TSTP Solution File: LCL490+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL490+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 : Sun Sep 18 04:56:29 EDT 2022
% Result : Theorem 127.46s 82.17s
% Output : Proof 127.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL490+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 : Thu Sep 1 22:14:19 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 127.46/82.17 % SZS status Theorem
% 127.46/82.17 % SZS output start Proof
% 127.46/82.17 tff(is_a_theorem_type, type, (
% 127.46/82.17 is_a_theorem: $i > $o)).
% 127.46/82.17 tff(or_type, type, (
% 127.46/82.17 or: ( $i * $i ) > $i)).
% 127.46/82.17 tff(not_type, type, (
% 127.46/82.17 not: $i > $i)).
% 127.46/82.17 tff(tptp_fun_X_1_type, type, (
% 127.46/82.17 tptp_fun_X_1: $i)).
% 127.46/82.17 tff(tptp_fun_Y_0_type, type, (
% 127.46/82.17 tptp_fun_Y_0: $i)).
% 127.46/82.17 tff(implies_type, type, (
% 127.46/82.17 implies: ( $i * $i ) > $i)).
% 127.46/82.17 tff(op_implies_or_type, type, (
% 127.46/82.17 op_implies_or: $o)).
% 127.46/82.17 tff(and_type, type, (
% 127.46/82.17 and: ( $i * $i ) > $i)).
% 127.46/82.17 tff(op_or_type, type, (
% 127.46/82.17 op_or: $o)).
% 127.46/82.17 tff(equiv_type, type, (
% 127.46/82.17 equiv: ( $i * $i ) > $i)).
% 127.46/82.17 tff(op_equiv_type, type, (
% 127.46/82.17 op_equiv: $o)).
% 127.46/82.17 tff(op_implies_and_type, type, (
% 127.46/82.17 op_implies_and: $o)).
% 127.46/82.17 tff(op_and_type, type, (
% 127.46/82.17 op_and: $o)).
% 127.46/82.17 tff(r3_type, type, (
% 127.46/82.17 r3: $o)).
% 127.46/82.17 tff(r4_type, type, (
% 127.46/82.17 r4: $o)).
% 127.46/82.17 tff(modus_ponens_type, type, (
% 127.46/82.17 modus_ponens: $o)).
% 127.46/82.17 tff(substitution_of_equivalents_type, type, (
% 127.46/82.17 substitution_of_equivalents: $o)).
% 127.46/82.17 tff(or_1_type, type, (
% 127.46/82.17 or_1: $o)).
% 127.46/82.17 tff(r2_type, type, (
% 127.46/82.17 r2: $o)).
% 127.46/82.17 tff(1,plain,
% 127.46/82.17 (^[X: $i, Y: $i] : refl((implies(X, Y) = or(not(X), Y)) <=> (implies(X, Y) = or(not(X), Y)))),
% 127.46/82.17 inference(bind,[status(th)],[])).
% 127.46/82.17 tff(2,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 127.46/82.17 inference(quant_intro,[status(thm)],[1])).
% 127.46/82.17 tff(3,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(4,plain,
% 127.46/82.17 (($false | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(5,plain,
% 127.46/82.17 ((~$true) <=> $false),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(6,axiom,(op_implies_or), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_op_implies_or')).
% 127.46/82.17 tff(7,plain,
% 127.46/82.17 (op_implies_or <=> $true),
% 127.46/82.17 inference(iff_true,[status(thm)],[6])).
% 127.46/82.17 tff(8,plain,
% 127.46/82.17 ((~op_implies_or) <=> (~$true)),
% 127.46/82.17 inference(monotonicity,[status(thm)],[7])).
% 127.46/82.17 tff(9,plain,
% 127.46/82.17 ((~op_implies_or) <=> $false),
% 127.46/82.17 inference(transitivity,[status(thm)],[8, 5])).
% 127.46/82.17 tff(10,plain,
% 127.46/82.17 (((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ($false | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)))),
% 127.46/82.17 inference(monotonicity,[status(thm)],[9])).
% 127.46/82.17 tff(11,plain,
% 127.46/82.17 (((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 127.46/82.17 inference(transitivity,[status(thm)],[10, 4])).
% 127.46/82.17 tff(12,plain,
% 127.46/82.17 (((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(13,plain,
% 127.46/82.17 ((op_implies_or => ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(14,axiom,(op_implies_or => ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_implies_or')).
% 127.46/82.17 tff(15,plain,
% 127.46/82.17 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[14, 13])).
% 127.46/82.17 tff(16,plain,
% 127.46/82.17 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[15, 12])).
% 127.46/82.17 tff(17,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[16, 11])).
% 127.46/82.17 tff(18,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[17, 3])).
% 127.46/82.17 tff(19,plain,(
% 127.46/82.17 ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 127.46/82.17 inference(skolemize,[status(sab)],[18])).
% 127.46/82.17 tff(20,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[19, 2])).
% 127.46/82.17 tff(21,plain,
% 127.46/82.17 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(X!1, or(X!1, Y!0)) = or(not(X!1), or(X!1, Y!0)))),
% 127.46/82.17 inference(quant_inst,[status(thm)],[])).
% 127.46/82.17 tff(22,plain,
% 127.46/82.17 (implies(X!1, or(X!1, Y!0)) = or(not(X!1), or(X!1, Y!0))),
% 127.46/82.17 inference(unit_resolution,[status(thm)],[21, 20])).
% 127.46/82.17 tff(23,plain,
% 127.46/82.17 (or(not(X!1), or(X!1, Y!0)) = implies(X!1, or(X!1, Y!0))),
% 127.46/82.17 inference(symmetry,[status(thm)],[22])).
% 127.46/82.17 tff(24,plain,
% 127.46/82.17 (^[X: $i, Y: $i] : refl((or(X, Y) = not(and(not(X), not(Y)))) <=> (or(X, Y) = not(and(not(X), not(Y)))))),
% 127.46/82.17 inference(bind,[status(th)],[])).
% 127.46/82.17 tff(25,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 127.46/82.17 inference(quant_intro,[status(thm)],[24])).
% 127.46/82.17 tff(26,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(27,plain,
% 127.46/82.17 (($false | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) <=> ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(28,axiom,(op_or), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','hilbert_op_or')).
% 127.46/82.17 tff(29,plain,
% 127.46/82.17 (op_or <=> $true),
% 127.46/82.17 inference(iff_true,[status(thm)],[28])).
% 127.46/82.17 tff(30,plain,
% 127.46/82.17 ((~op_or) <=> (~$true)),
% 127.46/82.17 inference(monotonicity,[status(thm)],[29])).
% 127.46/82.17 tff(31,plain,
% 127.46/82.17 ((~op_or) <=> $false),
% 127.46/82.17 inference(transitivity,[status(thm)],[30, 5])).
% 127.46/82.17 tff(32,plain,
% 127.46/82.17 (((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) <=> ($false | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y)))))),
% 127.46/82.17 inference(monotonicity,[status(thm)],[31])).
% 127.46/82.17 tff(33,plain,
% 127.46/82.17 (((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) <=> ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 127.46/82.17 inference(transitivity,[status(thm)],[32, 27])).
% 127.46/82.17 tff(34,plain,
% 127.46/82.17 (((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) <=> ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y)))))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(35,plain,
% 127.46/82.17 ((op_or => ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) <=> ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y)))))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(36,axiom,(op_or => ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_or')).
% 127.46/82.17 tff(37,plain,
% 127.46/82.17 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[36, 35])).
% 127.46/82.17 tff(38,plain,
% 127.46/82.17 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[37, 34])).
% 127.46/82.17 tff(39,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[38, 33])).
% 127.46/82.17 tff(40,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[39, 26])).
% 127.46/82.17 tff(41,plain,(
% 127.46/82.17 ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 127.46/82.17 inference(skolemize,[status(sab)],[40])).
% 127.46/82.17 tff(42,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[41, 25])).
% 127.46/82.17 tff(43,plain,
% 127.46/82.17 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(X!1, Y!0) = not(and(not(X!1), not(Y!0))))),
% 127.46/82.17 inference(quant_inst,[status(thm)],[])).
% 127.46/82.17 tff(44,plain,
% 127.46/82.17 (or(X!1, Y!0) = not(and(not(X!1), not(Y!0)))),
% 127.46/82.17 inference(unit_resolution,[status(thm)],[43, 42])).
% 127.46/82.17 tff(45,plain,
% 127.46/82.17 (not(and(not(X!1), not(Y!0))) = or(X!1, Y!0)),
% 127.46/82.17 inference(symmetry,[status(thm)],[44])).
% 127.46/82.17 tff(46,plain,
% 127.46/82.17 (^[X: $i, Y: $i] : refl((equiv(X, Y) = and(implies(X, Y), implies(Y, X))) <=> (equiv(X, Y) = and(implies(X, Y), implies(Y, X))))),
% 127.46/82.17 inference(bind,[status(th)],[])).
% 127.46/82.17 tff(47,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))) <=> ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 127.46/82.17 inference(quant_intro,[status(thm)],[46])).
% 127.46/82.17 tff(48,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))) <=> ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(49,plain,
% 127.46/82.17 (($false | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(50,axiom,(op_equiv), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_op_equiv')).
% 127.46/82.17 tff(51,plain,
% 127.46/82.17 (op_equiv <=> $true),
% 127.46/82.17 inference(iff_true,[status(thm)],[50])).
% 127.46/82.17 tff(52,plain,
% 127.46/82.17 ((~op_equiv) <=> (~$true)),
% 127.46/82.17 inference(monotonicity,[status(thm)],[51])).
% 127.46/82.17 tff(53,plain,
% 127.46/82.17 ((~op_equiv) <=> $false),
% 127.46/82.17 inference(transitivity,[status(thm)],[52, 5])).
% 127.46/82.17 tff(54,plain,
% 127.46/82.17 (((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ($false | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))))),
% 127.46/82.17 inference(monotonicity,[status(thm)],[53])).
% 127.46/82.17 tff(55,plain,
% 127.46/82.17 (((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 127.46/82.17 inference(transitivity,[status(thm)],[54, 49])).
% 127.46/82.17 tff(56,plain,
% 127.46/82.17 (((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(57,plain,
% 127.46/82.17 ((op_equiv => ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(58,axiom,(op_equiv => ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_equiv')).
% 127.46/82.17 tff(59,plain,
% 127.46/82.17 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[58, 57])).
% 127.46/82.17 tff(60,plain,
% 127.46/82.17 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[59, 56])).
% 127.46/82.17 tff(61,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[60, 55])).
% 127.46/82.17 tff(62,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[61, 48])).
% 127.46/82.17 tff(63,plain,(
% 127.46/82.17 ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 127.46/82.17 inference(skolemize,[status(sab)],[62])).
% 127.46/82.17 tff(64,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[63, 47])).
% 127.46/82.17 tff(65,plain,
% 127.46/82.17 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0)))) = and(implies(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0)))), implies(not(and(not(X!1), not(Y!0))), not(not(or(Y!0, X!1))))))),
% 127.46/82.17 inference(quant_inst,[status(thm)],[])).
% 127.46/82.17 tff(66,plain,
% 127.46/82.17 (equiv(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0)))) = and(implies(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0)))), implies(not(and(not(X!1), not(Y!0))), not(not(or(Y!0, X!1)))))),
% 127.46/82.17 inference(unit_resolution,[status(thm)],[65, 64])).
% 127.46/82.17 tff(67,plain,
% 127.46/82.17 (and(implies(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0)))), implies(not(and(not(X!1), not(Y!0))), not(not(or(Y!0, X!1))))) = equiv(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0))))),
% 127.46/82.17 inference(symmetry,[status(thm)],[66])).
% 127.46/82.17 tff(68,plain,
% 127.46/82.17 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(X!1), not(Y!0))), not(not(or(Y!0, X!1)))) = or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))),
% 127.46/82.17 inference(quant_inst,[status(thm)],[])).
% 127.46/82.17 tff(69,plain,
% 127.46/82.17 (implies(not(and(not(X!1), not(Y!0))), not(not(or(Y!0, X!1)))) = or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))),
% 127.46/82.17 inference(unit_resolution,[status(thm)],[68, 20])).
% 127.46/82.17 tff(70,plain,
% 127.46/82.17 (or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))) = implies(not(and(not(X!1), not(Y!0))), not(not(or(Y!0, X!1))))),
% 127.46/82.17 inference(symmetry,[status(thm)],[69])).
% 127.46/82.17 tff(71,plain,
% 127.46/82.17 (^[X: $i, Y: $i] : refl((implies(X, Y) = not(and(X, not(Y)))) <=> (implies(X, Y) = not(and(X, not(Y)))))),
% 127.46/82.17 inference(bind,[status(th)],[])).
% 127.46/82.17 tff(72,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 127.46/82.17 inference(quant_intro,[status(thm)],[71])).
% 127.46/82.17 tff(73,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(74,plain,
% 127.46/82.17 (($false | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(75,axiom,(op_implies_and), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','hilbert_op_implies_and')).
% 127.46/82.17 tff(76,plain,
% 127.46/82.17 (op_implies_and <=> $true),
% 127.46/82.17 inference(iff_true,[status(thm)],[75])).
% 127.46/82.17 tff(77,plain,
% 127.46/82.17 ((~op_implies_and) <=> (~$true)),
% 127.46/82.17 inference(monotonicity,[status(thm)],[76])).
% 127.46/82.17 tff(78,plain,
% 127.46/82.17 ((~op_implies_and) <=> $false),
% 127.46/82.17 inference(transitivity,[status(thm)],[77, 5])).
% 127.46/82.17 tff(79,plain,
% 127.46/82.17 (((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ($false | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))))),
% 127.46/82.17 inference(monotonicity,[status(thm)],[78])).
% 127.46/82.17 tff(80,plain,
% 127.46/82.17 (((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 127.46/82.17 inference(transitivity,[status(thm)],[79, 74])).
% 127.46/82.17 tff(81,plain,
% 127.46/82.17 (((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(82,plain,
% 127.46/82.17 ((op_implies_and => ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(83,axiom,(op_implies_and => ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_implies_and')).
% 127.46/82.17 tff(84,plain,
% 127.46/82.17 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[83, 82])).
% 127.46/82.17 tff(85,plain,
% 127.46/82.17 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[84, 81])).
% 127.46/82.17 tff(86,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[85, 80])).
% 127.46/82.17 tff(87,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[86, 73])).
% 127.46/82.17 tff(88,plain,(
% 127.46/82.17 ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 127.46/82.17 inference(skolemize,[status(sab)],[87])).
% 127.46/82.17 tff(89,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[88, 72])).
% 127.46/82.17 tff(90,plain,
% 127.46/82.17 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0)))) = not(and(not(not(or(Y!0, X!1))), not(not(and(not(X!1), not(Y!0)))))))),
% 127.46/82.17 inference(quant_inst,[status(thm)],[])).
% 127.46/82.17 tff(91,plain,
% 127.46/82.17 (implies(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0)))) = not(and(not(not(or(Y!0, X!1))), not(not(and(not(X!1), not(Y!0))))))),
% 127.46/82.17 inference(unit_resolution,[status(thm)],[90, 89])).
% 127.46/82.17 tff(92,plain,
% 127.46/82.17 (not(and(not(not(or(Y!0, X!1))), not(not(and(not(X!1), not(Y!0)))))) = implies(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0))))),
% 127.46/82.17 inference(symmetry,[status(thm)],[91])).
% 127.46/82.17 tff(93,plain,
% 127.46/82.17 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))) = not(and(not(not(or(Y!0, X!1))), not(not(and(not(X!1), not(Y!0)))))))),
% 127.46/82.17 inference(quant_inst,[status(thm)],[])).
% 127.46/82.17 tff(94,plain,
% 127.46/82.17 (or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))) = not(and(not(not(or(Y!0, X!1))), not(not(and(not(X!1), not(Y!0))))))),
% 127.46/82.17 inference(unit_resolution,[status(thm)],[93, 42])).
% 127.46/82.17 tff(95,plain,
% 127.46/82.17 (or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))) = implies(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0))))),
% 127.46/82.17 inference(transitivity,[status(thm)],[94, 92])).
% 127.46/82.17 tff(96,plain,
% 127.46/82.17 (and(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))) = and(implies(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0)))), implies(not(and(not(X!1), not(Y!0))), not(not(or(Y!0, X!1)))))),
% 127.46/82.17 inference(monotonicity,[status(thm)],[95, 70])).
% 127.46/82.17 tff(97,plain,
% 127.46/82.17 (^[X: $i, Y: $i] : refl((and(X, Y) = not(or(not(X), not(Y)))) <=> (and(X, Y) = not(or(not(X), not(Y)))))),
% 127.46/82.17 inference(bind,[status(th)],[])).
% 127.46/82.17 tff(98,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 127.46/82.17 inference(quant_intro,[status(thm)],[97])).
% 127.46/82.17 tff(99,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(100,plain,
% 127.46/82.17 (($false | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) <=> ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(101,axiom,(op_and), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_op_and')).
% 127.46/82.17 tff(102,plain,
% 127.46/82.17 (op_and <=> $true),
% 127.46/82.17 inference(iff_true,[status(thm)],[101])).
% 127.46/82.17 tff(103,plain,
% 127.46/82.17 ((~op_and) <=> (~$true)),
% 127.46/82.17 inference(monotonicity,[status(thm)],[102])).
% 127.46/82.17 tff(104,plain,
% 127.46/82.17 ((~op_and) <=> $false),
% 127.46/82.17 inference(transitivity,[status(thm)],[103, 5])).
% 127.46/82.17 tff(105,plain,
% 127.46/82.17 (((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) <=> ($false | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))))),
% 127.46/82.17 inference(monotonicity,[status(thm)],[104])).
% 127.46/82.17 tff(106,plain,
% 127.46/82.17 (((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) <=> ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 127.46/82.17 inference(transitivity,[status(thm)],[105, 100])).
% 127.46/82.17 tff(107,plain,
% 127.46/82.17 (((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) <=> ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(108,plain,
% 127.46/82.17 ((op_and => ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) <=> ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))))),
% 127.46/82.17 inference(rewrite,[status(thm)],[])).
% 127.46/82.17 tff(109,axiom,(op_and => ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_and')).
% 127.46/82.17 tff(110,plain,
% 127.46/82.17 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[109, 108])).
% 127.46/82.17 tff(111,plain,
% 127.46/82.17 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[110, 107])).
% 127.46/82.17 tff(112,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[111, 106])).
% 127.46/82.17 tff(113,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[112, 99])).
% 127.46/82.17 tff(114,plain,(
% 127.46/82.17 ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 127.46/82.17 inference(skolemize,[status(sab)],[113])).
% 127.46/82.17 tff(115,plain,
% 127.46/82.17 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 127.46/82.17 inference(modus_ponens,[status(thm)],[114, 98])).
% 127.46/82.17 tff(116,plain,
% 127.46/82.17 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))) = not(or(not(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))),
% 127.46/82.17 inference(quant_inst,[status(thm)],[])).
% 127.46/82.17 tff(117,plain,
% 127.46/82.17 (and(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))) = not(or(not(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))),
% 127.46/82.17 inference(unit_resolution,[status(thm)],[116, 115])).
% 127.46/82.17 tff(118,plain,
% 127.46/82.17 (not(or(not(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))) = and(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))),
% 127.46/82.17 inference(symmetry,[status(thm)],[117])).
% 127.46/82.17 tff(119,plain,
% 127.46/82.17 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))) = or(not(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))),
% 127.46/82.17 inference(quant_inst,[status(thm)],[])).
% 127.46/82.17 tff(120,plain,
% 127.46/82.17 (implies(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))) = or(not(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))),
% 127.46/82.17 inference(unit_resolution,[status(thm)],[119, 20])).
% 127.46/82.17 tff(121,plain,
% 127.46/82.17 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))) = not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))),
% 127.46/82.17 inference(quant_inst,[status(thm)],[])).
% 127.46/82.17 tff(122,plain,
% 127.46/82.17 (and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))) = not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))),
% 127.46/82.17 inference(unit_resolution,[status(thm)],[121, 115])).
% 127.46/82.17 tff(123,plain,
% 127.46/82.17 (not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))) = and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))),
% 127.46/82.17 inference(symmetry,[status(thm)],[122])).
% 127.46/82.17 tff(124,plain,
% 127.46/82.17 (implies(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))) = implies(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))),
% 127.46/82.17 inference(monotonicity,[status(thm)],[123])).
% 127.46/82.17 tff(125,plain,
% 127.46/82.17 (implies(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))) = implies(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))),
% 127.46/82.17 inference(symmetry,[status(thm)],[124])).
% 127.46/82.17 tff(126,plain,
% 127.46/82.17 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))) = not(and(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))))),
% 127.46/82.17 inference(quant_inst,[status(thm)],[])).
% 127.46/82.17 tff(127,plain,
% 127.46/82.17 (implies(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))) = not(and(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))),
% 127.46/82.17 inference(unit_resolution,[status(thm)],[126, 89])).
% 127.46/82.17 tff(128,plain,
% 127.46/82.17 (not(and(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))) = implies(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))),
% 127.46/82.17 inference(symmetry,[status(thm)],[127])).
% 127.46/82.17 tff(129,plain,
% 127.46/82.17 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(and(not(X!1), not(Y!0))), or(Y!0, X!1)) = not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))),
% 127.46/82.17 inference(quant_inst,[status(thm)],[])).
% 127.46/82.17 tff(130,plain,
% 127.46/82.17 (implies(not(and(not(X!1), not(Y!0))), or(Y!0, X!1)) = not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))),
% 127.46/82.17 inference(unit_resolution,[status(thm)],[129, 89])).
% 127.46/82.17 tff(131,plain,
% 127.46/82.17 (not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))) = implies(not(and(not(X!1), not(Y!0))), or(Y!0, X!1))),
% 127.46/82.17 inference(symmetry,[status(thm)],[130])).
% 127.46/82.17 tff(132,plain,
% 127.46/82.17 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(Y!0, X!1), not(and(not(X!1), not(Y!0)))) = not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))),
% 127.46/82.18 inference(quant_inst,[status(thm)],[])).
% 127.46/82.18 tff(133,plain,
% 127.46/82.18 (implies(or(Y!0, X!1), not(and(not(X!1), not(Y!0)))) = not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))),
% 127.46/82.18 inference(unit_resolution,[status(thm)],[132, 89])).
% 127.46/82.18 tff(134,plain,
% 127.46/82.18 (not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))) = implies(or(Y!0, X!1), not(and(not(X!1), not(Y!0))))),
% 127.46/82.18 inference(symmetry,[status(thm)],[133])).
% 127.46/82.18 tff(135,plain,
% 127.46/82.18 (and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))) = and(implies(or(Y!0, X!1), not(and(not(X!1), not(Y!0)))), implies(not(and(not(X!1), not(Y!0))), or(Y!0, X!1)))),
% 127.46/82.18 inference(monotonicity,[status(thm)],[134, 131])).
% 127.46/82.18 tff(136,plain,
% 127.46/82.18 (and(implies(or(Y!0, X!1), not(and(not(X!1), not(Y!0)))), implies(not(and(not(X!1), not(Y!0))), or(Y!0, X!1))) = and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))),
% 127.46/82.18 inference(symmetry,[status(thm)],[135])).
% 127.46/82.18 tff(137,plain,
% 127.46/82.18 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(Y!0, X!1), not(and(not(X!1), not(Y!0)))) = or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))))),
% 127.46/82.18 inference(quant_inst,[status(thm)],[])).
% 127.46/82.18 tff(138,plain,
% 127.46/82.18 (implies(or(Y!0, X!1), not(and(not(X!1), not(Y!0)))) = or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0))))),
% 127.46/82.18 inference(unit_resolution,[status(thm)],[137, 20])).
% 127.46/82.18 tff(139,plain,
% 127.46/82.18 (or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))) = implies(or(Y!0, X!1), not(and(not(X!1), not(Y!0))))),
% 127.46/82.18 inference(symmetry,[status(thm)],[138])).
% 127.46/82.18 tff(140,plain,
% 127.46/82.18 (and(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))) = and(implies(or(Y!0, X!1), not(and(not(X!1), not(Y!0)))), implies(not(and(not(X!1), not(Y!0))), or(Y!0, X!1)))),
% 127.46/82.18 inference(monotonicity,[status(thm)],[139, 131])).
% 127.46/82.18 tff(141,plain,
% 127.46/82.18 (and(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))) = and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))),
% 127.46/82.18 inference(transitivity,[status(thm)],[140, 136])).
% 127.46/82.18 tff(142,plain,
% 127.46/82.18 (not(and(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))) = not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))),
% 127.46/82.18 inference(monotonicity,[status(thm)],[141])).
% 127.46/82.18 tff(143,plain,
% 127.46/82.18 (not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))) = not(and(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))),
% 127.46/82.18 inference(symmetry,[status(thm)],[142])).
% 127.46/82.18 tff(144,plain,
% 127.46/82.18 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))) = not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))))),
% 127.46/82.18 inference(quant_inst,[status(thm)],[])).
% 127.46/82.18 tff(145,plain,
% 127.46/82.18 (or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))) = not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))),
% 127.46/82.18 inference(unit_resolution,[status(thm)],[144, 42])).
% 127.46/82.18 tff(146,plain,
% 127.46/82.18 (not(not(and(not(X!1), not(Y!0)))) = not(or(X!1, Y!0))),
% 127.46/82.18 inference(monotonicity,[status(thm)],[45])).
% 127.46/82.18 tff(147,plain,
% 127.46/82.18 (not(or(X!1, Y!0)) = not(not(and(not(X!1), not(Y!0))))),
% 127.46/82.18 inference(symmetry,[status(thm)],[146])).
% 127.46/82.18 tff(148,plain,
% 127.46/82.18 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(Y!0, X!1) = not(and(not(Y!0), not(X!1))))),
% 127.46/82.18 inference(quant_inst,[status(thm)],[])).
% 127.46/82.18 tff(149,plain,
% 127.46/82.18 (or(Y!0, X!1) = not(and(not(Y!0), not(X!1)))),
% 127.46/82.18 inference(unit_resolution,[status(thm)],[148, 42])).
% 127.46/82.18 tff(150,plain,
% 127.46/82.18 (not(and(not(Y!0), not(X!1))) = or(Y!0, X!1)),
% 127.46/82.18 inference(symmetry,[status(thm)],[149])).
% 127.46/82.18 tff(151,plain,
% 127.46/82.18 (and(not(and(not(Y!0), not(X!1))), not(or(X!1, Y!0))) = and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))),
% 127.46/82.18 inference(monotonicity,[status(thm)],[150, 147])).
% 127.46/82.18 tff(152,plain,
% 127.46/82.18 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(Y!0), not(X!1))), not(or(X!1, Y!0))) = not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))))),
% 127.46/82.18 inference(quant_inst,[status(thm)],[])).
% 127.46/82.18 tff(153,plain,
% 127.46/82.18 (and(not(and(not(Y!0), not(X!1))), not(or(X!1, Y!0))) = not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))))),
% 127.46/82.18 inference(unit_resolution,[status(thm)],[152, 115])).
% 127.46/82.18 tff(154,plain,
% 127.46/82.18 (not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))) = and(not(and(not(Y!0), not(X!1))), not(or(X!1, Y!0)))),
% 127.46/82.18 inference(symmetry,[status(thm)],[153])).
% 127.46/82.18 tff(155,plain,
% 127.46/82.18 (not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))) = and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))),
% 127.46/82.18 inference(transitivity,[status(thm)],[154, 151])).
% 127.46/82.18 tff(156,plain,
% 127.46/82.18 (or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))) = or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))),
% 127.46/82.18 inference(monotonicity,[status(thm)],[155, 123])).
% 127.46/82.18 tff(157,plain,
% 127.46/82.18 (or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))) = or(not(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))),
% 127.46/82.18 inference(transitivity,[status(thm)],[156, 145, 143, 128, 125, 120])).
% 127.46/82.18 tff(158,plain,
% 127.46/82.18 (not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))) = not(or(not(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))),
% 127.46/82.18 inference(monotonicity,[status(thm)],[157])).
% 127.46/82.18 tff(159,plain,
% 127.46/82.18 (not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))) = equiv(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0))))),
% 127.46/82.18 inference(transitivity,[status(thm)],[158, 118, 96, 67])).
% 127.46/82.18 tff(160,plain,
% 127.46/82.18 (is_a_theorem(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))) <=> is_a_theorem(equiv(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0)))))),
% 127.46/82.18 inference(monotonicity,[status(thm)],[159])).
% 127.46/82.18 tff(161,plain,
% 127.46/82.18 (or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))) = or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))),
% 127.46/82.18 inference(monotonicity,[status(thm)],[155])).
% 127.46/82.18 tff(162,plain,
% 127.46/82.18 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))) = or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))))),
% 127.46/82.18 inference(quant_inst,[status(thm)],[])).
% 127.46/82.18 tff(163,plain,
% 127.46/82.18 (implies(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))) = or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))),
% 127.46/82.18 inference(unit_resolution,[status(thm)],[162, 20])).
% 127.46/82.18 tff(164,plain,
% 127.46/82.18 (implies(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))) = or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))),
% 127.46/82.18 inference(transitivity,[status(thm)],[163, 161])).
% 127.46/82.18 tff(165,plain,
% 127.46/82.18 (is_a_theorem(implies(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))) <=> is_a_theorem(or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))))),
% 127.46/82.18 inference(monotonicity,[status(thm)],[164])).
% 127.46/82.18 tff(166,plain,
% 127.46/82.18 (is_a_theorem(or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))) <=> is_a_theorem(implies(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))))),
% 127.46/82.18 inference(symmetry,[status(thm)],[165])).
% 127.46/82.18 tff(167,plain,
% 127.46/82.18 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))) = not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))),
% 127.46/82.18 inference(quant_inst,[status(thm)],[])).
% 127.46/82.18 tff(168,plain,
% 127.46/82.18 (or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))) = not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))),
% 127.46/82.18 inference(unit_resolution,[status(thm)],[167, 42])).
% 127.46/82.18 tff(169,plain,
% 127.46/82.18 (implies(or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))) = implies(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))), or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))))),
% 127.46/82.18 inference(monotonicity,[status(thm)],[168])).
% 127.46/82.18 tff(170,plain,
% 127.46/82.18 (is_a_theorem(implies(or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))))) <=> is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))), or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))))),
% 127.46/82.18 inference(monotonicity,[status(thm)],[169])).
% 127.46/82.18 tff(171,plain,
% 127.46/82.18 (^[P: $i, Q: $i] : refl(is_a_theorem(implies(or(P, Q), or(Q, P))) <=> is_a_theorem(implies(or(P, Q), or(Q, P))))),
% 127.46/82.18 inference(bind,[status(th)],[])).
% 127.46/82.18 tff(172,plain,
% 127.46/82.18 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 127.46/82.18 inference(quant_intro,[status(thm)],[171])).
% 127.46/82.18 tff(173,plain,
% 127.46/82.18 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 127.46/82.18 inference(rewrite,[status(thm)],[])).
% 127.46/82.18 tff(174,plain,
% 127.46/82.18 (($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 127.46/82.18 inference(rewrite,[status(thm)],[])).
% 127.46/82.18 tff(175,axiom,(r3), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_r3')).
% 127.46/82.18 tff(176,plain,
% 127.46/82.18 (r3 <=> $true),
% 127.46/82.18 inference(iff_true,[status(thm)],[175])).
% 127.46/82.18 tff(177,plain,
% 127.46/82.18 ((r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) <=> ($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))))),
% 127.46/82.18 inference(monotonicity,[status(thm)],[176])).
% 127.46/82.18 tff(178,plain,
% 127.46/82.18 ((r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 127.46/82.18 inference(transitivity,[status(thm)],[177, 174])).
% 127.46/82.18 tff(179,plain,
% 127.46/82.18 ((r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) <=> (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))))),
% 127.46/82.18 inference(rewrite,[status(thm)],[])).
% 127.46/82.18 tff(180,axiom,(r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','r3')).
% 127.46/82.18 tff(181,plain,
% 127.46/82.18 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 127.46/82.18 inference(modus_ponens,[status(thm)],[180, 179])).
% 127.46/82.18 tff(182,plain,
% 127.46/82.18 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 127.46/82.18 inference(modus_ponens,[status(thm)],[181, 179])).
% 127.46/82.18 tff(183,plain,
% 127.46/82.18 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 127.46/82.18 inference(modus_ponens,[status(thm)],[182, 178])).
% 127.46/82.18 tff(184,plain,
% 127.46/82.18 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 127.46/82.18 inference(modus_ponens,[status(thm)],[183, 173])).
% 127.46/82.18 tff(185,plain,(
% 127.46/82.18 ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 127.46/82.18 inference(skolemize,[status(sab)],[184])).
% 127.46/82.18 tff(186,plain,
% 127.46/82.18 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 127.46/82.18 inference(modus_ponens,[status(thm)],[185, 172])).
% 127.46/82.18 tff(187,plain,
% 127.46/82.18 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))))),
% 127.46/82.18 inference(quant_inst,[status(thm)],[])).
% 127.46/82.18 tff(188,plain,
% 127.46/82.18 (is_a_theorem(implies(or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))))),
% 127.46/82.18 inference(unit_resolution,[status(thm)],[187, 186])).
% 127.46/82.18 tff(189,plain,
% 127.46/82.18 (is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))), or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))))),
% 127.46/82.18 inference(modus_ponens,[status(thm)],[188, 170])).
% 127.46/82.18 tff(190,plain,
% 127.46/82.18 (or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1)))) = or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1))),
% 127.46/82.18 inference(monotonicity,[status(thm)],[150])).
% 127.46/82.18 tff(191,plain,
% 127.46/82.18 (or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)) = or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))),
% 127.46/82.18 inference(symmetry,[status(thm)],[190])).
% 127.46/82.18 tff(192,plain,
% 127.46/82.18 (not(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1))) = not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1)))))),
% 127.46/82.18 inference(monotonicity,[status(thm)],[191])).
% 127.46/82.18 tff(193,plain,
% 127.46/82.18 (not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))) = not(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)))),
% 127.46/82.18 inference(symmetry,[status(thm)],[192])).
% 127.46/82.18 tff(194,plain,
% 127.46/82.18 (or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))) = or(not(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))),
% 127.46/82.18 inference(monotonicity,[status(thm)],[193])).
% 127.46/82.18 tff(195,plain,
% 127.46/82.18 (or(not(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))) = or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))),
% 127.46/82.18 inference(symmetry,[status(thm)],[194])).
% 127.46/82.18 tff(196,plain,
% 127.46/82.18 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))) = or(not(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))),
% 127.46/82.18 inference(quant_inst,[status(thm)],[])).
% 127.46/82.18 tff(197,plain,
% 127.46/82.18 (implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))) = or(not(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))),
% 127.46/82.18 inference(unit_resolution,[status(thm)],[196, 20])).
% 127.46/82.18 tff(198,plain,
% 127.46/82.18 (implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))) = implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))),
% 127.46/82.19 inference(monotonicity,[status(thm)],[168])).
% 127.46/82.19 tff(199,plain,
% 127.46/82.19 (implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) = implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))),
% 127.46/82.19 inference(symmetry,[status(thm)],[198])).
% 127.46/82.19 tff(200,plain,
% 127.46/82.19 (implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) = or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))),
% 127.46/82.19 inference(transitivity,[status(thm)],[199, 197, 195])).
% 127.46/82.19 tff(201,plain,
% 127.46/82.19 (is_a_theorem(implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))) <=> is_a_theorem(or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))),
% 127.46/82.19 inference(monotonicity,[status(thm)],[200])).
% 127.46/82.19 tff(202,plain,
% 127.46/82.19 (is_a_theorem(or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))) <=> is_a_theorem(implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))),
% 127.46/82.19 inference(symmetry,[status(thm)],[201])).
% 127.46/82.19 tff(203,plain,
% 127.46/82.19 (and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))) = and(implies(not(and(not(X!1), not(Y!0))), or(Y!0, X!1)), implies(or(Y!0, X!1), not(and(not(X!1), not(Y!0)))))),
% 127.46/82.19 inference(monotonicity,[status(thm)],[131, 134])).
% 127.46/82.19 tff(204,plain,
% 127.46/82.19 (and(implies(not(and(not(X!1), not(Y!0))), or(Y!0, X!1)), implies(or(Y!0, X!1), not(and(not(X!1), not(Y!0))))) = and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))),
% 127.46/82.19 inference(symmetry,[status(thm)],[203])).
% 127.46/82.19 tff(205,plain,
% 127.46/82.19 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(X!1), not(Y!0))), or(Y!0, X!1)) = or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)))),
% 127.46/82.19 inference(quant_inst,[status(thm)],[])).
% 127.46/82.19 tff(206,plain,
% 127.46/82.19 (implies(not(and(not(X!1), not(Y!0))), or(Y!0, X!1)) = or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1))),
% 127.46/82.19 inference(unit_resolution,[status(thm)],[205, 20])).
% 127.46/82.19 tff(207,plain,
% 127.46/82.19 (or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)) = implies(not(and(not(X!1), not(Y!0))), or(Y!0, X!1))),
% 127.46/82.19 inference(symmetry,[status(thm)],[206])).
% 127.46/82.19 tff(208,plain,
% 127.46/82.19 (and(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))) = and(implies(not(and(not(X!1), not(Y!0))), or(Y!0, X!1)), implies(or(Y!0, X!1), not(and(not(X!1), not(Y!0)))))),
% 127.46/82.19 inference(monotonicity,[status(thm)],[207, 134])).
% 127.46/82.19 tff(209,plain,
% 127.46/82.19 (and(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))) = and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))),
% 127.46/82.19 inference(transitivity,[status(thm)],[208, 204])).
% 127.46/82.19 tff(210,plain,
% 127.46/82.19 (not(and(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))) = not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))),
% 127.46/82.19 inference(monotonicity,[status(thm)],[209])).
% 127.46/82.19 tff(211,plain,
% 127.46/82.19 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))) = not(and(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))),
% 127.46/82.19 inference(quant_inst,[status(thm)],[])).
% 127.46/82.19 tff(212,plain,
% 127.46/82.19 (implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))) = not(and(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))),
% 127.46/82.19 inference(unit_resolution,[status(thm)],[211, 89])).
% 127.46/82.19 tff(213,plain,
% 127.46/82.19 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))) = or(not(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))),
% 127.46/82.19 inference(quant_inst,[status(thm)],[])).
% 127.46/82.19 tff(214,plain,
% 127.46/82.19 (implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))) = or(not(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))),
% 127.46/82.19 inference(unit_resolution,[status(thm)],[213, 20])).
% 127.46/82.19 tff(215,plain,
% 127.46/82.19 (or(not(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))) = implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))),
% 127.46/82.19 inference(symmetry,[status(thm)],[214])).
% 127.46/82.19 tff(216,plain,
% 127.46/82.19 (or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))) = or(not(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))),
% 127.46/82.19 inference(monotonicity,[status(thm)],[193])).
% 127.46/82.19 tff(217,plain,
% 127.46/82.19 (or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))) = not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))),
% 127.46/82.19 inference(transitivity,[status(thm)],[216, 215, 212, 210])).
% 127.46/82.19 tff(218,plain,
% 127.46/82.19 (or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))) = or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))),
% 127.46/82.19 inference(symmetry,[status(thm)],[156])).
% 127.46/82.19 tff(219,plain,
% 127.46/82.19 (not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))) = or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))),
% 127.46/82.19 inference(symmetry,[status(thm)],[145])).
% 127.46/82.19 tff(220,plain,
% 127.46/82.19 (not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))) = or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))),
% 127.46/82.19 inference(transitivity,[status(thm)],[219, 218])).
% 127.46/82.19 tff(221,plain,
% 127.46/82.19 (not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))) = not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))),
% 127.46/82.19 inference(monotonicity,[status(thm)],[220])).
% 127.46/82.19 tff(222,plain,
% 127.46/82.19 (not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))) = not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))))),
% 127.46/82.19 inference(symmetry,[status(thm)],[221])).
% 127.46/82.19 tff(223,plain,
% 127.46/82.19 (or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))) = or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))),
% 127.46/82.19 inference(monotonicity,[status(thm)],[222, 217])).
% 127.46/82.19 tff(224,plain,
% 127.46/82.19 (or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) = or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))),
% 127.46/82.19 inference(symmetry,[status(thm)],[223])).
% 127.46/82.19 tff(225,plain,
% 127.46/82.19 (implies(or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))) = implies(or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))),
% 127.46/82.19 inference(monotonicity,[status(thm)],[224])).
% 127.46/82.19 tff(226,plain,
% 127.46/82.19 (implies(or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))) = implies(or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))),
% 127.46/82.19 inference(symmetry,[status(thm)],[225])).
% 127.46/82.19 tff(227,plain,
% 127.46/82.19 (is_a_theorem(implies(or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) <=> is_a_theorem(implies(or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))),
% 127.46/82.19 inference(monotonicity,[status(thm)],[226])).
% 127.46/82.19 tff(228,plain,
% 127.46/82.19 (^[P: $i, Q: $i, R: $i] : refl(is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R)))) <=> is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R)))))),
% 127.46/82.19 inference(bind,[status(th)],[])).
% 127.46/82.19 tff(229,plain,
% 127.46/82.19 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R)))) <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 127.46/82.19 inference(quant_intro,[status(thm)],[228])).
% 127.46/82.19 tff(230,plain,
% 127.46/82.19 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R)))) <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 127.46/82.19 inference(rewrite,[status(thm)],[])).
% 127.46/82.19 tff(231,plain,
% 127.46/82.19 (($true <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 127.46/82.19 inference(rewrite,[status(thm)],[])).
% 127.46/82.19 tff(232,axiom,(r4), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_r4')).
% 127.46/82.19 tff(233,plain,
% 127.46/82.19 (r4 <=> $true),
% 127.46/82.19 inference(iff_true,[status(thm)],[232])).
% 127.46/82.19 tff(234,plain,
% 127.46/82.19 ((r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) <=> ($true <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R)))))),
% 127.46/82.19 inference(monotonicity,[status(thm)],[233])).
% 127.46/82.19 tff(235,plain,
% 127.46/82.19 ((r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 127.46/82.19 inference(transitivity,[status(thm)],[234, 231])).
% 127.46/82.19 tff(236,plain,
% 127.46/82.19 ((r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) <=> (r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R)))))),
% 127.46/82.19 inference(rewrite,[status(thm)],[])).
% 127.46/82.19 tff(237,axiom,(r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','r4')).
% 127.46/82.19 tff(238,plain,
% 127.46/82.19 (r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 127.46/82.19 inference(modus_ponens,[status(thm)],[237, 236])).
% 127.46/82.19 tff(239,plain,
% 127.46/82.19 (r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 127.46/82.19 inference(modus_ponens,[status(thm)],[238, 236])).
% 127.46/82.19 tff(240,plain,
% 127.46/82.19 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 127.46/82.19 inference(modus_ponens,[status(thm)],[239, 235])).
% 127.46/82.19 tff(241,plain,
% 127.46/82.19 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 127.46/82.19 inference(modus_ponens,[status(thm)],[240, 230])).
% 127.46/82.19 tff(242,plain,(
% 127.46/82.19 ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 127.46/82.19 inference(skolemize,[status(sab)],[241])).
% 127.46/82.19 tff(243,plain,
% 127.46/82.19 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 127.46/82.19 inference(modus_ponens,[status(thm)],[242, 229])).
% 127.46/82.19 tff(244,plain,
% 127.46/82.19 ((~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) | is_a_theorem(implies(or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))),
% 127.46/82.19 inference(quant_inst,[status(thm)],[])).
% 127.46/82.19 tff(245,plain,
% 127.46/82.19 (is_a_theorem(implies(or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))),
% 127.46/82.19 inference(unit_resolution,[status(thm)],[244, 243])).
% 127.46/82.19 tff(246,plain,
% 127.46/82.19 (is_a_theorem(implies(or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))),
% 127.46/82.19 inference(modus_ponens,[status(thm)],[245, 227])).
% 127.46/82.19 tff(247,plain,
% 127.46/82.19 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) = or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))),
% 127.46/82.19 inference(quant_inst,[status(thm)],[])).
% 127.46/82.19 tff(248,plain,
% 127.46/82.19 (implies(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) = or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))),
% 127.46/82.19 inference(unit_resolution,[status(thm)],[247, 20])).
% 127.46/82.19 tff(249,plain,
% 127.46/82.19 (or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) = implies(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))),
% 127.46/82.19 inference(symmetry,[status(thm)],[248])).
% 127.46/82.19 tff(250,plain,
% 127.46/82.19 (is_a_theorem(or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))) <=> is_a_theorem(implies(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))),
% 127.46/82.19 inference(monotonicity,[status(thm)],[249])).
% 127.46/82.19 tff(251,plain,
% 127.46/82.19 (is_a_theorem(implies(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))) <=> is_a_theorem(or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))),
% 127.46/82.19 inference(symmetry,[status(thm)],[250])).
% 127.46/82.19 tff(252,plain,
% 127.46/82.19 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))) = not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))),
% 127.46/82.19 inference(quant_inst,[status(thm)],[])).
% 127.46/82.19 tff(253,plain,
% 127.46/82.19 (or(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))) = not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))),
% 127.46/82.19 inference(unit_resolution,[status(thm)],[252, 42])).
% 127.46/82.19 tff(254,plain,
% 127.46/82.19 (or(not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))) = or(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))),
% 127.46/82.19 inference(monotonicity,[status(thm)],[123])).
% 127.46/82.19 tff(255,plain,
% 127.46/82.19 (or(not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))) = not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))),
% 127.46/82.19 inference(transitivity,[status(thm)],[254, 253])).
% 127.46/82.19 tff(256,plain,
% 127.46/82.19 (or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))) = or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))),
% 127.46/82.19 inference(monotonicity,[status(thm)],[123])).
% 127.46/82.19 tff(257,plain,
% 127.46/82.19 (or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))) = not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))),
% 127.46/82.19 inference(transitivity,[status(thm)],[256, 145])).
% 127.46/82.19 tff(258,plain,
% 127.46/82.19 (implies(or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))) = implies(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))),
% 127.46/82.20 inference(monotonicity,[status(thm)],[257, 255])).
% 127.46/82.20 tff(259,plain,
% 127.46/82.20 (is_a_theorem(implies(or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))) <=> is_a_theorem(implies(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))),
% 127.46/82.20 inference(monotonicity,[status(thm)],[258])).
% 127.46/82.20 tff(260,plain,
% 127.46/82.20 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))),
% 127.46/82.20 inference(quant_inst,[status(thm)],[])).
% 127.46/82.20 tff(261,plain,
% 127.46/82.20 (is_a_theorem(implies(or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))),
% 127.46/82.20 inference(unit_resolution,[status(thm)],[260, 186])).
% 127.46/82.20 tff(262,plain,
% 127.46/82.20 (is_a_theorem(implies(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))),
% 127.46/82.20 inference(modus_ponens,[status(thm)],[261, 259])).
% 127.46/82.20 tff(263,plain,
% 127.46/82.20 (is_a_theorem(or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))),
% 127.46/82.20 inference(modus_ponens,[status(thm)],[262, 251])).
% 127.46/82.20 tff(264,plain,
% 127.46/82.20 (^[X: $i, Y: $i] : refl((is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))) <=> (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))),
% 127.46/82.20 inference(bind,[status(th)],[])).
% 127.46/82.20 tff(265,plain,
% 127.46/82.20 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 127.46/82.20 inference(quant_intro,[status(thm)],[264])).
% 127.46/82.20 tff(266,plain,
% 127.46/82.20 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((is_a_theorem(X) & is_a_theorem(implies(X, Y))) <=> (~((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))), ((~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))) <=> (~(~((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))))), rewrite((~(~((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))) <=> ((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))), ((~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))) <=> ((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))), ((is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> (is_a_theorem(Y) | ((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))))), rewrite((is_a_theorem(Y) | ((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) <=> (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))), ((is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))))),
% 127.46/82.20 inference(bind,[status(th)],[])).
% 127.46/82.20 tff(267,plain,
% 127.46/82.20 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 127.46/82.20 inference(quant_intro,[status(thm)],[266])).
% 127.46/82.20 tff(268,plain,
% 127.46/82.20 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 127.46/82.20 inference(rewrite,[status(thm)],[])).
% 127.46/82.20 tff(269,plain,
% 127.46/82.20 (($true <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 127.46/82.20 inference(rewrite,[status(thm)],[])).
% 127.46/82.20 tff(270,axiom,(modus_ponens), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_modus_ponens')).
% 127.46/82.20 tff(271,plain,
% 127.46/82.20 (modus_ponens <=> $true),
% 127.46/82.20 inference(iff_true,[status(thm)],[270])).
% 127.46/82.20 tff(272,plain,
% 127.46/82.20 ((modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) <=> ($true <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))))),
% 127.46/82.20 inference(monotonicity,[status(thm)],[271])).
% 127.46/82.20 tff(273,plain,
% 127.46/82.20 ((modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 127.46/82.20 inference(transitivity,[status(thm)],[272, 269])).
% 127.46/82.20 tff(274,plain,
% 127.46/82.20 ((modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) <=> (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))))),
% 127.46/82.20 inference(rewrite,[status(thm)],[])).
% 127.46/82.20 tff(275,plain,
% 127.46/82.20 ((modus_ponens <=> ![X: $i, Y: $i] : ((is_a_theorem(X) & is_a_theorem(implies(X, Y))) => is_a_theorem(Y))) <=> (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))))),
% 127.46/82.20 inference(rewrite,[status(thm)],[])).
% 127.46/82.20 tff(276,axiom,(modus_ponens <=> ![X: $i, Y: $i] : ((is_a_theorem(X) & is_a_theorem(implies(X, Y))) => is_a_theorem(Y))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','modus_ponens')).
% 127.46/82.20 tff(277,plain,
% 127.46/82.20 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 127.46/82.20 inference(modus_ponens,[status(thm)],[276, 275])).
% 127.46/82.20 tff(278,plain,
% 127.46/82.20 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 127.46/82.20 inference(modus_ponens,[status(thm)],[277, 274])).
% 127.46/82.20 tff(279,plain,
% 127.46/82.20 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 127.46/82.20 inference(modus_ponens,[status(thm)],[278, 273])).
% 127.46/82.20 tff(280,plain,
% 127.46/82.20 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 127.46/82.20 inference(modus_ponens,[status(thm)],[279, 268])).
% 127.46/82.20 tff(281,plain,(
% 127.46/82.20 ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 127.46/82.20 inference(skolemize,[status(sab)],[280])).
% 127.46/82.20 tff(282,plain,
% 127.46/82.20 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 127.46/82.20 inference(modus_ponens,[status(thm)],[281, 267])).
% 127.46/82.20 tff(283,plain,
% 127.46/82.20 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 127.46/82.20 inference(modus_ponens,[status(thm)],[282, 265])).
% 127.46/82.20 tff(284,plain,
% 127.46/82.20 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))) | (~is_a_theorem(or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))) | (~is_a_theorem(or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))))),
% 127.46/82.20 inference(rewrite,[status(thm)],[])).
% 127.46/82.20 tff(285,plain,
% 127.46/82.20 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))) | (~is_a_theorem(or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))))),
% 127.46/82.20 inference(quant_inst,[status(thm)],[])).
% 127.46/82.20 tff(286,plain,
% 127.46/82.20 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))) | (~is_a_theorem(or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))),
% 127.51/82.20 inference(modus_ponens,[status(thm)],[285, 284])).
% 127.51/82.20 tff(287,plain,
% 127.51/82.20 (is_a_theorem(or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))) | (~is_a_theorem(or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))), not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))), not(and(not(and(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))), or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))),
% 127.51/82.20 inference(unit_resolution,[status(thm)],[286, 283])).
% 127.51/82.20 tff(288,plain,
% 127.51/82.20 (is_a_theorem(or(not(or(not(not(and(not(X!1), not(Y!0)))), not(and(not(Y!0), not(X!1))))), or(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))), and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))),
% 127.51/82.20 inference(unit_resolution,[status(thm)],[287, 263, 246])).
% 127.51/82.20 tff(289,plain,
% 127.51/82.20 (is_a_theorem(implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))),
% 127.51/82.20 inference(modus_ponens,[status(thm)],[288, 202])).
% 127.51/82.20 tff(290,plain,
% 127.51/82.20 (is_a_theorem(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1))) <=> is_a_theorem(implies(not(and(not(X!1), not(Y!0))), or(Y!0, X!1)))),
% 127.51/82.20 inference(monotonicity,[status(thm)],[207])).
% 127.51/82.20 tff(291,plain,
% 127.51/82.20 (is_a_theorem(implies(not(and(not(X!1), not(Y!0))), or(Y!0, X!1))) <=> is_a_theorem(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)))),
% 127.51/82.20 inference(symmetry,[status(thm)],[290])).
% 127.51/82.20 tff(292,plain,
% 127.51/82.20 (implies(or(X!1, Y!0), or(Y!0, X!1)) = implies(not(and(not(X!1), not(Y!0))), or(Y!0, X!1))),
% 127.51/82.20 inference(monotonicity,[status(thm)],[44])).
% 127.51/82.20 tff(293,plain,
% 127.51/82.20 (is_a_theorem(implies(or(X!1, Y!0), or(Y!0, X!1))) <=> is_a_theorem(implies(not(and(not(X!1), not(Y!0))), or(Y!0, X!1)))),
% 127.51/82.20 inference(monotonicity,[status(thm)],[292])).
% 127.51/82.20 tff(294,plain,
% 127.51/82.20 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(X!1, Y!0), or(Y!0, X!1)))),
% 127.51/82.20 inference(quant_inst,[status(thm)],[])).
% 127.51/82.20 tff(295,plain,
% 127.51/82.20 (is_a_theorem(implies(or(X!1, Y!0), or(Y!0, X!1)))),
% 127.51/82.20 inference(unit_resolution,[status(thm)],[294, 186])).
% 127.51/82.20 tff(296,plain,
% 127.51/82.20 (is_a_theorem(implies(not(and(not(X!1), not(Y!0))), or(Y!0, X!1)))),
% 127.51/82.20 inference(modus_ponens,[status(thm)],[295, 293])).
% 127.51/82.20 tff(297,plain,
% 127.51/82.20 (is_a_theorem(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)))),
% 127.51/82.20 inference(modus_ponens,[status(thm)],[296, 291])).
% 127.51/82.20 tff(298,plain,
% 127.51/82.20 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))))),
% 127.51/82.20 inference(rewrite,[status(thm)],[])).
% 127.51/82.20 tff(299,plain,
% 127.51/82.20 ((is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) | (~is_a_theorem(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)))) | (~is_a_theorem(implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))))) <=> ((~is_a_theorem(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))))),
% 127.51/82.20 inference(rewrite,[status(thm)],[])).
% 127.51/82.20 tff(300,plain,
% 127.51/82.20 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) | (~is_a_theorem(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)))) | (~is_a_theorem(implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))))))),
% 127.51/82.20 inference(monotonicity,[status(thm)],[299])).
% 127.51/82.20 tff(301,plain,
% 127.51/82.20 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) | (~is_a_theorem(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)))) | (~is_a_theorem(implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))))),
% 127.51/82.21 inference(transitivity,[status(thm)],[300, 298])).
% 127.51/82.21 tff(302,plain,
% 127.51/82.21 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) | (~is_a_theorem(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)))) | (~is_a_theorem(implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))))))),
% 127.51/82.21 inference(quant_inst,[status(thm)],[])).
% 127.51/82.21 tff(303,plain,
% 127.51/82.21 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))))),
% 127.51/82.21 inference(modus_ponens,[status(thm)],[302, 301])).
% 127.51/82.21 tff(304,plain,
% 127.51/82.21 (is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(X!1), not(Y!0)))), or(Y!0, X!1)), not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))))),
% 127.51/82.21 inference(unit_resolution,[status(thm)],[303, 283, 297])).
% 127.51/82.21 tff(305,plain,
% 127.51/82.21 (is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))),
% 127.51/82.21 inference(unit_resolution,[status(thm)],[304, 289])).
% 127.51/82.21 tff(306,plain,
% 127.51/82.21 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))), or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))), or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))))))),
% 127.51/82.21 inference(rewrite,[status(thm)],[])).
% 127.51/82.21 tff(307,plain,
% 127.51/82.21 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))), or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))))))),
% 127.51/82.21 inference(quant_inst,[status(thm)],[])).
% 127.51/82.21 tff(308,plain,
% 127.51/82.21 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))), or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))))))),
% 127.51/82.21 inference(modus_ponens,[status(thm)],[307, 306])).
% 127.51/82.21 tff(309,plain,
% 127.51/82.21 (is_a_theorem(or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))), not(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0)))))))), or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))))))),
% 127.51/82.21 inference(unit_resolution,[status(thm)],[308, 283])).
% 127.51/82.21 tff(310,plain,
% 127.51/82.21 (is_a_theorem(or(and(or(Y!0, X!1), not(not(and(not(X!1), not(Y!0))))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))))),
% 127.51/82.21 inference(unit_resolution,[status(thm)],[309, 305, 189])).
% 127.51/82.21 tff(311,plain,
% 127.51/82.21 (is_a_theorem(implies(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))))),
% 127.51/82.21 inference(modus_ponens,[status(thm)],[310, 166])).
% 127.51/82.21 tff(312,plain,
% 127.51/82.21 (not(not(and(not(Y!0), not(X!1)))) = not(or(Y!0, X!1))),
% 127.51/82.21 inference(monotonicity,[status(thm)],[150])).
% 127.51/82.21 tff(313,plain,
% 127.51/82.21 (not(or(Y!0, X!1)) = not(not(and(not(Y!0), not(X!1))))),
% 127.51/82.21 inference(symmetry,[status(thm)],[312])).
% 127.51/82.21 tff(314,plain,
% 127.51/82.21 (or(not(or(Y!0, X!1)), not(not(or(X!1, Y!0)))) = or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))),
% 127.51/82.21 inference(monotonicity,[status(thm)],[313])).
% 127.51/82.21 tff(315,plain,
% 127.51/82.21 (implies(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))), or(not(or(Y!0, X!1)), not(not(or(X!1, Y!0))))) = implies(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))), or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))))),
% 127.51/82.21 inference(monotonicity,[status(thm)],[314])).
% 127.51/82.21 tff(316,plain,
% 127.51/82.21 (is_a_theorem(implies(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))), or(not(or(Y!0, X!1)), not(not(or(X!1, Y!0)))))) <=> is_a_theorem(implies(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))), or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))))),
% 127.51/82.21 inference(monotonicity,[status(thm)],[315])).
% 127.51/82.21 tff(317,plain,
% 127.51/82.21 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))), or(not(or(Y!0, X!1)), not(not(or(X!1, Y!0))))))),
% 127.51/82.21 inference(quant_inst,[status(thm)],[])).
% 127.51/82.21 tff(318,plain,
% 127.51/82.21 (is_a_theorem(implies(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))), or(not(or(Y!0, X!1)), not(not(or(X!1, Y!0))))))),
% 127.51/82.21 inference(unit_resolution,[status(thm)],[317, 186])).
% 127.51/82.21 tff(319,plain,
% 127.51/82.21 (is_a_theorem(implies(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))), or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))))),
% 127.51/82.21 inference(modus_ponens,[status(thm)],[318, 316])).
% 127.51/82.21 tff(320,plain,
% 127.51/82.21 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))) = not(and(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))),
% 127.51/82.21 inference(quant_inst,[status(thm)],[])).
% 127.51/82.21 tff(321,plain,
% 127.51/82.21 (or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))) = not(and(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))),
% 127.51/82.21 inference(unit_resolution,[status(thm)],[320, 42])).
% 127.51/82.21 tff(322,plain,
% 127.51/82.21 (not(and(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))) = or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))),
% 127.51/82.21 inference(symmetry,[status(thm)],[321])).
% 127.51/82.21 tff(323,plain,
% 127.51/82.21 (and(not(or(X!1, Y!0)), not(not(or(Y!0, X!1)))) = and(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))),
% 127.51/82.21 inference(monotonicity,[status(thm)],[147])).
% 127.51/82.21 tff(324,plain,
% 127.51/82.21 (not(and(not(or(X!1, Y!0)), not(not(or(Y!0, X!1))))) = not(and(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))),
% 127.51/82.21 inference(monotonicity,[status(thm)],[323])).
% 127.51/82.21 tff(325,plain,
% 127.51/82.21 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(or(X!1, Y!0)), not(or(Y!0, X!1))) = not(and(not(or(X!1, Y!0)), not(not(or(Y!0, X!1))))))),
% 127.51/82.21 inference(quant_inst,[status(thm)],[])).
% 127.51/82.21 tff(326,plain,
% 127.51/82.21 (implies(not(or(X!1, Y!0)), not(or(Y!0, X!1))) = not(and(not(or(X!1, Y!0)), not(not(or(Y!0, X!1)))))),
% 127.51/82.21 inference(unit_resolution,[status(thm)],[325, 89])).
% 127.51/82.21 tff(327,plain,
% 127.51/82.21 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(X!1, Y!0)), not(or(Y!0, X!1))) = or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))))),
% 127.51/82.21 inference(quant_inst,[status(thm)],[])).
% 127.51/82.21 tff(328,plain,
% 127.51/82.21 (implies(not(or(X!1, Y!0)), not(or(Y!0, X!1))) = or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1)))),
% 127.51/82.21 inference(unit_resolution,[status(thm)],[327, 20])).
% 127.51/82.21 tff(329,plain,
% 127.51/82.21 (or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))) = implies(not(or(X!1, Y!0)), not(or(Y!0, X!1)))),
% 127.51/82.21 inference(symmetry,[status(thm)],[328])).
% 127.51/82.21 tff(330,plain,
% 127.51/82.21 (or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))) = or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))),
% 127.51/82.21 inference(transitivity,[status(thm)],[329, 326, 324, 322])).
% 127.51/82.21 tff(331,plain,
% 127.51/82.21 (is_a_theorem(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1)))) <=> is_a_theorem(or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))),
% 127.51/82.21 inference(monotonicity,[status(thm)],[330])).
% 127.51/82.21 tff(332,plain,
% 127.51/82.21 (is_a_theorem(or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))) <=> is_a_theorem(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))))),
% 127.51/82.21 inference(symmetry,[status(thm)],[331])).
% 127.51/82.21 tff(333,plain,
% 127.51/82.21 (is_a_theorem(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0))))) <=> is_a_theorem(implies(or(Y!0, X!1), not(and(not(X!1), not(Y!0)))))),
% 127.51/82.21 inference(monotonicity,[status(thm)],[139])).
% 127.51/82.21 tff(334,plain,
% 127.51/82.21 (is_a_theorem(implies(or(Y!0, X!1), not(and(not(X!1), not(Y!0))))) <=> is_a_theorem(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))))),
% 127.51/82.21 inference(symmetry,[status(thm)],[333])).
% 127.51/82.21 tff(335,plain,
% 127.51/82.21 (implies(or(Y!0, X!1), or(X!1, Y!0)) = implies(or(Y!0, X!1), not(and(not(X!1), not(Y!0))))),
% 127.51/82.21 inference(monotonicity,[status(thm)],[44])).
% 127.51/82.21 tff(336,plain,
% 127.51/82.21 (is_a_theorem(implies(or(Y!0, X!1), or(X!1, Y!0))) <=> is_a_theorem(implies(or(Y!0, X!1), not(and(not(X!1), not(Y!0)))))),
% 127.51/82.21 inference(monotonicity,[status(thm)],[335])).
% 127.51/82.21 tff(337,plain,
% 127.51/82.21 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(Y!0, X!1), or(X!1, Y!0)))),
% 127.51/82.21 inference(quant_inst,[status(thm)],[])).
% 127.51/82.21 tff(338,plain,
% 127.51/82.21 (is_a_theorem(implies(or(Y!0, X!1), or(X!1, Y!0)))),
% 127.51/82.21 inference(unit_resolution,[status(thm)],[337, 186])).
% 127.51/82.21 tff(339,plain,
% 127.51/82.21 (is_a_theorem(implies(or(Y!0, X!1), not(and(not(X!1), not(Y!0)))))),
% 127.51/82.21 inference(modus_ponens,[status(thm)],[338, 336])).
% 127.51/82.21 tff(340,plain,
% 127.51/82.21 (is_a_theorem(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))))),
% 127.51/82.21 inference(modus_ponens,[status(thm)],[339, 334])).
% 127.51/82.21 tff(341,plain,
% 127.51/82.21 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))),
% 127.51/82.21 inference(quant_inst,[status(thm)],[])).
% 127.51/82.21 tff(342,plain,
% 127.51/82.21 (is_a_theorem(implies(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))),
% 127.51/82.21 inference(unit_resolution,[status(thm)],[341, 186])).
% 127.51/82.21 tff(343,plain,
% 127.51/82.21 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))) | (~is_a_theorem(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))))) | (~is_a_theorem(implies(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))) | (~is_a_theorem(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))))) | (~is_a_theorem(implies(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))))),
% 127.51/82.21 inference(rewrite,[status(thm)],[])).
% 127.51/82.21 tff(344,plain,
% 127.51/82.21 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))) | (~is_a_theorem(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))))) | (~is_a_theorem(implies(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))))))),
% 127.51/82.21 inference(quant_inst,[status(thm)],[])).
% 127.51/82.21 tff(345,plain,
% 127.51/82.21 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))) | (~is_a_theorem(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))))) | (~is_a_theorem(implies(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0)))), or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))))),
% 127.51/82.21 inference(modus_ponens,[status(thm)],[344, 343])).
% 127.51/82.21 tff(346,plain,
% 127.51/82.21 (is_a_theorem(or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1)))) | (~is_a_theorem(or(not(or(Y!0, X!1)), not(and(not(X!1), not(Y!0))))))),
% 127.51/82.21 inference(unit_resolution,[status(thm)],[345, 283, 342])).
% 127.51/82.21 tff(347,plain,
% 127.51/82.21 (is_a_theorem(or(not(and(not(X!1), not(Y!0))), not(or(Y!0, X!1))))),
% 127.51/82.21 inference(unit_resolution,[status(thm)],[346, 340])).
% 127.51/82.21 tff(348,plain,
% 127.51/82.21 (is_a_theorem(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))))),
% 127.51/82.21 inference(modus_ponens,[status(thm)],[347, 332])).
% 127.51/82.21 tff(349,plain,
% 127.51/82.21 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))) | (~is_a_theorem(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))))) | (~is_a_theorem(implies(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))), or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))) | (~is_a_theorem(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))))) | (~is_a_theorem(implies(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))), or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))))))),
% 127.51/82.21 inference(rewrite,[status(thm)],[])).
% 127.51/82.21 tff(350,plain,
% 127.51/82.21 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))) | (~is_a_theorem(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))))) | (~is_a_theorem(implies(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))), or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))))))),
% 127.51/82.21 inference(quant_inst,[status(thm)],[])).
% 127.51/82.21 tff(351,plain,
% 127.51/82.21 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))) | (~is_a_theorem(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))))) | (~is_a_theorem(implies(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))), or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))))))),
% 127.51/82.21 inference(modus_ponens,[status(thm)],[350, 349])).
% 127.51/82.21 tff(352,plain,
% 127.51/82.21 (is_a_theorem(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))) | (~is_a_theorem(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))))) | (~is_a_theorem(implies(or(not(not(or(X!1, Y!0))), not(or(Y!0, X!1))), or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))))))),
% 127.51/82.21 inference(unit_resolution,[status(thm)],[351, 283])).
% 127.51/82.21 tff(353,plain,
% 127.51/82.21 (is_a_theorem(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))))),
% 127.51/82.21 inference(unit_resolution,[status(thm)],[352, 348, 319])).
% 127.51/82.21 tff(354,plain,
% 127.51/82.21 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))))) | is_a_theorem(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))) | (~is_a_theorem(implies(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))))) | is_a_theorem(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))) | (~is_a_theorem(implies(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))))))),
% 127.51/82.21 inference(rewrite,[status(thm)],[])).
% 127.51/82.21 tff(355,plain,
% 127.51/82.21 ((is_a_theorem(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))) | (~is_a_theorem(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))))) | (~is_a_theorem(implies(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))))) <=> ((~is_a_theorem(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))))) | is_a_theorem(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))) | (~is_a_theorem(implies(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))))))),
% 127.51/82.21 inference(rewrite,[status(thm)],[])).
% 127.51/82.21 tff(356,plain,
% 127.51/82.21 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))) | (~is_a_theorem(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))))) | (~is_a_theorem(implies(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))))) | is_a_theorem(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))) | (~is_a_theorem(implies(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))))))),
% 127.51/82.21 inference(monotonicity,[status(thm)],[355])).
% 127.51/82.21 tff(357,plain,
% 127.51/82.21 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))) | (~is_a_theorem(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))))) | (~is_a_theorem(implies(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))))) | is_a_theorem(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))) | (~is_a_theorem(implies(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))))))),
% 127.51/82.21 inference(transitivity,[status(thm)],[356, 354])).
% 127.51/82.22 tff(358,plain,
% 127.51/82.22 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))) | (~is_a_theorem(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))))) | (~is_a_theorem(implies(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))))))),
% 127.51/82.22 inference(quant_inst,[status(thm)],[])).
% 127.51/82.22 tff(359,plain,
% 127.51/82.22 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))))) | is_a_theorem(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))) | (~is_a_theorem(implies(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[358, 357])).
% 127.51/82.22 tff(360,plain,
% 127.51/82.22 (is_a_theorem(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1)))))))) | (~is_a_theorem(implies(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0)))), not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))))),
% 127.51/82.22 inference(unit_resolution,[status(thm)],[359, 283, 353])).
% 127.51/82.22 tff(361,plain,
% 127.51/82.22 (is_a_theorem(not(or(not(or(not(not(and(not(Y!0), not(X!1)))), not(not(or(X!1, Y!0))))), not(or(not(not(and(not(X!1), not(Y!0)))), not(not(or(Y!0, X!1))))))))),
% 127.51/82.22 inference(unit_resolution,[status(thm)],[360, 311])).
% 127.51/82.22 tff(362,plain,
% 127.51/82.22 (is_a_theorem(equiv(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0)))))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[361, 160])).
% 127.51/82.22 tff(363,plain,
% 127.51/82.22 (^[X: $i, Y: $i] : refl(((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ((~is_a_theorem(equiv(X, Y))) | (X = Y)))),
% 127.51/82.22 inference(bind,[status(th)],[])).
% 127.51/82.22 tff(364,plain,
% 127.51/82.22 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 127.51/82.22 inference(quant_intro,[status(thm)],[363])).
% 127.51/82.22 tff(365,plain,
% 127.51/82.22 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 127.51/82.22 inference(rewrite,[status(thm)],[])).
% 127.51/82.22 tff(366,plain,
% 127.51/82.22 (($true <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 127.51/82.22 inference(rewrite,[status(thm)],[])).
% 127.51/82.22 tff(367,axiom,(substitution_of_equivalents), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','substitution_of_equivalents')).
% 127.51/82.22 tff(368,plain,
% 127.51/82.22 (substitution_of_equivalents <=> $true),
% 127.51/82.22 inference(iff_true,[status(thm)],[367])).
% 127.51/82.22 tff(369,plain,
% 127.51/82.22 ((substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) <=> ($true <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)))),
% 127.51/82.22 inference(monotonicity,[status(thm)],[368])).
% 127.51/82.22 tff(370,plain,
% 127.51/82.22 ((substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 127.51/82.22 inference(transitivity,[status(thm)],[369, 366])).
% 127.51/82.22 tff(371,plain,
% 127.51/82.22 ((substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) <=> (substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)))),
% 127.51/82.22 inference(rewrite,[status(thm)],[])).
% 127.51/82.22 tff(372,plain,
% 127.51/82.22 ((substitution_of_equivalents <=> ![X: $i, Y: $i] : (is_a_theorem(equiv(X, Y)) => (X = Y))) <=> (substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)))),
% 127.51/82.22 inference(rewrite,[status(thm)],[])).
% 127.51/82.22 tff(373,axiom,(substitution_of_equivalents <=> ![X: $i, Y: $i] : (is_a_theorem(equiv(X, Y)) => (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','substitution_of_equivalents')).
% 127.51/82.22 tff(374,plain,
% 127.51/82.22 (substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[373, 372])).
% 127.51/82.22 tff(375,plain,
% 127.51/82.22 (substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[374, 371])).
% 127.51/82.22 tff(376,plain,
% 127.51/82.22 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[375, 370])).
% 127.51/82.22 tff(377,plain,
% 127.51/82.22 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[376, 365])).
% 127.51/82.22 tff(378,plain,(
% 127.51/82.22 ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 127.51/82.22 inference(skolemize,[status(sab)],[377])).
% 127.51/82.22 tff(379,plain,
% 127.51/82.22 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[378, 364])).
% 127.51/82.22 tff(380,plain,
% 127.51/82.22 (((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0)))))) | (not(not(or(Y!0, X!1))) = not(and(not(X!1), not(Y!0)))))) <=> ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0)))))) | (not(not(or(Y!0, X!1))) = not(and(not(X!1), not(Y!0)))))),
% 127.51/82.22 inference(rewrite,[status(thm)],[])).
% 127.51/82.22 tff(381,plain,
% 127.51/82.22 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0)))))) | (not(not(or(Y!0, X!1))) = not(and(not(X!1), not(Y!0)))))),
% 127.51/82.22 inference(quant_inst,[status(thm)],[])).
% 127.51/82.22 tff(382,plain,
% 127.51/82.22 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0)))))) | (not(not(or(Y!0, X!1))) = not(and(not(X!1), not(Y!0))))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[381, 380])).
% 127.51/82.22 tff(383,plain,
% 127.51/82.22 ((~is_a_theorem(equiv(not(not(or(Y!0, X!1))), not(and(not(X!1), not(Y!0)))))) | (not(not(or(Y!0, X!1))) = not(and(not(X!1), not(Y!0))))),
% 127.51/82.22 inference(unit_resolution,[status(thm)],[382, 379])).
% 127.51/82.22 tff(384,plain,
% 127.51/82.22 (not(not(or(Y!0, X!1))) = not(and(not(X!1), not(Y!0)))),
% 127.51/82.22 inference(unit_resolution,[status(thm)],[383, 362])).
% 127.51/82.22 tff(385,plain,
% 127.51/82.22 (not(not(or(Y!0, X!1))) = or(X!1, Y!0)),
% 127.51/82.22 inference(transitivity,[status(thm)],[384, 45])).
% 127.51/82.22 tff(386,plain,
% 127.51/82.22 (or(not(X!1), not(not(or(Y!0, X!1)))) = or(not(X!1), or(X!1, Y!0))),
% 127.51/82.22 inference(monotonicity,[status(thm)],[385])).
% 127.51/82.22 tff(387,plain,
% 127.51/82.22 (or(not(X!1), not(not(or(Y!0, X!1)))) = implies(X!1, or(X!1, Y!0))),
% 127.51/82.22 inference(transitivity,[status(thm)],[386, 23])).
% 127.51/82.22 tff(388,plain,
% 127.51/82.22 (is_a_theorem(or(not(X!1), not(not(or(Y!0, X!1))))) <=> is_a_theorem(implies(X!1, or(X!1, Y!0)))),
% 127.51/82.22 inference(monotonicity,[status(thm)],[387])).
% 127.51/82.22 tff(389,plain,
% 127.51/82.22 (is_a_theorem(implies(X!1, or(X!1, Y!0))) <=> is_a_theorem(or(not(X!1), not(not(or(Y!0, X!1)))))),
% 127.51/82.22 inference(symmetry,[status(thm)],[388])).
% 127.51/82.22 tff(390,plain,
% 127.51/82.22 ((~is_a_theorem(implies(X!1, or(X!1, Y!0)))) <=> (~is_a_theorem(or(not(X!1), not(not(or(Y!0, X!1))))))),
% 127.51/82.22 inference(monotonicity,[status(thm)],[389])).
% 127.51/82.22 tff(391,plain,
% 127.51/82.22 ((~![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y))))),
% 127.51/82.22 inference(rewrite,[status(thm)],[])).
% 127.51/82.22 tff(392,plain,
% 127.51/82.22 (($false <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y))))),
% 127.51/82.22 inference(rewrite,[status(thm)],[])).
% 127.51/82.22 tff(393,axiom,(~or_1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','hilbert_or_1')).
% 127.51/82.22 tff(394,plain,
% 127.51/82.22 (or_1 <=> $false),
% 127.51/82.22 inference(iff_false,[status(thm)],[393])).
% 127.51/82.22 tff(395,plain,
% 127.51/82.22 ((or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))) <=> ($false <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y))))),
% 127.51/82.22 inference(monotonicity,[status(thm)],[394])).
% 127.51/82.22 tff(396,plain,
% 127.51/82.22 ((or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y))))),
% 127.51/82.22 inference(transitivity,[status(thm)],[395, 392])).
% 127.51/82.22 tff(397,plain,
% 127.51/82.22 ((or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))) <=> (or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y))))),
% 127.51/82.22 inference(rewrite,[status(thm)],[])).
% 127.51/82.22 tff(398,axiom,(or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','or_1')).
% 127.51/82.22 tff(399,plain,
% 127.51/82.22 (or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[398, 397])).
% 127.51/82.22 tff(400,plain,
% 127.51/82.22 (or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[399, 397])).
% 127.51/82.22 tff(401,plain,
% 127.51/82.22 (~![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[400, 396])).
% 127.51/82.22 tff(402,plain,
% 127.51/82.22 (~![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[401, 391])).
% 127.51/82.22 tff(403,plain,
% 127.51/82.22 (~![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[402, 391])).
% 127.51/82.22 tff(404,plain,
% 127.51/82.22 (~![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[403, 391])).
% 127.51/82.22 tff(405,plain,
% 127.51/82.22 (~![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[404, 391])).
% 127.51/82.22 tff(406,plain,
% 127.51/82.22 (~![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[405, 391])).
% 127.51/82.22 tff(407,plain,
% 127.51/82.22 (~![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[406, 391])).
% 127.51/82.22 tff(408,plain,(
% 127.51/82.22 ~is_a_theorem(implies(X!1, or(X!1, Y!0)))),
% 127.51/82.22 inference(skolemize,[status(sab)],[407])).
% 127.51/82.22 tff(409,plain,
% 127.51/82.22 (~is_a_theorem(or(not(X!1), not(not(or(Y!0, X!1)))))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[408, 390])).
% 127.51/82.22 tff(410,plain,
% 127.51/82.22 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(and(not(Y!0), not(X!1))), not(X!1)) = not(and(not(not(and(not(Y!0), not(X!1)))), not(not(X!1)))))),
% 127.51/82.22 inference(quant_inst,[status(thm)],[])).
% 127.51/82.22 tff(411,plain,
% 127.51/82.22 (or(not(and(not(Y!0), not(X!1))), not(X!1)) = not(and(not(not(and(not(Y!0), not(X!1)))), not(not(X!1))))),
% 127.51/82.22 inference(unit_resolution,[status(thm)],[410, 42])).
% 127.51/82.22 tff(412,plain,
% 127.51/82.22 (not(and(not(not(and(not(Y!0), not(X!1)))), not(not(X!1)))) = or(not(and(not(Y!0), not(X!1))), not(X!1))),
% 127.51/82.22 inference(symmetry,[status(thm)],[411])).
% 127.51/82.22 tff(413,plain,
% 127.51/82.22 (and(not(not(and(not(Y!0), not(X!1)))), not(not(X!1))) = and(not(or(Y!0, X!1)), not(not(X!1)))),
% 127.51/82.22 inference(monotonicity,[status(thm)],[312])).
% 127.51/82.22 tff(414,plain,
% 127.51/82.22 (not(and(not(not(and(not(Y!0), not(X!1)))), not(not(X!1)))) = not(and(not(or(Y!0, X!1)), not(not(X!1))))),
% 127.51/82.22 inference(monotonicity,[status(thm)],[413])).
% 127.51/82.22 tff(415,plain,
% 127.51/82.22 (not(and(not(or(Y!0, X!1)), not(not(X!1)))) = not(and(not(not(and(not(Y!0), not(X!1)))), not(not(X!1))))),
% 127.51/82.22 inference(symmetry,[status(thm)],[414])).
% 127.51/82.22 tff(416,plain,
% 127.51/82.22 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(or(Y!0, X!1)), not(X!1)) = not(and(not(or(Y!0, X!1)), not(not(X!1)))))),
% 127.51/82.22 inference(quant_inst,[status(thm)],[])).
% 127.51/82.22 tff(417,plain,
% 127.51/82.22 (implies(not(or(Y!0, X!1)), not(X!1)) = not(and(not(or(Y!0, X!1)), not(not(X!1))))),
% 127.51/82.22 inference(unit_resolution,[status(thm)],[416, 89])).
% 127.51/82.22 tff(418,plain,
% 127.51/82.22 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(Y!0, X!1)), not(X!1)) = or(not(not(or(Y!0, X!1))), not(X!1)))),
% 127.51/82.22 inference(quant_inst,[status(thm)],[])).
% 127.51/82.22 tff(419,plain,
% 127.51/82.22 (implies(not(or(Y!0, X!1)), not(X!1)) = or(not(not(or(Y!0, X!1))), not(X!1))),
% 127.51/82.22 inference(unit_resolution,[status(thm)],[418, 20])).
% 127.51/82.22 tff(420,plain,
% 127.51/82.22 (or(not(not(or(Y!0, X!1))), not(X!1)) = implies(not(or(Y!0, X!1)), not(X!1))),
% 127.51/82.22 inference(symmetry,[status(thm)],[419])).
% 127.51/82.22 tff(421,plain,
% 127.51/82.22 (or(not(not(or(Y!0, X!1))), not(X!1)) = or(not(and(not(Y!0), not(X!1))), not(X!1))),
% 127.51/82.22 inference(transitivity,[status(thm)],[420, 417, 415, 412])).
% 127.51/82.22 tff(422,plain,
% 127.51/82.22 (is_a_theorem(or(not(not(or(Y!0, X!1))), not(X!1))) <=> is_a_theorem(or(not(and(not(Y!0), not(X!1))), not(X!1)))),
% 127.51/82.22 inference(monotonicity,[status(thm)],[421])).
% 127.51/82.22 tff(423,plain,
% 127.51/82.22 (is_a_theorem(or(not(and(not(Y!0), not(X!1))), not(X!1))) <=> is_a_theorem(or(not(not(or(Y!0, X!1))), not(X!1)))),
% 127.51/82.22 inference(symmetry,[status(thm)],[422])).
% 127.51/82.22 tff(424,plain,
% 127.51/82.22 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(X!1, not(and(not(Y!0), not(X!1)))) = or(not(X!1), not(and(not(Y!0), not(X!1)))))),
% 127.51/82.22 inference(quant_inst,[status(thm)],[])).
% 127.51/82.22 tff(425,plain,
% 127.51/82.22 (implies(X!1, not(and(not(Y!0), not(X!1)))) = or(not(X!1), not(and(not(Y!0), not(X!1))))),
% 127.51/82.22 inference(unit_resolution,[status(thm)],[424, 20])).
% 127.51/82.22 tff(426,plain,
% 127.51/82.22 (or(not(X!1), not(and(not(Y!0), not(X!1)))) = implies(X!1, not(and(not(Y!0), not(X!1))))),
% 127.51/82.22 inference(symmetry,[status(thm)],[425])).
% 127.51/82.22 tff(427,plain,
% 127.51/82.22 (is_a_theorem(or(not(X!1), not(and(not(Y!0), not(X!1))))) <=> is_a_theorem(implies(X!1, not(and(not(Y!0), not(X!1)))))),
% 127.51/82.22 inference(monotonicity,[status(thm)],[426])).
% 127.51/82.22 tff(428,plain,
% 127.51/82.22 (is_a_theorem(implies(X!1, not(and(not(Y!0), not(X!1))))) <=> is_a_theorem(or(not(X!1), not(and(not(Y!0), not(X!1)))))),
% 127.51/82.22 inference(symmetry,[status(thm)],[427])).
% 127.51/82.22 tff(429,plain,
% 127.51/82.22 (implies(X!1, not(and(not(Y!0), not(X!1)))) = implies(X!1, or(Y!0, X!1))),
% 127.51/82.22 inference(monotonicity,[status(thm)],[150])).
% 127.51/82.22 tff(430,plain,
% 127.51/82.22 (implies(X!1, or(Y!0, X!1)) = implies(X!1, not(and(not(Y!0), not(X!1))))),
% 127.51/82.22 inference(symmetry,[status(thm)],[429])).
% 127.51/82.22 tff(431,plain,
% 127.51/82.22 (is_a_theorem(implies(X!1, or(Y!0, X!1))) <=> is_a_theorem(implies(X!1, not(and(not(Y!0), not(X!1)))))),
% 127.51/82.22 inference(monotonicity,[status(thm)],[430])).
% 127.51/82.22 tff(432,plain,
% 127.51/82.22 (^[P: $i, Q: $i] : refl(is_a_theorem(implies(Q, or(P, Q))) <=> is_a_theorem(implies(Q, or(P, Q))))),
% 127.51/82.22 inference(bind,[status(th)],[])).
% 127.51/82.22 tff(433,plain,
% 127.51/82.22 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 127.51/82.22 inference(quant_intro,[status(thm)],[432])).
% 127.51/82.22 tff(434,plain,
% 127.51/82.22 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 127.51/82.22 inference(rewrite,[status(thm)],[])).
% 127.51/82.22 tff(435,plain,
% 127.51/82.22 (($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 127.51/82.22 inference(rewrite,[status(thm)],[])).
% 127.51/82.22 tff(436,axiom,(r2), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_r2')).
% 127.51/82.22 tff(437,plain,
% 127.51/82.22 (r2 <=> $true),
% 127.51/82.22 inference(iff_true,[status(thm)],[436])).
% 127.51/82.22 tff(438,plain,
% 127.51/82.22 ((r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> ($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))))),
% 127.51/82.22 inference(monotonicity,[status(thm)],[437])).
% 127.51/82.22 tff(439,plain,
% 127.51/82.22 ((r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 127.51/82.22 inference(transitivity,[status(thm)],[438, 435])).
% 127.51/82.22 tff(440,plain,
% 127.51/82.22 ((r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))))),
% 127.51/82.22 inference(rewrite,[status(thm)],[])).
% 127.51/82.22 tff(441,axiom,(r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','r2')).
% 127.51/82.22 tff(442,plain,
% 127.51/82.22 (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[441, 440])).
% 127.51/82.22 tff(443,plain,
% 127.51/82.22 (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[442, 440])).
% 127.51/82.22 tff(444,plain,
% 127.51/82.22 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[443, 439])).
% 127.51/82.22 tff(445,plain,
% 127.51/82.22 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[444, 434])).
% 127.51/82.22 tff(446,plain,(
% 127.51/82.22 ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 127.51/82.22 inference(skolemize,[status(sab)],[445])).
% 127.51/82.22 tff(447,plain,
% 127.51/82.22 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[446, 433])).
% 127.51/82.22 tff(448,plain,
% 127.51/82.22 ((~![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) | is_a_theorem(implies(X!1, or(Y!0, X!1)))),
% 127.51/82.22 inference(quant_inst,[status(thm)],[])).
% 127.51/82.22 tff(449,plain,
% 127.51/82.22 (is_a_theorem(implies(X!1, or(Y!0, X!1)))),
% 127.51/82.22 inference(unit_resolution,[status(thm)],[448, 447])).
% 127.51/82.22 tff(450,plain,
% 127.51/82.22 (is_a_theorem(implies(X!1, not(and(not(Y!0), not(X!1)))))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[449, 431])).
% 127.51/82.22 tff(451,plain,
% 127.51/82.22 (is_a_theorem(or(not(X!1), not(and(not(Y!0), not(X!1)))))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[450, 428])).
% 127.51/82.22 tff(452,plain,
% 127.51/82.22 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(X!1), not(and(not(Y!0), not(X!1)))), or(not(and(not(Y!0), not(X!1))), not(X!1))))),
% 127.51/82.22 inference(quant_inst,[status(thm)],[])).
% 127.51/82.22 tff(453,plain,
% 127.51/82.22 (is_a_theorem(implies(or(not(X!1), not(and(not(Y!0), not(X!1)))), or(not(and(not(Y!0), not(X!1))), not(X!1))))),
% 127.51/82.22 inference(unit_resolution,[status(thm)],[452, 186])).
% 127.51/82.22 tff(454,plain,
% 127.51/82.22 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(and(not(Y!0), not(X!1))), not(X!1))) | (~is_a_theorem(or(not(X!1), not(and(not(Y!0), not(X!1)))))) | (~is_a_theorem(implies(or(not(X!1), not(and(not(Y!0), not(X!1)))), or(not(and(not(Y!0), not(X!1))), not(X!1))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(and(not(Y!0), not(X!1))), not(X!1))) | (~is_a_theorem(or(not(X!1), not(and(not(Y!0), not(X!1)))))) | (~is_a_theorem(implies(or(not(X!1), not(and(not(Y!0), not(X!1)))), or(not(and(not(Y!0), not(X!1))), not(X!1))))))),
% 127.51/82.22 inference(rewrite,[status(thm)],[])).
% 127.51/82.22 tff(455,plain,
% 127.51/82.22 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(and(not(Y!0), not(X!1))), not(X!1))) | (~is_a_theorem(or(not(X!1), not(and(not(Y!0), not(X!1)))))) | (~is_a_theorem(implies(or(not(X!1), not(and(not(Y!0), not(X!1)))), or(not(and(not(Y!0), not(X!1))), not(X!1))))))),
% 127.51/82.22 inference(quant_inst,[status(thm)],[])).
% 127.51/82.22 tff(456,plain,
% 127.51/82.22 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(and(not(Y!0), not(X!1))), not(X!1))) | (~is_a_theorem(or(not(X!1), not(and(not(Y!0), not(X!1)))))) | (~is_a_theorem(implies(or(not(X!1), not(and(not(Y!0), not(X!1)))), or(not(and(not(Y!0), not(X!1))), not(X!1)))))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[455, 454])).
% 127.51/82.22 tff(457,plain,
% 127.51/82.22 (is_a_theorem(or(not(and(not(Y!0), not(X!1))), not(X!1))) | (~is_a_theorem(or(not(X!1), not(and(not(Y!0), not(X!1))))))),
% 127.51/82.22 inference(unit_resolution,[status(thm)],[456, 283, 453])).
% 127.51/82.22 tff(458,plain,
% 127.51/82.22 (is_a_theorem(or(not(and(not(Y!0), not(X!1))), not(X!1)))),
% 127.51/82.22 inference(unit_resolution,[status(thm)],[457, 451])).
% 127.51/82.22 tff(459,plain,
% 127.51/82.22 (is_a_theorem(or(not(not(or(Y!0, X!1))), not(X!1)))),
% 127.51/82.22 inference(modus_ponens,[status(thm)],[458, 423])).
% 127.51/82.22 tff(460,plain,
% 127.51/82.22 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(not(or(Y!0, X!1))), not(X!1)), or(not(X!1), not(not(or(Y!0, X!1))))))),
% 127.51/82.22 inference(quant_inst,[status(thm)],[])).
% 127.51/82.22 tff(461,plain,
% 127.51/82.22 (is_a_theorem(implies(or(not(not(or(Y!0, X!1))), not(X!1)), or(not(X!1), not(not(or(Y!0, X!1))))))),
% 127.51/82.22 inference(unit_resolution,[status(thm)],[460, 186])).
% 127.51/82.22 tff(462,plain,
% 127.51/82.22 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(X!1), not(not(or(Y!0, X!1))))) | (~is_a_theorem(or(not(not(or(Y!0, X!1))), not(X!1)))) | (~is_a_theorem(implies(or(not(not(or(Y!0, X!1))), not(X!1)), or(not(X!1), not(not(or(Y!0, X!1))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(X!1), not(not(or(Y!0, X!1))))) | (~is_a_theorem(or(not(not(or(Y!0, X!1))), not(X!1)))) | (~is_a_theorem(implies(or(not(not(or(Y!0, X!1))), not(X!1)), or(not(X!1), not(not(or(Y!0, X!1))))))))),
% 127.55/82.25 inference(rewrite,[status(thm)],[])).
% 127.55/82.25 tff(463,plain,
% 127.55/82.25 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(X!1), not(not(or(Y!0, X!1))))) | (~is_a_theorem(or(not(not(or(Y!0, X!1))), not(X!1)))) | (~is_a_theorem(implies(or(not(not(or(Y!0, X!1))), not(X!1)), or(not(X!1), not(not(or(Y!0, X!1))))))))),
% 127.55/82.25 inference(quant_inst,[status(thm)],[])).
% 127.55/82.25 tff(464,plain,
% 127.55/82.25 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(X!1), not(not(or(Y!0, X!1))))) | (~is_a_theorem(or(not(not(or(Y!0, X!1))), not(X!1)))) | (~is_a_theorem(implies(or(not(not(or(Y!0, X!1))), not(X!1)), or(not(X!1), not(not(or(Y!0, X!1)))))))),
% 127.55/82.25 inference(modus_ponens,[status(thm)],[463, 462])).
% 127.55/82.25 tff(465,plain,
% 127.55/82.25 (is_a_theorem(or(not(X!1), not(not(or(Y!0, X!1))))) | (~is_a_theorem(or(not(not(or(Y!0, X!1))), not(X!1))))),
% 127.55/82.25 inference(unit_resolution,[status(thm)],[464, 283, 461])).
% 127.55/82.25 tff(466,plain,
% 127.55/82.25 (is_a_theorem(or(not(X!1), not(not(or(Y!0, X!1)))))),
% 127.55/82.25 inference(unit_resolution,[status(thm)],[465, 459])).
% 127.55/82.25 tff(467,plain,
% 127.55/82.25 ($false),
% 127.55/82.25 inference(unit_resolution,[status(thm)],[466, 409])).
% 127.55/82.25 % SZS output end Proof
%------------------------------------------------------------------------------