 82.49/53.55 % SZS output start Proof
% 82.49/53.55 tff(tptp_fun_X0_0_type, type, (
% 82.49/53.55 tptp_fun_X0_0: $i)).
% 82.49/53.55 tff(join_type, type, (
% 82.49/53.55 join: ( $i * $i ) > $i)).
% 82.49/53.55 tff(zero_type, type, (
% 82.49/53.55 zero: $i)).
% 82.49/53.55 tff(complement_type, type, (
% 82.49/53.55 complement: $i > $i)).
% 82.49/53.55 tff(meet_type, type, (
% 82.49/53.55 meet: ( $i * $i ) > $i)).
% 82.49/53.55 tff(top_type, type, (
% 82.49/53.55 top: $i)).
% 82.49/53.55 tff(1,plain,
% 82.49/53.55 (^[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)))))),
% 82.49/53.55 inference(bind,[status(th)],[])).
% 82.49/53.55 tff(2,plain,
% 82.49/53.55 (![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))))),
% 82.49/53.55 inference(quant_intro,[status(thm)],[1])).
% 82.49/53.55 tff(3,plain,
% 82.49/53.55 (![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))))),
% 82.49/53.56 inference(rewrite,[status(thm)],[])).
% 82.49/53.56 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')).
% 82.49/53.56 tff(5,plain,
% 82.49/53.56 (![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))),
% 82.49/53.56 inference(modus_ponens,[status(thm)],[4, 3])).
% 82.49/53.56 tff(6,plain,(
% 82.49/53.56 ![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))),
% 82.49/53.56 inference(skolemize,[status(sab)],[5])).
% 82.49/53.56 tff(7,plain,
% 82.49/53.56 (![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))),
% 82.49/53.56 inference(modus_ponens,[status(thm)],[6, 2])).
% 82.49/53.56 tff(8,plain,
% 82.49/53.56 ((~![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(X0!0))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.56 inference(quant_inst,[status(thm)],[])).
% 82.49/53.56 tff(9,plain,
% 82.49/53.56 (X0!0 = join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.56 inference(unit_resolution,[status(thm)],[8, 7])).
% 82.49/53.56 tff(10,plain,
% 82.49/53.56 (join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))) = X0!0),
% 82.49/53.56 inference(symmetry,[status(thm)],[9])).
% 82.49/53.56 tff(11,plain,
% 82.49/53.56 ((~![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))) | (join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))))))),
% 82.49/53.56 inference(quant_inst,[status(thm)],[])).
% 82.49/53.56 tff(12,plain,
% 82.49/53.56 (join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))))),
% 82.49/53.56 inference(unit_resolution,[status(thm)],[11, 7])).
% 82.49/53.56 tff(13,plain,
% 82.49/53.56 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))))) = join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.56 inference(symmetry,[status(thm)],[12])).
% 82.49/53.56 tff(14,plain,
% 82.49/53.56 (^[X0: $i] : refl((zero = meet(X0, complement(X0))) <=> (zero = meet(X0, complement(X0))))),
% 82.49/53.56 inference(bind,[status(th)],[])).
% 82.49/53.56 tff(15,plain,
% 82.49/53.56 (![X0: $i] : (zero = meet(X0, complement(X0))) <=> ![X0: $i] : (zero = meet(X0, complement(X0)))),
% 82.49/53.56 inference(quant_intro,[status(thm)],[14])).
% 82.49/53.56 tff(16,plain,
% 82.49/53.56 (![X0: $i] : (zero = meet(X0, complement(X0))) <=> ![X0: $i] : (zero = meet(X0, complement(X0)))),
% 82.49/53.56 inference(rewrite,[status(thm)],[])).
% 82.49/53.56 tff(17,axiom,(![X0: $i] : (zero = meet(X0, complement(X0)))), file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax','def_zero')).
% 82.49/53.56 tff(18,plain,
% 82.49/53.56 (![X0: $i] : (zero = meet(X0, complement(X0)))),
% 82.49/53.56 inference(modus_ponens,[status(thm)],[17, 16])).
% 82.49/53.56 tff(19,plain,(
% 82.49/53.56 ![X0: $i] : (zero = meet(X0, complement(X0)))),
% 82.49/53.56 inference(skolemize,[status(sab)],[18])).
% 82.49/53.56 tff(20,plain,
% 82.49/53.56 (![X0: $i] : (zero = meet(X0, complement(X0)))),
% 82.49/53.56 inference(modus_ponens,[status(thm)],[19, 15])).
% 82.49/53.56 tff(21,plain,
% 82.49/53.56 ((~![X0: $i] : (zero = meet(X0, complement(X0)))) | (zero = meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.56 inference(quant_inst,[status(thm)],[])).
% 82.49/53.56 tff(22,plain,
% 82.49/53.56 (zero = meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.56 inference(unit_resolution,[status(thm)],[21, 20])).
% 82.49/53.56 tff(23,plain,
% 82.49/53.56 ((~![X0: $i] : (zero = meet(X0, complement(X0)))) | (zero = meet(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.56 inference(quant_inst,[status(thm)],[])).
% 82.49/53.56 tff(24,plain,
% 82.49/53.56 (zero = meet(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))),
% 82.49/53.56 inference(unit_resolution,[status(thm)],[23, 20])).
% 82.49/53.56 tff(25,plain,
% 82.49/53.56 (meet(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))) = zero),
% 82.49/53.56 inference(symmetry,[status(thm)],[24])).
% 82.49/53.56 tff(26,plain,
% 82.49/53.56 (^[X0: $i, X1: $i] : refl((meet(X0, X1) = complement(join(complement(X0), complement(X1)))) <=> (meet(X0, X1) = complement(join(complement(X0), complement(X1)))))),
% 82.49/53.56 inference(bind,[status(th)],[])).
% 82.49/53.56 tff(27,plain,
% 82.49/53.56 (![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))))),
% 82.49/53.56 inference(quant_intro,[status(thm)],[26])).
% 82.49/53.56 tff(28,plain,
% 82.49/53.56 (![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))))),
% 82.49/53.56 inference(rewrite,[status(thm)],[])).
% 82.49/53.56 tff(29,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')).
% 82.49/53.56 tff(30,plain,
% 82.49/53.56 (![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))),
% 82.49/53.56 inference(modus_ponens,[status(thm)],[29, 28])).
% 82.49/53.56 tff(31,plain,(
% 82.49/53.56 ![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))),
% 82.49/53.56 inference(skolemize,[status(sab)],[30])).
% 82.49/53.56 tff(32,plain,
% 82.49/53.56 (![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))),
% 82.49/53.56 inference(modus_ponens,[status(thm)],[31, 27])).
% 82.49/53.56 tff(33,plain,
% 82.49/53.56 ((~![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))) | (meet(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))) = complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))))),
% 82.49/53.56 inference(quant_inst,[status(thm)],[])).
% 82.49/53.56 tff(34,plain,
% 82.49/53.56 (meet(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))) = complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))))),
% 82.49/53.56 inference(unit_resolution,[status(thm)],[33, 32])).
% 82.49/53.56 tff(35,plain,
% 82.49/53.56 (complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = meet(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))),
% 82.49/53.56 inference(symmetry,[status(thm)],[34])).
% 82.49/53.56 tff(36,plain,
% 82.49/53.56 (^[X0: $i] : refl((top = join(X0, complement(X0))) <=> (top = join(X0, complement(X0))))),
% 82.49/53.56 inference(bind,[status(th)],[])).
% 82.49/53.56 tff(37,plain,
% 82.49/53.56 (![X0: $i] : (top = join(X0, complement(X0))) <=> ![X0: $i] : (top = join(X0, complement(X0)))),
% 82.49/53.56 inference(quant_intro,[status(thm)],[36])).
% 82.49/53.56 tff(38,plain,
% 82.49/53.56 (![X0: $i] : (top = join(X0, complement(X0))) <=> ![X0: $i] : (top = join(X0, complement(X0)))),
% 82.49/53.56 inference(rewrite,[status(thm)],[])).
% 82.49/53.56 tff(39,axiom,(![X0: $i] : (top = join(X0, complement(X0)))), file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax','def_top')).
% 82.49/53.56 tff(40,plain,
% 82.49/53.56 (![X0: $i] : (top = join(X0, complement(X0)))),
% 82.49/53.56 inference(modus_ponens,[status(thm)],[39, 38])).
% 82.49/53.56 tff(41,plain,(
% 82.49/53.56 ![X0: $i] : (top = join(X0, complement(X0)))),
% 82.49/53.56 inference(skolemize,[status(sab)],[40])).
% 82.49/53.56 tff(42,plain,
% 82.49/53.56 (![X0: $i] : (top = join(X0, complement(X0)))),
% 82.49/53.56 inference(modus_ponens,[status(thm)],[41, 37])).
% 82.49/53.56 tff(43,plain,
% 82.49/53.56 ((~![X0: $i] : (top = join(X0, complement(X0)))) | (top = join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))))),
% 82.49/53.56 inference(quant_inst,[status(thm)],[])).
% 82.49/53.56 tff(44,plain,
% 82.49/53.56 (top = join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.56 inference(unit_resolution,[status(thm)],[43, 42])).
% 82.49/53.56 tff(45,plain,
% 82.49/53.56 ((~![X0: $i] : (top = join(X0, complement(X0)))) | (top = join(X0!0, complement(X0!0)))),
% 82.49/53.56 inference(quant_inst,[status(thm)],[])).
% 82.49/53.56 tff(46,plain,
% 82.49/53.56 (top = join(X0!0, complement(X0!0))),
% 82.49/53.56 inference(unit_resolution,[status(thm)],[45, 42])).
% 82.49/53.56 tff(47,plain,
% 82.49/53.56 (join(X0!0, complement(X0!0)) = top),
% 82.49/53.56 inference(symmetry,[status(thm)],[46])).
% 82.49/53.56 tff(48,plain,
% 82.49/53.56 (join(X0!0, complement(X0!0)) = join(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))), complement(X0!0))),
% 82.49/53.56 inference(monotonicity,[status(thm)],[9])).
% 82.49/53.56 tff(49,plain,
% 82.49/53.56 (join(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))), complement(X0!0)) = join(X0!0, complement(X0!0))),
% 82.49/53.56 inference(symmetry,[status(thm)],[48])).
% 82.49/53.56 tff(50,plain,
% 82.49/53.56 (^[X0: $i, X1: $i] : refl((join(X0, X1) = join(X1, X0)) <=> (join(X0, X1) = join(X1, X0)))),
% 82.49/53.56 inference(bind,[status(th)],[])).
% 82.49/53.56 tff(51,plain,
% 82.49/53.56 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0)) <=> ![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 82.49/53.56 inference(quant_intro,[status(thm)],[50])).
% 82.49/53.56 tff(52,plain,
% 82.49/53.56 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0)) <=> ![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 82.49/53.56 inference(rewrite,[status(thm)],[])).
% 82.49/53.56 tff(53,axiom,(![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))), file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax','maddux1_join_commutativity')).
% 82.49/53.56 tff(54,plain,
% 82.49/53.56 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 82.49/53.56 inference(modus_ponens,[status(thm)],[53, 52])).
% 82.49/53.56 tff(55,plain,(
% 82.49/53.56 ![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 82.49/53.56 inference(skolemize,[status(sab)],[54])).
% 82.49/53.56 tff(56,plain,
% 82.49/53.56 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 82.49/53.56 inference(modus_ponens,[status(thm)],[55, 51])).
% 82.49/53.56 tff(57,plain,
% 82.49/53.56 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(X0!0), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))) = join(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))), complement(X0!0)))),
% 82.49/53.56 inference(quant_inst,[status(thm)],[])).
% 82.49/53.56 tff(58,plain,
% 82.49/53.56 (join(complement(X0!0), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))) = join(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))), complement(X0!0))),
% 82.49/53.56 inference(unit_resolution,[status(thm)],[57, 56])).
% 82.49/53.56 tff(59,plain,
% 82.49/53.56 (join(complement(X0!0), X0!0) = join(complement(X0!0), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.56 inference(monotonicity,[status(thm)],[9])).
% 82.49/53.56 tff(60,plain,
% 82.49/53.56 (join(complement(X0!0), X0!0) = join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.56 inference(transitivity,[status(thm)],[59, 58, 49, 47, 44])).
% 82.49/53.56 tff(61,plain,
% 82.49/53.56 (complement(join(complement(X0!0), X0!0)) = complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))))),
% 82.49/53.56 inference(monotonicity,[status(thm)],[60])).
% 82.49/53.56 tff(62,plain,
% 82.49/53.56 (join(complement(X0!0), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))) = join(complement(X0!0), X0!0)),
% 82.49/53.56 inference(symmetry,[status(thm)],[59])).
% 82.49/53.56 tff(63,plain,
% 82.49/53.56 (^[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)))),
% 82.49/53.56 inference(bind,[status(th)],[])).
% 82.49/53.56 tff(64,plain,
% 82.49/53.56 (![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))),
% 82.49/53.56 inference(quant_intro,[status(thm)],[63])).
% 82.49/53.56 tff(65,plain,
% 82.49/53.56 (![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))),
% 82.49/53.56 inference(rewrite,[status(thm)],[])).
% 82.49/53.56 tff(66,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')).
% 82.49/53.56 tff(67,plain,
% 82.49/53.56 (![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 82.49/53.56 inference(modus_ponens,[status(thm)],[66, 65])).
% 82.49/53.56 tff(68,plain,(
% 82.49/53.56 ![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 82.49/53.56 inference(skolemize,[status(sab)],[67])).
% 82.49/53.56 tff(69,plain,
% 82.49/53.56 (![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 82.49/53.56 inference(modus_ponens,[status(thm)],[68, 64])).
% 82.49/53.56 tff(70,plain,
% 82.49/53.56 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(X0!0), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))) = join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.56 inference(quant_inst,[status(thm)],[])).
% 82.49/53.56 tff(71,plain,
% 82.49/53.56 (join(complement(X0!0), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))) = join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.56 inference(unit_resolution,[status(thm)],[70, 69])).
% 82.49/53.56 tff(72,plain,
% 82.49/53.56 (join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))) = join(complement(X0!0), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.56 inference(symmetry,[status(thm)],[71])).
% 82.49/53.56 tff(73,plain,
% 82.49/53.56 ((~![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))) | (join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))) = join(complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))))),
% 82.49/53.56 inference(quant_inst,[status(thm)],[])).
% 82.49/53.56 tff(74,plain,
% 82.49/53.56 (join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))) = join(complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))))),
% 82.49/53.56 inference(unit_resolution,[status(thm)],[73, 7])).
% 82.49/53.56 tff(75,plain,
% 82.49/53.56 (join(complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))) = join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.56 inference(symmetry,[status(thm)],[74])).
% 82.49/53.56 tff(76,plain,
% 82.49/53.56 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))) = join(complement(join(complement(X0!0), X0!0)), complement(join(complement(X0!0), complement(X0!0)))))),
% 82.49/53.56 inference(quant_inst,[status(thm)],[])).
% 82.49/53.56 tff(77,plain,
% 82.49/53.56 (join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))) = join(complement(join(complement(X0!0), X0!0)), complement(join(complement(X0!0), complement(X0!0))))),
% 82.49/53.56 inference(unit_resolution,[status(thm)],[76, 56])).
% 82.49/53.56 tff(78,plain,
% 82.49/53.56 (join(complement(join(complement(X0!0), X0!0)), complement(join(complement(X0!0), complement(X0!0)))) = join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.56 inference(symmetry,[status(thm)],[77])).
% 82.49/53.56 tff(79,plain,
% 82.49/53.56 ((~![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))) | (join(complement(X0!0), complement(X0!0)) = join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))),
% 82.49/53.56 inference(quant_inst,[status(thm)],[])).
% 82.49/53.56 tff(80,plain,
% 82.49/53.56 (join(complement(X0!0), complement(X0!0)) = join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))),
% 82.49/53.56 inference(unit_resolution,[status(thm)],[79, 7])).
% 82.49/53.56 tff(81,plain,
% 82.49/53.56 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))) = join(complement(X0!0), complement(X0!0))),
% 82.49/53.56 inference(symmetry,[status(thm)],[80])).
% 82.49/53.56 tff(82,plain,
% 82.49/53.56 (complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))) = complement(join(complement(X0!0), complement(X0!0)))),
% 82.49/53.56 inference(monotonicity,[status(thm)],[81])).
% 82.49/53.56 tff(83,plain,
% 82.49/53.56 (join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))) = join(complement(X0!0), X0!0)),
% 82.49/53.56 inference(transitivity,[status(thm)],[72, 62])).
% 82.49/53.56 tff(84,plain,
% 82.49/53.56 (complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))) = complement(join(complement(X0!0), X0!0))),
% 82.49/53.56 inference(monotonicity,[status(thm)],[83])).
% 82.49/53.56 tff(85,plain,
% 82.49/53.56 (join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))) = join(complement(join(complement(X0!0), X0!0)), complement(join(complement(X0!0), complement(X0!0))))),
% 82.49/53.56 inference(monotonicity,[status(thm)],[84, 82])).
% 82.49/53.56 tff(86,plain,
% 82.49/53.56 (join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))) = X0!0),
% 82.49/53.56 inference(transitivity,[status(thm)],[85, 78, 10])).
% 82.49/53.56 tff(87,plain,
% 82.49/53.56 (complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))) = complement(X0!0)),
% 82.49/53.56 inference(monotonicity,[status(thm)],[86])).
% 82.49/53.56 tff(88,plain,
% 82.49/53.56 (complement(X0!0) = complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))))),
% 82.49/53.56 inference(symmetry,[status(thm)],[87])).
% 82.49/53.56 tff(89,plain,
% 82.49/53.56 (complement(X0!0) = complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.56 inference(monotonicity,[status(thm)],[9])).
% 82.49/53.56 tff(90,plain,
% 82.49/53.56 (complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))) = complement(X0!0)),
% 82.49/53.56 inference(symmetry,[status(thm)],[89])).
% 82.49/53.56 tff(91,plain,
% 82.49/53.56 (complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))) = complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))))),
% 82.49/53.56 inference(transitivity,[status(thm)],[90, 88])).
% 82.49/53.56 tff(92,plain,
% 82.49/53.56 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))) = join(complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))))),
% 82.49/53.56 inference(monotonicity,[status(thm)],[91])).
% 82.49/53.56 tff(93,plain,
% 82.49/53.56 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))) = join(complement(X0!0), X0!0)),
% 82.49/53.56 inference(transitivity,[status(thm)],[92, 75, 72, 62])).
% 82.49/53.56 tff(94,plain,
% 82.49/53.56 (complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))))) = complement(join(complement(X0!0), X0!0))),
% 82.49/53.56 inference(monotonicity,[status(thm)],[93])).
% 82.49/53.56 tff(95,plain,
% 82.49/53.56 (complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))))) = meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.56 inference(transitivity,[status(thm)],[94, 61, 35, 25, 22])).
% 82.49/53.56 tff(96,plain,
% 82.49/53.56 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))))) = join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))))),
% 82.49/53.56 inference(monotonicity,[status(thm)],[95])).
% 82.49/53.56 tff(97,plain,
% 82.49/53.56 (join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))))),
% 82.49/53.56 inference(symmetry,[status(thm)],[96])).
% 82.49/53.56 tff(98,plain,
% 82.49/53.56 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))))),
% 82.49/53.56 inference(quant_inst,[status(thm)],[])).
% 82.49/53.56 tff(99,plain,
% 82.49/53.56 (join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.57 inference(unit_resolution,[status(thm)],[98, 56])).
% 82.49/53.57 tff(100,plain,
% 82.49/53.57 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))) = join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))))),
% 82.49/53.57 inference(symmetry,[status(thm)],[99])).
% 82.49/53.57 tff(101,plain,
% 82.49/53.57 (join(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))), complement(X0!0)) = join(complement(X0!0), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.57 inference(symmetry,[status(thm)],[58])).
% 82.49/53.57 tff(102,plain,
% 82.49/53.57 ((~![X0: $i] : (top = join(X0, complement(X0)))) | (top = join(complement(join(complement(X0!0), X0!0)), complement(complement(join(complement(X0!0), X0!0)))))),
% 82.49/53.57 inference(quant_inst,[status(thm)],[])).
% 82.49/53.57 tff(103,plain,
% 82.49/53.57 (top = join(complement(join(complement(X0!0), X0!0)), complement(complement(join(complement(X0!0), X0!0))))),
% 82.49/53.57 inference(unit_resolution,[status(thm)],[102, 42])).
% 82.49/53.57 tff(104,plain,
% 82.49/53.57 (join(complement(join(complement(X0!0), X0!0)), complement(complement(join(complement(X0!0), X0!0)))) = top),
% 82.49/53.57 inference(symmetry,[status(thm)],[103])).
% 82.49/53.57 tff(105,plain,
% 82.49/53.57 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(join(complement(X0!0), X0!0)), complement(complement(join(complement(X0!0), X0!0)))) = join(complement(complement(join(complement(X0!0), X0!0))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.57 inference(quant_inst,[status(thm)],[])).
% 82.49/53.57 tff(106,plain,
% 82.49/53.57 (join(complement(join(complement(X0!0), X0!0)), complement(complement(join(complement(X0!0), X0!0)))) = join(complement(complement(join(complement(X0!0), X0!0))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.57 inference(unit_resolution,[status(thm)],[105, 56])).
% 82.49/53.57 tff(107,plain,
% 82.49/53.57 (join(complement(complement(join(complement(X0!0), X0!0))), complement(join(complement(X0!0), X0!0))) = join(complement(join(complement(X0!0), X0!0)), complement(complement(join(complement(X0!0), X0!0))))),
% 82.49/53.57 inference(symmetry,[status(thm)],[106])).
% 82.49/53.57 tff(108,plain,
% 82.49/53.57 (complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = complement(join(complement(X0!0), X0!0))),
% 82.49/53.57 inference(symmetry,[status(thm)],[61])).
% 82.49/53.57 tff(109,plain,
% 82.49/53.57 (meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))) = zero),
% 82.49/53.57 inference(symmetry,[status(thm)],[22])).
% 82.49/53.57 tff(110,plain,
% 82.49/53.57 (meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))) = complement(join(complement(X0!0), X0!0))),
% 82.49/53.57 inference(transitivity,[status(thm)],[109, 24, 34, 108])).
% 82.49/53.57 tff(111,plain,
% 82.49/53.57 (complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))) = complement(complement(join(complement(X0!0), X0!0)))),
% 82.49/53.57 inference(monotonicity,[status(thm)],[110])).
% 82.49/53.57 tff(112,plain,
% 82.49/53.57 (join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))))) = join(complement(complement(join(complement(X0!0), X0!0))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.57 inference(monotonicity,[status(thm)],[111, 84])).
% 82.49/53.57 tff(113,plain,
% 82.49/53.57 (join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))))) = join(complement(X0!0), X0!0)),
% 82.49/53.57 inference(transitivity,[status(thm)],[112, 107, 104, 46, 48, 101, 62])).
% 82.49/53.57 tff(114,plain,
% 82.49/53.57 (complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))))) = complement(join(complement(X0!0), X0!0))),
% 82.49/53.57 inference(monotonicity,[status(thm)],[113])).
% 82.49/53.57 tff(115,plain,
% 82.49/53.57 (complement(join(complement(X0!0), X0!0)) = complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.57 inference(symmetry,[status(thm)],[114])).
% 82.49/53.57 tff(116,plain,
% 82.49/53.57 (meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))) = complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.57 inference(transitivity,[status(thm)],[109, 24, 34, 108, 115])).
% 82.49/53.57 tff(117,plain,
% 82.49/53.57 (join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))))) = join(complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.57 inference(monotonicity,[status(thm)],[116])).
% 82.49/53.57 tff(118,plain,
% 82.49/53.57 (join(complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))))) = join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.57 inference(symmetry,[status(thm)],[117])).
% 82.49/53.57 tff(119,plain,
% 82.49/53.57 ((~![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))) | (meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))) = join(complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))))))),
% 82.49/53.57 inference(quant_inst,[status(thm)],[])).
% 82.49/53.57 tff(120,plain,
% 82.49/53.57 (meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))) = join(complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.57 inference(unit_resolution,[status(thm)],[119, 7])).
% 82.49/53.57 tff(121,plain,
% 82.49/53.57 (meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))) = join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.57 inference(transitivity,[status(thm)],[120, 118])).
% 82.49/53.57 tff(122,plain,
% 82.49/53.57 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))))))),
% 82.49/53.57 inference(monotonicity,[status(thm)],[121])).
% 82.49/53.57 tff(123,plain,
% 82.49/53.57 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))))))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.57 inference(symmetry,[status(thm)],[122])).
% 82.49/53.57 tff(124,plain,
% 82.49/53.57 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))))))) = join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))))))),
% 82.49/53.57 inference(quant_inst,[status(thm)],[])).
% 82.49/53.57 tff(125,plain,
% 82.49/53.57 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))))))) = join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.57 inference(unit_resolution,[status(thm)],[124, 69])).
% 82.49/53.57 tff(126,plain,
% 82.49/53.57 (join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))))))),
% 82.49/53.57 inference(symmetry,[status(thm)],[125])).
% 82.49/53.57 tff(127,plain,
% 82.49/53.57 ((~![X0: $i] : (top = join(X0, complement(X0)))) | (top = join(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.57 inference(quant_inst,[status(thm)],[])).
% 82.49/53.57 tff(128,plain,
% 82.49/53.57 (top = join(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.57 inference(unit_resolution,[status(thm)],[127, 42])).
% 82.49/53.57 tff(129,plain,
% 82.49/53.57 (join(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))) = top),
% 82.49/53.57 inference(symmetry,[status(thm)],[128])).
% 82.49/53.57 tff(130,plain,
% 82.49/53.57 ((~![X0: $i] : (top = join(X0, complement(X0)))) | (top = join(join(complement(X0!0), complement(X0!0)), complement(join(complement(X0!0), complement(X0!0)))))),
% 82.49/53.57 inference(quant_inst,[status(thm)],[])).
% 82.49/53.57 tff(131,plain,
% 82.49/53.57 (top = join(join(complement(X0!0), complement(X0!0)), complement(join(complement(X0!0), complement(X0!0))))),
% 82.49/53.57 inference(unit_resolution,[status(thm)],[130, 42])).
% 82.49/53.57 tff(132,plain,
% 82.49/53.57 (join(join(complement(X0!0), complement(X0!0)), complement(join(complement(X0!0), complement(X0!0)))) = top),
% 82.49/53.57 inference(symmetry,[status(thm)],[131])).
% 82.49/53.57 tff(133,plain,
% 82.49/53.57 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))) = join(complement(X0!0), complement(X0!0))),
% 82.49/53.57 inference(monotonicity,[status(thm)],[90, 90])).
% 82.49/53.57 tff(134,plain,
% 82.49/53.57 (join(complement(X0!0), complement(X0!0)) = join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))),
% 82.49/53.57 inference(symmetry,[status(thm)],[133])).
% 82.49/53.57 tff(135,plain,
% 82.49/53.57 (complement(join(complement(X0!0), complement(X0!0))) = complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.57 inference(monotonicity,[status(thm)],[134])).
% 82.49/53.57 tff(136,plain,
% 82.49/53.57 (complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))) = complement(join(complement(X0!0), complement(X0!0)))),
% 82.49/53.57 inference(symmetry,[status(thm)],[135])).
% 82.49/53.57 tff(137,plain,
% 82.49/53.57 (join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = join(join(complement(X0!0), complement(X0!0)), complement(join(complement(X0!0), complement(X0!0))))),
% 82.49/53.57 inference(monotonicity,[status(thm)],[81, 136])).
% 82.49/53.57 tff(138,plain,
% 82.49/53.57 (join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = join(complement(X0!0), X0!0)),
% 82.49/53.57 inference(transitivity,[status(thm)],[137, 132, 46, 48, 101, 62])).
% 82.49/53.57 tff(139,plain,
% 82.49/53.57 (join(join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))), complement(join(complement(X0!0), X0!0))) = join(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.57 inference(monotonicity,[status(thm)],[138])).
% 82.49/53.57 tff(140,plain,
% 82.49/53.57 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(X0!0), X0!0)))) = join(join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.57 inference(quant_inst,[status(thm)],[])).
% 82.49/53.57 tff(141,plain,
% 82.49/53.57 (join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(X0!0), X0!0)))) = join(join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.57 inference(unit_resolution,[status(thm)],[140, 69])).
% 82.49/53.57 tff(142,plain,
% 82.49/53.57 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(X0!0), X0!0))) = join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.57 inference(monotonicity,[status(thm)],[136])).
% 82.49/53.57 tff(143,plain,
% 82.49/53.57 (join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.57 inference(symmetry,[status(thm)],[142])).
% 82.49/53.57 tff(144,plain,
% 82.49/53.57 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))) = join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))),
% 82.49/53.57 inference(transitivity,[status(thm)],[133, 80])).
% 82.49/53.57 tff(145,plain,
% 82.49/53.57 (join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))) = join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.57 inference(monotonicity,[status(thm)],[144, 143])).
% 82.49/53.57 tff(146,plain,
% 82.49/53.57 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))) = join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))),
% 82.49/53.57 inference(quant_inst,[status(thm)],[])).
% 82.49/53.57 tff(147,plain,
% 82.49/53.57 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))) = join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.58 inference(unit_resolution,[status(thm)],[146, 69])).
% 82.49/53.58 tff(148,plain,
% 82.49/53.58 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))) = join(complement(X0!0), X0!0)),
% 82.49/53.58 inference(monotonicity,[status(thm)],[90, 10])).
% 82.49/53.58 tff(149,plain,
% 82.49/53.58 (join(complement(X0!0), X0!0) = join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.58 inference(symmetry,[status(thm)],[148])).
% 82.49/53.58 tff(150,plain,
% 82.49/53.58 ((~![X0: $i] : (top = join(X0, complement(X0)))) | (top = join(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))),
% 82.49/53.58 inference(quant_inst,[status(thm)],[])).
% 82.49/53.58 tff(151,plain,
% 82.49/53.58 (top = join(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))),
% 82.49/53.58 inference(unit_resolution,[status(thm)],[150, 42])).
% 82.49/53.58 tff(152,plain,
% 82.49/53.58 (join(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))) = top),
% 82.49/53.58 inference(symmetry,[status(thm)],[151])).
% 82.49/53.58 tff(153,plain,
% 82.49/53.58 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))) = join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))),
% 82.49/53.58 inference(monotonicity,[status(thm)],[136, 83])).
% 82.49/53.58 tff(154,plain,
% 82.49/53.58 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))) = join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))))),
% 82.49/53.58 inference(quant_inst,[status(thm)],[])).
% 82.49/53.58 tff(155,plain,
% 82.49/53.58 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))) = join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))))),
% 82.49/53.58 inference(unit_resolution,[status(thm)],[154, 56])).
% 82.49/53.58 tff(156,plain,
% 82.49/53.58 (join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.58 inference(symmetry,[status(thm)],[155])).
% 82.49/53.58 tff(157,plain,
% 82.49/53.58 (join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))),
% 82.49/53.58 inference(transitivity,[status(thm)],[156, 153])).
% 82.49/53.58 tff(158,plain,
% 82.49/53.58 (join(join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))) = join(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))),
% 82.49/53.58 inference(monotonicity,[status(thm)],[157])).
% 82.49/53.58 tff(159,plain,
% 82.49/53.58 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))) = join(join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))),
% 82.49/53.58 inference(quant_inst,[status(thm)],[])).
% 82.49/53.58 tff(160,plain,
% 82.49/53.58 (join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))) = join(join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))),
% 82.49/53.58 inference(unit_resolution,[status(thm)],[159, 69])).
% 82.49/53.58 tff(161,plain,
% 82.49/53.58 (join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(X0!0), X0!0))) = join(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.58 inference(monotonicity,[status(thm)],[83])).
% 82.49/53.58 tff(162,plain,
% 82.49/53.58 (join(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))) = join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.58 inference(symmetry,[status(thm)],[161])).
% 82.49/53.58 tff(163,plain,
% 82.49/53.58 (join(complement(X0!0), X0!0) = join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.58 inference(transitivity,[status(thm)],[59, 58, 49, 47, 128, 162])).
% 82.49/53.58 tff(164,plain,
% 82.49/53.58 (join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.58 inference(monotonicity,[status(thm)],[135, 163])).
% 82.49/53.58 tff(165,plain,
% 82.49/53.58 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(X0!0), X0!0)))) = join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))),
% 82.49/53.58 inference(symmetry,[status(thm)],[164])).
% 82.49/53.58 tff(166,plain,
% 82.49/53.58 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(X0!0), X0!0)))) = join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.58 inference(quant_inst,[status(thm)],[])).
% 82.49/53.58 tff(167,plain,
% 82.49/53.58 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(X0!0), X0!0)))) = join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.58 inference(unit_resolution,[status(thm)],[166, 69])).
% 82.49/53.58 tff(168,plain,
% 82.49/53.58 (join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(X0!0), X0!0))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.58 inference(symmetry,[status(thm)],[167])).
% 82.49/53.58 tff(169,plain,
% 82.49/53.58 (join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(X0!0), X0!0))) = join(join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.58 inference(monotonicity,[status(thm)],[155])).
% 82.49/53.58 tff(170,plain,
% 82.49/53.58 (join(join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))), complement(join(complement(X0!0), X0!0))) = join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.58 inference(symmetry,[status(thm)],[169])).
% 82.49/53.58 tff(171,plain,
% 82.49/53.58 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(X0!0), X0!0)))) = join(join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.58 inference(quant_inst,[status(thm)],[])).
% 82.49/53.58 tff(172,plain,
% 82.49/53.58 (join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(X0!0), X0!0)))) = join(join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.58 inference(unit_resolution,[status(thm)],[171, 69])).
% 82.49/53.58 tff(173,plain,
% 82.49/53.58 (join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = join(join(complement(X0!0), complement(X0!0)), complement(join(complement(X0!0), complement(X0!0))))),
% 82.49/53.58 inference(monotonicity,[status(thm)],[133, 136])).
% 82.49/53.58 tff(174,plain,
% 82.49/53.58 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))))) = join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))))),
% 82.49/53.58 inference(quant_inst,[status(thm)],[])).
% 82.49/53.58 tff(175,plain,
% 82.49/53.58 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))))) = join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))))),
% 82.49/53.58 inference(unit_resolution,[status(thm)],[174, 69])).
% 82.49/53.58 tff(176,plain,
% 82.49/53.58 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.58 inference(quant_inst,[status(thm)],[])).
% 82.49/53.58 tff(177,plain,
% 82.49/53.58 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))),
% 82.49/53.58 inference(unit_resolution,[status(thm)],[176, 56])).
% 82.49/53.58 tff(178,plain,
% 82.49/53.58 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))) = join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))))),
% 82.49/53.58 inference(symmetry,[status(thm)],[177])).
% 82.49/53.58 tff(179,plain,
% 82.49/53.58 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))) = join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))))),
% 82.49/53.58 inference(monotonicity,[status(thm)],[178])).
% 82.49/53.58 tff(180,plain,
% 82.49/53.58 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))) = join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.58 inference(transitivity,[status(thm)],[179, 175, 173, 132, 46, 48, 101, 71])).
% 82.49/53.58 tff(181,plain,
% 82.49/53.58 (join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))) = join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.58 inference(monotonicity,[status(thm)],[180, 143])).
% 82.49/53.58 tff(182,plain,
% 82.49/53.58 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))) = join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))),
% 82.49/53.58 inference(quant_inst,[status(thm)],[])).
% 82.49/53.58 tff(183,plain,
% 82.49/53.58 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))) = join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.58 inference(unit_resolution,[status(thm)],[182, 69])).
% 82.49/53.58 tff(184,plain,
% 82.49/53.58 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))) = join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))),
% 82.49/53.58 inference(quant_inst,[status(thm)],[])).
% 82.49/53.58 tff(185,plain,
% 82.49/53.58 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))) = join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.58 inference(unit_resolution,[status(thm)],[184, 69])).
% 82.49/53.58 tff(186,plain,
% 82.49/53.58 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))) = join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))),
% 82.49/53.58 inference(monotonicity,[status(thm)],[136, 148])).
% 82.49/53.58 tff(187,plain,
% 82.49/53.58 (join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))),
% 82.49/53.58 inference(symmetry,[status(thm)],[186])).
% 82.49/53.58 tff(188,plain,
% 82.49/53.58 (join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)) = join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.58 inference(transitivity,[status(thm)],[187, 185])).
% 82.49/53.58 tff(189,plain,
% 82.49/53.58 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))) = join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))),
% 82.49/53.58 inference(monotonicity,[status(thm)],[188])).
% 82.49/53.59 tff(190,plain,
% 82.49/53.59 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))) = join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))),
% 82.49/53.59 inference(transitivity,[status(thm)],[189, 183, 181, 172, 170, 168, 165])).
% 82.49/53.59 tff(191,plain,
% 82.49/53.59 (complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))) = complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))),
% 82.49/53.59 inference(monotonicity,[status(thm)],[190])).
% 82.49/53.59 tff(192,plain,
% 82.49/53.59 (complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))) = complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))),
% 82.49/53.59 inference(symmetry,[status(thm)],[191])).
% 82.49/53.59 tff(193,plain,
% 82.49/53.59 (complement(join(complement(X0!0), complement(X0!0))) = complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))),
% 82.49/53.59 inference(symmetry,[status(thm)],[82])).
% 82.49/53.59 tff(194,plain,
% 82.49/53.59 (complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))) = complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))),
% 82.49/53.59 inference(transitivity,[status(thm)],[136, 193])).
% 82.49/53.59 tff(195,plain,
% 82.49/53.59 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))),
% 82.49/53.59 inference(monotonicity,[status(thm)],[194, 192])).
% 82.49/53.59 tff(196,plain,
% 82.49/53.59 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))),
% 82.49/53.59 inference(symmetry,[status(thm)],[195])).
% 82.49/53.59 tff(197,plain,
% 82.49/53.59 ((~![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))) | (join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))),
% 82.49/53.59 inference(quant_inst,[status(thm)],[])).
% 82.49/53.59 tff(198,plain,
% 82.49/53.59 (join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))),
% 82.49/53.59 inference(unit_resolution,[status(thm)],[197, 7])).
% 82.49/53.59 tff(199,plain,
% 82.49/53.59 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(X0!0), X0!0))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))),
% 82.49/53.59 inference(transitivity,[status(thm)],[142, 198, 196])).
% 82.49/53.59 tff(200,plain,
% 82.49/53.59 (join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(X0!0), X0!0)))) = join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0)))))),
% 82.49/53.59 inference(monotonicity,[status(thm)],[199])).
% 82.49/53.59 tff(201,plain,
% 82.49/53.59 (join(join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))), complement(join(complement(X0!0), X0!0))) = join(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.59 inference(symmetry,[status(thm)],[172])).
% 82.49/53.59 tff(202,plain,
% 82.49/53.59 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))) = join(complement(X0!0), X0!0)),
% 82.49/53.59 inference(transitivity,[status(thm)],[179, 175, 173, 132, 46, 48, 101, 62])).
% 82.49/53.59 tff(203,plain,
% 82.49/53.59 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))),
% 82.49/53.59 inference(monotonicity,[status(thm)],[136, 202])).
% 82.49/53.59 tff(204,plain,
% 82.49/53.59 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))))),
% 82.49/53.59 inference(quant_inst,[status(thm)],[])).
% 82.49/53.59 tff(205,plain,
% 82.49/53.59 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.59 inference(unit_resolution,[status(thm)],[204, 69])).
% 82.49/53.59 tff(206,plain,
% 82.49/53.59 (join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))) = join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))))),
% 82.49/53.59 inference(symmetry,[status(thm)],[205])).
% 82.49/53.59 tff(207,plain,
% 82.49/53.59 (join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))) = join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))),
% 82.49/53.59 inference(transitivity,[status(thm)],[206, 203, 164, 167, 169, 201, 200, 160, 158, 152, 46, 48, 101, 62, 149])).
% 82.49/53.59 tff(208,plain,
% 82.49/53.59 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))),
% 82.49/53.59 inference(monotonicity,[status(thm)],[207])).
% 82.49/53.59 tff(209,plain,
% 82.49/53.59 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))))),
% 82.49/53.59 inference(quant_inst,[status(thm)],[])).
% 82.49/53.59 tff(210,plain,
% 82.49/53.59 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.59 inference(unit_resolution,[status(thm)],[209, 69])).
% 82.49/53.59 tff(211,plain,
% 82.49/53.59 (join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))) = join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))))),
% 82.49/53.59 inference(symmetry,[status(thm)],[210])).
% 82.49/53.59 tff(212,plain,
% 82.49/53.59 (join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))))) = join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.59 inference(symmetry,[status(thm)],[179])).
% 82.49/53.59 tff(213,plain,
% 82.49/53.59 (join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))))),
% 82.49/53.59 inference(symmetry,[status(thm)],[175])).
% 82.49/53.59 tff(214,plain,
% 82.49/53.59 (join(join(complement(X0!0), complement(X0!0)), complement(join(complement(X0!0), complement(X0!0)))) = join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))))),
% 82.49/53.59 inference(symmetry,[status(thm)],[173])).
% 82.49/53.59 tff(215,plain,
% 82.49/53.59 (join(complement(complement(join(complement(X0!0), X0!0))), meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))) = join(complement(complement(join(complement(X0!0), X0!0))), complement(join(complement(X0!0), X0!0)))),
% 82.49/53.59 inference(monotonicity,[status(thm)],[110])).
% 82.49/53.59 tff(216,plain,
% 82.49/53.59 (join(complement(complement(join(complement(X0!0), X0!0))), meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))) = join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.59 inference(transitivity,[status(thm)],[215, 107, 104, 131, 214, 213, 212])).
% 82.49/53.59 tff(217,plain,
% 82.49/53.59 (join(join(complement(complement(join(complement(X0!0), X0!0))), meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))) = join(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.59 inference(monotonicity,[status(thm)],[216])).
% 82.49/53.59 tff(218,plain,
% 82.49/53.59 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(complement(join(complement(X0!0), X0!0))), join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = join(join(complement(complement(join(complement(X0!0), X0!0))), meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))))),
% 82.49/53.59 inference(quant_inst,[status(thm)],[])).
% 82.49/53.59 tff(219,plain,
% 82.49/53.59 (join(complement(complement(join(complement(X0!0), X0!0))), join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = join(join(complement(complement(join(complement(X0!0), X0!0))), meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.59 inference(unit_resolution,[status(thm)],[218, 69])).
% 82.49/53.59 tff(220,plain,
% 82.49/53.59 (join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))) = join(complement(join(complement(X0!0), X0!0)), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.59 inference(monotonicity,[status(thm)],[110])).
% 82.49/53.59 tff(221,plain,
% 82.49/53.59 (join(complement(join(complement(X0!0), X0!0)), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))) = join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.59 inference(symmetry,[status(thm)],[220])).
% 82.49/53.59 tff(222,plain,
% 82.49/53.59 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(complement(join(complement(X0!0), X0!0)), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))) = join(join(complement(join(complement(X0!0), X0!0)), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.59 inference(quant_inst,[status(thm)],[])).
% 82.49/53.59 tff(223,plain,
% 82.49/53.59 (join(complement(join(complement(X0!0), X0!0)), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))) = join(join(complement(join(complement(X0!0), X0!0)), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))),
% 82.49/53.60 inference(unit_resolution,[status(thm)],[222, 69])).
% 82.49/53.60 tff(224,plain,
% 82.49/53.60 (join(join(complement(join(complement(X0!0), X0!0)), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))) = join(complement(join(complement(X0!0), X0!0)), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.60 inference(symmetry,[status(thm)],[223])).
% 82.49/53.60 tff(225,plain,
% 82.49/53.60 (join(complement(join(complement(X0!0), X0!0)), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = join(complement(join(complement(X0!0), X0!0)), complement(join(complement(X0!0), complement(X0!0))))),
% 82.49/53.60 inference(monotonicity,[status(thm)],[136])).
% 82.49/53.60 tff(226,plain,
% 82.49/53.60 (join(complement(join(complement(X0!0), X0!0)), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))) = X0!0),
% 82.49/53.60 inference(transitivity,[status(thm)],[225, 78, 10])).
% 82.49/53.60 tff(227,plain,
% 82.49/53.60 (join(join(complement(join(complement(X0!0), X0!0)), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))) = join(X0!0, complement(X0!0))),
% 82.49/53.60 inference(monotonicity,[status(thm)],[226, 90])).
% 82.49/53.60 tff(228,plain,
% 82.49/53.60 (join(X0!0, complement(X0!0)) = join(join(complement(join(complement(X0!0), X0!0)), complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))),
% 82.49/53.60 inference(symmetry,[status(thm)],[227])).
% 82.49/53.60 tff(229,plain,
% 82.49/53.60 (join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))) = join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.60 inference(transitivity,[status(thm)],[72, 58, 49, 228, 224, 221])).
% 82.49/53.60 tff(230,plain,
% 82.49/53.60 (join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))) = join(complement(complement(join(complement(X0!0), X0!0))), join(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0))), join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))), complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))))))),
% 82.49/53.60 inference(monotonicity,[status(thm)],[111, 229])).
% 82.49/53.60 tff(231,plain,
% 82.49/53.60 (join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))) = join(complement(X0!0), X0!0)),
% 82.49/53.60 inference(transitivity,[status(thm)],[230, 219, 217, 211, 208, 147, 145, 141, 139, 129, 46, 48, 101, 62])).
% 82.49/53.60 tff(232,plain,
% 82.49/53.60 (complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))))) = complement(join(complement(X0!0), X0!0))),
% 82.49/53.60 inference(monotonicity,[status(thm)],[231])).
% 82.49/53.60 tff(233,plain,
% 82.49/53.60 (complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))))) = zero),
% 82.49/53.60 inference(transitivity,[status(thm)],[232, 61, 35, 25])).
% 82.49/53.60 tff(234,plain,
% 82.49/53.60 (join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))) = X0!0),
% 82.49/53.60 inference(transitivity,[status(thm)],[100, 97, 13, 10])).
% 82.49/53.60 tff(235,plain,
% 82.49/53.60 (join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))))) = join(X0!0, zero)),
% 82.49/53.60 inference(monotonicity,[status(thm)],[234, 233])).
% 82.49/53.60 tff(236,plain,
% 82.49/53.60 (join(X0!0, zero) = join(join(complement(join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), join(complement(join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0)))), join(complement(join(complement(join(complement(X0!0), complement(X0!0))), complement(join(complement(X0!0), X0!0)))), complement(join(complement(join(complement(X0!0), complement(X0!0))), join(complement(X0!0), X0!0))))))), meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), complement(join(complement(meet(join(complement(X0!0), X0!0), complement(join(complement(X0!0), X0!0)))), join(join(complement(X0!0), complement(join(complement(X0!0), complement(X0!0)))), complement(join(complement(X0!0), X0!0))))))),
% 82.49/53.60 inference(symmetry,[status(thm)],[235])).
% 82.49/53.60 tff(237,plain,
% 82.49/53.60 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(zero, X0!0) = join(X0!0, zero))),
% 82.49/53.60 inference(quant_inst,[status(thm)],[])).
% 82.49/53.60 tff(238,plain,
% 82.49/53.60 (join(zero, X0!0) = join(X0!0, zero)),
% 82.49/53.60 inference(unit_resolution,[status(thm)],[237, 56])).
% 82.49/53.60 tff(239,plain,
% 82.49/53.60 (join(zero, X0!0) = X0!0),
% 82.49/53.60 inference(transitivity,[status(thm)],[238, 236, 126, 123, 100, 97, 13, 10])).
% 82.49/53.60 tff(240,plain,
% 82.49/53.60 ((~![X0: $i] : (join(zero, X0) = X0)) <=> (~![X0: $i] : (join(zero, X0) = X0))),
% 82.49/53.60 inference(rewrite,[status(thm)],[])).
% 82.49/53.60 tff(241,axiom,(~![X0: $i] : (join(zero, X0) = X0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 82.49/53.60 tff(242,plain,
% 82.49/53.60 (~![X0: $i] : (join(zero, X0) = X0)),
% 82.49/53.60 inference(modus_ponens,[status(thm)],[241, 240])).
% 82.49/53.60 tff(243,plain,
% 82.49/53.60 (~![X0: $i] : (join(zero, X0) = X0)),
% 82.49/53.60 inference(modus_ponens,[status(thm)],[242, 240])).
% 82.49/53.60 tff(244,plain,
% 82.49/53.60 (~![X0: $i] : (join(zero, X0) = X0)),
% 82.49/53.60 inference(modus_ponens,[status(thm)],[243, 240])).
% 82.49/53.60 tff(245,plain,
% 82.49/53.60 (~![X0: $i] : (join(zero, X0) = X0)),
% 82.49/53.60 inference(modus_ponens,[status(thm)],[244, 240])).
% 82.49/53.60 tff(246,plain,
% 82.49/53.60 (~![X0: $i] : (join(zero, X0) = X0)),
% 82.49/53.60 inference(modus_ponens,[status(thm)],[245, 240])).
% 82.49/53.60 tff(247,plain,
% 82.49/53.60 (~![X0: $i] : (join(zero, X0) = X0)),
% 82.49/53.60 inference(modus_ponens,[status(thm)],[246, 240])).
% 82.49/53.60 tff(248,plain,
% 82.49/53.60 (~![X0: $i] : (join(zero, X0) = X0)),
% 82.49/53.60 inference(modus_ponens,[status(thm)],[247, 240])).
% 82.49/53.60 tff(249,plain,(
% 82.49/53.60 ~(join(zero, X0!0) = X0!0)),
% 82.49/53.60 inference(skolemize,[status(sab)],[248])).
% 82.49/53.60 tff(250,plain,
% 82.49/53.60 ($false),
% 82.49/53.60 inference(unit_resolution,[status(thm)],[249, 239])).
% 82.49/53.60 % SZS output end Proof
%------------------------------------------------------------------------------