TSTP Solution File: LCL500+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL500+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 04:56:31 EDT 2022
% Result : Theorem 64.59s 41.51s
% Output : Proof 64.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL500+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n013.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 21:50:47 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 64.59/41.51 % SZS status Theorem
% 64.59/41.51 % SZS output start Proof
% 64.59/41.51 tff(is_a_theorem_type, type, (
% 64.59/41.51 is_a_theorem: $i > $o)).
% 64.59/41.51 tff(or_type, type, (
% 64.59/41.51 or: ( $i * $i ) > $i)).
% 64.59/41.51 tff(not_type, type, (
% 64.59/41.51 not: $i > $i)).
% 64.59/41.51 tff(tptp_fun_P_1_type, type, (
% 64.59/41.51 tptp_fun_P_1: $i)).
% 64.59/41.51 tff(tptp_fun_Q_0_type, type, (
% 64.59/41.51 tptp_fun_Q_0: $i)).
% 64.59/41.51 tff(implies_type, type, (
% 64.59/41.51 implies: ( $i * $i ) > $i)).
% 64.59/41.51 tff(op_implies_or_type, type, (
% 64.59/41.51 op_implies_or: $o)).
% 64.59/41.51 tff(and_type, type, (
% 64.59/41.51 and: ( $i * $i ) > $i)).
% 64.59/41.51 tff(equiv_type, type, (
% 64.59/41.51 equiv: ( $i * $i ) > $i)).
% 64.59/41.51 tff(op_or_type, type, (
% 64.59/41.51 op_or: $o)).
% 64.59/41.51 tff(op_equiv_type, type, (
% 64.59/41.51 op_equiv: $o)).
% 64.59/41.51 tff(op_implies_and_type, type, (
% 64.59/41.51 op_implies_and: $o)).
% 64.59/41.51 tff(op_and_type, type, (
% 64.59/41.51 op_and: $o)).
% 64.59/41.51 tff(r4_type, type, (
% 64.59/41.51 r4: $o)).
% 64.59/41.51 tff(r3_type, type, (
% 64.59/41.51 r3: $o)).
% 64.59/41.51 tff(modus_ponens_type, type, (
% 64.59/41.51 modus_ponens: $o)).
% 64.59/41.51 tff(substitution_of_equivalents_type, type, (
% 64.59/41.51 substitution_of_equivalents: $o)).
% 64.59/41.51 tff(kn2_type, type, (
% 64.59/41.51 kn2: $o)).
% 64.59/41.51 tff(r2_type, type, (
% 64.59/41.51 r2: $o)).
% 64.59/41.51 tff(1,plain,
% 64.59/41.51 (^[X: $i, Y: $i] : refl((implies(X, Y) = or(not(X), Y)) <=> (implies(X, Y) = or(not(X), Y)))),
% 64.59/41.51 inference(bind,[status(th)],[])).
% 64.59/41.51 tff(2,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 64.59/41.51 inference(quant_intro,[status(thm)],[1])).
% 64.59/41.51 tff(3,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(4,plain,
% 64.59/41.51 (($false | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(5,plain,
% 64.59/41.51 ((~$true) <=> $false),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(6,axiom,(op_implies_or), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_op_implies_or')).
% 64.59/41.51 tff(7,plain,
% 64.59/41.51 (op_implies_or <=> $true),
% 64.59/41.51 inference(iff_true,[status(thm)],[6])).
% 64.59/41.51 tff(8,plain,
% 64.59/41.51 ((~op_implies_or) <=> (~$true)),
% 64.59/41.51 inference(monotonicity,[status(thm)],[7])).
% 64.59/41.51 tff(9,plain,
% 64.59/41.51 ((~op_implies_or) <=> $false),
% 64.59/41.51 inference(transitivity,[status(thm)],[8, 5])).
% 64.59/41.51 tff(10,plain,
% 64.59/41.51 (((~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)))),
% 64.59/41.51 inference(monotonicity,[status(thm)],[9])).
% 64.59/41.51 tff(11,plain,
% 64.59/41.51 (((~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))),
% 64.59/41.51 inference(transitivity,[status(thm)],[10, 4])).
% 64.59/41.51 tff(12,plain,
% 64.59/41.51 (((~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)))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(13,plain,
% 64.59/41.51 ((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)))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(14,axiom,(op_implies_or => ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax','op_implies_or')).
% 64.59/41.51 tff(15,plain,
% 64.59/41.51 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[14, 13])).
% 64.59/41.51 tff(16,plain,
% 64.59/41.51 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[15, 12])).
% 64.59/41.51 tff(17,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[16, 11])).
% 64.59/41.51 tff(18,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[17, 3])).
% 64.59/41.51 tff(19,plain,(
% 64.59/41.51 ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 64.59/41.51 inference(skolemize,[status(sab)],[18])).
% 64.59/41.51 tff(20,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[19, 2])).
% 64.59/41.51 tff(21,plain,
% 64.59/41.51 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(not(P!1), not(Q!0))), not(not(P!1))) = or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))),
% 64.59/41.51 inference(quant_inst,[status(thm)],[])).
% 64.59/41.51 tff(22,plain,
% 64.59/41.51 (implies(not(or(not(P!1), not(Q!0))), not(not(P!1))) = or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))),
% 64.59/41.51 inference(unit_resolution,[status(thm)],[21, 20])).
% 64.59/41.51 tff(23,plain,
% 64.59/41.51 (or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))) = implies(not(or(not(P!1), not(Q!0))), not(not(P!1)))),
% 64.59/41.51 inference(symmetry,[status(thm)],[22])).
% 64.59/41.51 tff(24,plain,
% 64.59/41.51 (^[X: $i, Y: $i] : refl((or(X, Y) = not(and(not(X), not(Y)))) <=> (or(X, Y) = not(and(not(X), not(Y)))))),
% 64.59/41.51 inference(bind,[status(th)],[])).
% 64.59/41.51 tff(25,plain,
% 64.59/41.51 (![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))))),
% 64.59/41.51 inference(quant_intro,[status(thm)],[24])).
% 64.59/41.51 tff(26,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(27,plain,
% 64.59/41.51 (($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))))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(28,axiom,(op_or), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rosser_op_or')).
% 64.59/41.51 tff(29,plain,
% 64.59/41.51 (op_or <=> $true),
% 64.59/41.51 inference(iff_true,[status(thm)],[28])).
% 64.59/41.51 tff(30,plain,
% 64.59/41.51 ((~op_or) <=> (~$true)),
% 64.59/41.51 inference(monotonicity,[status(thm)],[29])).
% 64.59/41.51 tff(31,plain,
% 64.59/41.51 ((~op_or) <=> $false),
% 64.59/41.51 inference(transitivity,[status(thm)],[30, 5])).
% 64.59/41.51 tff(32,plain,
% 64.59/41.51 (((~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)))))),
% 64.59/41.51 inference(monotonicity,[status(thm)],[31])).
% 64.59/41.51 tff(33,plain,
% 64.59/41.51 (((~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))))),
% 64.59/41.51 inference(transitivity,[status(thm)],[32, 27])).
% 64.59/41.51 tff(34,plain,
% 64.59/41.51 (((~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)))))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(35,plain,
% 64.59/41.51 ((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)))))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(36,axiom,(op_or => ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax','op_or')).
% 64.59/41.51 tff(37,plain,
% 64.59/41.51 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[36, 35])).
% 64.59/41.51 tff(38,plain,
% 64.59/41.51 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[37, 34])).
% 64.59/41.51 tff(39,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[38, 33])).
% 64.59/41.51 tff(40,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[39, 26])).
% 64.59/41.51 tff(41,plain,(
% 64.59/41.51 ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 64.59/41.51 inference(skolemize,[status(sab)],[40])).
% 64.59/41.51 tff(42,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[41, 25])).
% 64.59/41.51 tff(43,plain,
% 64.59/41.51 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(P!1, or(not(P!1), not(Q!0))) = not(and(not(P!1), not(or(not(P!1), not(Q!0))))))),
% 64.59/41.51 inference(quant_inst,[status(thm)],[])).
% 64.59/41.51 tff(44,plain,
% 64.59/41.51 (or(P!1, or(not(P!1), not(Q!0))) = not(and(not(P!1), not(or(not(P!1), not(Q!0)))))),
% 64.59/41.51 inference(unit_resolution,[status(thm)],[43, 42])).
% 64.59/41.51 tff(45,plain,
% 64.59/41.51 (not(and(not(P!1), not(or(not(P!1), not(Q!0))))) = or(P!1, or(not(P!1), not(Q!0)))),
% 64.59/41.51 inference(symmetry,[status(thm)],[44])).
% 64.59/41.51 tff(46,plain,
% 64.59/41.51 (equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(and(P!1, Q!0)), P!1)) = equiv(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1))),
% 64.59/41.51 inference(monotonicity,[status(thm)],[45])).
% 64.59/41.51 tff(47,plain,
% 64.59/41.51 (equiv(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)) = equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(and(P!1, Q!0)), P!1))),
% 64.59/41.51 inference(symmetry,[status(thm)],[46])).
% 64.59/41.51 tff(48,plain,
% 64.59/41.51 (^[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))))),
% 64.59/41.51 inference(bind,[status(th)],[])).
% 64.59/41.51 tff(49,plain,
% 64.59/41.51 (![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)))),
% 64.59/41.51 inference(quant_intro,[status(thm)],[48])).
% 64.59/41.51 tff(50,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))) <=> ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(51,plain,
% 64.59/41.51 (($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)))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(52,axiom,(op_equiv), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_op_equiv')).
% 64.59/41.51 tff(53,plain,
% 64.59/41.51 (op_equiv <=> $true),
% 64.59/41.51 inference(iff_true,[status(thm)],[52])).
% 64.59/41.51 tff(54,plain,
% 64.59/41.51 ((~op_equiv) <=> (~$true)),
% 64.59/41.51 inference(monotonicity,[status(thm)],[53])).
% 64.59/41.51 tff(55,plain,
% 64.59/41.51 ((~op_equiv) <=> $false),
% 64.59/41.51 inference(transitivity,[status(thm)],[54, 5])).
% 64.59/41.51 tff(56,plain,
% 64.59/41.51 (((~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))))),
% 64.59/41.51 inference(monotonicity,[status(thm)],[55])).
% 64.59/41.51 tff(57,plain,
% 64.59/41.51 (((~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)))),
% 64.59/41.51 inference(transitivity,[status(thm)],[56, 51])).
% 64.59/41.51 tff(58,plain,
% 64.59/41.51 (((~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))))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(59,plain,
% 64.59/41.51 ((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))))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(60,axiom,(op_equiv => ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax','op_equiv')).
% 64.59/41.51 tff(61,plain,
% 64.59/41.51 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[60, 59])).
% 64.59/41.51 tff(62,plain,
% 64.59/41.51 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[61, 58])).
% 64.59/41.51 tff(63,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[62, 57])).
% 64.59/41.51 tff(64,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[63, 50])).
% 64.59/41.51 tff(65,plain,(
% 64.59/41.51 ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 64.59/41.51 inference(skolemize,[status(sab)],[64])).
% 64.59/41.51 tff(66,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[65, 49])).
% 64.59/41.51 tff(67,plain,
% 64.59/41.51 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)) = and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))),
% 64.59/41.51 inference(quant_inst,[status(thm)],[])).
% 64.59/41.51 tff(68,plain,
% 64.59/41.51 (equiv(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)) = and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))),
% 64.59/41.51 inference(unit_resolution,[status(thm)],[67, 66])).
% 64.59/41.51 tff(69,plain,
% 64.59/41.51 (and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))) = equiv(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1))),
% 64.59/41.51 inference(symmetry,[status(thm)],[68])).
% 64.59/41.51 tff(70,plain,
% 64.59/41.51 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))) = or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))),
% 64.59/41.51 inference(quant_inst,[status(thm)],[])).
% 64.59/41.51 tff(71,plain,
% 64.59/41.51 (implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))) = or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))),
% 64.59/41.51 inference(unit_resolution,[status(thm)],[70, 20])).
% 64.59/41.51 tff(72,plain,
% 64.59/41.51 (or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))) = implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))),
% 64.59/41.51 inference(symmetry,[status(thm)],[71])).
% 64.59/41.51 tff(73,plain,
% 64.59/41.51 (^[X: $i, Y: $i] : refl((implies(X, Y) = not(and(X, not(Y)))) <=> (implies(X, Y) = not(and(X, not(Y)))))),
% 64.59/41.51 inference(bind,[status(th)],[])).
% 64.59/41.51 tff(74,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 64.59/41.51 inference(quant_intro,[status(thm)],[73])).
% 64.59/41.51 tff(75,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(76,plain,
% 64.59/41.51 (($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))))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(77,axiom,(op_implies_and), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rosser_op_implies_and')).
% 64.59/41.51 tff(78,plain,
% 64.59/41.51 (op_implies_and <=> $true),
% 64.59/41.51 inference(iff_true,[status(thm)],[77])).
% 64.59/41.51 tff(79,plain,
% 64.59/41.51 ((~op_implies_and) <=> (~$true)),
% 64.59/41.51 inference(monotonicity,[status(thm)],[78])).
% 64.59/41.51 tff(80,plain,
% 64.59/41.51 ((~op_implies_and) <=> $false),
% 64.59/41.51 inference(transitivity,[status(thm)],[79, 5])).
% 64.59/41.51 tff(81,plain,
% 64.59/41.51 (((~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)))))),
% 64.59/41.51 inference(monotonicity,[status(thm)],[80])).
% 64.59/41.51 tff(82,plain,
% 64.59/41.51 (((~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))))),
% 64.59/41.51 inference(transitivity,[status(thm)],[81, 76])).
% 64.59/41.51 tff(83,plain,
% 64.59/41.51 (((~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)))))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(84,plain,
% 64.59/41.51 ((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)))))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(85,axiom,(op_implies_and => ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax','op_implies_and')).
% 64.59/41.51 tff(86,plain,
% 64.59/41.51 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[85, 84])).
% 64.59/41.51 tff(87,plain,
% 64.59/41.51 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[86, 83])).
% 64.59/41.51 tff(88,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[87, 82])).
% 64.59/41.51 tff(89,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[88, 75])).
% 64.59/41.51 tff(90,plain,(
% 64.59/41.51 ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 64.59/41.51 inference(skolemize,[status(sab)],[89])).
% 64.59/41.51 tff(91,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[90, 74])).
% 64.59/41.51 tff(92,plain,
% 64.59/41.51 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)) = not(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.59/41.51 inference(quant_inst,[status(thm)],[])).
% 64.59/41.51 tff(93,plain,
% 64.59/41.51 (implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)) = not(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))),
% 64.59/41.51 inference(unit_resolution,[status(thm)],[92, 91])).
% 64.59/41.51 tff(94,plain,
% 64.59/41.51 (not(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))) = implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1))),
% 64.59/41.51 inference(symmetry,[status(thm)],[93])).
% 64.59/41.51 tff(95,plain,
% 64.59/41.51 (^[X: $i, Y: $i] : refl((and(X, Y) = not(or(not(X), not(Y)))) <=> (and(X, Y) = not(or(not(X), not(Y)))))),
% 64.59/41.51 inference(bind,[status(th)],[])).
% 64.59/41.51 tff(96,plain,
% 64.59/41.51 (![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))))),
% 64.59/41.51 inference(quant_intro,[status(thm)],[95])).
% 64.59/41.51 tff(97,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(98,plain,
% 64.59/41.51 (($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))))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(99,axiom,(op_and), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_op_and')).
% 64.59/41.51 tff(100,plain,
% 64.59/41.51 (op_and <=> $true),
% 64.59/41.51 inference(iff_true,[status(thm)],[99])).
% 64.59/41.51 tff(101,plain,
% 64.59/41.51 ((~op_and) <=> (~$true)),
% 64.59/41.51 inference(monotonicity,[status(thm)],[100])).
% 64.59/41.51 tff(102,plain,
% 64.59/41.51 ((~op_and) <=> $false),
% 64.59/41.51 inference(transitivity,[status(thm)],[101, 5])).
% 64.59/41.51 tff(103,plain,
% 64.59/41.51 (((~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)))))),
% 64.59/41.51 inference(monotonicity,[status(thm)],[102])).
% 64.59/41.51 tff(104,plain,
% 64.59/41.51 (((~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))))),
% 64.59/41.51 inference(transitivity,[status(thm)],[103, 98])).
% 64.59/41.51 tff(105,plain,
% 64.59/41.51 (((~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)))))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(106,plain,
% 64.59/41.51 ((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)))))),
% 64.59/41.51 inference(rewrite,[status(thm)],[])).
% 64.59/41.51 tff(107,axiom,(op_and => ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax','op_and')).
% 64.59/41.51 tff(108,plain,
% 64.59/41.51 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[107, 106])).
% 64.59/41.51 tff(109,plain,
% 64.59/41.51 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[108, 105])).
% 64.59/41.51 tff(110,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[109, 104])).
% 64.59/41.51 tff(111,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[110, 97])).
% 64.59/41.51 tff(112,plain,(
% 64.59/41.51 ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 64.59/41.51 inference(skolemize,[status(sab)],[111])).
% 64.59/41.51 tff(113,plain,
% 64.59/41.51 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 64.59/41.51 inference(modus_ponens,[status(thm)],[112, 96])).
% 64.59/41.51 tff(114,plain,
% 64.59/41.51 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(P!1), not(or(not(P!1), not(Q!0)))) = not(or(not(not(P!1)), not(not(or(not(P!1), not(Q!0)))))))),
% 64.59/41.51 inference(quant_inst,[status(thm)],[])).
% 64.59/41.51 tff(115,plain,
% 64.59/41.51 (and(not(P!1), not(or(not(P!1), not(Q!0)))) = not(or(not(not(P!1)), not(not(or(not(P!1), not(Q!0))))))),
% 64.59/41.51 inference(unit_resolution,[status(thm)],[114, 113])).
% 64.59/41.51 tff(116,plain,
% 64.59/41.51 (not(or(not(not(P!1)), not(not(or(not(P!1), not(Q!0)))))) = and(not(P!1), not(or(not(P!1), not(Q!0))))),
% 64.59/41.51 inference(symmetry,[status(thm)],[115])).
% 64.59/41.51 tff(117,plain,
% 64.59/41.51 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(P!1, not(and(P!1, Q!0))) = not(and(not(P!1), not(not(and(P!1, Q!0))))))),
% 64.59/41.51 inference(quant_inst,[status(thm)],[])).
% 64.59/41.51 tff(118,plain,
% 64.59/41.51 (or(P!1, not(and(P!1, Q!0))) = not(and(not(P!1), not(not(and(P!1, Q!0)))))),
% 64.59/41.51 inference(unit_resolution,[status(thm)],[117, 42])).
% 64.59/41.51 tff(119,plain,
% 64.59/41.51 (not(and(not(P!1), not(not(and(P!1, Q!0))))) = or(P!1, not(and(P!1, Q!0)))),
% 64.59/41.51 inference(symmetry,[status(thm)],[118])).
% 64.59/41.51 tff(120,plain,
% 64.59/41.51 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(P!1), not(and(P!1, Q!0))) = not(and(not(P!1), not(not(and(P!1, Q!0))))))),
% 64.59/41.51 inference(quant_inst,[status(thm)],[])).
% 64.59/41.51 tff(121,plain,
% 64.59/41.51 (implies(not(P!1), not(and(P!1, Q!0))) = not(and(not(P!1), not(not(and(P!1, Q!0)))))),
% 64.59/41.51 inference(unit_resolution,[status(thm)],[120, 91])).
% 64.59/41.51 tff(122,plain,
% 64.59/41.51 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(P!1), not(and(P!1, Q!0))) = or(not(not(P!1)), not(and(P!1, Q!0))))),
% 64.59/41.51 inference(quant_inst,[status(thm)],[])).
% 64.59/41.51 tff(123,plain,
% 64.59/41.51 (implies(not(P!1), not(and(P!1, Q!0))) = or(not(not(P!1)), not(and(P!1, Q!0)))),
% 64.59/41.51 inference(unit_resolution,[status(thm)],[122, 20])).
% 64.59/41.51 tff(124,plain,
% 64.59/41.51 (or(not(not(P!1)), not(and(P!1, Q!0))) = implies(not(P!1), not(and(P!1, Q!0)))),
% 64.59/41.51 inference(symmetry,[status(thm)],[123])).
% 64.59/41.51 tff(125,plain,
% 64.59/41.51 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(P!1, Q!0) = not(or(not(P!1), not(Q!0))))),
% 64.59/41.51 inference(quant_inst,[status(thm)],[])).
% 64.59/41.51 tff(126,plain,
% 64.59/41.51 (and(P!1, Q!0) = not(or(not(P!1), not(Q!0)))),
% 64.59/41.51 inference(unit_resolution,[status(thm)],[125, 113])).
% 64.59/41.51 tff(127,plain,
% 64.59/41.51 (not(or(not(P!1), not(Q!0))) = and(P!1, Q!0)),
% 64.59/41.51 inference(symmetry,[status(thm)],[126])).
% 64.59/41.51 tff(128,plain,
% 64.59/41.51 (not(not(or(not(P!1), not(Q!0)))) = not(and(P!1, Q!0))),
% 64.59/41.51 inference(monotonicity,[status(thm)],[127])).
% 64.59/41.51 tff(129,plain,
% 64.59/41.51 (or(not(not(P!1)), not(not(or(not(P!1), not(Q!0))))) = or(not(not(P!1)), not(and(P!1, Q!0)))),
% 64.59/41.51 inference(monotonicity,[status(thm)],[128])).
% 64.59/41.51 tff(130,plain,
% 64.59/41.51 (or(not(not(P!1)), not(not(or(not(P!1), not(Q!0))))) = or(P!1, not(and(P!1, Q!0)))),
% 64.59/41.51 inference(transitivity,[status(thm)],[129, 124, 121, 119])).
% 64.59/41.51 tff(131,plain,
% 64.59/41.51 (not(or(not(not(P!1)), not(not(or(not(P!1), not(Q!0)))))) = not(or(P!1, not(and(P!1, Q!0))))),
% 64.59/41.51 inference(monotonicity,[status(thm)],[130])).
% 64.59/41.51 tff(132,plain,
% 64.59/41.51 (not(or(P!1, not(and(P!1, Q!0)))) = not(or(not(not(P!1)), not(not(or(not(P!1), not(Q!0))))))),
% 64.59/41.51 inference(symmetry,[status(thm)],[131])).
% 64.59/41.51 tff(133,plain,
% 64.59/41.51 (not(or(P!1, not(and(P!1, Q!0)))) = and(not(P!1), not(or(not(P!1), not(Q!0))))),
% 64.59/41.51 inference(transitivity,[status(thm)],[132, 116])).
% 64.59/41.51 tff(134,plain,
% 64.59/41.51 (not(not(or(P!1, not(and(P!1, Q!0))))) = not(and(not(P!1), not(or(not(P!1), not(Q!0)))))),
% 64.59/41.51 inference(monotonicity,[status(thm)],[133])).
% 64.59/41.51 tff(135,plain,
% 64.59/41.51 (not(not(or(P!1, not(and(P!1, Q!0))))) = or(P!1, or(not(P!1), not(Q!0)))),
% 64.59/41.51 inference(transitivity,[status(thm)],[134, 45])).
% 64.59/41.51 tff(136,plain,
% 64.59/41.51 (and(not(not(or(P!1, not(and(P!1, Q!0))))), not(or(not(and(P!1, Q!0)), P!1))) = and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))),
% 64.59/41.51 inference(monotonicity,[status(thm)],[135])).
% 64.59/41.51 tff(137,plain,
% 64.59/41.51 (and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))) = and(not(not(or(P!1, not(and(P!1, Q!0))))), not(or(not(and(P!1, Q!0)), P!1)))),
% 64.59/41.51 inference(symmetry,[status(thm)],[136])).
% 64.59/41.51 tff(138,plain,
% 64.59/41.51 (not(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))) = not(and(not(not(or(P!1, not(and(P!1, Q!0))))), not(or(not(and(P!1, Q!0)), P!1))))),
% 64.59/41.51 inference(monotonicity,[status(thm)],[137])).
% 64.59/41.51 tff(139,plain,
% 64.59/41.51 (not(and(not(not(or(P!1, not(and(P!1, Q!0))))), not(or(not(and(P!1, Q!0)), P!1)))) = not(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))),
% 64.59/41.51 inference(symmetry,[status(thm)],[138])).
% 64.59/41.51 tff(140,plain,
% 64.59/41.51 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)) = not(and(not(not(or(P!1, not(and(P!1, Q!0))))), not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.59/41.51 inference(quant_inst,[status(thm)],[])).
% 64.59/41.51 tff(141,plain,
% 64.59/41.51 (or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)) = not(and(not(not(or(P!1, not(and(P!1, Q!0))))), not(or(not(and(P!1, Q!0)), P!1))))),
% 64.59/41.52 inference(unit_resolution,[status(thm)],[140, 42])).
% 64.59/41.52 tff(142,plain,
% 64.59/41.52 (or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)) = implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1))),
% 64.59/41.52 inference(transitivity,[status(thm)],[141, 139, 94])).
% 64.59/41.52 tff(143,plain,
% 64.59/41.52 (and(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))) = and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[142, 72])).
% 64.59/41.52 tff(144,plain,
% 64.59/41.52 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))) = not(or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))))))),
% 64.59/41.52 inference(quant_inst,[status(thm)],[])).
% 64.59/41.52 tff(145,plain,
% 64.59/41.52 (and(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))) = not(or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))))),
% 64.59/41.52 inference(unit_resolution,[status(thm)],[144, 113])).
% 64.59/41.52 tff(146,plain,
% 64.59/41.52 (not(or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))))) = and(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))),
% 64.59/41.52 inference(symmetry,[status(thm)],[145])).
% 64.59/41.52 tff(147,plain,
% 64.59/41.52 (or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))) = or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[135])).
% 64.59/41.52 tff(148,plain,
% 64.59/41.52 (or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))) = or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))),
% 64.59/41.52 inference(symmetry,[status(thm)],[147])).
% 64.59/41.52 tff(149,plain,
% 64.59/41.52 (not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))) = not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[148])).
% 64.59/41.52 tff(150,plain,
% 64.59/41.52 (or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))) = or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[149])).
% 64.59/41.52 tff(151,plain,
% 64.59/41.52 (or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))))),
% 64.59/41.52 inference(symmetry,[status(thm)],[150])).
% 64.59/41.52 tff(152,plain,
% 64.59/41.52 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(and(P!1, Q!0), P!1) = or(not(and(P!1, Q!0)), P!1))),
% 64.59/41.52 inference(quant_inst,[status(thm)],[])).
% 64.59/41.52 tff(153,plain,
% 64.59/41.52 (implies(and(P!1, Q!0), P!1) = or(not(and(P!1, Q!0)), P!1)),
% 64.59/41.52 inference(unit_resolution,[status(thm)],[152, 20])).
% 64.59/41.52 tff(154,plain,
% 64.59/41.52 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(and(P!1, Q!0), P!1) = not(and(and(P!1, Q!0), not(P!1))))),
% 64.59/41.52 inference(quant_inst,[status(thm)],[])).
% 64.59/41.52 tff(155,plain,
% 64.59/41.52 (implies(and(P!1, Q!0), P!1) = not(and(and(P!1, Q!0), not(P!1)))),
% 64.59/41.52 inference(unit_resolution,[status(thm)],[154, 91])).
% 64.59/41.52 tff(156,plain,
% 64.59/41.52 (not(and(and(P!1, Q!0), not(P!1))) = implies(and(P!1, Q!0), P!1)),
% 64.59/41.52 inference(symmetry,[status(thm)],[155])).
% 64.59/41.52 tff(157,plain,
% 64.59/41.52 (and(and(P!1, Q!0), not(P!1)) = and(not(or(not(P!1), not(Q!0))), not(P!1))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[126])).
% 64.59/41.52 tff(158,plain,
% 64.59/41.52 (and(not(or(not(P!1), not(Q!0))), not(P!1)) = and(and(P!1, Q!0), not(P!1))),
% 64.59/41.52 inference(symmetry,[status(thm)],[157])).
% 64.59/41.52 tff(159,plain,
% 64.59/41.52 (not(and(not(or(not(P!1), not(Q!0))), not(P!1))) = not(and(and(P!1, Q!0), not(P!1)))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[158])).
% 64.59/41.52 tff(160,plain,
% 64.59/41.52 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(or(not(P!1), not(Q!0))), not(P!1)) = not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.59/41.52 inference(quant_inst,[status(thm)],[])).
% 64.59/41.52 tff(161,plain,
% 64.59/41.52 (and(not(or(not(P!1), not(Q!0))), not(P!1)) = not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))),
% 64.59/41.52 inference(unit_resolution,[status(thm)],[160, 113])).
% 64.59/41.52 tff(162,plain,
% 64.59/41.52 (not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))) = and(not(or(not(P!1), not(Q!0))), not(P!1))),
% 64.59/41.52 inference(symmetry,[status(thm)],[161])).
% 64.59/41.52 tff(163,plain,
% 64.59/41.52 (not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))) = not(and(not(or(not(P!1), not(Q!0))), not(P!1)))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[162])).
% 64.59/41.52 tff(164,plain,
% 64.59/41.52 (not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))) = or(not(and(P!1, Q!0)), P!1)),
% 64.59/41.52 inference(transitivity,[status(thm)],[163, 159, 156, 153])).
% 64.59/41.52 tff(165,plain,
% 64.59/41.52 (not(not(and(not(P!1), not(not(and(P!1, Q!0)))))) = not(or(P!1, not(and(P!1, Q!0))))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[119])).
% 64.59/41.52 tff(166,plain,
% 64.59/41.52 (or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))) = or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[165, 164])).
% 64.59/41.52 tff(167,plain,
% 64.59/41.52 (not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))) = not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[166])).
% 64.59/41.52 tff(168,plain,
% 64.59/41.52 (or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[167])).
% 64.59/41.52 tff(169,plain,
% 64.59/41.52 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = not(and(not(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))),
% 64.59/41.52 inference(quant_inst,[status(thm)],[])).
% 64.59/41.52 tff(170,plain,
% 64.59/41.52 (or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = not(and(not(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.59/41.52 inference(unit_resolution,[status(thm)],[169, 42])).
% 64.59/41.52 tff(171,plain,
% 64.59/41.52 (not(and(not(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))) = or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.59/41.52 inference(symmetry,[status(thm)],[170])).
% 64.59/41.52 tff(172,plain,
% 64.59/41.52 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(P!1)), not(and(P!1, Q!0))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))) = or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.59/41.52 inference(quant_inst,[status(thm)],[])).
% 64.59/41.52 tff(173,plain,
% 64.59/41.52 (implies(or(not(not(P!1)), not(and(P!1, Q!0))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))) = or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))),
% 64.59/41.52 inference(unit_resolution,[status(thm)],[172, 20])).
% 64.59/41.52 tff(174,plain,
% 64.59/41.52 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(not(P!1)), not(and(P!1, Q!0))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))) = not(and(or(not(not(P!1)), not(and(P!1, Q!0))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))))),
% 64.59/41.52 inference(quant_inst,[status(thm)],[])).
% 64.59/41.52 tff(175,plain,
% 64.59/41.52 (implies(or(not(not(P!1)), not(and(P!1, Q!0))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))) = not(and(or(not(not(P!1)), not(and(P!1, Q!0))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))),
% 64.59/41.52 inference(unit_resolution,[status(thm)],[174, 91])).
% 64.59/41.52 tff(176,plain,
% 64.59/41.52 (not(and(or(not(not(P!1)), not(and(P!1, Q!0))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))) = implies(or(not(not(P!1)), not(and(P!1, Q!0))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))),
% 64.59/41.52 inference(symmetry,[status(thm)],[175])).
% 64.59/41.52 tff(177,plain,
% 64.59/41.52 (or(not(not(P!1)), not(and(P!1, Q!0))) = not(and(not(P!1), not(not(and(P!1, Q!0)))))),
% 64.59/41.52 inference(transitivity,[status(thm)],[124, 121])).
% 64.59/41.52 tff(178,plain,
% 64.59/41.52 (and(or(not(not(P!1)), not(and(P!1, Q!0))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))) = and(not(and(not(P!1), not(not(and(P!1, Q!0))))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[177])).
% 64.59/41.52 tff(179,plain,
% 64.59/41.52 (and(not(and(not(P!1), not(not(and(P!1, Q!0))))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))) = and(or(not(not(P!1)), not(and(P!1, Q!0))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.59/41.52 inference(symmetry,[status(thm)],[178])).
% 64.59/41.52 tff(180,plain,
% 64.59/41.52 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(P!1), not(not(and(P!1, Q!0))))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))) = not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))))),
% 64.59/41.52 inference(quant_inst,[status(thm)],[])).
% 64.59/41.52 tff(181,plain,
% 64.59/41.52 (and(not(and(not(P!1), not(not(and(P!1, Q!0))))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))) = not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))))),
% 64.59/41.52 inference(unit_resolution,[status(thm)],[180, 113])).
% 64.59/41.52 tff(182,plain,
% 64.59/41.52 (not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))) = and(not(and(not(P!1), not(not(and(P!1, Q!0))))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.59/41.52 inference(symmetry,[status(thm)],[181])).
% 64.59/41.52 tff(183,plain,
% 64.59/41.52 (not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))) = and(or(not(not(P!1)), not(and(P!1, Q!0))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.59/41.52 inference(transitivity,[status(thm)],[182, 179])).
% 64.59/41.52 tff(184,plain,
% 64.59/41.52 (not(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))))) = not(and(or(not(not(P!1)), not(and(P!1, Q!0))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[183])).
% 64.59/41.52 tff(185,plain,
% 64.59/41.52 (not(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))))) = or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))),
% 64.59/41.52 inference(transitivity,[status(thm)],[184, 176, 173])).
% 64.59/41.52 tff(186,plain,
% 64.59/41.52 (and(not(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))) = and(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[185])).
% 64.59/41.52 tff(187,plain,
% 64.59/41.52 (and(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))) = and(not(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.59/41.52 inference(symmetry,[status(thm)],[186])).
% 64.59/41.52 tff(188,plain,
% 64.59/41.52 (not(and(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))) = not(and(not(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[187])).
% 64.59/41.52 tff(189,plain,
% 64.59/41.52 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = not(and(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))),
% 64.59/41.52 inference(quant_inst,[status(thm)],[])).
% 64.59/41.52 tff(190,plain,
% 64.59/41.52 (implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = not(and(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.59/41.52 inference(unit_resolution,[status(thm)],[189, 91])).
% 64.59/41.52 tff(191,plain,
% 64.59/41.52 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = or(not(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.59/41.52 inference(quant_inst,[status(thm)],[])).
% 64.59/41.52 tff(192,plain,
% 64.59/41.52 (implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = or(not(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.59/41.52 inference(unit_resolution,[status(thm)],[191, 20])).
% 64.59/41.52 tff(193,plain,
% 64.59/41.52 (or(not(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.59/41.52 inference(symmetry,[status(thm)],[192])).
% 64.59/41.52 tff(194,plain,
% 64.59/41.52 (or(not(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))) = or(not(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[149])).
% 64.59/41.52 tff(195,plain,
% 64.59/41.52 (or(not(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))) = or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))))),
% 64.59/41.52 inference(transitivity,[status(thm)],[194, 193, 190, 188, 171, 168, 151])).
% 64.59/41.52 tff(196,plain,
% 64.59/41.52 (not(or(not(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))))) = not(or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[195])).
% 64.59/41.52 tff(197,plain,
% 64.59/41.52 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))) = not(or(not(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))))))),
% 64.59/41.52 inference(quant_inst,[status(thm)],[])).
% 64.59/41.52 tff(198,plain,
% 64.59/41.52 (and(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))) = not(or(not(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))))),
% 64.59/41.52 inference(unit_resolution,[status(thm)],[197, 113])).
% 64.59/41.52 tff(199,plain,
% 64.59/41.52 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))) = not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, or(not(P!1), not(Q!0)))))))),
% 64.59/41.52 inference(quant_inst,[status(thm)],[])).
% 64.59/41.52 tff(200,plain,
% 64.59/41.52 (implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))) = not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, or(not(P!1), not(Q!0))))))),
% 64.59/41.52 inference(unit_resolution,[status(thm)],[199, 91])).
% 64.59/41.52 tff(201,plain,
% 64.59/41.52 (not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, or(not(P!1), not(Q!0)))))) = implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))),
% 64.59/41.52 inference(symmetry,[status(thm)],[200])).
% 64.59/41.52 tff(202,plain,
% 64.59/41.52 (not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))) = not(or(P!1, or(not(P!1), not(Q!0))))),
% 64.59/41.52 inference(monotonicity,[status(thm)],[45])).
% 64.59/41.52 tff(203,plain,
% 64.59/41.52 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(or(not(P!1), not(Q!0)), P!1) = not(and(not(or(not(P!1), not(Q!0))), not(P!1))))),
% 64.59/41.52 inference(quant_inst,[status(thm)],[])).
% 64.59/41.52 tff(204,plain,
% 64.59/41.52 (or(or(not(P!1), not(Q!0)), P!1) = not(and(not(or(not(P!1), not(Q!0))), not(P!1)))),
% 64.59/41.52 inference(unit_resolution,[status(thm)],[203, 42])).
% 64.59/41.52 tff(205,plain,
% 64.59/41.52 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(P!1), not(Q!0)) = not(and(not(not(P!1)), not(not(Q!0)))))),
% 64.59/41.52 inference(quant_inst,[status(thm)],[])).
% 64.59/41.52 tff(206,plain,
% 64.59/41.52 (or(not(P!1), not(Q!0)) = not(and(not(not(P!1)), not(not(Q!0))))),
% 64.59/41.52 inference(unit_resolution,[status(thm)],[205, 42])).
% 64.59/41.52 tff(207,plain,
% 64.59/41.52 (not(and(not(not(P!1)), not(not(Q!0)))) = or(not(P!1), not(Q!0))),
% 64.59/41.52 inference(symmetry,[status(thm)],[206])).
% 64.59/41.52 tff(208,plain,
% 64.59/41.52 (or(not(and(not(not(P!1)), not(not(Q!0)))), P!1) = or(or(not(P!1), not(Q!0)), P!1)),
% 64.59/41.52 inference(monotonicity,[status(thm)],[207])).
% 64.59/41.52 tff(209,plain,
% 64.59/41.52 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(and(not(not(P!1)), not(not(Q!0))), P!1) = or(not(and(not(not(P!1)), not(not(Q!0)))), P!1))),
% 64.59/41.53 inference(quant_inst,[status(thm)],[])).
% 64.59/41.53 tff(210,plain,
% 64.59/41.53 (implies(and(not(not(P!1)), not(not(Q!0))), P!1) = or(not(and(not(not(P!1)), not(not(Q!0)))), P!1)),
% 64.59/41.53 inference(unit_resolution,[status(thm)],[209, 20])).
% 64.59/41.53 tff(211,plain,
% 64.59/41.53 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(not(P!1)), not(not(Q!0))) = not(or(not(not(not(P!1))), not(not(not(Q!0))))))),
% 64.59/41.53 inference(quant_inst,[status(thm)],[])).
% 64.59/41.53 tff(212,plain,
% 64.59/41.53 (and(not(not(P!1)), not(not(Q!0))) = not(or(not(not(not(P!1))), not(not(not(Q!0)))))),
% 64.59/41.53 inference(unit_resolution,[status(thm)],[211, 113])).
% 64.59/41.53 tff(213,plain,
% 64.59/41.53 (not(or(not(not(not(P!1))), not(not(not(Q!0))))) = and(not(not(P!1)), not(not(Q!0)))),
% 64.59/41.53 inference(symmetry,[status(thm)],[212])).
% 64.59/41.53 tff(214,plain,
% 64.59/41.53 (implies(not(or(not(not(not(P!1))), not(not(not(Q!0))))), P!1) = implies(and(not(not(P!1)), not(not(Q!0))), P!1)),
% 64.59/41.53 inference(monotonicity,[status(thm)],[213])).
% 64.59/41.53 tff(215,plain,
% 64.59/41.53 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(or(not(not(not(P!1))), not(not(not(Q!0))))), P!1) = not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1))))),
% 64.59/41.53 inference(quant_inst,[status(thm)],[])).
% 64.59/41.53 tff(216,plain,
% 64.59/41.53 (implies(not(or(not(not(not(P!1))), not(not(not(Q!0))))), P!1) = not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1)))),
% 64.59/41.53 inference(unit_resolution,[status(thm)],[215, 91])).
% 64.59/41.53 tff(217,plain,
% 64.59/41.53 (not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1))) = implies(not(or(not(not(not(P!1))), not(not(not(Q!0))))), P!1)),
% 64.59/41.53 inference(symmetry,[status(thm)],[216])).
% 64.59/41.53 tff(218,plain,
% 64.59/41.53 (not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1))) = or(not(and(P!1, Q!0)), P!1)),
% 64.59/41.53 inference(transitivity,[status(thm)],[217, 214, 210, 208, 204, 159, 156, 153])).
% 64.59/41.53 tff(219,plain,
% 64.59/41.53 (and(not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1))), not(not(and(not(P!1), not(or(not(P!1), not(Q!0))))))) = and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, or(not(P!1), not(Q!0)))))),
% 64.59/41.53 inference(monotonicity,[status(thm)],[218, 202])).
% 64.59/41.53 tff(220,plain,
% 64.59/41.53 (not(and(not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1))), not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))))) = not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, or(not(P!1), not(Q!0))))))),
% 64.59/41.53 inference(monotonicity,[status(thm)],[219])).
% 64.59/41.53 tff(221,plain,
% 64.59/41.53 (implies(and(not(not(P!1)), not(not(Q!0))), P!1) = implies(not(or(not(not(not(P!1))), not(not(not(Q!0))))), P!1)),
% 64.59/41.53 inference(symmetry,[status(thm)],[214])).
% 64.59/41.53 tff(222,plain,
% 64.59/41.53 (or(not(and(not(not(P!1)), not(not(Q!0)))), P!1) = implies(and(not(not(P!1)), not(not(Q!0))), P!1)),
% 64.59/41.53 inference(symmetry,[status(thm)],[210])).
% 64.59/41.53 tff(223,plain,
% 64.59/41.53 (or(or(not(P!1), not(Q!0)), P!1) = or(not(and(not(not(P!1)), not(not(Q!0)))), P!1)),
% 64.59/41.53 inference(symmetry,[status(thm)],[208])).
% 64.59/41.53 tff(224,plain,
% 64.59/41.53 (not(and(not(or(not(P!1), not(Q!0))), not(P!1))) = or(or(not(P!1), not(Q!0)), P!1)),
% 64.59/41.53 inference(symmetry,[status(thm)],[204])).
% 64.59/41.53 tff(225,plain,
% 64.59/41.53 (not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))) = not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1)))),
% 64.59/41.53 inference(transitivity,[status(thm)],[163, 224, 223, 222, 221, 216])).
% 64.59/41.53 tff(226,plain,
% 64.59/41.53 (and(not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(not(and(not(P!1), not(or(not(P!1), not(Q!0))))))) = and(not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1))), not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))))),
% 64.59/41.53 inference(monotonicity,[status(thm)],[225])).
% 64.59/41.53 tff(227,plain,
% 64.59/41.53 (not(and(not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))))) = not(and(not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1))), not(not(and(not(P!1), not(or(not(P!1), not(Q!0))))))))),
% 64.59/41.53 inference(monotonicity,[status(thm)],[226])).
% 64.59/41.53 tff(228,plain,
% 64.59/41.53 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))) = not(and(not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))))))),
% 64.59/41.53 inference(quant_inst,[status(thm)],[])).
% 64.59/41.53 tff(229,plain,
% 64.59/41.53 (or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))) = not(and(not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(not(and(not(P!1), not(or(not(P!1), not(Q!0))))))))),
% 64.59/41.53 inference(unit_resolution,[status(thm)],[228, 42])).
% 64.59/41.53 tff(230,plain,
% 64.59/41.53 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))) = or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))))),
% 64.59/41.53 inference(quant_inst,[status(thm)],[])).
% 64.59/41.53 tff(231,plain,
% 64.59/41.53 (implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))) = or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(P!1), not(or(not(P!1), not(Q!0))))))),
% 64.59/41.53 inference(unit_resolution,[status(thm)],[230, 20])).
% 64.59/41.53 tff(232,plain,
% 64.59/41.53 (implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))) = or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))),
% 64.59/41.53 inference(transitivity,[status(thm)],[231, 229, 227, 220, 201, 71])).
% 64.59/41.53 tff(233,plain,
% 64.59/41.53 (not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))) = not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))))),
% 64.59/41.53 inference(symmetry,[status(thm)],[167])).
% 64.59/41.53 tff(234,plain,
% 64.59/41.53 (or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1)))) = or(not(or(P!1, or(not(P!1), not(Q!0)))), or(not(and(P!1, Q!0)), P!1))),
% 64.59/41.53 inference(monotonicity,[status(thm)],[202, 218])).
% 64.59/41.53 tff(235,plain,
% 64.59/41.53 (or(not(or(P!1, or(not(P!1), not(Q!0)))), or(not(and(P!1, Q!0)), P!1)) = or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1))))),
% 64.59/41.53 inference(symmetry,[status(thm)],[234])).
% 64.59/41.53 tff(236,plain,
% 64.59/41.53 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)) = or(not(or(P!1, or(not(P!1), not(Q!0)))), or(not(and(P!1, Q!0)), P!1)))),
% 64.59/41.53 inference(quant_inst,[status(thm)],[])).
% 64.59/41.53 tff(237,plain,
% 64.59/41.53 (implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)) = or(not(or(P!1, or(not(P!1), not(Q!0)))), or(not(and(P!1, Q!0)), P!1))),
% 64.59/41.53 inference(unit_resolution,[status(thm)],[236, 20])).
% 64.59/41.53 tff(238,plain,
% 64.59/41.53 (or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)) = or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1))))),
% 64.59/41.53 inference(transitivity,[status(thm)],[141, 139, 94, 237, 235])).
% 64.59/41.53 tff(239,plain,
% 64.59/41.53 (not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))) = not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1)))))),
% 64.59/41.53 inference(monotonicity,[status(thm)],[238])).
% 64.59/41.53 tff(240,plain,
% 64.59/41.53 (not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1))))) = not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)))),
% 64.59/41.53 inference(symmetry,[status(thm)],[239])).
% 64.59/41.53 tff(241,plain,
% 64.59/41.53 (or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))) = or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1))))),
% 64.59/41.53 inference(monotonicity,[status(thm)],[225])).
% 64.59/41.53 tff(242,plain,
% 64.59/41.53 (or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1)))) = or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))),
% 64.59/41.53 inference(symmetry,[status(thm)],[241])).
% 64.59/41.53 tff(243,plain,
% 64.59/41.53 (not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1))))) = not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))))),
% 64.59/41.53 inference(monotonicity,[status(thm)],[242])).
% 64.59/41.53 tff(244,plain,
% 64.59/41.53 (not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))) = not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(and(not(or(not(not(not(P!1))), not(not(not(Q!0))))), not(P!1)))))),
% 64.59/41.53 inference(symmetry,[status(thm)],[243])).
% 64.59/41.53 tff(245,plain,
% 64.59/41.53 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))) = not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))))),
% 64.59/41.53 inference(quant_inst,[status(thm)],[])).
% 64.59/41.53 tff(246,plain,
% 64.59/41.53 (and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))) = not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))))),
% 64.59/41.53 inference(unit_resolution,[status(thm)],[245, 113])).
% 64.59/41.53 tff(247,plain,
% 64.59/41.53 (and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))) = and(or(not(not(P!1)), not(and(P!1, Q!0))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.59/41.53 inference(transitivity,[status(thm)],[246, 244, 240, 233, 182, 179])).
% 64.59/41.53 tff(248,plain,
% 64.59/41.53 (not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))) = not(and(or(not(not(P!1)), not(and(P!1, Q!0))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))),
% 64.59/41.53 inference(monotonicity,[status(thm)],[247])).
% 64.59/41.53 tff(249,plain,
% 64.59/41.53 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))) = not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))))),
% 64.59/41.53 inference(quant_inst,[status(thm)],[])).
% 64.59/41.53 tff(250,plain,
% 64.59/41.53 (implies(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))) = not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))),
% 64.59/41.53 inference(unit_resolution,[status(thm)],[249, 91])).
% 64.59/41.53 tff(251,plain,
% 64.59/41.53 (implies(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))) = or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))),
% 64.59/41.53 inference(transitivity,[status(thm)],[250, 248, 176, 173])).
% 64.59/41.53 tff(252,plain,
% 64.59/41.53 (and(implies(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), not(and(not(P!1), not(or(not(P!1), not(Q!0))))))) = and(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))),
% 64.59/41.53 inference(monotonicity,[status(thm)],[251, 232])).
% 64.59/41.53 tff(253,plain,
% 64.59/41.53 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))) = and(implies(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), not(and(not(P!1), not(or(not(P!1), not(Q!0))))))))),
% 64.59/41.53 inference(quant_inst,[status(thm)],[])).
% 64.59/41.53 tff(254,plain,
% 64.59/41.53 (equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))) = and(implies(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))))),
% 64.59/41.53 inference(unit_resolution,[status(thm)],[253, 66])).
% 64.59/41.53 tff(255,plain,
% 64.59/41.53 (equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))) = equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(and(P!1, Q!0)), P!1))),
% 64.59/41.53 inference(transitivity,[status(thm)],[254, 252, 198, 196, 146, 143, 69, 47])).
% 64.59/41.53 tff(256,plain,
% 64.59/41.53 (is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))) <=> is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(and(P!1, Q!0)), P!1)))),
% 64.59/41.53 inference(monotonicity,[status(thm)],[255])).
% 64.59/41.53 tff(257,plain,
% 64.59/41.53 (is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(and(P!1, Q!0)), P!1))) <=> is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.59/41.53 inference(symmetry,[status(thm)],[256])).
% 64.59/41.53 tff(258,plain,
% 64.59/41.53 (and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))) = equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(and(P!1, Q!0)), P!1))),
% 64.59/41.53 inference(transitivity,[status(thm)],[69, 47])).
% 64.59/41.53 tff(259,plain,
% 64.59/41.53 (is_a_theorem(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) <=> is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(and(P!1, Q!0)), P!1)))),
% 64.59/41.53 inference(monotonicity,[status(thm)],[258])).
% 64.59/41.53 tff(260,plain,
% 64.59/41.53 (is_a_theorem(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) <=> is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.59/41.53 inference(transitivity,[status(thm)],[259, 257])).
% 64.59/41.53 tff(261,plain,
% 64.59/41.53 (and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))) = and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(or(not(and(P!1, Q!0)), P!1)))),
% 64.59/41.53 inference(monotonicity,[status(thm)],[44])).
% 64.59/41.53 tff(262,plain,
% 64.59/41.53 (and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(or(not(and(P!1, Q!0)), P!1))) = and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))),
% 64.59/41.53 inference(symmetry,[status(thm)],[261])).
% 64.59/41.53 tff(263,plain,
% 64.59/41.53 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(or(not(and(P!1, Q!0)), P!1))) = not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.59/41.53 inference(quant_inst,[status(thm)],[])).
% 64.59/41.53 tff(264,plain,
% 64.59/41.53 (and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(or(not(and(P!1, Q!0)), P!1))) = not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.59/41.53 inference(unit_resolution,[status(thm)],[263, 113])).
% 64.59/41.53 tff(265,plain,
% 64.59/41.53 (not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))) = and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(or(not(and(P!1, Q!0)), P!1)))),
% 64.59/41.53 inference(symmetry,[status(thm)],[264])).
% 64.59/41.53 tff(266,plain,
% 64.59/41.53 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))) = or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.59/41.53 inference(quant_inst,[status(thm)],[])).
% 64.59/41.53 tff(267,plain,
% 64.59/41.53 (implies(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))) = or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))),
% 64.59/41.53 inference(unit_resolution,[status(thm)],[266, 20])).
% 64.59/41.53 tff(268,plain,
% 64.59/41.53 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))) = not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.59/41.53 inference(quant_inst,[status(thm)],[])).
% 64.59/41.53 tff(269,plain,
% 64.59/41.53 (implies(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))) = not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.59/41.53 inference(unit_resolution,[status(thm)],[268, 91])).
% 64.59/41.53 tff(270,plain,
% 64.59/41.53 (not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))) = implies(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1))))),
% 64.59/41.53 inference(symmetry,[status(thm)],[269])).
% 64.59/41.53 tff(271,plain,
% 64.59/41.53 (not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))) = or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))),
% 64.59/41.53 inference(transitivity,[status(thm)],[270, 267])).
% 64.59/41.53 tff(272,plain,
% 64.59/41.53 (not(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1))))))) = not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.59/41.53 inference(monotonicity,[status(thm)],[271])).
% 64.59/41.53 tff(273,plain,
% 64.59/41.53 (not(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1))))))) = and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))),
% 64.59/41.53 inference(transitivity,[status(thm)],[272, 265, 262])).
% 64.59/41.53 tff(274,plain,
% 64.59/41.53 (or(not(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1))))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) = or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))),
% 64.59/41.53 inference(monotonicity,[status(thm)],[273])).
% 64.59/41.53 tff(275,plain,
% 64.59/41.53 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) = or(not(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1))))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))))),
% 64.59/41.53 inference(quant_inst,[status(thm)],[])).
% 64.59/41.53 tff(276,plain,
% 64.59/41.53 (implies(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) = or(not(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1))))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))),
% 64.59/41.53 inference(unit_resolution,[status(thm)],[275, 20])).
% 64.59/41.53 tff(277,plain,
% 64.59/41.53 (implies(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) = or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))),
% 64.59/41.53 inference(transitivity,[status(thm)],[276, 274])).
% 64.59/41.53 tff(278,plain,
% 64.59/41.53 (is_a_theorem(implies(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))) <=> is_a_theorem(or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))))),
% 64.64/41.54 inference(monotonicity,[status(thm)],[277])).
% 64.64/41.54 tff(279,plain,
% 64.64/41.54 (is_a_theorem(or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))) <=> is_a_theorem(implies(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))))),
% 64.64/41.54 inference(symmetry,[status(thm)],[278])).
% 64.64/41.54 tff(280,plain,
% 64.64/41.54 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(and(P!1, Q!0)), P!1), or(P!1, not(and(P!1, Q!0)))) = or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0)))))),
% 64.64/41.54 inference(quant_inst,[status(thm)],[])).
% 64.64/41.54 tff(281,plain,
% 64.64/41.54 (implies(or(not(and(P!1, Q!0)), P!1), or(P!1, not(and(P!1, Q!0)))) = or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0))))),
% 64.64/41.54 inference(unit_resolution,[status(thm)],[280, 20])).
% 64.64/41.54 tff(282,plain,
% 64.64/41.54 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(and(P!1, Q!0)), P!1), or(P!1, not(and(P!1, Q!0)))) = not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))),
% 64.64/41.54 inference(quant_inst,[status(thm)],[])).
% 64.64/41.54 tff(283,plain,
% 64.64/41.54 (implies(or(not(and(P!1, Q!0)), P!1), or(P!1, not(and(P!1, Q!0)))) = not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))),
% 64.64/41.54 inference(unit_resolution,[status(thm)],[282, 91])).
% 64.64/41.54 tff(284,plain,
% 64.64/41.54 (not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))) = implies(or(not(and(P!1, Q!0)), P!1), or(P!1, not(and(P!1, Q!0))))),
% 64.64/41.54 inference(symmetry,[status(thm)],[283])).
% 64.64/41.54 tff(285,plain,
% 64.64/41.54 (and(not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(not(and(not(P!1), not(not(and(P!1, Q!0))))))) = and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))),
% 64.64/41.54 inference(monotonicity,[status(thm)],[164, 165])).
% 64.64/41.54 tff(286,plain,
% 64.64/41.54 (not(and(not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(not(and(not(P!1), not(not(and(P!1, Q!0)))))))) = not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))),
% 64.64/41.54 inference(monotonicity,[status(thm)],[285])).
% 64.64/41.54 tff(287,plain,
% 64.64/41.54 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(P!1), not(not(and(P!1, Q!0)))))) = not(and(not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(not(and(not(P!1), not(not(and(P!1, Q!0)))))))))),
% 64.64/41.54 inference(quant_inst,[status(thm)],[])).
% 64.64/41.54 tff(288,plain,
% 64.64/41.54 (or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(P!1), not(not(and(P!1, Q!0)))))) = not(and(not(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(not(and(not(P!1), not(not(and(P!1, Q!0))))))))),
% 64.64/41.54 inference(unit_resolution,[status(thm)],[287, 42])).
% 64.64/41.54 tff(289,plain,
% 64.64/41.54 (or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))) = or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(P!1), not(not(and(P!1, Q!0))))))),
% 64.64/41.54 inference(monotonicity,[status(thm)],[177])).
% 64.64/41.54 tff(290,plain,
% 64.64/41.54 (or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))) = or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0))))),
% 64.64/41.54 inference(transitivity,[status(thm)],[289, 288, 286, 284, 281])).
% 64.64/41.54 tff(291,plain,
% 64.64/41.54 (not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))) = not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0)))))),
% 64.64/41.54 inference(monotonicity,[status(thm)],[290])).
% 64.64/41.54 tff(292,plain,
% 64.64/41.54 (not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0))))) = not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))))),
% 64.64/41.54 inference(symmetry,[status(thm)],[291])).
% 64.64/41.54 tff(293,plain,
% 64.64/41.54 (or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0)))))) = or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0))))),
% 64.64/41.54 inference(monotonicity,[status(thm)],[119])).
% 64.64/41.54 tff(294,plain,
% 64.64/41.54 (not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))) = not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0)))))),
% 64.64/41.54 inference(monotonicity,[status(thm)],[293])).
% 64.64/41.54 tff(295,plain,
% 64.64/41.54 (not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))) = not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))))),
% 64.64/41.54 inference(transitivity,[status(thm)],[294, 292])).
% 64.64/41.54 tff(296,plain,
% 64.64/41.54 (or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) = or(not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.64/41.54 inference(monotonicity,[status(thm)],[295])).
% 64.64/41.54 tff(297,plain,
% 64.64/41.54 (or(not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) = or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.64/41.54 inference(symmetry,[status(thm)],[296])).
% 64.64/41.54 tff(298,plain,
% 64.64/41.54 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) = or(not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.64/41.54 inference(quant_inst,[status(thm)],[])).
% 64.64/41.54 tff(299,plain,
% 64.64/41.54 (implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) = or(not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.64/41.54 inference(unit_resolution,[status(thm)],[298, 20])).
% 64.64/41.54 tff(300,plain,
% 64.64/41.54 (implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) = or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.64/41.54 inference(transitivity,[status(thm)],[299, 297])).
% 64.64/41.54 tff(301,plain,
% 64.64/41.54 (is_a_theorem(implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) <=> is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.64/41.54 inference(monotonicity,[status(thm)],[300])).
% 64.64/41.54 tff(302,plain,
% 64.64/41.54 (is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) <=> is_a_theorem(implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.64/41.54 inference(symmetry,[status(thm)],[301])).
% 64.64/41.54 tff(303,plain,
% 64.64/41.54 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)) = not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.64/41.54 inference(quant_inst,[status(thm)],[])).
% 64.64/41.54 tff(304,plain,
% 64.64/41.54 (implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)) = not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))),
% 64.64/41.54 inference(unit_resolution,[status(thm)],[303, 91])).
% 64.64/41.54 tff(305,plain,
% 64.64/41.54 (not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))) = implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1))),
% 64.64/41.54 inference(symmetry,[status(thm)],[304])).
% 64.64/41.54 tff(306,plain,
% 64.64/41.54 (and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) = and(implies(or(not(and(P!1, Q!0)), P!1), or(P!1, not(and(P!1, Q!0)))), implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)))),
% 64.64/41.54 inference(monotonicity,[status(thm)],[284, 305])).
% 64.64/41.54 tff(307,plain,
% 64.64/41.54 (and(implies(or(not(and(P!1, Q!0)), P!1), or(P!1, not(and(P!1, Q!0)))), implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1))) = and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.64/41.54 inference(symmetry,[status(thm)],[306])).
% 64.64/41.54 tff(308,plain,
% 64.64/41.54 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)) = or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)))),
% 64.64/41.54 inference(quant_inst,[status(thm)],[])).
% 64.64/41.54 tff(309,plain,
% 64.64/41.54 (implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)) = or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))),
% 64.64/41.54 inference(unit_resolution,[status(thm)],[308, 20])).
% 64.64/41.54 tff(310,plain,
% 64.64/41.54 (or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)) = implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1))),
% 64.64/41.54 inference(symmetry,[status(thm)],[309])).
% 64.64/41.54 tff(311,plain,
% 64.64/41.54 (not(and(not(not(or(P!1, not(and(P!1, Q!0))))), not(or(not(and(P!1, Q!0)), P!1)))) = or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))),
% 64.64/41.54 inference(symmetry,[status(thm)],[141])).
% 64.64/41.54 tff(312,plain,
% 64.64/41.54 (not(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))) = implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1))),
% 64.64/41.54 inference(transitivity,[status(thm)],[138, 311, 310])).
% 64.64/41.54 tff(313,plain,
% 64.64/41.54 (or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))) = implies(or(not(and(P!1, Q!0)), P!1), or(P!1, not(and(P!1, Q!0))))),
% 64.64/41.54 inference(transitivity,[status(thm)],[289, 288, 286, 284])).
% 64.64/41.54 tff(314,plain,
% 64.64/41.54 (and(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), not(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) = and(implies(or(not(and(P!1, Q!0)), P!1), or(P!1, not(and(P!1, Q!0)))), implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)))),
% 64.64/41.54 inference(monotonicity,[status(thm)],[313, 312])).
% 64.64/41.54 tff(315,plain,
% 64.64/41.54 (and(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), not(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) = and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.64/41.54 inference(transitivity,[status(thm)],[314, 307])).
% 64.64/41.54 tff(316,plain,
% 64.64/41.54 (not(and(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), not(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) = not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.64/41.54 inference(monotonicity,[status(thm)],[315])).
% 64.64/41.54 tff(317,plain,
% 64.64/41.54 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))) = not(and(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), not(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.64/41.54 inference(quant_inst,[status(thm)],[])).
% 64.64/41.54 tff(318,plain,
% 64.64/41.54 (implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))) = not(and(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), not(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.64/41.54 inference(unit_resolution,[status(thm)],[317, 91])).
% 64.64/41.54 tff(319,plain,
% 64.64/41.54 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))) = or(not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.64/41.54 inference(quant_inst,[status(thm)],[])).
% 64.64/41.54 tff(320,plain,
% 64.64/41.54 (implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))) = or(not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))),
% 64.64/41.54 inference(unit_resolution,[status(thm)],[319, 20])).
% 64.64/41.54 tff(321,plain,
% 64.64/41.54 (or(not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))) = implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))),
% 64.64/41.54 inference(symmetry,[status(thm)],[320])).
% 64.64/41.54 tff(322,plain,
% 64.64/41.54 (or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))) = or(not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))),
% 64.64/41.54 inference(monotonicity,[status(thm)],[295])).
% 64.64/41.54 tff(323,plain,
% 64.64/41.54 (or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))) = not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.64/41.54 inference(transitivity,[status(thm)],[322, 321, 318, 316])).
% 64.64/41.54 tff(324,plain,
% 64.64/41.54 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.64/41.54 inference(quant_inst,[status(thm)],[])).
% 64.64/41.54 tff(325,plain,
% 64.64/41.54 (implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.64/41.54 inference(unit_resolution,[status(thm)],[324, 20])).
% 64.64/41.54 tff(326,plain,
% 64.64/41.54 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))) = not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.64/41.54 inference(quant_inst,[status(thm)],[])).
% 64.64/41.54 tff(327,plain,
% 64.64/41.54 (and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))) = not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))),
% 64.64/41.54 inference(unit_resolution,[status(thm)],[326, 113])).
% 64.64/41.54 tff(328,plain,
% 64.64/41.54 (not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))) = and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))),
% 64.64/41.54 inference(symmetry,[status(thm)],[327])).
% 64.64/41.54 tff(329,plain,
% 64.64/41.54 (implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))),
% 64.64/41.54 inference(monotonicity,[status(thm)],[328])).
% 64.64/41.54 tff(330,plain,
% 64.64/41.54 (implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))) = implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.64/41.54 inference(symmetry,[status(thm)],[329])).
% 64.64/41.54 tff(331,plain,
% 64.64/41.54 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))) = not(and(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.64/41.54 inference(quant_inst,[status(thm)],[])).
% 64.64/41.54 tff(332,plain,
% 64.64/41.54 (implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))) = not(and(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.65/41.55 inference(unit_resolution,[status(thm)],[331, 91])).
% 64.65/41.55 tff(333,plain,
% 64.65/41.55 (not(and(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))) = implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))),
% 64.65/41.55 inference(symmetry,[status(thm)],[332])).
% 64.65/41.55 tff(334,plain,
% 64.65/41.55 (and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))) = and(implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, not(and(P!1, Q!0)))))),
% 64.65/41.55 inference(monotonicity,[status(thm)],[305, 284])).
% 64.65/41.55 tff(335,plain,
% 64.65/41.55 (and(implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, not(and(P!1, Q!0))))) = and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))),
% 64.65/41.55 inference(symmetry,[status(thm)],[334])).
% 64.65/41.55 tff(336,plain,
% 64.65/41.55 (and(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))) = and(implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, not(and(P!1, Q!0)))))),
% 64.65/41.55 inference(monotonicity,[status(thm)],[310, 284])).
% 64.65/41.55 tff(337,plain,
% 64.65/41.55 (and(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))) = and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))),
% 64.65/41.55 inference(transitivity,[status(thm)],[336, 335])).
% 64.65/41.55 tff(338,plain,
% 64.65/41.55 (not(and(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))) = not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.65/41.55 inference(monotonicity,[status(thm)],[337])).
% 64.65/41.55 tff(339,plain,
% 64.65/41.55 (not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))) = not(and(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.65/41.55 inference(symmetry,[status(thm)],[338])).
% 64.65/41.55 tff(340,plain,
% 64.65/41.55 (not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))) = or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))))),
% 64.65/41.55 inference(transitivity,[status(thm)],[339, 333, 330, 325, 151])).
% 64.65/41.55 tff(341,plain,
% 64.65/41.55 (not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))) = not(or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))))),
% 64.65/41.55 inference(monotonicity,[status(thm)],[340])).
% 64.65/41.55 tff(342,plain,
% 64.65/41.55 (not(or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))))) = not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.65/41.55 inference(symmetry,[status(thm)],[341])).
% 64.65/41.55 tff(343,plain,
% 64.65/41.55 (and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))) = and(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))),
% 64.65/41.55 inference(symmetry,[status(thm)],[143])).
% 64.65/41.55 tff(344,plain,
% 64.65/41.55 (and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))) = not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.65/41.55 inference(transitivity,[status(thm)],[343, 145, 342])).
% 64.65/41.55 tff(345,plain,
% 64.65/41.55 (or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) = or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.55 inference(monotonicity,[status(thm)],[344, 323])).
% 64.65/41.55 tff(346,plain,
% 64.65/41.55 (or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))) = or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.65/41.55 inference(symmetry,[status(thm)],[345])).
% 64.65/41.55 tff(347,plain,
% 64.65/41.55 (implies(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) = implies(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.65/41.55 inference(monotonicity,[status(thm)],[346])).
% 64.65/41.55 tff(348,plain,
% 64.65/41.55 (implies(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) = implies(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.65/41.55 inference(symmetry,[status(thm)],[347])).
% 64.65/41.55 tff(349,plain,
% 64.65/41.55 (is_a_theorem(implies(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))) <=> is_a_theorem(implies(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.55 inference(monotonicity,[status(thm)],[348])).
% 64.65/41.55 tff(350,plain,
% 64.65/41.55 (^[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)))))),
% 64.65/41.55 inference(bind,[status(th)],[])).
% 64.65/41.55 tff(351,plain,
% 64.65/41.55 (![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))))),
% 64.65/41.55 inference(quant_intro,[status(thm)],[350])).
% 64.65/41.55 tff(352,plain,
% 64.65/41.55 (![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: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 64.65/41.55 inference(rewrite,[status(thm)],[])).
% 64.65/41.55 tff(353,plain,
% 64.65/41.55 (($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))))),
% 64.65/41.55 inference(rewrite,[status(thm)],[])).
% 64.65/41.55 tff(354,axiom,(r4), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_r4')).
% 64.65/41.55 tff(355,plain,
% 64.65/41.55 (r4 <=> $true),
% 64.65/41.55 inference(iff_true,[status(thm)],[354])).
% 64.65/41.55 tff(356,plain,
% 64.65/41.55 ((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)))))),
% 64.65/41.55 inference(monotonicity,[status(thm)],[355])).
% 64.65/41.55 tff(357,plain,
% 64.65/41.55 ((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))))),
% 64.65/41.55 inference(transitivity,[status(thm)],[356, 353])).
% 64.65/41.55 tff(358,plain,
% 64.65/41.55 ((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)))))),
% 64.65/41.55 inference(rewrite,[status(thm)],[])).
% 64.65/41.55 tff(359,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/sandbox/benchmark/Axioms/LCL006+0.ax','r4')).
% 64.65/41.55 tff(360,plain,
% 64.65/41.55 (r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 64.65/41.55 inference(modus_ponens,[status(thm)],[359, 358])).
% 64.65/41.55 tff(361,plain,
% 64.65/41.55 (r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 64.65/41.55 inference(modus_ponens,[status(thm)],[360, 358])).
% 64.65/41.55 tff(362,plain,
% 64.65/41.55 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 64.65/41.55 inference(modus_ponens,[status(thm)],[361, 357])).
% 64.65/41.55 tff(363,plain,
% 64.65/41.55 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 64.65/41.55 inference(modus_ponens,[status(thm)],[362, 352])).
% 64.65/41.55 tff(364,plain,(
% 64.65/41.55 ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 64.65/41.55 inference(skolemize,[status(sab)],[363])).
% 64.65/41.55 tff(365,plain,
% 64.65/41.55 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 64.65/41.55 inference(modus_ponens,[status(thm)],[364, 351])).
% 64.65/41.55 tff(366,plain,
% 64.65/41.55 ((~![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(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.55 inference(quant_inst,[status(thm)],[])).
% 64.65/41.55 tff(367,plain,
% 64.65/41.55 (is_a_theorem(implies(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.55 inference(unit_resolution,[status(thm)],[366, 365])).
% 64.65/41.55 tff(368,plain,
% 64.65/41.55 (is_a_theorem(implies(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.55 inference(modus_ponens,[status(thm)],[367, 349])).
% 64.65/41.55 tff(369,plain,
% 64.65/41.55 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))) = or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.65/41.55 inference(quant_inst,[status(thm)],[])).
% 64.65/41.55 tff(370,plain,
% 64.65/41.55 (implies(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))) = or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.56 inference(unit_resolution,[status(thm)],[369, 20])).
% 64.65/41.56 tff(371,plain,
% 64.65/41.56 (or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))) = implies(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.56 inference(symmetry,[status(thm)],[370])).
% 64.65/41.56 tff(372,plain,
% 64.65/41.56 (is_a_theorem(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))) <=> is_a_theorem(implies(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.65/41.56 inference(monotonicity,[status(thm)],[371])).
% 64.65/41.56 tff(373,plain,
% 64.65/41.56 (is_a_theorem(implies(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))) <=> is_a_theorem(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.65/41.56 inference(symmetry,[status(thm)],[372])).
% 64.65/41.56 tff(374,plain,
% 64.65/41.56 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))), and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))) = not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.56 inference(quant_inst,[status(thm)],[])).
% 64.65/41.56 tff(375,plain,
% 64.65/41.56 (or(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))), and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))) = not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.65/41.56 inference(unit_resolution,[status(thm)],[374, 42])).
% 64.65/41.56 tff(376,plain,
% 64.65/41.56 (and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))) = and(not(and(not(P!1), not(not(and(P!1, Q!0))))), not(or(not(and(P!1, Q!0)), P!1)))),
% 64.65/41.56 inference(monotonicity,[status(thm)],[118])).
% 64.65/41.56 tff(377,plain,
% 64.65/41.56 (and(not(and(not(P!1), not(not(and(P!1, Q!0))))), not(or(not(and(P!1, Q!0)), P!1))) = and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))),
% 64.65/41.56 inference(symmetry,[status(thm)],[376])).
% 64.65/41.56 tff(378,plain,
% 64.65/41.56 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(P!1), not(not(and(P!1, Q!0))))), not(or(not(and(P!1, Q!0)), P!1))) = not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.65/41.56 inference(quant_inst,[status(thm)],[])).
% 64.65/41.56 tff(379,plain,
% 64.65/41.56 (and(not(and(not(P!1), not(not(and(P!1, Q!0))))), not(or(not(and(P!1, Q!0)), P!1))) = not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.65/41.56 inference(unit_resolution,[status(thm)],[378, 113])).
% 64.65/41.56 tff(380,plain,
% 64.65/41.56 (not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))) = and(not(and(not(P!1), not(not(and(P!1, Q!0))))), not(or(not(and(P!1, Q!0)), P!1)))),
% 64.65/41.56 inference(symmetry,[status(thm)],[379])).
% 64.65/41.56 tff(381,plain,
% 64.65/41.56 (not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))) = and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))),
% 64.65/41.56 inference(transitivity,[status(thm)],[380, 377])).
% 64.65/41.56 tff(382,plain,
% 64.65/41.56 (or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))) = or(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))), and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))),
% 64.65/41.56 inference(monotonicity,[status(thm)],[328, 381])).
% 64.65/41.56 tff(383,plain,
% 64.65/41.56 (or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))) = not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.65/41.56 inference(transitivity,[status(thm)],[382, 375])).
% 64.65/41.56 tff(384,plain,
% 64.65/41.56 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))) = not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.65/41.56 inference(quant_inst,[status(thm)],[])).
% 64.65/41.56 tff(385,plain,
% 64.65/41.56 (or(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))) = not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.65/41.56 inference(unit_resolution,[status(thm)],[384, 42])).
% 64.65/41.56 tff(386,plain,
% 64.65/41.56 (or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = or(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))),
% 64.65/41.56 inference(monotonicity,[status(thm)],[381, 328])).
% 64.65/41.56 tff(387,plain,
% 64.65/41.56 (or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.65/41.56 inference(transitivity,[status(thm)],[386, 385])).
% 64.65/41.56 tff(388,plain,
% 64.65/41.56 (implies(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))) = implies(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.56 inference(monotonicity,[status(thm)],[387, 383])).
% 64.65/41.56 tff(389,plain,
% 64.65/41.56 (is_a_theorem(implies(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) <=> is_a_theorem(implies(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.65/41.56 inference(monotonicity,[status(thm)],[388])).
% 64.65/41.56 tff(390,plain,
% 64.65/41.56 (^[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))))),
% 64.65/41.56 inference(bind,[status(th)],[])).
% 64.65/41.56 tff(391,plain,
% 64.65/41.56 (![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)))),
% 64.65/41.56 inference(quant_intro,[status(thm)],[390])).
% 64.65/41.56 tff(392,plain,
% 64.65/41.56 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 64.65/41.56 inference(rewrite,[status(thm)],[])).
% 64.65/41.56 tff(393,plain,
% 64.65/41.56 (($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)))),
% 64.65/41.56 inference(rewrite,[status(thm)],[])).
% 64.65/41.56 tff(394,axiom,(r3), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_r3')).
% 64.65/41.56 tff(395,plain,
% 64.65/41.56 (r3 <=> $true),
% 64.65/41.56 inference(iff_true,[status(thm)],[394])).
% 64.65/41.56 tff(396,plain,
% 64.65/41.56 ((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))))),
% 64.65/41.56 inference(monotonicity,[status(thm)],[395])).
% 64.65/41.56 tff(397,plain,
% 64.65/41.56 ((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)))),
% 64.65/41.56 inference(transitivity,[status(thm)],[396, 393])).
% 64.65/41.56 tff(398,plain,
% 64.65/41.56 ((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))))),
% 64.65/41.56 inference(rewrite,[status(thm)],[])).
% 64.65/41.56 tff(399,axiom,(r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','r3')).
% 64.65/41.56 tff(400,plain,
% 64.65/41.56 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 64.65/41.56 inference(modus_ponens,[status(thm)],[399, 398])).
% 64.65/41.56 tff(401,plain,
% 64.65/41.56 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 64.65/41.56 inference(modus_ponens,[status(thm)],[400, 398])).
% 64.65/41.56 tff(402,plain,
% 64.65/41.56 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 64.65/41.56 inference(modus_ponens,[status(thm)],[401, 397])).
% 64.65/41.56 tff(403,plain,
% 64.65/41.56 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 64.65/41.56 inference(modus_ponens,[status(thm)],[402, 392])).
% 64.65/41.56 tff(404,plain,(
% 64.65/41.56 ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 64.65/41.56 inference(skolemize,[status(sab)],[403])).
% 64.65/41.56 tff(405,plain,
% 64.65/41.56 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 64.65/41.56 inference(modus_ponens,[status(thm)],[404, 391])).
% 64.65/41.56 tff(406,plain,
% 64.65/41.56 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.65/41.56 inference(quant_inst,[status(thm)],[])).
% 64.65/41.56 tff(407,plain,
% 64.65/41.56 (is_a_theorem(implies(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.65/41.56 inference(unit_resolution,[status(thm)],[406, 405])).
% 64.65/41.56 tff(408,plain,
% 64.65/41.56 (is_a_theorem(implies(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.65/41.56 inference(modus_ponens,[status(thm)],[407, 389])).
% 64.65/41.56 tff(409,plain,
% 64.65/41.56 (is_a_theorem(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.65/41.56 inference(modus_ponens,[status(thm)],[408, 373])).
% 64.65/41.56 tff(410,plain,
% 64.65/41.56 (^[X: $i, Y: $i] : refl((is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X))) <=> (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X))))),
% 64.65/41.56 inference(bind,[status(th)],[])).
% 64.65/41.56 tff(411,plain,
% 64.65/41.56 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))),
% 64.65/41.56 inference(quant_intro,[status(thm)],[410])).
% 64.65/41.56 tff(412,plain,
% 64.65/41.56 (^[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(implies(X, Y))) | (~is_a_theorem(X)))), ((is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))))),
% 64.65/41.56 inference(bind,[status(th)],[])).
% 64.65/41.56 tff(413,plain,
% 64.65/41.56 (![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(implies(X, Y))) | (~is_a_theorem(X)))),
% 64.65/41.56 inference(quant_intro,[status(thm)],[412])).
% 64.65/41.56 tff(414,plain,
% 64.65/41.56 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 64.65/41.56 inference(rewrite,[status(thm)],[])).
% 64.65/41.56 tff(415,plain,
% 64.65/41.56 (($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)))))),
% 64.65/41.56 inference(rewrite,[status(thm)],[])).
% 64.65/41.56 tff(416,axiom,(modus_ponens), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_modus_ponens')).
% 64.65/41.56 tff(417,plain,
% 64.65/41.56 (modus_ponens <=> $true),
% 64.65/41.56 inference(iff_true,[status(thm)],[416])).
% 64.65/41.56 tff(418,plain,
% 64.65/41.56 ((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))))))),
% 64.65/41.56 inference(monotonicity,[status(thm)],[417])).
% 64.65/41.56 tff(419,plain,
% 64.65/41.56 ((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)))))),
% 64.65/41.56 inference(transitivity,[status(thm)],[418, 415])).
% 64.65/41.56 tff(420,plain,
% 64.65/41.56 ((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))))))),
% 64.65/41.56 inference(rewrite,[status(thm)],[])).
% 64.65/41.56 tff(421,plain,
% 64.65/41.56 ((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))))))),
% 64.65/41.56 inference(rewrite,[status(thm)],[])).
% 64.65/41.56 tff(422,axiom,(modus_ponens <=> ![X: $i, Y: $i] : ((is_a_theorem(X) & is_a_theorem(implies(X, Y))) => is_a_theorem(Y))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','modus_ponens')).
% 64.65/41.56 tff(423,plain,
% 64.65/41.56 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 64.65/41.56 inference(modus_ponens,[status(thm)],[422, 421])).
% 64.65/41.56 tff(424,plain,
% 64.65/41.56 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 64.65/41.56 inference(modus_ponens,[status(thm)],[423, 420])).
% 64.65/41.56 tff(425,plain,
% 64.65/41.56 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 64.65/41.56 inference(modus_ponens,[status(thm)],[424, 419])).
% 64.65/41.56 tff(426,plain,
% 64.65/41.56 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 64.65/41.56 inference(modus_ponens,[status(thm)],[425, 414])).
% 64.65/41.56 tff(427,plain,(
% 64.65/41.56 ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 64.65/41.56 inference(skolemize,[status(sab)],[426])).
% 64.65/41.56 tff(428,plain,
% 64.65/41.56 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))),
% 64.65/41.56 inference(modus_ponens,[status(thm)],[427, 413])).
% 64.65/41.56 tff(429,plain,
% 64.65/41.56 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))),
% 64.65/41.56 inference(modus_ponens,[status(thm)],[428, 411])).
% 64.65/41.56 tff(430,plain,
% 64.65/41.56 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))) | is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))) | is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))))),
% 64.65/41.57 inference(rewrite,[status(thm)],[])).
% 64.65/41.57 tff(431,plain,
% 64.65/41.57 ((is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))) | (~is_a_theorem(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))))) <=> ((~is_a_theorem(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))) | is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))))),
% 64.65/41.57 inference(rewrite,[status(thm)],[])).
% 64.65/41.57 tff(432,plain,
% 64.65/41.57 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))) | (~is_a_theorem(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))) | is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))))),
% 64.65/41.57 inference(monotonicity,[status(thm)],[431])).
% 64.65/41.57 tff(433,plain,
% 64.65/41.57 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))) | (~is_a_theorem(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))) | is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))))),
% 64.65/41.57 inference(transitivity,[status(thm)],[432, 430])).
% 64.65/41.57 tff(434,plain,
% 64.65/41.57 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))) | (~is_a_theorem(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))))),
% 64.65/41.57 inference(quant_inst,[status(thm)],[])).
% 64.65/41.57 tff(435,plain,
% 64.65/41.57 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))) | is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.65/41.57 inference(modus_ponens,[status(thm)],[434, 433])).
% 64.65/41.57 tff(436,plain,
% 64.65/41.57 ((~is_a_theorem(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))) | is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.65/41.57 inference(unit_resolution,[status(thm)],[435, 429])).
% 64.65/41.57 tff(437,plain,
% 64.65/41.57 (is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.65/41.57 inference(unit_resolution,[status(thm)],[436, 409, 368])).
% 64.65/41.57 tff(438,plain,
% 64.65/41.57 (is_a_theorem(implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.65/41.57 inference(modus_ponens,[status(thm)],[437, 302])).
% 64.65/41.57 tff(439,plain,
% 64.65/41.57 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), or(not(not(P!1)), not(and(P!1, Q!0)))) = or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))))),
% 64.65/41.57 inference(quant_inst,[status(thm)],[])).
% 64.65/41.57 tff(440,plain,
% 64.65/41.57 (implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), or(not(not(P!1)), not(and(P!1, Q!0)))) = or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))),
% 64.65/41.57 inference(unit_resolution,[status(thm)],[439, 20])).
% 64.65/41.57 tff(441,plain,
% 64.65/41.57 (or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))) = implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), or(not(not(P!1)), not(and(P!1, Q!0))))),
% 64.65/41.57 inference(symmetry,[status(thm)],[440])).
% 64.65/41.57 tff(442,plain,
% 64.65/41.57 (is_a_theorem(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))) <=> is_a_theorem(implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), or(not(not(P!1)), not(and(P!1, Q!0)))))),
% 64.65/41.57 inference(monotonicity,[status(thm)],[441])).
% 64.65/41.57 tff(443,plain,
% 64.65/41.57 (is_a_theorem(implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), or(not(not(P!1)), not(and(P!1, Q!0))))) <=> is_a_theorem(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))))),
% 64.65/41.57 inference(symmetry,[status(thm)],[442])).
% 64.65/41.57 tff(444,plain,
% 64.65/41.57 (not(and(P!1, Q!0)) = not(not(or(not(P!1), not(Q!0))))),
% 64.65/41.57 inference(symmetry,[status(thm)],[128])).
% 64.65/41.57 tff(445,plain,
% 64.65/41.58 (or(not(and(P!1, Q!0)), not(not(P!1))) = or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))),
% 64.65/41.58 inference(monotonicity,[status(thm)],[444])).
% 64.65/41.58 tff(446,plain,
% 64.65/41.58 (implies(or(not(and(P!1, Q!0)), not(not(P!1))), or(not(not(P!1)), not(and(P!1, Q!0)))) = implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), or(not(not(P!1)), not(and(P!1, Q!0))))),
% 64.65/41.58 inference(monotonicity,[status(thm)],[445])).
% 64.65/41.58 tff(447,plain,
% 64.65/41.58 (is_a_theorem(implies(or(not(and(P!1, Q!0)), not(not(P!1))), or(not(not(P!1)), not(and(P!1, Q!0))))) <=> is_a_theorem(implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), or(not(not(P!1)), not(and(P!1, Q!0)))))),
% 64.65/41.58 inference(monotonicity,[status(thm)],[446])).
% 64.65/41.58 tff(448,plain,
% 64.65/41.58 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(and(P!1, Q!0)), not(not(P!1))), or(not(not(P!1)), not(and(P!1, Q!0)))))),
% 64.65/41.58 inference(quant_inst,[status(thm)],[])).
% 64.65/41.58 tff(449,plain,
% 64.65/41.58 (is_a_theorem(implies(or(not(and(P!1, Q!0)), not(not(P!1))), or(not(not(P!1)), not(and(P!1, Q!0)))))),
% 64.65/41.58 inference(unit_resolution,[status(thm)],[448, 405])).
% 64.65/41.58 tff(450,plain,
% 64.65/41.58 (is_a_theorem(implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), or(not(not(P!1)), not(and(P!1, Q!0)))))),
% 64.65/41.58 inference(modus_ponens,[status(thm)],[449, 447])).
% 64.65/41.58 tff(451,plain,
% 64.65/41.58 (is_a_theorem(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))))),
% 64.65/41.58 inference(modus_ponens,[status(thm)],[450, 443])).
% 64.65/41.58 tff(452,plain,
% 64.65/41.58 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))))) | is_a_theorem(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) | (~is_a_theorem(implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))))) | is_a_theorem(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) | (~is_a_theorem(implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.65/41.58 inference(rewrite,[status(thm)],[])).
% 64.65/41.58 tff(453,plain,
% 64.65/41.58 ((is_a_theorem(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) | (~is_a_theorem(implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))) | (~is_a_theorem(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))))) <=> ((~is_a_theorem(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))))) | is_a_theorem(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) | (~is_a_theorem(implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.65/41.58 inference(rewrite,[status(thm)],[])).
% 64.65/41.58 tff(454,plain,
% 64.65/41.58 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) | (~is_a_theorem(implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))) | (~is_a_theorem(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))))) | is_a_theorem(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) | (~is_a_theorem(implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))))),
% 64.65/41.58 inference(monotonicity,[status(thm)],[453])).
% 64.65/41.58 tff(455,plain,
% 64.65/41.58 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) | (~is_a_theorem(implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))) | (~is_a_theorem(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))))) | is_a_theorem(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) | (~is_a_theorem(implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.65/41.58 inference(transitivity,[status(thm)],[454, 452])).
% 64.65/41.58 tff(456,plain,
% 64.65/41.58 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) | (~is_a_theorem(implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))) | (~is_a_theorem(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))))))),
% 64.65/41.58 inference(quant_inst,[status(thm)],[])).
% 64.65/41.58 tff(457,plain,
% 64.65/41.58 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))))) | is_a_theorem(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) | (~is_a_theorem(implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.58 inference(modus_ponens,[status(thm)],[456, 455])).
% 64.65/41.58 tff(458,plain,
% 64.65/41.58 (is_a_theorem(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) | (~is_a_theorem(implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.58 inference(unit_resolution,[status(thm)],[457, 429, 451])).
% 64.65/41.58 tff(459,plain,
% 64.65/41.58 (is_a_theorem(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.65/41.58 inference(unit_resolution,[status(thm)],[458, 438])).
% 64.65/41.58 tff(460,plain,
% 64.65/41.58 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))))),
% 64.65/41.58 inference(quant_inst,[status(thm)],[])).
% 64.65/41.58 tff(461,plain,
% 64.65/41.58 (is_a_theorem(implies(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))))),
% 64.65/41.58 inference(unit_resolution,[status(thm)],[460, 405])).
% 64.65/41.58 tff(462,plain,
% 64.65/41.58 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))) | (~is_a_theorem(implies(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))))) | (~is_a_theorem(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | is_a_theorem(or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))) | (~is_a_theorem(implies(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))))) | (~is_a_theorem(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.58 inference(rewrite,[status(thm)],[])).
% 64.65/41.58 tff(463,plain,
% 64.65/41.58 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))) | (~is_a_theorem(implies(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))))) | (~is_a_theorem(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.58 inference(quant_inst,[status(thm)],[])).
% 64.65/41.58 tff(464,plain,
% 64.65/41.58 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | is_a_theorem(or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))) | (~is_a_theorem(implies(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))))) | (~is_a_theorem(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.65/41.58 inference(modus_ponens,[status(thm)],[463, 462])).
% 64.65/41.58 tff(465,plain,
% 64.65/41.58 (is_a_theorem(or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))) | (~is_a_theorem(or(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))), and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.65/41.58 inference(unit_resolution,[status(thm)],[464, 429, 461])).
% 64.65/41.58 tff(466,plain,
% 64.65/41.58 (is_a_theorem(or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))))),
% 64.65/41.58 inference(unit_resolution,[status(thm)],[465, 459])).
% 64.65/41.58 tff(467,plain,
% 64.65/41.58 (is_a_theorem(implies(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))))),
% 64.65/41.58 inference(modus_ponens,[status(thm)],[466, 279])).
% 64.65/41.58 tff(468,plain,
% 64.65/41.58 (not(or(P!1, not(and(P!1, Q!0)))) = not(not(and(not(P!1), not(not(and(P!1, Q!0))))))),
% 64.65/41.58 inference(symmetry,[status(thm)],[165])).
% 64.65/41.58 tff(469,plain,
% 64.65/41.58 (or(not(or(P!1, not(and(P!1, Q!0)))), not(not(or(not(and(P!1, Q!0)), P!1)))) = or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))),
% 64.65/41.58 inference(monotonicity,[status(thm)],[468])).
% 64.65/41.58 tff(470,plain,
% 64.65/41.58 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(P!1, not(and(P!1, Q!0)))), not(not(or(not(and(P!1, Q!0)), P!1)))) = not(and(not(not(or(P!1, not(and(P!1, Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.58 inference(quant_inst,[status(thm)],[])).
% 64.65/41.58 tff(471,plain,
% 64.65/41.58 (or(not(or(P!1, not(and(P!1, Q!0)))), not(not(or(not(and(P!1, Q!0)), P!1)))) = not(and(not(not(or(P!1, not(and(P!1, Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.65/41.58 inference(unit_resolution,[status(thm)],[470, 42])).
% 64.65/41.58 tff(472,plain,
% 64.65/41.58 (not(and(not(not(or(P!1, not(and(P!1, Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))) = or(not(or(P!1, not(and(P!1, Q!0)))), not(not(or(not(and(P!1, Q!0)), P!1))))),
% 64.65/41.58 inference(symmetry,[status(thm)],[471])).
% 64.65/41.58 tff(473,plain,
% 64.65/41.58 (not(and(not(P!1), not(or(not(P!1), not(Q!0))))) = not(not(or(P!1, not(and(P!1, Q!0)))))),
% 64.65/41.58 inference(symmetry,[status(thm)],[134])).
% 64.65/41.58 tff(474,plain,
% 64.65/41.58 (and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1))))) = and(not(not(or(P!1, not(and(P!1, Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.65/41.58 inference(monotonicity,[status(thm)],[473])).
% 64.65/41.58 tff(475,plain,
% 64.65/41.58 (not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))) = not(and(not(not(or(P!1, not(and(P!1, Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.65/41.58 inference(monotonicity,[status(thm)],[474])).
% 64.65/41.58 tff(476,plain,
% 64.65/41.58 (not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))) = or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))),
% 64.65/41.58 inference(transitivity,[status(thm)],[475, 472, 469])).
% 64.65/41.58 tff(477,plain,
% 64.65/41.58 (is_a_theorem(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1))))))) <=> is_a_theorem(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.65/41.58 inference(monotonicity,[status(thm)],[476])).
% 64.65/41.58 tff(478,plain,
% 64.65/41.58 (is_a_theorem(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))) <=> is_a_theorem(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.58 inference(symmetry,[status(thm)],[477])).
% 64.65/41.58 tff(479,plain,
% 64.65/41.58 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))) = not(and(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.65/41.59 inference(quant_inst,[status(thm)],[])).
% 64.65/41.59 tff(480,plain,
% 64.65/41.59 (or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))) = not(and(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))),
% 64.65/41.59 inference(unit_resolution,[status(thm)],[479, 42])).
% 64.65/41.59 tff(481,plain,
% 64.65/41.59 (not(and(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))) = or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))),
% 64.65/41.59 inference(symmetry,[status(thm)],[480])).
% 64.65/41.59 tff(482,plain,
% 64.65/41.59 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(or(not(and(P!1, Q!0)), P!1)), not(or(P!1, not(and(P!1, Q!0))))) = not(and(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.65/41.59 inference(quant_inst,[status(thm)],[])).
% 64.65/41.59 tff(483,plain,
% 64.65/41.59 (implies(not(or(not(and(P!1, Q!0)), P!1)), not(or(P!1, not(and(P!1, Q!0))))) = not(and(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))),
% 64.65/41.59 inference(unit_resolution,[status(thm)],[482, 91])).
% 64.65/41.59 tff(484,plain,
% 64.65/41.59 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(not(and(P!1, Q!0)), P!1)), not(or(P!1, not(and(P!1, Q!0))))) = or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))))),
% 64.65/41.59 inference(quant_inst,[status(thm)],[])).
% 64.65/41.59 tff(485,plain,
% 64.65/41.59 (implies(not(or(not(and(P!1, Q!0)), P!1)), not(or(P!1, not(and(P!1, Q!0))))) = or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0)))))),
% 64.65/41.59 inference(unit_resolution,[status(thm)],[484, 20])).
% 64.65/41.59 tff(486,plain,
% 64.65/41.59 (or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))) = implies(not(or(not(and(P!1, Q!0)), P!1)), not(or(P!1, not(and(P!1, Q!0)))))),
% 64.65/41.59 inference(symmetry,[status(thm)],[485])).
% 64.65/41.59 tff(487,plain,
% 64.65/41.59 (or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))) = or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))),
% 64.65/41.59 inference(transitivity,[status(thm)],[486, 483, 481])).
% 64.65/41.59 tff(488,plain,
% 64.65/41.59 (is_a_theorem(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0)))))) <=> is_a_theorem(or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))),
% 64.65/41.59 inference(monotonicity,[status(thm)],[487])).
% 64.65/41.59 tff(489,plain,
% 64.65/41.59 (is_a_theorem(or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))) <=> is_a_theorem(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))))),
% 64.65/41.59 inference(symmetry,[status(thm)],[488])).
% 64.65/41.59 tff(490,plain,
% 64.65/41.59 (is_a_theorem(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))) <=> is_a_theorem(implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)))),
% 64.65/41.59 inference(monotonicity,[status(thm)],[310])).
% 64.65/41.59 tff(491,plain,
% 64.65/41.59 (is_a_theorem(implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1))) <=> is_a_theorem(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)))),
% 64.65/41.59 inference(symmetry,[status(thm)],[490])).
% 64.65/41.59 tff(492,plain,
% 64.65/41.59 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)))),
% 64.65/41.59 inference(quant_inst,[status(thm)],[])).
% 64.65/41.59 tff(493,plain,
% 64.65/41.59 (is_a_theorem(implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)))),
% 64.65/41.59 inference(unit_resolution,[status(thm)],[492, 405])).
% 64.65/41.59 tff(494,plain,
% 64.65/41.59 (is_a_theorem(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)))),
% 64.65/41.59 inference(modus_ponens,[status(thm)],[493, 491])).
% 64.65/41.59 tff(495,plain,
% 64.65/41.59 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))),
% 64.65/41.59 inference(quant_inst,[status(thm)],[])).
% 64.65/41.59 tff(496,plain,
% 64.65/41.59 (is_a_theorem(implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))),
% 64.65/41.59 inference(unit_resolution,[status(thm)],[495, 405])).
% 64.65/41.59 tff(497,plain,
% 64.65/41.59 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)))) | is_a_theorem(or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))) | (~is_a_theorem(implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)))) | is_a_theorem(or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))) | (~is_a_theorem(implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.65/41.59 inference(rewrite,[status(thm)],[])).
% 64.65/41.59 tff(498,plain,
% 64.65/41.59 ((is_a_theorem(or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))) | (~is_a_theorem(implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))) | (~is_a_theorem(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))))) <=> ((~is_a_theorem(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)))) | is_a_theorem(or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))) | (~is_a_theorem(implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.65/41.59 inference(rewrite,[status(thm)],[])).
% 64.65/41.59 tff(499,plain,
% 64.65/41.59 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))) | (~is_a_theorem(implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))) | (~is_a_theorem(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)))) | is_a_theorem(or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))) | (~is_a_theorem(implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.65/41.59 inference(monotonicity,[status(thm)],[498])).
% 64.65/41.59 tff(500,plain,
% 64.65/41.59 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))) | (~is_a_theorem(implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))) | (~is_a_theorem(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)))) | is_a_theorem(or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))) | (~is_a_theorem(implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.65/41.59 inference(transitivity,[status(thm)],[499, 497])).
% 64.65/41.59 tff(501,plain,
% 64.65/41.59 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))) | (~is_a_theorem(implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))) | (~is_a_theorem(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)))))),
% 64.65/41.59 inference(quant_inst,[status(thm)],[])).
% 64.65/41.59 tff(502,plain,
% 64.65/41.59 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)))) | is_a_theorem(or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))) | (~is_a_theorem(implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.65/41.59 inference(modus_ponens,[status(thm)],[501, 500])).
% 64.65/41.59 tff(503,plain,
% 64.65/41.59 ((~is_a_theorem(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)))) | is_a_theorem(or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))),
% 64.65/41.59 inference(unit_resolution,[status(thm)],[502, 429, 496])).
% 64.65/41.59 tff(504,plain,
% 64.65/41.59 (is_a_theorem(or(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))),
% 64.65/41.59 inference(unit_resolution,[status(thm)],[503, 494])).
% 64.65/41.59 tff(505,plain,
% 64.65/41.59 (is_a_theorem(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))))),
% 64.65/41.59 inference(modus_ponens,[status(thm)],[504, 489])).
% 64.65/41.59 tff(506,plain,
% 64.65/41.59 (implies(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))), or(not(or(P!1, not(and(P!1, Q!0)))), not(not(or(not(and(P!1, Q!0)), P!1))))) = implies(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))), or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.65/41.59 inference(monotonicity,[status(thm)],[469])).
% 64.65/41.59 tff(507,plain,
% 64.65/41.59 (is_a_theorem(implies(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))), or(not(or(P!1, not(and(P!1, Q!0)))), not(not(or(not(and(P!1, Q!0)), P!1)))))) <=> is_a_theorem(implies(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))), or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.65/41.59 inference(monotonicity,[status(thm)],[506])).
% 64.65/41.59 tff(508,plain,
% 64.65/41.59 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))), or(not(or(P!1, not(and(P!1, Q!0)))), not(not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.65/41.59 inference(quant_inst,[status(thm)],[])).
% 64.65/41.59 tff(509,plain,
% 64.65/41.59 (is_a_theorem(implies(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))), or(not(or(P!1, not(and(P!1, Q!0)))), not(not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.65/41.59 inference(unit_resolution,[status(thm)],[508, 405])).
% 64.65/41.59 tff(510,plain,
% 64.65/41.59 (is_a_theorem(implies(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))), or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.65/41.59 inference(modus_ponens,[status(thm)],[509, 507])).
% 64.65/41.59 tff(511,plain,
% 64.65/41.59 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))) | (~is_a_theorem(implies(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))), or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))) | (~is_a_theorem(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | is_a_theorem(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))) | (~is_a_theorem(implies(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))), or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))) | (~is_a_theorem(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.65/41.59 inference(rewrite,[status(thm)],[])).
% 64.65/41.59 tff(512,plain,
% 64.65/41.59 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))) | (~is_a_theorem(implies(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))), or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))) | (~is_a_theorem(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.65/41.59 inference(quant_inst,[status(thm)],[])).
% 64.65/41.59 tff(513,plain,
% 64.65/41.59 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | is_a_theorem(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))) | (~is_a_theorem(implies(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))), or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))) | (~is_a_theorem(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0)))))))),
% 64.65/41.59 inference(modus_ponens,[status(thm)],[512, 511])).
% 64.65/41.59 tff(514,plain,
% 64.65/41.59 (is_a_theorem(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))) | (~is_a_theorem(implies(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))), or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))) | (~is_a_theorem(or(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0)))))))),
% 64.65/41.59 inference(unit_resolution,[status(thm)],[513, 429])).
% 64.65/41.59 tff(515,plain,
% 64.65/41.59 (is_a_theorem(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.65/41.59 inference(unit_resolution,[status(thm)],[514, 510, 505])).
% 64.65/41.59 tff(516,plain,
% 64.65/41.59 (is_a_theorem(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.59 inference(modus_ponens,[status(thm)],[515, 478])).
% 64.65/41.59 tff(517,plain,
% 64.65/41.59 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))))) | is_a_theorem(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) | (~is_a_theorem(implies(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))))) | is_a_theorem(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) | (~is_a_theorem(implies(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))))))),
% 64.65/41.59 inference(rewrite,[status(thm)],[])).
% 64.65/41.59 tff(518,plain,
% 64.65/41.59 ((is_a_theorem(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) | (~is_a_theorem(implies(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))))) | (~is_a_theorem(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1))))))))) <=> ((~is_a_theorem(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))))) | is_a_theorem(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) | (~is_a_theorem(implies(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))))))),
% 64.65/41.59 inference(rewrite,[status(thm)],[])).
% 64.65/41.59 tff(519,plain,
% 64.65/41.59 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) | (~is_a_theorem(implies(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))))) | (~is_a_theorem(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))))) | is_a_theorem(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) | (~is_a_theorem(implies(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))))))),
% 64.65/41.59 inference(monotonicity,[status(thm)],[518])).
% 64.65/41.59 tff(520,plain,
% 64.65/41.59 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) | (~is_a_theorem(implies(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))))) | (~is_a_theorem(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))))) | is_a_theorem(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) | (~is_a_theorem(implies(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))))))),
% 64.65/41.59 inference(transitivity,[status(thm)],[519, 517])).
% 64.65/41.59 tff(521,plain,
% 64.65/41.59 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) | (~is_a_theorem(implies(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))))) | (~is_a_theorem(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))))))),
% 64.65/41.59 inference(quant_inst,[status(thm)],[])).
% 64.65/41.59 tff(522,plain,
% 64.65/41.59 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))))) | is_a_theorem(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) | (~is_a_theorem(implies(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))))),
% 64.65/41.60 inference(modus_ponens,[status(thm)],[521, 520])).
% 64.65/41.60 tff(523,plain,
% 64.65/41.60 (is_a_theorem(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) | (~is_a_theorem(implies(not(and(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(not(or(not(and(P!1, Q!0)), P!1)))))), and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))))),
% 64.65/41.60 inference(unit_resolution,[status(thm)],[522, 429, 516])).
% 64.65/41.60 tff(524,plain,
% 64.65/41.60 (is_a_theorem(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))))),
% 64.65/41.60 inference(unit_resolution,[status(thm)],[523, 467])).
% 64.65/41.60 tff(525,plain,
% 64.65/41.60 (is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.65/41.60 inference(modus_ponens,[status(thm)],[524, 260])).
% 64.65/41.60 tff(526,plain,
% 64.65/41.60 (^[X: $i, Y: $i] : refl(((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ((~is_a_theorem(equiv(X, Y))) | (X = Y)))),
% 64.65/41.60 inference(bind,[status(th)],[])).
% 64.65/41.60 tff(527,plain,
% 64.65/41.60 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 64.65/41.60 inference(quant_intro,[status(thm)],[526])).
% 64.65/41.60 tff(528,plain,
% 64.65/41.60 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 64.65/41.60 inference(rewrite,[status(thm)],[])).
% 64.65/41.60 tff(529,plain,
% 64.65/41.60 (($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))),
% 64.65/41.60 inference(rewrite,[status(thm)],[])).
% 64.65/41.60 tff(530,axiom,(substitution_of_equivalents), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','substitution_of_equivalents')).
% 64.65/41.60 tff(531,plain,
% 64.65/41.60 (substitution_of_equivalents <=> $true),
% 64.65/41.60 inference(iff_true,[status(thm)],[530])).
% 64.65/41.60 tff(532,plain,
% 64.65/41.60 ((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)))),
% 64.65/41.60 inference(monotonicity,[status(thm)],[531])).
% 64.65/41.60 tff(533,plain,
% 64.65/41.60 ((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))),
% 64.65/41.60 inference(transitivity,[status(thm)],[532, 529])).
% 64.65/41.60 tff(534,plain,
% 64.65/41.60 ((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)))),
% 64.65/41.60 inference(rewrite,[status(thm)],[])).
% 64.65/41.60 tff(535,plain,
% 64.65/41.60 ((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)))),
% 64.65/41.60 inference(rewrite,[status(thm)],[])).
% 64.65/41.60 tff(536,axiom,(substitution_of_equivalents <=> ![X: $i, Y: $i] : (is_a_theorem(equiv(X, Y)) => (X = Y))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','substitution_of_equivalents')).
% 64.65/41.60 tff(537,plain,
% 64.65/41.60 (substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 64.65/41.60 inference(modus_ponens,[status(thm)],[536, 535])).
% 64.65/41.60 tff(538,plain,
% 64.65/41.60 (substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 64.65/41.60 inference(modus_ponens,[status(thm)],[537, 534])).
% 64.65/41.60 tff(539,plain,
% 64.65/41.60 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 64.65/41.60 inference(modus_ponens,[status(thm)],[538, 533])).
% 64.65/41.60 tff(540,plain,
% 64.65/41.60 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 64.65/41.60 inference(modus_ponens,[status(thm)],[539, 528])).
% 64.65/41.60 tff(541,plain,(
% 64.65/41.60 ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 64.65/41.60 inference(skolemize,[status(sab)],[540])).
% 64.65/41.60 tff(542,plain,
% 64.65/41.60 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 64.65/41.60 inference(modus_ponens,[status(thm)],[541, 527])).
% 64.65/41.60 tff(543,plain,
% 64.65/41.60 (((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))) | (not(and(not(P!1), not(or(not(P!1), not(Q!0))))) = or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))) <=> ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))) | (not(and(not(P!1), not(or(not(P!1), not(Q!0))))) = or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.65/41.60 inference(rewrite,[status(thm)],[])).
% 64.65/41.60 tff(544,plain,
% 64.65/41.60 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))) | (not(and(not(P!1), not(or(not(P!1), not(Q!0))))) = or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.65/41.60 inference(quant_inst,[status(thm)],[])).
% 64.65/41.60 tff(545,plain,
% 64.65/41.60 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))) | (not(and(not(P!1), not(or(not(P!1), not(Q!0))))) = or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))),
% 64.65/41.60 inference(modus_ponens,[status(thm)],[544, 543])).
% 64.65/41.60 tff(546,plain,
% 64.65/41.60 ((~is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))) | (not(and(not(P!1), not(or(not(P!1), not(Q!0))))) = or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))),
% 64.65/41.60 inference(unit_resolution,[status(thm)],[545, 542])).
% 64.65/41.60 tff(547,plain,
% 64.65/41.60 (not(and(not(P!1), not(or(not(P!1), not(Q!0))))) = or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))),
% 64.65/41.60 inference(unit_resolution,[status(thm)],[546, 525])).
% 64.65/41.60 tff(548,plain,
% 64.65/41.60 (or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0)))) = implies(or(not(and(P!1, Q!0)), P!1), or(P!1, not(and(P!1, Q!0))))),
% 64.65/41.60 inference(symmetry,[status(thm)],[281])).
% 64.65/41.60 tff(549,plain,
% 64.65/41.60 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0)))))) = not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0)))))))))),
% 64.65/41.60 inference(quant_inst,[status(thm)],[])).
% 64.65/41.60 tff(550,plain,
% 64.65/41.60 (or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0)))))) = not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0))))))))),
% 64.65/41.60 inference(unit_resolution,[status(thm)],[549, 42])).
% 64.65/41.60 tff(551,plain,
% 64.65/41.60 (not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0)))))))) = or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))),
% 64.65/41.60 inference(symmetry,[status(thm)],[550])).
% 64.65/41.60 tff(552,plain,
% 64.65/41.60 (not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0)))))))) = implies(or(not(and(P!1, Q!0)), P!1), or(P!1, not(and(P!1, Q!0))))),
% 64.65/41.60 inference(transitivity,[status(thm)],[551, 293, 548])).
% 64.65/41.60 tff(553,plain,
% 64.65/41.60 (and(not(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0))))))))) = and(implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, not(and(P!1, Q!0)))))),
% 64.65/41.60 inference(monotonicity,[status(thm)],[312, 552])).
% 64.65/41.60 tff(554,plain,
% 64.65/41.60 (and(not(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0))))))))) = and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))),
% 64.65/41.60 inference(transitivity,[status(thm)],[553, 335])).
% 64.65/41.60 tff(555,plain,
% 64.65/41.60 (not(and(not(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0)))))))))) = not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.65/41.60 inference(monotonicity,[status(thm)],[554])).
% 64.65/41.60 tff(556,plain,
% 64.65/41.60 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0)))))))) = not(and(not(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0)))))))))))),
% 64.65/41.60 inference(quant_inst,[status(thm)],[])).
% 64.65/41.60 tff(557,plain,
% 64.65/41.60 (or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0)))))))) = not(and(not(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0))))))))))),
% 64.65/41.60 inference(unit_resolution,[status(thm)],[556, 42])).
% 64.65/41.60 tff(558,plain,
% 64.65/41.60 (and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0))))))) = and(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0)))))),
% 64.65/41.60 inference(monotonicity,[status(thm)],[165])).
% 64.65/41.60 tff(559,plain,
% 64.65/41.60 (and(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))) = and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0)))))))),
% 64.65/41.60 inference(symmetry,[status(thm)],[558])).
% 64.65/41.60 tff(560,plain,
% 64.65/41.60 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))) = not(or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.65/41.60 inference(quant_inst,[status(thm)],[])).
% 64.65/41.60 tff(561,plain,
% 64.65/41.60 (and(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0))))) = not(or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(not(or(P!1, not(and(P!1, Q!0)))))))),
% 64.65/41.60 inference(unit_resolution,[status(thm)],[560, 113])).
% 64.65/41.60 tff(562,plain,
% 64.65/41.60 (not(or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(not(or(P!1, not(and(P!1, Q!0))))))) = and(not(not(or(not(and(P!1, Q!0)), P!1))), not(or(P!1, not(and(P!1, Q!0)))))),
% 64.65/41.60 inference(symmetry,[status(thm)],[561])).
% 64.65/41.60 tff(563,plain,
% 64.65/41.60 (not(or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(not(or(P!1, not(and(P!1, Q!0))))))) = and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0)))))))),
% 64.65/41.60 inference(transitivity,[status(thm)],[562, 559])).
% 64.65/41.60 tff(564,plain,
% 64.65/41.60 (not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))) = and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1)))),
% 64.65/41.60 inference(transitivity,[status(thm)],[265, 262])).
% 64.65/41.60 tff(565,plain,
% 64.65/41.60 (or(not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))), not(or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(not(or(P!1, not(and(P!1, Q!0)))))))) = or(and(or(P!1, or(not(P!1), not(Q!0))), not(or(not(and(P!1, Q!0)), P!1))), and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0))))))))),
% 64.65/41.60 inference(monotonicity,[status(thm)],[564, 563])).
% 64.65/41.60 tff(566,plain,
% 64.65/41.60 (or(not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))), not(or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(not(or(P!1, not(and(P!1, Q!0)))))))) = or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))))),
% 64.65/41.60 inference(transitivity,[status(thm)],[565, 557, 555, 339, 333, 330, 325, 151])).
% 64.65/41.60 tff(567,plain,
% 64.65/41.60 (not(or(not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))), not(or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(not(or(P!1, not(and(P!1, Q!0))))))))) = not(or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))))),
% 64.65/41.60 inference(monotonicity,[status(thm)],[566])).
% 64.65/41.60 tff(568,plain,
% 64.65/41.60 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))), or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(not(or(P!1, not(and(P!1, Q!0))))))) = not(or(not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))), not(or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.65/41.60 inference(quant_inst,[status(thm)],[])).
% 64.65/41.60 tff(569,plain,
% 64.65/41.60 (and(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))), or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(not(or(P!1, not(and(P!1, Q!0))))))) = not(or(not(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))), not(or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.65/41.60 inference(unit_resolution,[status(thm)],[568, 113])).
% 64.65/41.60 tff(570,plain,
% 64.65/41.60 (or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(not(or(P!1, not(and(P!1, Q!0)))))) = or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(and(not(P!1), not(or(not(P!1), not(Q!0))))))),
% 64.65/41.60 inference(monotonicity,[status(thm)],[134])).
% 64.65/41.60 tff(571,plain,
% 64.65/41.60 (or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))) = or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(not(or(P!1, not(and(P!1, Q!0))))))),
% 64.65/41.60 inference(symmetry,[status(thm)],[570])).
% 64.65/41.60 tff(572,plain,
% 64.65/41.60 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))) = or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))))),
% 64.65/41.60 inference(quant_inst,[status(thm)],[])).
% 64.65/41.60 tff(573,plain,
% 64.65/41.60 (implies(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))) = or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(and(not(P!1), not(or(not(P!1), not(Q!0))))))),
% 64.65/41.60 inference(unit_resolution,[status(thm)],[572, 20])).
% 64.65/41.60 tff(574,plain,
% 64.65/41.60 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))) = not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))))))),
% 64.65/41.60 inference(quant_inst,[status(thm)],[])).
% 64.65/41.60 tff(575,plain,
% 64.65/41.60 (implies(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))) = not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(or(not(P!1), not(Q!0))))))))),
% 64.65/41.60 inference(unit_resolution,[status(thm)],[574, 91])).
% 64.65/41.60 tff(576,plain,
% 64.65/41.60 (not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))))) = implies(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(or(not(P!1), not(Q!0))))))),
% 64.65/41.60 inference(symmetry,[status(thm)],[575])).
% 64.65/41.60 tff(577,plain,
% 64.65/41.60 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))) = not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))))))),
% 64.65/41.60 inference(quant_inst,[status(thm)],[])).
% 64.65/41.60 tff(578,plain,
% 64.65/41.60 (or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))) = not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(or(not(P!1), not(Q!0))))))))),
% 64.65/41.60 inference(unit_resolution,[status(thm)],[577, 42])).
% 64.65/41.60 tff(579,plain,
% 64.65/41.60 (or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))) = or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))),
% 64.65/41.60 inference(monotonicity,[status(thm)],[45])).
% 64.65/41.60 tff(580,plain,
% 64.65/41.60 (or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))) = or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(or(not(P!1), not(Q!0))))))),
% 64.65/41.60 inference(symmetry,[status(thm)],[579])).
% 64.65/41.60 tff(581,plain,
% 64.65/41.60 (or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))) = or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(not(or(P!1, not(and(P!1, Q!0))))))),
% 64.65/41.60 inference(transitivity,[status(thm)],[580, 578, 576, 573, 571])).
% 64.65/41.60 tff(582,plain,
% 64.65/41.60 (and(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))), or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))) = and(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))), or(not(not(not(or(not(and(P!1, Q!0)), P!1)))), not(not(or(P!1, not(and(P!1, Q!0)))))))),
% 64.65/41.60 inference(monotonicity,[status(thm)],[581])).
% 64.65/41.60 tff(583,plain,
% 64.65/41.60 (not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))))) = or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(or(not(P!1), not(Q!0))))))),
% 64.65/41.60 inference(symmetry,[status(thm)],[578])).
% 64.65/41.60 tff(584,plain,
% 64.65/41.60 (implies(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))) = or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))),
% 64.65/41.60 inference(transitivity,[status(thm)],[575, 583, 579])).
% 64.65/41.60 tff(585,plain,
% 64.65/41.60 (and(implies(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))), implies(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(or(not(P!1), not(Q!0))))))) = and(or(not(not(and(not(P!1), not(or(not(P!1), not(Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))), or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))),
% 64.65/41.60 inference(monotonicity,[status(thm)],[267, 584])).
% 64.65/41.60 tff(586,plain,
% 64.65/41.60 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))) = and(implies(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))), implies(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(or(not(P!1), not(Q!0))))))))),
% 64.65/41.60 inference(quant_inst,[status(thm)],[])).
% 64.65/41.60 tff(587,plain,
% 64.65/41.60 (equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))) = and(implies(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))), implies(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(or(not(P!1), not(Q!0)))))))),
% 64.65/41.60 inference(unit_resolution,[status(thm)],[586, 66])).
% 64.65/41.60 tff(588,plain,
% 64.65/41.60 (equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))) = equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(and(P!1, Q!0)), P!1))),
% 64.65/41.60 inference(transitivity,[status(thm)],[587, 585, 582, 569, 567, 146, 143, 69, 47])).
% 64.65/41.60 tff(589,plain,
% 64.65/41.60 (is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1))))) <=> is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(and(P!1, Q!0)), P!1)))),
% 64.65/41.60 inference(monotonicity,[status(thm)],[588])).
% 64.65/41.60 tff(590,plain,
% 64.65/41.60 (is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), or(not(and(P!1, Q!0)), P!1))) <=> is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.65/41.60 inference(symmetry,[status(thm)],[589])).
% 64.65/41.60 tff(591,plain,
% 64.65/41.60 (is_a_theorem(and(implies(or(P!1, or(not(P!1), not(Q!0))), or(not(and(P!1, Q!0)), P!1)), implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))) <=> is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.65/41.60 inference(transitivity,[status(thm)],[259, 590])).
% 64.65/41.60 tff(592,plain,
% 64.65/41.60 (is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.65/41.60 inference(modus_ponens,[status(thm)],[524, 591])).
% 64.65/41.60 tff(593,plain,
% 64.65/41.60 (((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))))) | (not(and(not(P!1), not(or(not(P!1), not(Q!0))))) = not(not(or(not(and(P!1, Q!0)), P!1)))))) <=> ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))))) | (not(and(not(P!1), not(or(not(P!1), not(Q!0))))) = not(not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.65/41.61 inference(rewrite,[status(thm)],[])).
% 64.65/41.61 tff(594,plain,
% 64.65/41.61 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))))) | (not(and(not(P!1), not(or(not(P!1), not(Q!0))))) = not(not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.65/41.61 inference(quant_inst,[status(thm)],[])).
% 64.65/41.61 tff(595,plain,
% 64.65/41.61 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))))) | (not(and(not(P!1), not(or(not(P!1), not(Q!0))))) = not(not(or(not(and(P!1, Q!0)), P!1))))),
% 64.65/41.61 inference(modus_ponens,[status(thm)],[594, 593])).
% 64.65/41.61 tff(596,plain,
% 64.65/41.61 ((~is_a_theorem(equiv(not(and(not(P!1), not(or(not(P!1), not(Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))))) | (not(and(not(P!1), not(or(not(P!1), not(Q!0))))) = not(not(or(not(and(P!1, Q!0)), P!1))))),
% 64.65/41.61 inference(unit_resolution,[status(thm)],[595, 542])).
% 64.65/41.61 tff(597,plain,
% 64.65/41.61 (not(and(not(P!1), not(or(not(P!1), not(Q!0))))) = not(not(or(not(and(P!1, Q!0)), P!1)))),
% 64.65/41.61 inference(unit_resolution,[status(thm)],[596, 592])).
% 64.65/41.61 tff(598,plain,
% 64.65/41.61 (not(not(or(not(and(P!1, Q!0)), P!1))) = not(and(not(P!1), not(or(not(P!1), not(Q!0)))))),
% 64.65/41.61 inference(symmetry,[status(thm)],[597])).
% 64.65/41.61 tff(599,plain,
% 64.65/41.61 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0)))))) = and(implies(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0)))))), implies(not(and(not(P!1), not(not(and(P!1, Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.65/41.61 inference(quant_inst,[status(thm)],[])).
% 64.65/41.61 tff(600,plain,
% 64.65/41.61 (equiv(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0)))))) = and(implies(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0)))))), implies(not(and(not(P!1), not(not(and(P!1, Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.65/41.61 inference(unit_resolution,[status(thm)],[599, 66])).
% 64.65/41.61 tff(601,plain,
% 64.65/41.61 (and(implies(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0)))))), implies(not(and(not(P!1), not(not(and(P!1, Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1))))) = equiv(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0))))))),
% 64.65/41.61 inference(symmetry,[status(thm)],[600])).
% 64.65/41.61 tff(602,plain,
% 64.65/41.61 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(P!1), not(not(and(P!1, Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))) = or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.65/41.61 inference(quant_inst,[status(thm)],[])).
% 64.65/41.61 tff(603,plain,
% 64.65/41.61 (implies(not(and(not(P!1), not(not(and(P!1, Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))) = or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))),
% 64.65/41.61 inference(unit_resolution,[status(thm)],[602, 20])).
% 64.65/41.61 tff(604,plain,
% 64.65/41.61 (or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))) = implies(not(and(not(P!1), not(not(and(P!1, Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1))))),
% 64.65/41.61 inference(symmetry,[status(thm)],[603])).
% 64.65/41.61 tff(605,plain,
% 64.65/41.61 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0)))))) = not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0)))))))))),
% 64.65/41.61 inference(quant_inst,[status(thm)],[])).
% 64.65/41.61 tff(606,plain,
% 64.65/41.61 (implies(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0)))))) = not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0))))))))),
% 64.65/41.61 inference(unit_resolution,[status(thm)],[605, 91])).
% 64.65/41.61 tff(607,plain,
% 64.65/41.61 (not(and(not(not(or(not(and(P!1, Q!0)), P!1))), not(not(and(not(P!1), not(not(and(P!1, Q!0)))))))) = implies(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0))))))),
% 64.65/41.61 inference(symmetry,[status(thm)],[606])).
% 64.65/41.61 tff(608,plain,
% 64.65/41.61 (or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0)))) = or(not(or(not(and(P!1, Q!0)), P!1)), not(and(not(P!1), not(not(and(P!1, Q!0))))))),
% 64.65/41.61 inference(symmetry,[status(thm)],[293])).
% 64.65/41.61 tff(609,plain,
% 64.65/41.61 (or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))) = implies(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0))))))),
% 64.65/41.61 inference(transitivity,[status(thm)],[289, 288, 286, 284, 281, 608, 550, 607])).
% 64.65/41.61 tff(610,plain,
% 64.65/41.61 (and(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))) = and(implies(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0)))))), implies(not(and(not(P!1), not(not(and(P!1, Q!0))))), not(not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.65/41.61 inference(monotonicity,[status(thm)],[609, 604])).
% 64.65/41.61 tff(611,plain,
% 64.65/41.61 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))) = not(or(not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.65/41.61 inference(quant_inst,[status(thm)],[])).
% 64.65/41.61 tff(612,plain,
% 64.65/41.61 (and(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))) = not(or(not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.61 inference(unit_resolution,[status(thm)],[611, 113])).
% 64.65/41.61 tff(613,plain,
% 64.65/41.61 (not(or(not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))) = and(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.65/41.61 inference(symmetry,[status(thm)],[612])).
% 64.65/41.61 tff(614,plain,
% 64.65/41.61 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))) = or(not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.65/41.61 inference(quant_inst,[status(thm)],[])).
% 64.65/41.61 tff(615,plain,
% 64.65/41.61 (implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))) = or(not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.65/41.61 inference(unit_resolution,[status(thm)],[614, 20])).
% 64.72/41.61 tff(616,plain,
% 64.72/41.61 (implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))) = implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0)))), and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))),
% 64.72/41.61 inference(monotonicity,[status(thm)],[290, 381])).
% 64.72/41.61 tff(617,plain,
% 64.72/41.61 (implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0)))), and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))) = implies(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0)))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.72/41.61 inference(symmetry,[status(thm)],[616])).
% 64.72/41.61 tff(618,plain,
% 64.72/41.61 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0)))), and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))) = not(and(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0)))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.72/41.61 inference(quant_inst,[status(thm)],[])).
% 64.72/41.61 tff(619,plain,
% 64.72/41.61 (implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0)))), and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))) = not(and(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0)))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.72/41.61 inference(unit_resolution,[status(thm)],[618, 91])).
% 64.72/41.61 tff(620,plain,
% 64.72/41.61 (not(and(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0)))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) = implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0)))), and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))),
% 64.72/41.61 inference(symmetry,[status(thm)],[619])).
% 64.72/41.61 tff(621,plain,
% 64.72/41.61 (and(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0)))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) = and(implies(or(not(and(P!1, Q!0)), P!1), or(P!1, not(and(P!1, Q!0)))), implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)))),
% 64.72/41.61 inference(monotonicity,[status(thm)],[548, 305])).
% 64.72/41.61 tff(622,plain,
% 64.72/41.61 (and(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0)))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))) = and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))),
% 64.72/41.61 inference(transitivity,[status(thm)],[621, 307])).
% 64.72/41.61 tff(623,plain,
% 64.72/41.61 (not(and(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0)))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) = not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.72/41.61 inference(monotonicity,[status(thm)],[622])).
% 64.72/41.61 tff(624,plain,
% 64.72/41.61 (not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) = not(and(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, not(and(P!1, Q!0)))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.72/41.61 inference(symmetry,[status(thm)],[623])).
% 64.72/41.61 tff(625,plain,
% 64.72/41.61 (not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))) = and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))),
% 64.72/41.61 inference(transitivity,[status(thm)],[149, 328])).
% 64.72/41.61 tff(626,plain,
% 64.72/41.61 (or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))) = or(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))), and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))),
% 64.72/41.61 inference(monotonicity,[status(thm)],[625, 381])).
% 64.72/41.61 tff(627,plain,
% 64.72/41.61 (or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))) = or(not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.72/41.61 inference(transitivity,[status(thm)],[626, 375, 624, 620, 617, 615])).
% 64.72/41.61 tff(628,plain,
% 64.72/41.61 (not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))) = not(or(not(or(not(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(not(P!1)), not(and(P!1, Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.72/41.61 inference(monotonicity,[status(thm)],[627])).
% 64.72/41.61 tff(629,plain,
% 64.72/41.61 (not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))) = equiv(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0))))))),
% 64.72/41.61 inference(transitivity,[status(thm)],[628, 613, 610, 601])).
% 64.72/41.61 tff(630,plain,
% 64.72/41.61 (is_a_theorem(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) <=> is_a_theorem(equiv(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0)))))))),
% 64.72/41.61 inference(monotonicity,[status(thm)],[629])).
% 64.72/41.61 tff(631,plain,
% 64.72/41.61 (not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))) = not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))),
% 64.72/41.61 inference(symmetry,[status(thm)],[149])).
% 64.72/41.61 tff(632,plain,
% 64.72/41.61 (or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) = or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.72/41.61 inference(monotonicity,[status(thm)],[631])).
% 64.72/41.61 tff(633,plain,
% 64.72/41.61 (or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) = or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.72/41.61 inference(symmetry,[status(thm)],[632])).
% 64.72/41.61 tff(634,plain,
% 64.72/41.61 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) = or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))))),
% 64.72/41.61 inference(quant_inst,[status(thm)],[])).
% 64.72/41.61 tff(635,plain,
% 64.72/41.61 (implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) = or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.72/41.62 inference(unit_resolution,[status(thm)],[634, 20])).
% 64.72/41.62 tff(636,plain,
% 64.72/41.62 (implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) = or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.72/41.62 inference(transitivity,[status(thm)],[635, 633])).
% 64.72/41.62 tff(637,plain,
% 64.72/41.62 (is_a_theorem(implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))) <=> is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))))),
% 64.72/41.62 inference(monotonicity,[status(thm)],[636])).
% 64.72/41.62 tff(638,plain,
% 64.72/41.62 (is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))) <=> is_a_theorem(implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))))),
% 64.72/41.62 inference(symmetry,[status(thm)],[637])).
% 64.72/41.62 tff(639,plain,
% 64.72/41.62 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))),
% 64.72/41.62 inference(quant_inst,[status(thm)],[])).
% 64.72/41.62 tff(640,plain,
% 64.72/41.62 (or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.72/41.62 inference(unit_resolution,[status(thm)],[639, 42])).
% 64.72/41.62 tff(641,plain,
% 64.72/41.62 (implies(or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))) = implies(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))))),
% 64.72/41.62 inference(monotonicity,[status(thm)],[640])).
% 64.72/41.62 tff(642,plain,
% 64.72/41.62 (is_a_theorem(implies(or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))))) <=> is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))))),
% 64.72/41.62 inference(monotonicity,[status(thm)],[641])).
% 64.72/41.62 tff(643,plain,
% 64.72/41.62 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))))),
% 64.72/41.62 inference(quant_inst,[status(thm)],[])).
% 64.72/41.62 tff(644,plain,
% 64.72/41.62 (is_a_theorem(implies(or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))))),
% 64.72/41.62 inference(unit_resolution,[status(thm)],[643, 405])).
% 64.72/41.62 tff(645,plain,
% 64.72/41.62 (is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))))),
% 64.72/41.62 inference(modus_ponens,[status(thm)],[644, 642])).
% 64.72/41.62 tff(646,plain,
% 64.72/41.62 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(and(P!1, Q!0)), not(not(P!1))) = not(and(not(not(and(P!1, Q!0))), not(not(not(P!1))))))),
% 64.72/41.62 inference(quant_inst,[status(thm)],[])).
% 64.72/41.62 tff(647,plain,
% 64.72/41.62 (or(not(and(P!1, Q!0)), not(not(P!1))) = not(and(not(not(and(P!1, Q!0))), not(not(not(P!1)))))),
% 64.72/41.62 inference(unit_resolution,[status(thm)],[646, 42])).
% 64.72/41.62 tff(648,plain,
% 64.72/41.62 (not(and(not(not(and(P!1, Q!0))), not(not(not(P!1))))) = or(not(and(P!1, Q!0)), not(not(P!1)))),
% 64.72/41.62 inference(symmetry,[status(thm)],[647])).
% 64.72/41.62 tff(649,plain,
% 64.72/41.62 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(and(P!1, Q!0))), not(not(P!1))) = not(and(not(not(and(P!1, Q!0))), not(not(not(P!1))))))),
% 64.72/41.62 inference(quant_inst,[status(thm)],[])).
% 64.72/41.62 tff(650,plain,
% 64.72/41.62 (implies(not(not(and(P!1, Q!0))), not(not(P!1))) = not(and(not(not(and(P!1, Q!0))), not(not(not(P!1)))))),
% 64.72/41.62 inference(unit_resolution,[status(thm)],[649, 91])).
% 64.72/41.62 tff(651,plain,
% 64.72/41.62 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(not(and(P!1, Q!0))), not(not(P!1))) = or(not(not(not(and(P!1, Q!0)))), not(not(P!1))))),
% 64.72/41.62 inference(quant_inst,[status(thm)],[])).
% 64.72/41.62 tff(652,plain,
% 64.72/41.62 (implies(not(not(and(P!1, Q!0))), not(not(P!1))) = or(not(not(not(and(P!1, Q!0)))), not(not(P!1)))),
% 64.72/41.62 inference(unit_resolution,[status(thm)],[651, 20])).
% 64.72/41.62 tff(653,plain,
% 64.72/41.62 (or(not(not(not(and(P!1, Q!0)))), not(not(P!1))) = implies(not(not(and(P!1, Q!0))), not(not(P!1)))),
% 64.72/41.62 inference(symmetry,[status(thm)],[652])).
% 64.72/41.62 tff(654,plain,
% 64.72/41.62 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(not(not(and(P!1, Q!0)))), not(not(P!1))) = not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))),
% 64.72/41.62 inference(quant_inst,[status(thm)],[])).
% 64.72/41.62 tff(655,plain,
% 64.72/41.62 (or(not(not(not(and(P!1, Q!0)))), not(not(P!1))) = not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1)))))),
% 64.72/41.62 inference(unit_resolution,[status(thm)],[654, 42])).
% 64.72/41.62 tff(656,plain,
% 64.72/41.62 (not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))) = or(not(not(not(and(P!1, Q!0)))), not(not(P!1)))),
% 64.72/41.62 inference(symmetry,[status(thm)],[655])).
% 64.72/41.62 tff(657,plain,
% 64.72/41.62 (not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))) = or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))),
% 64.72/41.62 inference(transitivity,[status(thm)],[656, 653, 650, 648, 445])).
% 64.72/41.62 tff(658,plain,
% 64.72/41.62 (or(not(not(P!1)), not(and(P!1, Q!0))) = or(P!1, not(and(P!1, Q!0)))),
% 64.72/41.62 inference(transitivity,[status(thm)],[124, 121, 119])).
% 64.72/41.62 tff(659,plain,
% 64.72/41.62 (not(or(not(not(P!1)), not(and(P!1, Q!0)))) = not(or(P!1, not(and(P!1, Q!0))))),
% 64.72/41.62 inference(monotonicity,[status(thm)],[658])).
% 64.72/41.62 tff(660,plain,
% 64.72/41.62 (not(or(P!1, not(and(P!1, Q!0)))) = not(or(not(not(P!1)), not(and(P!1, Q!0))))),
% 64.72/41.62 inference(symmetry,[status(thm)],[659])).
% 64.72/41.62 tff(661,plain,
% 64.72/41.62 (not(not(and(not(P!1), not(not(and(P!1, Q!0)))))) = not(or(not(not(P!1)), not(and(P!1, Q!0))))),
% 64.72/41.62 inference(transitivity,[status(thm)],[165, 660])).
% 64.72/41.62 tff(662,plain,
% 64.72/41.62 (or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1)))))) = or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))),
% 64.72/41.62 inference(monotonicity,[status(thm)],[661, 657])).
% 64.72/41.62 tff(663,plain,
% 64.72/41.62 (or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))) = or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))),
% 64.72/41.62 inference(symmetry,[status(thm)],[662])).
% 64.72/41.62 tff(664,plain,
% 64.72/41.62 (not(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))) = not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1)))))))),
% 64.72/41.62 inference(monotonicity,[status(thm)],[663])).
% 64.72/41.62 tff(665,plain,
% 64.72/41.62 (not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))) = not(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.72/41.62 inference(symmetry,[status(thm)],[664])).
% 64.72/41.62 tff(666,plain,
% 64.72/41.62 (or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))) = or(not(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.72/41.62 inference(monotonicity,[status(thm)],[665])).
% 64.72/41.62 tff(667,plain,
% 64.72/41.62 (or(not(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))) = or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.72/41.62 inference(symmetry,[status(thm)],[666])).
% 64.72/41.62 tff(668,plain,
% 64.72/41.62 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))) = or(not(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.72/41.62 inference(quant_inst,[status(thm)],[])).
% 64.72/41.62 tff(669,plain,
% 64.72/41.62 (implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))) = or(not(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.72/41.62 inference(unit_resolution,[status(thm)],[668, 20])).
% 64.72/41.62 tff(670,plain,
% 64.72/41.62 (implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))) = implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))),
% 64.72/41.62 inference(monotonicity,[status(thm)],[640])).
% 64.72/41.62 tff(671,plain,
% 64.72/41.62 (implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))) = implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.72/41.62 inference(symmetry,[status(thm)],[670])).
% 64.72/41.62 tff(672,plain,
% 64.72/41.62 (implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))) = or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.72/41.62 inference(transitivity,[status(thm)],[671, 669, 667])).
% 64.72/41.62 tff(673,plain,
% 64.72/41.62 (is_a_theorem(implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))) <=> is_a_theorem(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.72/41.62 inference(monotonicity,[status(thm)],[672])).
% 64.72/41.62 tff(674,plain,
% 64.72/41.62 (is_a_theorem(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))) <=> is_a_theorem(implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))))),
% 64.72/41.62 inference(symmetry,[status(thm)],[673])).
% 64.72/41.62 tff(675,plain,
% 64.72/41.62 (or(not(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = implies(or(not(or(P!1, not(and(P!1, Q!0)))), or(not(and(P!1, Q!0)), P!1)), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.72/41.62 inference(symmetry,[status(thm)],[325])).
% 64.72/41.62 tff(676,plain,
% 64.72/41.62 (or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = or(not(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.72/41.63 inference(monotonicity,[status(thm)],[665])).
% 64.72/41.63 tff(677,plain,
% 64.72/41.63 (or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))) = not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))),
% 64.72/41.63 inference(transitivity,[status(thm)],[676, 193, 190, 188, 171, 168, 675, 329, 332, 338])).
% 64.72/41.63 tff(678,plain,
% 64.72/41.63 (or(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))), and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))) = or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.72/41.63 inference(symmetry,[status(thm)],[626])).
% 64.72/41.63 tff(679,plain,
% 64.72/41.63 (not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) = or(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))), and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))),
% 64.72/41.63 inference(symmetry,[status(thm)],[375])).
% 64.72/41.63 tff(680,plain,
% 64.72/41.63 (not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))) = or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))),
% 64.72/41.63 inference(transitivity,[status(thm)],[679, 678])).
% 64.72/41.63 tff(681,plain,
% 64.72/41.63 (not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))) = not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.72/41.63 inference(monotonicity,[status(thm)],[680])).
% 64.72/41.63 tff(682,plain,
% 64.72/41.63 (not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))) = not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))))),
% 64.72/41.63 inference(symmetry,[status(thm)],[681])).
% 64.72/41.63 tff(683,plain,
% 64.72/41.63 (or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))) = or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.72/41.63 inference(monotonicity,[status(thm)],[682, 677])).
% 64.72/41.63 tff(684,plain,
% 64.72/41.63 (or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))) = or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.72/41.63 inference(symmetry,[status(thm)],[683])).
% 64.72/41.63 tff(685,plain,
% 64.72/41.63 (implies(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))) = implies(or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.72/41.63 inference(monotonicity,[status(thm)],[684])).
% 64.72/41.63 tff(686,plain,
% 64.72/41.63 (implies(or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))) = implies(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.72/41.63 inference(symmetry,[status(thm)],[685])).
% 64.72/41.63 tff(687,plain,
% 64.72/41.63 (is_a_theorem(implies(or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))) <=> is_a_theorem(implies(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))),
% 64.72/41.63 inference(monotonicity,[status(thm)],[686])).
% 64.72/41.63 tff(688,plain,
% 64.72/41.63 ((~![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(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))),
% 64.72/41.63 inference(quant_inst,[status(thm)],[])).
% 64.72/41.63 tff(689,plain,
% 64.72/41.63 (is_a_theorem(implies(or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))),
% 64.72/41.63 inference(unit_resolution,[status(thm)],[688, 365])).
% 64.72/41.63 tff(690,plain,
% 64.72/41.63 (is_a_theorem(implies(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))),
% 64.72/41.63 inference(modus_ponens,[status(thm)],[689, 687])).
% 64.72/41.63 tff(691,plain,
% 64.72/41.63 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))) = or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.72/41.63 inference(quant_inst,[status(thm)],[])).
% 64.72/41.63 tff(692,plain,
% 64.72/41.63 (implies(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))) = or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.72/41.63 inference(unit_resolution,[status(thm)],[691, 20])).
% 64.72/41.63 tff(693,plain,
% 64.72/41.63 (or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))) = implies(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.72/41.63 inference(symmetry,[status(thm)],[692])).
% 64.72/41.63 tff(694,plain,
% 64.72/41.63 (is_a_theorem(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))))) <=> is_a_theorem(implies(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.72/41.63 inference(monotonicity,[status(thm)],[693])).
% 64.72/41.63 tff(695,plain,
% 64.72/41.63 (is_a_theorem(implies(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))))) <=> is_a_theorem(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.72/41.63 inference(symmetry,[status(thm)],[694])).
% 64.72/41.63 tff(696,plain,
% 64.72/41.63 (implies(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))) = implies(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))))),
% 64.72/41.63 inference(monotonicity,[status(thm)],[383, 387])).
% 64.72/41.63 tff(697,plain,
% 64.72/41.63 (is_a_theorem(implies(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))) <=> is_a_theorem(implies(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.72/41.64 inference(monotonicity,[status(thm)],[696])).
% 64.72/41.64 tff(698,plain,
% 64.72/41.64 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.72/41.64 inference(quant_inst,[status(thm)],[])).
% 64.72/41.64 tff(699,plain,
% 64.72/41.64 (is_a_theorem(implies(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.72/41.64 inference(unit_resolution,[status(thm)],[698, 405])).
% 64.72/41.64 tff(700,plain,
% 64.72/41.64 (is_a_theorem(implies(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.72/41.64 inference(modus_ponens,[status(thm)],[699, 697])).
% 64.72/41.64 tff(701,plain,
% 64.72/41.64 (is_a_theorem(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.72/41.64 inference(modus_ponens,[status(thm)],[700, 695])).
% 64.72/41.64 tff(702,plain,
% 64.72/41.64 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))))) | is_a_theorem(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))))) | is_a_theorem(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))))),
% 64.72/41.64 inference(rewrite,[status(thm)],[])).
% 64.72/41.64 tff(703,plain,
% 64.72/41.64 ((is_a_theorem(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))))))))) <=> ((~is_a_theorem(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))))) | is_a_theorem(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))))),
% 64.72/41.64 inference(rewrite,[status(thm)],[])).
% 64.72/41.64 tff(704,plain,
% 64.72/41.64 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))))) | is_a_theorem(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))))))),
% 64.72/41.64 inference(monotonicity,[status(thm)],[703])).
% 64.72/41.64 tff(705,plain,
% 64.72/41.64 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))))) | is_a_theorem(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))))),
% 64.72/41.64 inference(transitivity,[status(thm)],[704, 702])).
% 64.72/41.64 tff(706,plain,
% 64.72/41.64 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))))))),
% 64.72/41.65 inference(quant_inst,[status(thm)],[])).
% 64.72/41.65 tff(707,plain,
% 64.72/41.65 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))))) | is_a_theorem(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))))),
% 64.72/41.65 inference(modus_ponens,[status(thm)],[706, 705])).
% 64.72/41.65 tff(708,plain,
% 64.72/41.65 ((~is_a_theorem(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))))) | is_a_theorem(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0)))))), not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1))))))), not(and(not(and(or(P!1, not(and(P!1, Q!0))), not(or(not(and(P!1, Q!0)), P!1)))), not(and(or(not(and(P!1, Q!0)), P!1), not(or(P!1, not(and(P!1, Q!0))))))))), or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))))),
% 64.72/41.65 inference(unit_resolution,[status(thm)],[707, 429])).
% 64.72/41.65 tff(709,plain,
% 64.72/41.65 (is_a_theorem(or(not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(and(not(not(not(not(and(P!1, Q!0))))), not(not(not(P!1))))))), or(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))), not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))),
% 64.72/41.65 inference(unit_resolution,[status(thm)],[708, 701, 690])).
% 64.72/41.65 tff(710,plain,
% 64.72/41.65 (is_a_theorem(implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))))),
% 64.72/41.65 inference(modus_ponens,[status(thm)],[709, 674])).
% 64.72/41.65 tff(711,plain,
% 64.72/41.65 (or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))) = implies(or(not(not(P!1)), not(and(P!1, Q!0))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))),
% 64.72/41.65 inference(symmetry,[status(thm)],[173])).
% 64.72/41.65 tff(712,plain,
% 64.72/41.65 (is_a_theorem(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))) <=> is_a_theorem(implies(or(not(not(P!1)), not(and(P!1, Q!0))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.72/41.65 inference(monotonicity,[status(thm)],[711])).
% 64.72/41.65 tff(713,plain,
% 64.72/41.65 (is_a_theorem(implies(or(not(not(P!1)), not(and(P!1, Q!0))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))) <=> is_a_theorem(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.72/41.65 inference(symmetry,[status(thm)],[712])).
% 64.72/41.65 tff(714,plain,
% 64.72/41.65 (implies(or(not(not(P!1)), not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), not(not(P!1)))) = implies(or(not(not(P!1)), not(and(P!1, Q!0))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))),
% 64.72/41.65 inference(monotonicity,[status(thm)],[445])).
% 64.72/41.65 tff(715,plain,
% 64.72/41.65 (is_a_theorem(implies(or(not(not(P!1)), not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), not(not(P!1))))) <=> is_a_theorem(implies(or(not(not(P!1)), not(and(P!1, Q!0))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.72/41.65 inference(monotonicity,[status(thm)],[714])).
% 64.72/41.65 tff(716,plain,
% 64.72/41.65 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(not(P!1)), not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), not(not(P!1)))))),
% 64.72/41.65 inference(quant_inst,[status(thm)],[])).
% 64.72/41.65 tff(717,plain,
% 64.72/41.65 (is_a_theorem(implies(or(not(not(P!1)), not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), not(not(P!1)))))),
% 64.72/41.65 inference(unit_resolution,[status(thm)],[716, 405])).
% 64.72/41.65 tff(718,plain,
% 64.72/41.65 (is_a_theorem(implies(or(not(not(P!1)), not(and(P!1, Q!0))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.72/41.65 inference(modus_ponens,[status(thm)],[717, 715])).
% 64.72/41.65 tff(719,plain,
% 64.72/41.65 (is_a_theorem(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.72/41.65 inference(modus_ponens,[status(thm)],[718, 713])).
% 64.72/41.65 tff(720,plain,
% 64.72/41.65 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))))))),
% 64.72/41.65 inference(rewrite,[status(thm)],[])).
% 64.72/41.65 tff(721,plain,
% 64.72/41.65 ((is_a_theorem(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))))) | (~is_a_theorem(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))) <=> ((~is_a_theorem(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))))))),
% 64.72/41.65 inference(rewrite,[status(thm)],[])).
% 64.72/41.65 tff(722,plain,
% 64.72/41.65 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))))) | (~is_a_theorem(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))))))),
% 64.72/41.65 inference(monotonicity,[status(thm)],[721])).
% 64.72/41.65 tff(723,plain,
% 64.72/41.65 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))))) | (~is_a_theorem(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))))))),
% 64.72/41.65 inference(transitivity,[status(thm)],[722, 720])).
% 64.72/41.65 tff(724,plain,
% 64.72/41.65 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))))) | (~is_a_theorem(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))))),
% 64.72/41.65 inference(quant_inst,[status(thm)],[])).
% 64.72/41.65 tff(725,plain,
% 64.72/41.65 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))))),
% 64.72/41.65 inference(modus_ponens,[status(thm)],[724, 723])).
% 64.72/41.65 tff(726,plain,
% 64.72/41.65 (is_a_theorem(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!1)), not(and(P!1, Q!0)))), or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))), not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))))),
% 64.72/41.65 inference(unit_resolution,[status(thm)],[725, 429, 719])).
% 64.72/41.65 tff(727,plain,
% 64.72/41.65 (is_a_theorem(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))),
% 64.72/41.65 inference(unit_resolution,[status(thm)],[726, 710])).
% 64.72/41.65 tff(728,plain,
% 64.72/41.65 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))))),
% 64.72/41.65 inference(rewrite,[status(thm)],[])).
% 64.72/41.65 tff(729,plain,
% 64.72/41.65 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))))))),
% 64.72/41.66 inference(quant_inst,[status(thm)],[])).
% 64.72/41.66 tff(730,plain,
% 64.72/41.66 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))))),
% 64.72/41.66 inference(modus_ponens,[status(thm)],[729, 728])).
% 64.72/41.66 tff(731,plain,
% 64.72/41.66 (is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0)))))))))), or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))), not(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))))))))),
% 64.72/41.66 inference(unit_resolution,[status(thm)],[730, 429])).
% 64.72/41.66 tff(732,plain,
% 64.72/41.66 (is_a_theorem(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), not(not(or(P!1, not(and(P!1, Q!0))))))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))))),
% 64.72/41.66 inference(unit_resolution,[status(thm)],[731, 727, 645])).
% 64.72/41.66 tff(733,plain,
% 64.72/41.66 (is_a_theorem(implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))))),
% 64.76/41.66 inference(modus_ponens,[status(thm)],[732, 638])).
% 64.76/41.66 tff(734,plain,
% 64.76/41.66 (not(and(and(P!1, Q!0), not(P!1))) = not(and(not(or(not(P!1), not(Q!0))), not(P!1)))),
% 64.76/41.66 inference(symmetry,[status(thm)],[159])).
% 64.76/41.66 tff(735,plain,
% 64.76/41.66 (or(not(and(P!1, Q!0)), P!1) = implies(and(P!1, Q!0), P!1)),
% 64.76/41.66 inference(symmetry,[status(thm)],[153])).
% 64.76/41.66 tff(736,plain,
% 64.76/41.66 (or(not(and(P!1, Q!0)), P!1) = or(or(not(P!1), not(Q!0)), P!1)),
% 64.76/41.66 inference(transitivity,[status(thm)],[735, 155, 734, 224])).
% 64.76/41.66 tff(737,plain,
% 64.76/41.66 (implies(or(not(and(P!1, Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))) = implies(or(or(not(P!1), not(Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))),
% 64.76/41.66 inference(monotonicity,[status(thm)],[736])).
% 64.76/41.66 tff(738,plain,
% 64.76/41.66 (or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))) = implies(or(or(not(P!1), not(Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))),
% 64.76/41.66 inference(transitivity,[status(thm)],[72, 737])).
% 64.76/41.66 tff(739,plain,
% 64.76/41.66 (is_a_theorem(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))) <=> is_a_theorem(implies(or(or(not(P!1), not(Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))),
% 64.76/41.66 inference(monotonicity,[status(thm)],[738])).
% 64.76/41.66 tff(740,plain,
% 64.76/41.66 (is_a_theorem(implies(or(or(not(P!1), not(Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0))))) <=> is_a_theorem(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))),
% 64.76/41.66 inference(symmetry,[status(thm)],[739])).
% 64.76/41.66 tff(741,plain,
% 64.76/41.66 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(or(not(P!1), not(Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))),
% 64.76/41.66 inference(quant_inst,[status(thm)],[])).
% 64.76/41.66 tff(742,plain,
% 64.76/41.66 (is_a_theorem(implies(or(or(not(P!1), not(Q!0)), P!1), or(P!1, or(not(P!1), not(Q!0)))))),
% 64.76/41.66 inference(unit_resolution,[status(thm)],[741, 405])).
% 64.76/41.66 tff(743,plain,
% 64.76/41.66 (is_a_theorem(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))),
% 64.76/41.66 inference(modus_ponens,[status(thm)],[742, 740])).
% 64.76/41.66 tff(744,plain,
% 64.76/41.66 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))) | is_a_theorem(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) | (~is_a_theorem(implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))) | is_a_theorem(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) | (~is_a_theorem(implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))))))),
% 64.76/41.66 inference(rewrite,[status(thm)],[])).
% 64.76/41.66 tff(745,plain,
% 64.76/41.66 ((is_a_theorem(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) | (~is_a_theorem(implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))))) | (~is_a_theorem(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))))) <=> ((~is_a_theorem(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))) | is_a_theorem(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) | (~is_a_theorem(implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))))))),
% 64.76/41.66 inference(rewrite,[status(thm)],[])).
% 64.76/41.66 tff(746,plain,
% 64.76/41.66 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) | (~is_a_theorem(implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))))) | (~is_a_theorem(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))) | is_a_theorem(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) | (~is_a_theorem(implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))))))),
% 64.76/41.66 inference(monotonicity,[status(thm)],[745])).
% 64.76/41.66 tff(747,plain,
% 64.76/41.66 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) | (~is_a_theorem(implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))))) | (~is_a_theorem(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))) | is_a_theorem(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) | (~is_a_theorem(implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))))))),
% 64.76/41.66 inference(transitivity,[status(thm)],[746, 744])).
% 64.76/41.66 tff(748,plain,
% 64.76/41.66 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) | (~is_a_theorem(implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))))) | (~is_a_theorem(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))))),
% 64.76/41.66 inference(quant_inst,[status(thm)],[])).
% 64.76/41.66 tff(749,plain,
% 64.76/41.66 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))))) | is_a_theorem(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) | (~is_a_theorem(implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))))),
% 64.76/41.66 inference(modus_ponens,[status(thm)],[748, 747])).
% 64.76/41.66 tff(750,plain,
% 64.76/41.66 (is_a_theorem(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1)))))))) | (~is_a_theorem(implies(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0)))), not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))))),
% 64.76/41.66 inference(unit_resolution,[status(thm)],[749, 429, 743])).
% 64.76/41.66 tff(751,plain,
% 64.76/41.66 (is_a_theorem(not(or(not(or(not(or(not(and(P!1, Q!0)), P!1)), or(P!1, or(not(P!1), not(Q!0))))), not(or(not(not(and(not(P!1), not(not(and(P!1, Q!0)))))), not(not(or(not(and(P!1, Q!0)), P!1))))))))),
% 64.76/41.66 inference(unit_resolution,[status(thm)],[750, 733])).
% 64.76/41.66 tff(752,plain,
% 64.76/41.66 (is_a_theorem(equiv(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0)))))))),
% 64.76/41.66 inference(modus_ponens,[status(thm)],[751, 630])).
% 64.76/41.66 tff(753,plain,
% 64.76/41.66 (((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0)))))))) | (not(not(or(not(and(P!1, Q!0)), P!1))) = not(and(not(P!1), not(not(and(P!1, Q!0)))))))) <=> ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0)))))))) | (not(not(or(not(and(P!1, Q!0)), P!1))) = not(and(not(P!1), not(not(and(P!1, Q!0)))))))),
% 64.76/41.66 inference(rewrite,[status(thm)],[])).
% 64.76/41.66 tff(754,plain,
% 64.76/41.66 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0)))))))) | (not(not(or(not(and(P!1, Q!0)), P!1))) = not(and(not(P!1), not(not(and(P!1, Q!0)))))))),
% 64.76/41.66 inference(quant_inst,[status(thm)],[])).
% 64.76/41.66 tff(755,plain,
% 64.76/41.66 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0)))))))) | (not(not(or(not(and(P!1, Q!0)), P!1))) = not(and(not(P!1), not(not(and(P!1, Q!0))))))),
% 64.76/41.66 inference(modus_ponens,[status(thm)],[754, 753])).
% 64.76/41.66 tff(756,plain,
% 64.76/41.66 ((~is_a_theorem(equiv(not(not(or(not(and(P!1, Q!0)), P!1))), not(and(not(P!1), not(not(and(P!1, Q!0)))))))) | (not(not(or(not(and(P!1, Q!0)), P!1))) = not(and(not(P!1), not(not(and(P!1, Q!0))))))),
% 64.76/41.66 inference(unit_resolution,[status(thm)],[755, 542])).
% 64.76/41.66 tff(757,plain,
% 64.76/41.66 (not(not(or(not(and(P!1, Q!0)), P!1))) = not(and(not(P!1), not(not(and(P!1, Q!0)))))),
% 64.76/41.66 inference(unit_resolution,[status(thm)],[756, 752])).
% 64.76/41.66 tff(758,plain,
% 64.76/41.66 (not(and(not(P!1), not(not(and(P!1, Q!0))))) = not(not(or(not(and(P!1, Q!0)), P!1)))),
% 64.76/41.66 inference(symmetry,[status(thm)],[757])).
% 64.76/41.66 tff(759,plain,
% 64.76/41.66 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(not(not(or(not(Q!0), not(P!1)))), or(not(P!1), not(Q!0))) = and(implies(not(not(or(not(Q!0), not(P!1)))), or(not(P!1), not(Q!0))), implies(or(not(P!1), not(Q!0)), not(not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.66 inference(quant_inst,[status(thm)],[])).
% 64.76/41.66 tff(760,plain,
% 64.76/41.66 (equiv(not(not(or(not(Q!0), not(P!1)))), or(not(P!1), not(Q!0))) = and(implies(not(not(or(not(Q!0), not(P!1)))), or(not(P!1), not(Q!0))), implies(or(not(P!1), not(Q!0)), not(not(or(not(Q!0), not(P!1))))))),
% 64.76/41.66 inference(unit_resolution,[status(thm)],[759, 66])).
% 64.76/41.66 tff(761,plain,
% 64.76/41.66 (and(implies(not(not(or(not(Q!0), not(P!1)))), or(not(P!1), not(Q!0))), implies(or(not(P!1), not(Q!0)), not(not(or(not(Q!0), not(P!1)))))) = equiv(not(not(or(not(Q!0), not(P!1)))), or(not(P!1), not(Q!0)))),
% 64.76/41.66 inference(symmetry,[status(thm)],[760])).
% 64.76/41.66 tff(762,plain,
% 64.76/41.66 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(P!1), not(Q!0)), not(not(or(not(Q!0), not(P!1))))) = or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))),
% 64.76/41.66 inference(quant_inst,[status(thm)],[])).
% 64.76/41.66 tff(763,plain,
% 64.76/41.66 (implies(or(not(P!1), not(Q!0)), not(not(or(not(Q!0), not(P!1))))) = or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))),
% 64.76/41.66 inference(unit_resolution,[status(thm)],[762, 20])).
% 64.76/41.66 tff(764,plain,
% 64.76/41.66 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))) = not(and(not(not(or(not(Q!0), not(P!1)))), not(or(not(P!1), not(Q!0))))))),
% 64.76/41.66 inference(quant_inst,[status(thm)],[])).
% 64.76/41.66 tff(765,plain,
% 64.76/41.66 (or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))) = not(and(not(not(or(not(Q!0), not(P!1)))), not(or(not(P!1), not(Q!0)))))),
% 64.76/41.66 inference(unit_resolution,[status(thm)],[764, 42])).
% 64.76/41.66 tff(766,plain,
% 64.76/41.66 (not(and(not(not(or(not(Q!0), not(P!1)))), not(or(not(P!1), not(Q!0))))) = or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0)))),
% 64.76/41.66 inference(symmetry,[status(thm)],[765])).
% 64.76/41.66 tff(767,plain,
% 64.76/41.66 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(or(not(Q!0), not(P!1)))), or(not(P!1), not(Q!0))) = not(and(not(not(or(not(Q!0), not(P!1)))), not(or(not(P!1), not(Q!0))))))),
% 64.76/41.66 inference(quant_inst,[status(thm)],[])).
% 64.76/41.66 tff(768,plain,
% 64.76/41.66 (implies(not(not(or(not(Q!0), not(P!1)))), or(not(P!1), not(Q!0))) = not(and(not(not(or(not(Q!0), not(P!1)))), not(or(not(P!1), not(Q!0)))))),
% 64.76/41.66 inference(unit_resolution,[status(thm)],[767, 91])).
% 64.76/41.66 tff(769,plain,
% 64.76/41.66 (implies(not(not(or(not(Q!0), not(P!1)))), or(not(P!1), not(Q!0))) = or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0)))),
% 64.76/41.66 inference(transitivity,[status(thm)],[768, 766])).
% 64.76/41.66 tff(770,plain,
% 64.76/41.66 (and(implies(not(not(or(not(Q!0), not(P!1)))), or(not(P!1), not(Q!0))), implies(or(not(P!1), not(Q!0)), not(not(or(not(Q!0), not(P!1)))))) = and(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))),
% 64.76/41.66 inference(monotonicity,[status(thm)],[769, 763])).
% 64.76/41.66 tff(771,plain,
% 64.76/41.66 (and(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))) = and(implies(not(not(or(not(Q!0), not(P!1)))), or(not(P!1), not(Q!0))), implies(or(not(P!1), not(Q!0)), not(not(or(not(Q!0), not(P!1))))))),
% 64.76/41.66 inference(symmetry,[status(thm)],[770])).
% 64.76/41.66 tff(772,plain,
% 64.76/41.66 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))) = not(or(not(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0)))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))),
% 64.76/41.66 inference(quant_inst,[status(thm)],[])).
% 64.76/41.66 tff(773,plain,
% 64.76/41.66 (and(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))) = not(or(not(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0)))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))),
% 64.76/41.66 inference(unit_resolution,[status(thm)],[772, 113])).
% 64.76/41.66 tff(774,plain,
% 64.76/41.66 (not(or(not(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0)))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))) = and(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))),
% 64.76/41.67 inference(symmetry,[status(thm)],[773])).
% 64.76/41.67 tff(775,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))) = not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(776,plain,
% 64.76/41.67 (and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))) = not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[775, 113])).
% 64.76/41.67 tff(777,plain,
% 64.76/41.67 (not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))) = and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))),
% 64.76/41.67 inference(symmetry,[status(thm)],[776])).
% 64.76/41.67 tff(778,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))) = not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(779,plain,
% 64.76/41.67 (and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))) = not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[778, 113])).
% 64.76/41.67 tff(780,plain,
% 64.76/41.67 (not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))) = and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))),
% 64.76/41.67 inference(symmetry,[status(thm)],[779])).
% 64.76/41.67 tff(781,plain,
% 64.76/41.67 (or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))) = or(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))), and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))),
% 64.76/41.67 inference(monotonicity,[status(thm)],[780, 777])).
% 64.76/41.67 tff(782,plain,
% 64.76/41.67 (or(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))), and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))) = or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.67 inference(symmetry,[status(thm)],[781])).
% 64.76/41.67 tff(783,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))), and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))) = not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(784,plain,
% 64.76/41.67 (or(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))), and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))) = not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[783, 42])).
% 64.76/41.67 tff(785,plain,
% 64.76/41.67 (not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))) = or(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))), and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))),
% 64.76/41.67 inference(symmetry,[status(thm)],[784])).
% 64.76/41.67 tff(786,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1))) = not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(787,plain,
% 64.76/41.67 (implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1))) = not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[786, 91])).
% 64.76/41.67 tff(788,plain,
% 64.76/41.67 (not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))) = implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1)))),
% 64.76/41.67 inference(symmetry,[status(thm)],[787])).
% 64.76/41.67 tff(789,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0))) = not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(790,plain,
% 64.76/41.67 (implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0))) = not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[789, 91])).
% 64.76/41.67 tff(791,plain,
% 64.76/41.67 (not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))) = implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0)))),
% 64.76/41.67 inference(symmetry,[status(thm)],[790])).
% 64.76/41.67 tff(792,plain,
% 64.76/41.67 (and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))) = and(implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0))), implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1))))),
% 64.76/41.67 inference(monotonicity,[status(thm)],[791, 788])).
% 64.76/41.67 tff(793,plain,
% 64.76/41.67 (and(implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0))), implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1)))) = and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))),
% 64.76/41.67 inference(symmetry,[status(thm)],[792])).
% 64.76/41.67 tff(794,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0))) = or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(795,plain,
% 64.76/41.67 (implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0))) = or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0)))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[794, 20])).
% 64.76/41.67 tff(796,plain,
% 64.76/41.67 (or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))) = implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0)))),
% 64.76/41.67 inference(symmetry,[status(thm)],[795])).
% 64.76/41.67 tff(797,plain,
% 64.76/41.67 (and(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))) = and(implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0))), implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1))))),
% 64.76/41.67 inference(monotonicity,[status(thm)],[796, 788])).
% 64.76/41.67 tff(798,plain,
% 64.76/41.67 (and(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))) = and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))),
% 64.76/41.67 inference(transitivity,[status(thm)],[797, 793])).
% 64.76/41.67 tff(799,plain,
% 64.76/41.67 (not(and(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))) = not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.67 inference(monotonicity,[status(thm)],[798])).
% 64.76/41.67 tff(800,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))) = not(and(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(801,plain,
% 64.76/41.67 (implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))) = not(and(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[800, 91])).
% 64.76/41.67 tff(802,plain,
% 64.76/41.67 (implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))) = implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))),
% 64.76/41.67 inference(monotonicity,[status(thm)],[777])).
% 64.76/41.67 tff(803,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))) = or(not(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0)))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(804,plain,
% 64.76/41.67 (implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))) = or(not(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0)))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[803, 20])).
% 64.76/41.67 tff(805,plain,
% 64.76/41.67 (or(not(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0)))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))) = implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.67 inference(symmetry,[status(thm)],[804])).
% 64.76/41.67 tff(806,plain,
% 64.76/41.67 (or(not(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0)))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))) = or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.67 inference(transitivity,[status(thm)],[805, 802, 801, 799, 785, 782])).
% 64.76/41.67 tff(807,plain,
% 64.76/41.67 (not(or(not(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0)))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))) = not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))),
% 64.76/41.67 inference(monotonicity,[status(thm)],[806])).
% 64.76/41.67 tff(808,plain,
% 64.76/41.67 (not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))) = not(or(not(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0)))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))),
% 64.76/41.67 inference(symmetry,[status(thm)],[807])).
% 64.76/41.67 tff(809,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1))) = or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(810,plain,
% 64.76/41.67 (implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1))) = or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1)))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[809, 20])).
% 64.76/41.67 tff(811,plain,
% 64.76/41.67 (or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))) = implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1)))),
% 64.76/41.67 inference(symmetry,[status(thm)],[810])).
% 64.76/41.67 tff(812,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))) = not(and(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1))))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(813,plain,
% 64.76/41.67 (or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))) = not(and(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1)))))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[812, 42])).
% 64.76/41.67 tff(814,plain,
% 64.76/41.67 (not(and(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1))))) = or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1)))),
% 64.76/41.67 inference(symmetry,[status(thm)],[813])).
% 64.76/41.67 tff(815,plain,
% 64.76/41.67 (not(and(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1))))) = implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1)))),
% 64.76/41.67 inference(transitivity,[status(thm)],[814, 811])).
% 64.76/41.67 tff(816,plain,
% 64.76/41.67 (not(and(not(not(or(not(Q!0), not(P!1)))), not(or(not(P!1), not(Q!0))))) = implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0)))),
% 64.76/41.67 inference(transitivity,[status(thm)],[766, 796])).
% 64.76/41.67 tff(817,plain,
% 64.76/41.67 (and(not(and(not(not(or(not(Q!0), not(P!1)))), not(or(not(P!1), not(Q!0))))), not(and(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1)))))) = and(implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0))), implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1))))),
% 64.76/41.67 inference(monotonicity,[status(thm)],[816, 815])).
% 64.76/41.67 tff(818,plain,
% 64.76/41.67 (and(not(and(not(not(or(not(Q!0), not(P!1)))), not(or(not(P!1), not(Q!0))))), not(and(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1)))))) = and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))),
% 64.76/41.67 inference(transitivity,[status(thm)],[817, 793])).
% 64.76/41.67 tff(819,plain,
% 64.76/41.67 (not(and(not(and(not(not(or(not(Q!0), not(P!1)))), not(or(not(P!1), not(Q!0))))), not(and(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1))))))) = not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.67 inference(monotonicity,[status(thm)],[818])).
% 64.76/41.67 tff(820,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(not(not(or(not(Q!0), not(P!1)))), not(or(not(P!1), not(Q!0)))), and(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1))))) = not(and(not(and(not(not(or(not(Q!0), not(P!1)))), not(or(not(P!1), not(Q!0))))), not(and(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1))))))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(821,plain,
% 64.76/41.67 (or(and(not(not(or(not(Q!0), not(P!1)))), not(or(not(P!1), not(Q!0)))), and(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1))))) = not(and(not(and(not(not(or(not(Q!0), not(P!1)))), not(or(not(P!1), not(Q!0))))), not(and(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[820, 42])).
% 64.76/41.67 tff(822,plain,
% 64.76/41.67 (and(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1)))) = and(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1))))),
% 64.76/41.67 inference(monotonicity,[status(thm)],[128])).
% 64.76/41.67 tff(823,plain,
% 64.76/41.67 (and(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1)))) = and(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1))))),
% 64.76/41.67 inference(symmetry,[status(thm)],[822])).
% 64.76/41.67 tff(824,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1)))) = not(or(not(not(and(P!1, Q!0))), not(not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(825,plain,
% 64.76/41.67 (and(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1)))) = not(or(not(not(and(P!1, Q!0))), not(not(or(not(Q!0), not(P!1))))))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[824, 113])).
% 64.76/41.67 tff(826,plain,
% 64.76/41.67 (not(or(not(not(and(P!1, Q!0))), not(not(or(not(Q!0), not(P!1)))))) = and(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1))))),
% 64.76/41.67 inference(symmetry,[status(thm)],[825])).
% 64.76/41.67 tff(827,plain,
% 64.76/41.67 (not(or(not(not(and(P!1, Q!0))), not(not(or(not(Q!0), not(P!1)))))) = and(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1))))),
% 64.76/41.67 inference(transitivity,[status(thm)],[826, 823])).
% 64.76/41.67 tff(828,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(not(or(not(Q!0), not(P!1)))), not(or(not(P!1), not(Q!0)))) = not(or(not(not(not(or(not(Q!0), not(P!1))))), not(not(or(not(P!1), not(Q!0)))))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(829,plain,
% 64.76/41.67 (and(not(not(or(not(Q!0), not(P!1)))), not(or(not(P!1), not(Q!0)))) = not(or(not(not(not(or(not(Q!0), not(P!1))))), not(not(or(not(P!1), not(Q!0))))))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[828, 113])).
% 64.76/41.67 tff(830,plain,
% 64.76/41.67 (not(or(not(not(not(or(not(Q!0), not(P!1))))), not(not(or(not(P!1), not(Q!0)))))) = and(not(not(or(not(Q!0), not(P!1)))), not(or(not(P!1), not(Q!0))))),
% 64.76/41.67 inference(symmetry,[status(thm)],[829])).
% 64.76/41.67 tff(831,plain,
% 64.76/41.67 (or(not(or(not(not(not(or(not(Q!0), not(P!1))))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(not(and(P!1, Q!0))), not(not(or(not(Q!0), not(P!1))))))) = or(and(not(not(or(not(Q!0), not(P!1)))), not(or(not(P!1), not(Q!0)))), and(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1)))))),
% 64.76/41.67 inference(monotonicity,[status(thm)],[830, 827])).
% 64.76/41.67 tff(832,plain,
% 64.76/41.67 (or(not(or(not(not(not(or(not(Q!0), not(P!1))))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(not(and(P!1, Q!0))), not(not(or(not(Q!0), not(P!1))))))) = or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.67 inference(transitivity,[status(thm)],[831, 821, 819, 785, 782])).
% 64.76/41.67 tff(833,plain,
% 64.76/41.67 (not(or(not(or(not(not(not(or(not(Q!0), not(P!1))))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(not(and(P!1, Q!0))), not(not(or(not(Q!0), not(P!1)))))))) = not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))),
% 64.76/41.67 inference(monotonicity,[status(thm)],[832])).
% 64.76/41.67 tff(834,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(not(not(or(not(Q!0), not(P!1))))), not(not(or(not(P!1), not(Q!0))))), or(not(not(and(P!1, Q!0))), not(not(or(not(Q!0), not(P!1)))))) = not(or(not(or(not(not(not(or(not(Q!0), not(P!1))))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(not(and(P!1, Q!0))), not(not(or(not(Q!0), not(P!1)))))))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(835,plain,
% 64.76/41.67 (and(or(not(not(not(or(not(Q!0), not(P!1))))), not(not(or(not(P!1), not(Q!0))))), or(not(not(and(P!1, Q!0))), not(not(or(not(Q!0), not(P!1)))))) = not(or(not(or(not(not(not(or(not(Q!0), not(P!1))))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(not(and(P!1, Q!0))), not(not(or(not(Q!0), not(P!1))))))))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[834, 113])).
% 64.76/41.67 tff(836,plain,
% 64.76/41.67 (or(not(not(not(or(not(Q!0), not(P!1))))), not(not(or(not(P!1), not(Q!0))))) = or(not(not(not(or(not(Q!0), not(P!1))))), not(and(P!1, Q!0)))),
% 64.76/41.67 inference(monotonicity,[status(thm)],[128])).
% 64.76/41.67 tff(837,plain,
% 64.76/41.67 (or(not(not(not(or(not(Q!0), not(P!1))))), not(and(P!1, Q!0))) = or(not(not(not(or(not(Q!0), not(P!1))))), not(not(or(not(P!1), not(Q!0)))))),
% 64.76/41.67 inference(symmetry,[status(thm)],[836])).
% 64.76/41.67 tff(838,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))) = or(not(not(not(or(not(Q!0), not(P!1))))), not(and(P!1, Q!0))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(839,plain,
% 64.76/41.67 (implies(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))) = or(not(not(not(or(not(Q!0), not(P!1))))), not(and(P!1, Q!0)))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[838, 20])).
% 64.76/41.67 tff(840,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))) = not(and(not(not(or(not(Q!0), not(P!1)))), not(not(and(P!1, Q!0))))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(841,plain,
% 64.76/41.67 (implies(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))) = not(and(not(not(or(not(Q!0), not(P!1)))), not(not(and(P!1, Q!0)))))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[840, 91])).
% 64.76/41.67 tff(842,plain,
% 64.76/41.67 (not(and(not(not(or(not(Q!0), not(P!1)))), not(not(and(P!1, Q!0))))) = implies(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0)))),
% 64.76/41.67 inference(symmetry,[status(thm)],[841])).
% 64.76/41.67 tff(843,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))) = not(and(not(not(or(not(Q!0), not(P!1)))), not(not(and(P!1, Q!0))))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(844,plain,
% 64.76/41.67 (or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))) = not(and(not(not(or(not(Q!0), not(P!1)))), not(not(and(P!1, Q!0)))))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[843, 42])).
% 64.76/41.67 tff(845,plain,
% 64.76/41.67 (or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))) = or(not(not(not(or(not(Q!0), not(P!1))))), not(not(or(not(P!1), not(Q!0)))))),
% 64.76/41.67 inference(transitivity,[status(thm)],[844, 842, 839, 837])).
% 64.76/41.67 tff(846,plain,
% 64.76/41.67 (and(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), or(not(not(and(P!1, Q!0))), not(not(or(not(Q!0), not(P!1)))))) = and(or(not(not(not(or(not(Q!0), not(P!1))))), not(not(or(not(P!1), not(Q!0))))), or(not(not(and(P!1, Q!0))), not(not(or(not(Q!0), not(P!1))))))),
% 64.76/41.67 inference(monotonicity,[status(thm)],[845])).
% 64.76/41.67 tff(847,plain,
% 64.76/41.67 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(P!1, Q!0)), not(not(or(not(Q!0), not(P!1))))) = or(not(not(and(P!1, Q!0))), not(not(or(not(Q!0), not(P!1))))))),
% 64.76/41.67 inference(quant_inst,[status(thm)],[])).
% 64.76/41.67 tff(848,plain,
% 64.76/41.67 (implies(not(and(P!1, Q!0)), not(not(or(not(Q!0), not(P!1))))) = or(not(not(and(P!1, Q!0))), not(not(or(not(Q!0), not(P!1)))))),
% 64.76/41.67 inference(unit_resolution,[status(thm)],[847, 20])).
% 64.76/41.67 tff(849,plain,
% 64.76/41.67 (not(and(not(not(or(not(Q!0), not(P!1)))), not(not(and(P!1, Q!0))))) = or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))),
% 64.76/41.68 inference(symmetry,[status(thm)],[844])).
% 64.76/41.68 tff(850,plain,
% 64.76/41.68 (implies(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))) = or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))),
% 64.76/41.68 inference(transitivity,[status(thm)],[841, 849])).
% 64.76/41.68 tff(851,plain,
% 64.76/41.68 (and(implies(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))), implies(not(and(P!1, Q!0)), not(not(or(not(Q!0), not(P!1)))))) = and(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), or(not(not(and(P!1, Q!0))), not(not(or(not(Q!0), not(P!1))))))),
% 64.76/41.68 inference(monotonicity,[status(thm)],[850, 848])).
% 64.76/41.68 tff(852,plain,
% 64.76/41.68 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))) = and(implies(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))), implies(not(and(P!1, Q!0)), not(not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.68 inference(quant_inst,[status(thm)],[])).
% 64.76/41.68 tff(853,plain,
% 64.76/41.68 (equiv(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))) = and(implies(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))), implies(not(and(P!1, Q!0)), not(not(or(not(Q!0), not(P!1))))))),
% 64.76/41.68 inference(unit_resolution,[status(thm)],[852, 66])).
% 64.76/41.68 tff(854,plain,
% 64.76/41.68 (equiv(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))) = equiv(not(not(or(not(Q!0), not(P!1)))), or(not(P!1), not(Q!0)))),
% 64.76/41.68 inference(transitivity,[status(thm)],[853, 851, 846, 835, 833, 808, 774, 771, 761])).
% 64.76/41.68 tff(855,plain,
% 64.76/41.68 (is_a_theorem(equiv(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0)))) <=> is_a_theorem(equiv(not(not(or(not(Q!0), not(P!1)))), or(not(P!1), not(Q!0))))),
% 64.76/41.68 inference(monotonicity,[status(thm)],[854])).
% 64.76/41.68 tff(856,plain,
% 64.76/41.68 (is_a_theorem(equiv(not(not(or(not(Q!0), not(P!1)))), or(not(P!1), not(Q!0)))) <=> is_a_theorem(equiv(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))))),
% 64.76/41.68 inference(symmetry,[status(thm)],[855])).
% 64.76/41.68 tff(857,plain,
% 64.76/41.68 (not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))) = equiv(not(not(or(not(Q!0), not(P!1)))), or(not(P!1), not(Q!0)))),
% 64.76/41.68 inference(transitivity,[status(thm)],[808, 774, 771, 761])).
% 64.76/41.68 tff(858,plain,
% 64.76/41.68 (is_a_theorem(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))) <=> is_a_theorem(equiv(not(not(or(not(Q!0), not(P!1)))), or(not(P!1), not(Q!0))))),
% 64.76/41.68 inference(monotonicity,[status(thm)],[857])).
% 64.76/41.68 tff(859,plain,
% 64.76/41.68 (is_a_theorem(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))) <=> is_a_theorem(equiv(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))))),
% 64.76/41.68 inference(transitivity,[status(thm)],[858, 856])).
% 64.76/41.68 tff(860,plain,
% 64.76/41.68 (or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))) = or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))),
% 64.76/41.68 inference(monotonicity,[status(thm)],[444])).
% 64.76/41.68 tff(861,plain,
% 64.76/41.68 (not(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))) = not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))),
% 64.76/41.68 inference(monotonicity,[status(thm)],[860])).
% 64.76/41.68 tff(862,plain,
% 64.76/41.68 (or(not(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))) = or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))),
% 64.76/41.68 inference(monotonicity,[status(thm)],[861])).
% 64.76/41.68 tff(863,plain,
% 64.76/41.68 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))) = or(not(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))),
% 64.76/41.68 inference(quant_inst,[status(thm)],[])).
% 64.76/41.68 tff(864,plain,
% 64.76/41.68 (implies(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))) = or(not(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))),
% 64.76/41.68 inference(unit_resolution,[status(thm)],[863, 20])).
% 64.76/41.68 tff(865,plain,
% 64.76/41.68 (implies(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))) = or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))),
% 64.76/41.68 inference(transitivity,[status(thm)],[864, 862])).
% 64.76/41.68 tff(866,plain,
% 64.76/41.68 (is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))) <=> is_a_theorem(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))),
% 64.76/41.68 inference(monotonicity,[status(thm)],[865])).
% 64.76/41.68 tff(867,plain,
% 64.76/41.68 (is_a_theorem(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))) <=> is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))),
% 64.76/41.68 inference(symmetry,[status(thm)],[866])).
% 64.76/41.68 tff(868,plain,
% 64.76/41.68 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))) = not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))),
% 64.76/41.68 inference(quant_inst,[status(thm)],[])).
% 64.76/41.68 tff(869,plain,
% 64.76/41.68 (or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))) = not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))),
% 64.76/41.68 inference(unit_resolution,[status(thm)],[868, 42])).
% 64.76/41.68 tff(870,plain,
% 64.76/41.68 (implies(or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))) = implies(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))),
% 64.76/41.68 inference(monotonicity,[status(thm)],[869])).
% 64.76/41.68 tff(871,plain,
% 64.76/41.68 (is_a_theorem(implies(or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))) <=> is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))))),
% 64.76/41.68 inference(monotonicity,[status(thm)],[870])).
% 64.76/41.68 tff(872,plain,
% 64.76/41.68 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))))),
% 64.76/41.68 inference(quant_inst,[status(thm)],[])).
% 64.76/41.68 tff(873,plain,
% 64.76/41.68 (is_a_theorem(implies(or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))))),
% 64.76/41.68 inference(unit_resolution,[status(thm)],[872, 405])).
% 64.76/41.68 tff(874,plain,
% 64.76/41.68 (is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))))),
% 64.76/41.68 inference(modus_ponens,[status(thm)],[873, 871])).
% 64.76/41.68 tff(875,plain,
% 64.76/41.68 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(Q!0), not(P!1)) = not(and(not(not(Q!0)), not(not(P!1)))))),
% 64.76/41.68 inference(quant_inst,[status(thm)],[])).
% 64.76/41.68 tff(876,plain,
% 64.76/41.68 (or(not(Q!0), not(P!1)) = not(and(not(not(Q!0)), not(not(P!1))))),
% 64.76/41.68 inference(unit_resolution,[status(thm)],[875, 42])).
% 64.76/41.68 tff(877,plain,
% 64.76/41.68 (not(and(not(not(Q!0)), not(not(P!1)))) = or(not(Q!0), not(P!1))),
% 64.76/41.68 inference(symmetry,[status(thm)],[876])).
% 64.76/41.68 tff(878,plain,
% 64.76/41.68 (or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1))))) = or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1)))),
% 64.76/41.68 inference(monotonicity,[status(thm)],[877])).
% 64.76/41.68 tff(879,plain,
% 64.76/41.68 (or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))) = or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))),
% 64.76/41.68 inference(symmetry,[status(thm)],[878])).
% 64.76/41.68 tff(880,plain,
% 64.76/41.68 (not(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1)))) = not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1))))))),
% 64.76/41.68 inference(monotonicity,[status(thm)],[879])).
% 64.76/41.68 tff(881,plain,
% 64.76/41.68 (not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))) = not(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))))),
% 64.76/41.68 inference(symmetry,[status(thm)],[880])).
% 64.76/41.68 tff(882,plain,
% 64.76/41.68 (or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))) = or(not(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1)))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))),
% 64.76/41.68 inference(monotonicity,[status(thm)],[881])).
% 64.76/41.68 tff(883,plain,
% 64.76/41.68 (or(not(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1)))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))) = or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))),
% 64.76/41.68 inference(symmetry,[status(thm)],[882])).
% 64.76/41.68 tff(884,plain,
% 64.76/41.68 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))) = or(not(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1)))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))),
% 64.76/41.68 inference(quant_inst,[status(thm)],[])).
% 64.76/41.68 tff(885,plain,
% 64.76/41.68 (implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))) = or(not(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1)))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))),
% 64.76/41.68 inference(unit_resolution,[status(thm)],[884, 20])).
% 64.76/41.68 tff(886,plain,
% 64.76/41.68 (implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))) = implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))),
% 64.76/41.68 inference(monotonicity,[status(thm)],[869])).
% 64.76/41.68 tff(887,plain,
% 64.76/41.68 (implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))) = implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))),
% 64.76/41.68 inference(symmetry,[status(thm)],[886])).
% 64.76/41.68 tff(888,plain,
% 64.76/41.68 (implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))) = or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))),
% 64.76/41.68 inference(transitivity,[status(thm)],[887, 885, 883])).
% 64.76/41.68 tff(889,plain,
% 64.76/41.68 (is_a_theorem(implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))) <=> is_a_theorem(or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))),
% 64.76/41.68 inference(monotonicity,[status(thm)],[888])).
% 64.76/41.68 tff(890,plain,
% 64.76/41.68 (is_a_theorem(or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))) <=> is_a_theorem(implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))))),
% 64.76/41.68 inference(symmetry,[status(thm)],[889])).
% 64.76/41.68 tff(891,plain,
% 64.76/41.68 (and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))) = and(implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1))), implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0))))),
% 64.76/41.68 inference(monotonicity,[status(thm)],[788, 791])).
% 64.76/41.68 tff(892,plain,
% 64.76/41.68 (and(implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1))), implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0)))) = and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))))),
% 64.76/41.68 inference(symmetry,[status(thm)],[891])).
% 64.76/41.68 tff(893,plain,
% 64.76/41.68 (and(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))) = and(implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1))), implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0))))),
% 64.76/41.68 inference(monotonicity,[status(thm)],[811, 791])).
% 64.76/41.68 tff(894,plain,
% 64.76/41.68 (and(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))) = and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))))),
% 64.76/41.68 inference(transitivity,[status(thm)],[893, 892])).
% 64.76/41.68 tff(895,plain,
% 64.76/41.68 (not(and(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))))) = not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))),
% 64.76/41.69 inference(monotonicity,[status(thm)],[894])).
% 64.76/41.69 tff(896,plain,
% 64.76/41.69 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))) = not(and(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))))))),
% 64.76/41.69 inference(quant_inst,[status(thm)],[])).
% 64.76/41.69 tff(897,plain,
% 64.76/41.69 (implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))) = not(and(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))),
% 64.76/41.69 inference(unit_resolution,[status(thm)],[896, 91])).
% 64.76/41.69 tff(898,plain,
% 64.76/41.69 (implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))) = implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))),
% 64.76/41.69 inference(monotonicity,[status(thm)],[780])).
% 64.76/41.69 tff(899,plain,
% 64.76/41.69 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))) = or(not(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1)))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))),
% 64.76/41.69 inference(quant_inst,[status(thm)],[])).
% 64.76/41.69 tff(900,plain,
% 64.76/41.69 (implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))) = or(not(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1)))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))),
% 64.76/41.69 inference(unit_resolution,[status(thm)],[899, 20])).
% 64.76/41.69 tff(901,plain,
% 64.76/41.69 (or(not(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1)))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))) = implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))),
% 64.76/41.69 inference(symmetry,[status(thm)],[900])).
% 64.76/41.69 tff(902,plain,
% 64.76/41.69 (or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))) = or(not(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1)))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))),
% 64.76/41.69 inference(monotonicity,[status(thm)],[881])).
% 64.76/41.69 tff(903,plain,
% 64.76/41.69 (or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))) = not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))),
% 64.76/41.69 inference(transitivity,[status(thm)],[902, 901, 898, 897, 895])).
% 64.76/41.69 tff(904,plain,
% 64.76/41.69 (not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))) = or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.69 inference(transitivity,[status(thm)],[785, 782])).
% 64.76/41.69 tff(905,plain,
% 64.76/41.69 (not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))) = not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))),
% 64.76/41.69 inference(monotonicity,[status(thm)],[904])).
% 64.76/41.69 tff(906,plain,
% 64.76/41.69 (not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))) = not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))))),
% 64.76/41.69 inference(symmetry,[status(thm)],[905])).
% 64.76/41.69 tff(907,plain,
% 64.76/41.69 (or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))) = or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))))))),
% 64.76/41.69 inference(monotonicity,[status(thm)],[906, 903])).
% 64.76/41.69 tff(908,plain,
% 64.76/41.69 (or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))) = or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))),
% 64.76/41.69 inference(symmetry,[status(thm)],[907])).
% 64.76/41.69 tff(909,plain,
% 64.76/41.69 (implies(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))) = implies(or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))),
% 64.76/41.69 inference(monotonicity,[status(thm)],[908])).
% 64.76/41.69 tff(910,plain,
% 64.76/41.69 (implies(or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))) = implies(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))),
% 64.76/41.69 inference(symmetry,[status(thm)],[909])).
% 64.76/41.69 tff(911,plain,
% 64.76/41.69 (is_a_theorem(implies(or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))) <=> is_a_theorem(implies(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))),
% 64.76/41.69 inference(monotonicity,[status(thm)],[910])).
% 64.76/41.69 tff(912,plain,
% 64.76/41.69 ((~![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(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))),
% 64.76/41.69 inference(quant_inst,[status(thm)],[])).
% 64.76/41.69 tff(913,plain,
% 64.76/41.69 (is_a_theorem(implies(or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))),
% 64.76/41.69 inference(unit_resolution,[status(thm)],[912, 365])).
% 64.76/41.69 tff(914,plain,
% 64.76/41.69 (is_a_theorem(implies(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))),
% 64.76/41.69 inference(modus_ponens,[status(thm)],[913, 911])).
% 64.76/41.69 tff(915,plain,
% 64.76/41.69 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))) = or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))))),
% 64.76/41.69 inference(quant_inst,[status(thm)],[])).
% 64.76/41.69 tff(916,plain,
% 64.76/41.69 (implies(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))) = or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))))))),
% 64.76/41.69 inference(unit_resolution,[status(thm)],[915, 20])).
% 64.76/41.69 tff(917,plain,
% 64.76/41.69 (or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))) = implies(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))))))),
% 64.76/41.69 inference(symmetry,[status(thm)],[916])).
% 64.76/41.69 tff(918,plain,
% 64.76/41.69 (is_a_theorem(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))))))) <=> is_a_theorem(implies(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))))),
% 64.76/41.69 inference(monotonicity,[status(thm)],[917])).
% 64.76/41.69 tff(919,plain,
% 64.76/41.69 (is_a_theorem(implies(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))))))) <=> is_a_theorem(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))))),
% 64.76/41.69 inference(symmetry,[status(thm)],[918])).
% 64.76/41.69 tff(920,plain,
% 64.76/41.69 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))), and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))) = not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))))))),
% 64.76/41.69 inference(quant_inst,[status(thm)],[])).
% 64.76/41.69 tff(921,plain,
% 64.76/41.69 (or(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))), and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))) = not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))),
% 64.76/41.69 inference(unit_resolution,[status(thm)],[920, 42])).
% 64.76/41.69 tff(922,plain,
% 64.76/41.69 (or(not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))) = or(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))), and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))),
% 64.76/41.69 inference(monotonicity,[status(thm)],[777, 780])).
% 64.76/41.69 tff(923,plain,
% 64.76/41.69 (or(not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))) = not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))),
% 64.76/41.69 inference(transitivity,[status(thm)],[922, 921])).
% 64.76/41.69 tff(924,plain,
% 64.76/41.69 (or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))) = not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.69 inference(transitivity,[status(thm)],[781, 784])).
% 64.76/41.69 tff(925,plain,
% 64.76/41.69 (implies(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))) = implies(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))))))),
% 64.76/41.69 inference(monotonicity,[status(thm)],[924, 923])).
% 64.76/41.69 tff(926,plain,
% 64.76/41.69 (is_a_theorem(implies(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))) <=> is_a_theorem(implies(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))))),
% 64.76/41.69 inference(monotonicity,[status(thm)],[925])).
% 64.76/41.69 tff(927,plain,
% 64.76/41.69 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))),
% 64.76/41.69 inference(quant_inst,[status(thm)],[])).
% 64.76/41.69 tff(928,plain,
% 64.76/41.69 (is_a_theorem(implies(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))),
% 64.76/41.69 inference(unit_resolution,[status(thm)],[927, 405])).
% 64.76/41.69 tff(929,plain,
% 64.76/41.69 (is_a_theorem(implies(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))))),
% 64.76/41.69 inference(modus_ponens,[status(thm)],[928, 926])).
% 64.76/41.69 tff(930,plain,
% 64.76/41.69 (is_a_theorem(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))))),
% 64.76/41.69 inference(modus_ponens,[status(thm)],[929, 919])).
% 64.76/41.69 tff(931,plain,
% 64.76/41.69 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))))) | is_a_theorem(or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))))) | is_a_theorem(or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))))),
% 64.76/41.70 inference(rewrite,[status(thm)],[])).
% 64.76/41.70 tff(932,plain,
% 64.76/41.70 ((is_a_theorem(or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))))))))) <=> ((~is_a_theorem(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))))) | is_a_theorem(or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))))),
% 64.76/41.70 inference(rewrite,[status(thm)],[])).
% 64.76/41.70 tff(933,plain,
% 64.76/41.70 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))))) | is_a_theorem(or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))))))),
% 64.76/41.70 inference(monotonicity,[status(thm)],[932])).
% 64.76/41.70 tff(934,plain,
% 64.76/41.70 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))))) | is_a_theorem(or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))))),
% 64.76/41.70 inference(transitivity,[status(thm)],[933, 931])).
% 64.76/41.70 tff(935,plain,
% 64.76/41.70 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))))))),
% 64.76/41.70 inference(quant_inst,[status(thm)],[])).
% 64.76/41.70 tff(936,plain,
% 64.76/41.70 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))))) | is_a_theorem(or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))))),
% 64.76/41.70 inference(modus_ponens,[status(thm)],[935, 934])).
% 64.76/41.70 tff(937,plain,
% 64.76/41.70 ((~is_a_theorem(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))))) | is_a_theorem(or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0))))), not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))), not(and(not(and(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))), not(and(or(not(Q!0), not(P!1)), not(or(not(P!1), not(Q!0)))))))), or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))))),
% 64.76/41.70 inference(unit_resolution,[status(thm)],[936, 429])).
% 64.76/41.70 tff(938,plain,
% 64.76/41.70 (is_a_theorem(or(not(or(not(or(not(P!1), not(Q!0))), not(and(not(not(Q!0)), not(not(P!1)))))), or(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))), not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))),
% 64.76/41.70 inference(unit_resolution,[status(thm)],[937, 930, 914])).
% 64.76/41.70 tff(939,plain,
% 64.76/41.70 (is_a_theorem(implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))))),
% 64.76/41.70 inference(modus_ponens,[status(thm)],[938, 890])).
% 64.76/41.70 tff(940,plain,
% 64.76/41.70 (is_a_theorem(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1)))) <=> is_a_theorem(implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1))))),
% 64.76/41.70 inference(monotonicity,[status(thm)],[811])).
% 64.76/41.70 tff(941,plain,
% 64.76/41.70 (is_a_theorem(implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1)))) <=> is_a_theorem(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))))),
% 64.76/41.70 inference(symmetry,[status(thm)],[940])).
% 64.76/41.70 tff(942,plain,
% 64.76/41.70 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1))))),
% 64.76/41.70 inference(quant_inst,[status(thm)],[])).
% 64.76/41.70 tff(943,plain,
% 64.76/41.70 (is_a_theorem(implies(or(not(P!1), not(Q!0)), or(not(Q!0), not(P!1))))),
% 64.76/41.70 inference(unit_resolution,[status(thm)],[942, 405])).
% 64.76/41.70 tff(944,plain,
% 64.76/41.70 (is_a_theorem(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))))),
% 64.76/41.70 inference(modus_ponens,[status(thm)],[943, 941])).
% 64.76/41.70 tff(945,plain,
% 64.76/41.70 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))) | (~is_a_theorem(implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))) | (~is_a_theorem(implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))))))),
% 64.76/41.70 inference(rewrite,[status(thm)],[])).
% 64.76/41.70 tff(946,plain,
% 64.76/41.70 ((is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))) | (~is_a_theorem(implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))))) | (~is_a_theorem(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1)))))) <=> ((~is_a_theorem(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))) | (~is_a_theorem(implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))))))),
% 64.76/41.70 inference(rewrite,[status(thm)],[])).
% 64.76/41.70 tff(947,plain,
% 64.76/41.70 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))) | (~is_a_theorem(implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))))) | (~is_a_theorem(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))) | (~is_a_theorem(implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))))))),
% 64.76/41.70 inference(monotonicity,[status(thm)],[946])).
% 64.76/41.70 tff(948,plain,
% 64.76/41.70 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))) | (~is_a_theorem(implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))))) | (~is_a_theorem(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))) | (~is_a_theorem(implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))))))),
% 64.76/41.71 inference(transitivity,[status(thm)],[947, 945])).
% 64.76/41.71 tff(949,plain,
% 64.76/41.71 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))) | (~is_a_theorem(implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))))) | (~is_a_theorem(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))))))),
% 64.76/41.71 inference(quant_inst,[status(thm)],[])).
% 64.76/41.71 tff(950,plain,
% 64.76/41.71 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))) | (~is_a_theorem(implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))))),
% 64.76/41.71 inference(modus_ponens,[status(thm)],[949, 948])).
% 64.76/41.71 tff(951,plain,
% 64.76/41.71 (is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))) | (~is_a_theorem(implies(or(not(or(not(P!1), not(Q!0))), or(not(Q!0), not(P!1))), not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))))),
% 64.76/41.71 inference(unit_resolution,[status(thm)],[950, 429, 944])).
% 64.76/41.71 tff(952,plain,
% 64.76/41.71 (is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))),
% 64.76/41.71 inference(unit_resolution,[status(thm)],[951, 939])).
% 64.76/41.71 tff(953,plain,
% 64.76/41.71 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))) | is_a_theorem(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))) | is_a_theorem(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))))))),
% 64.76/41.71 inference(rewrite,[status(thm)],[])).
% 64.76/41.71 tff(954,plain,
% 64.76/41.71 ((is_a_theorem(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))))))))) <=> ((~is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))) | is_a_theorem(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))))))),
% 64.76/41.71 inference(rewrite,[status(thm)],[])).
% 64.76/41.71 tff(955,plain,
% 64.76/41.71 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))) | is_a_theorem(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))))))),
% 64.76/41.71 inference(monotonicity,[status(thm)],[954])).
% 64.76/41.71 tff(956,plain,
% 64.76/41.71 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))) | is_a_theorem(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))))))),
% 64.76/41.71 inference(transitivity,[status(thm)],[955, 953])).
% 64.76/41.71 tff(957,plain,
% 64.76/41.71 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))))),
% 64.76/41.71 inference(quant_inst,[status(thm)],[])).
% 64.76/41.71 tff(958,plain,
% 64.76/41.71 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))) | is_a_theorem(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))))),
% 64.76/41.71 inference(modus_ponens,[status(thm)],[957, 956])).
% 64.76/41.71 tff(959,plain,
% 64.76/41.71 ((~is_a_theorem(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))))) | is_a_theorem(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))), not(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0))))))))), or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))))),
% 64.76/41.71 inference(unit_resolution,[status(thm)],[958, 429])).
% 64.76/41.71 tff(960,plain,
% 64.76/41.71 (is_a_theorem(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))),
% 64.76/41.71 inference(unit_resolution,[status(thm)],[959, 952, 874])).
% 64.76/41.71 tff(961,plain,
% 64.76/41.71 (is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))),
% 64.76/41.71 inference(modus_ponens,[status(thm)],[960, 867])).
% 64.76/41.71 tff(962,plain,
% 64.76/41.71 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))) = not(and(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.71 inference(quant_inst,[status(thm)],[])).
% 64.76/41.71 tff(963,plain,
% 64.76/41.71 (or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))) = not(and(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))),
% 64.76/41.71 inference(unit_resolution,[status(thm)],[962, 42])).
% 64.76/41.71 tff(964,plain,
% 64.76/41.71 (not(and(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))) = or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))),
% 64.76/41.71 inference(symmetry,[status(thm)],[963])).
% 64.76/41.71 tff(965,plain,
% 64.76/41.71 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(or(not(P!1), not(Q!0))), not(or(not(Q!0), not(P!1)))) = not(and(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.71 inference(quant_inst,[status(thm)],[])).
% 64.76/41.71 tff(966,plain,
% 64.76/41.71 (implies(not(or(not(P!1), not(Q!0))), not(or(not(Q!0), not(P!1)))) = not(and(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))),
% 64.76/41.71 inference(unit_resolution,[status(thm)],[965, 91])).
% 64.76/41.71 tff(967,plain,
% 64.76/41.71 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(not(P!1), not(Q!0))), not(or(not(Q!0), not(P!1)))) = or(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1)))))),
% 64.76/41.71 inference(quant_inst,[status(thm)],[])).
% 64.76/41.71 tff(968,plain,
% 64.76/41.71 (implies(not(or(not(P!1), not(Q!0))), not(or(not(Q!0), not(P!1)))) = or(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1))))),
% 64.76/41.71 inference(unit_resolution,[status(thm)],[967, 20])).
% 64.76/41.71 tff(969,plain,
% 64.76/41.71 (or(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1)))) = implies(not(or(not(P!1), not(Q!0))), not(or(not(Q!0), not(P!1))))),
% 64.76/41.71 inference(symmetry,[status(thm)],[968])).
% 64.76/41.71 tff(970,plain,
% 64.76/41.71 (or(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1)))) = or(not(not(or(not(P!1), not(Q!0)))), not(or(not(Q!0), not(P!1))))),
% 64.76/41.71 inference(monotonicity,[status(thm)],[444])).
% 64.76/41.71 tff(971,plain,
% 64.76/41.71 (or(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1)))) = or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))),
% 64.76/41.71 inference(transitivity,[status(thm)],[970, 969, 966, 964])).
% 64.76/41.71 tff(972,plain,
% 64.76/41.71 (is_a_theorem(or(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1))))) <=> is_a_theorem(or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))),
% 64.76/41.71 inference(monotonicity,[status(thm)],[971])).
% 64.76/41.71 tff(973,plain,
% 64.76/41.71 (is_a_theorem(or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))) <=> is_a_theorem(or(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1)))))),
% 64.76/41.71 inference(symmetry,[status(thm)],[972])).
% 64.76/41.71 tff(974,plain,
% 64.76/41.71 (is_a_theorem(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0)))) <=> is_a_theorem(implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0))))),
% 64.76/41.71 inference(monotonicity,[status(thm)],[796])).
% 64.76/41.71 tff(975,plain,
% 64.76/41.71 (is_a_theorem(implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0)))) <=> is_a_theorem(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))))),
% 64.76/41.71 inference(symmetry,[status(thm)],[974])).
% 64.76/41.71 tff(976,plain,
% 64.76/41.71 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0))))),
% 64.76/41.71 inference(quant_inst,[status(thm)],[])).
% 64.76/41.72 tff(977,plain,
% 64.76/41.72 (is_a_theorem(implies(or(not(Q!0), not(P!1)), or(not(P!1), not(Q!0))))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[976, 405])).
% 64.76/41.72 tff(978,plain,
% 64.76/41.72 (is_a_theorem(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[977, 975])).
% 64.76/41.72 tff(979,plain,
% 64.76/41.72 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))),
% 64.76/41.72 inference(quant_inst,[status(thm)],[])).
% 64.76/41.72 tff(980,plain,
% 64.76/41.72 (is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[979, 405])).
% 64.76/41.72 tff(981,plain,
% 64.76/41.72 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))))) | is_a_theorem(or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))))) | is_a_theorem(or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))))),
% 64.76/41.72 inference(rewrite,[status(thm)],[])).
% 64.76/41.72 tff(982,plain,
% 64.76/41.72 ((is_a_theorem(or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))) | (~is_a_theorem(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0)))))) <=> ((~is_a_theorem(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))))) | is_a_theorem(or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))))),
% 64.76/41.72 inference(rewrite,[status(thm)],[])).
% 64.76/41.72 tff(983,plain,
% 64.76/41.72 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))) | (~is_a_theorem(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))))) | is_a_theorem(or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))))),
% 64.76/41.72 inference(monotonicity,[status(thm)],[982])).
% 64.76/41.72 tff(984,plain,
% 64.76/41.72 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))) | (~is_a_theorem(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))))) | is_a_theorem(or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))))),
% 64.76/41.72 inference(transitivity,[status(thm)],[983, 981])).
% 64.76/41.72 tff(985,plain,
% 64.76/41.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))))) | (~is_a_theorem(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))))))),
% 64.76/41.72 inference(quant_inst,[status(thm)],[])).
% 64.76/41.72 tff(986,plain,
% 64.76/41.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))))) | is_a_theorem(or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))), or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[985, 984])).
% 64.76/41.72 tff(987,plain,
% 64.76/41.72 ((~is_a_theorem(or(not(or(not(Q!0), not(P!1))), or(not(P!1), not(Q!0))))) | is_a_theorem(or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[986, 429, 980])).
% 64.76/41.72 tff(988,plain,
% 64.76/41.72 (is_a_theorem(or(or(not(P!1), not(Q!0)), not(or(not(Q!0), not(P!1)))))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[987, 978])).
% 64.76/41.72 tff(989,plain,
% 64.76/41.72 (is_a_theorem(or(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1)))))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[988, 973])).
% 64.76/41.72 tff(990,plain,
% 64.76/41.72 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1)))), or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))))),
% 64.76/41.72 inference(quant_inst,[status(thm)],[])).
% 64.76/41.72 tff(991,plain,
% 64.76/41.72 (is_a_theorem(implies(or(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1)))), or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[990, 405])).
% 64.76/41.72 tff(992,plain,
% 64.76/41.72 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))) | (~is_a_theorem(implies(or(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1)))), or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))))) | (~is_a_theorem(or(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | is_a_theorem(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))) | (~is_a_theorem(implies(or(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1)))), or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))))) | (~is_a_theorem(or(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.72 inference(rewrite,[status(thm)],[])).
% 64.76/41.72 tff(993,plain,
% 64.76/41.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))) | (~is_a_theorem(implies(or(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1)))), or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))))) | (~is_a_theorem(or(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.72 inference(quant_inst,[status(thm)],[])).
% 64.76/41.72 tff(994,plain,
% 64.76/41.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | is_a_theorem(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))) | (~is_a_theorem(implies(or(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1)))), or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))))) | (~is_a_theorem(or(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1))))))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[993, 992])).
% 64.76/41.72 tff(995,plain,
% 64.76/41.72 (is_a_theorem(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))) | (~is_a_theorem(or(not(and(P!1, Q!0)), not(or(not(Q!0), not(P!1))))))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[994, 429, 991])).
% 64.76/41.72 tff(996,plain,
% 64.76/41.72 (is_a_theorem(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[995, 989])).
% 64.76/41.72 tff(997,plain,
% 64.76/41.72 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))))) | is_a_theorem(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))))) | is_a_theorem(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))))),
% 64.76/41.72 inference(rewrite,[status(thm)],[])).
% 64.76/41.72 tff(998,plain,
% 64.76/41.72 ((is_a_theorem(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))) | (~is_a_theorem(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0)))))) <=> ((~is_a_theorem(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))))) | is_a_theorem(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))))),
% 64.76/41.72 inference(rewrite,[status(thm)],[])).
% 64.76/41.72 tff(999,plain,
% 64.76/41.72 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))) | (~is_a_theorem(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))))) | is_a_theorem(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))))))),
% 64.76/41.72 inference(monotonicity,[status(thm)],[998])).
% 64.76/41.72 tff(1000,plain,
% 64.76/41.72 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))) | (~is_a_theorem(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))))) | is_a_theorem(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))))),
% 64.76/41.72 inference(transitivity,[status(thm)],[999, 997])).
% 64.76/41.72 tff(1001,plain,
% 64.76/41.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))))) | (~is_a_theorem(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))))))),
% 64.76/41.72 inference(quant_inst,[status(thm)],[])).
% 64.76/41.72 tff(1002,plain,
% 64.76/41.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))))) | is_a_theorem(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 64.76/41.72 tff(1003,plain,
% 64.76/41.72 (is_a_theorem(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1))))))))) | (~is_a_theorem(implies(or(not(or(not(Q!0), not(P!1))), not(and(P!1, Q!0))), not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[1002, 429, 996])).
% 64.76/41.72 tff(1004,plain,
% 64.76/41.72 (is_a_theorem(not(or(not(or(not(or(not(Q!0), not(P!1))), not(not(or(not(P!1), not(Q!0)))))), not(or(not(or(not(P!1), not(Q!0))), not(not(or(not(Q!0), not(P!1)))))))))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[1003, 961])).
% 64.76/41.72 tff(1005,plain,
% 64.76/41.72 (is_a_theorem(equiv(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1004, 859])).
% 64.76/41.72 tff(1006,plain,
% 64.76/41.72 (((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))))) | (not(not(or(not(Q!0), not(P!1)))) = not(and(P!1, Q!0))))) <=> ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))))) | (not(not(or(not(Q!0), not(P!1)))) = not(and(P!1, Q!0))))),
% 64.76/41.72 inference(rewrite,[status(thm)],[])).
% 64.76/41.72 tff(1007,plain,
% 64.76/41.72 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))))) | (not(not(or(not(Q!0), not(P!1)))) = not(and(P!1, Q!0))))),
% 64.76/41.72 inference(quant_inst,[status(thm)],[])).
% 64.76/41.72 tff(1008,plain,
% 64.76/41.72 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))))) | (not(not(or(not(Q!0), not(P!1)))) = not(and(P!1, Q!0)))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 64.76/41.72 tff(1009,plain,
% 64.76/41.72 ((~is_a_theorem(equiv(not(not(or(not(Q!0), not(P!1)))), not(and(P!1, Q!0))))) | (not(not(or(not(Q!0), not(P!1)))) = not(and(P!1, Q!0)))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[1008, 542])).
% 64.76/41.72 tff(1010,plain,
% 64.76/41.72 (not(not(or(not(Q!0), not(P!1)))) = not(and(P!1, Q!0))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[1009, 1005])).
% 64.76/41.72 tff(1011,plain,
% 64.76/41.72 (or(not(not(P!1)), not(not(or(not(Q!0), not(P!1))))) = or(not(not(P!1)), not(and(P!1, Q!0)))),
% 64.76/41.72 inference(monotonicity,[status(thm)],[1010])).
% 64.76/41.72 tff(1012,plain,
% 64.76/41.72 (or(not(not(P!1)), not(not(or(not(Q!0), not(P!1))))) = implies(not(or(not(P!1), not(Q!0))), not(not(P!1)))),
% 64.76/41.72 inference(transitivity,[status(thm)],[1011, 124, 121, 758, 598, 547, 23])).
% 64.76/41.72 tff(1013,plain,
% 64.76/41.72 (is_a_theorem(or(not(not(P!1)), not(not(or(not(Q!0), not(P!1)))))) <=> is_a_theorem(implies(not(or(not(P!1), not(Q!0))), not(not(P!1))))),
% 64.76/41.72 inference(monotonicity,[status(thm)],[1012])).
% 64.76/41.72 tff(1014,plain,
% 64.76/41.72 (is_a_theorem(implies(not(or(not(P!1), not(Q!0))), not(not(P!1)))) <=> is_a_theorem(or(not(not(P!1)), not(not(or(not(Q!0), not(P!1))))))),
% 64.76/41.72 inference(symmetry,[status(thm)],[1013])).
% 64.76/41.72 tff(1015,plain,
% 64.76/41.72 ((~is_a_theorem(implies(not(or(not(P!1), not(Q!0))), not(not(P!1))))) <=> (~is_a_theorem(or(not(not(P!1)), not(not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.72 inference(monotonicity,[status(thm)],[1014])).
% 64.76/41.72 tff(1016,plain,
% 64.76/41.72 (is_a_theorem(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))) <=> is_a_theorem(implies(not(or(not(P!1), not(Q!0))), not(not(P!1))))),
% 64.76/41.72 inference(monotonicity,[status(thm)],[23])).
% 64.76/41.72 tff(1017,plain,
% 64.76/41.72 ((~is_a_theorem(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))) <=> (~is_a_theorem(implies(not(or(not(P!1), not(Q!0))), not(not(P!1)))))),
% 64.76/41.72 inference(monotonicity,[status(thm)],[1016])).
% 64.76/41.72 tff(1018,plain,
% 64.76/41.72 (is_a_theorem(or(not(not(P!1)), not(and(P!1, Q!0)))) <=> is_a_theorem(or(P!1, not(and(P!1, Q!0))))),
% 64.76/41.72 inference(monotonicity,[status(thm)],[658])).
% 64.76/41.72 tff(1019,plain,
% 64.76/41.72 (is_a_theorem(or(P!1, not(and(P!1, Q!0)))) <=> is_a_theorem(or(not(not(P!1)), not(and(P!1, Q!0))))),
% 64.76/41.72 inference(symmetry,[status(thm)],[1018])).
% 64.76/41.72 tff(1020,plain,
% 64.76/41.72 ((~is_a_theorem(or(P!1, not(and(P!1, Q!0))))) <=> (~is_a_theorem(or(not(not(P!1)), not(and(P!1, Q!0)))))),
% 64.76/41.72 inference(monotonicity,[status(thm)],[1019])).
% 64.76/41.72 tff(1021,plain,
% 64.76/41.72 (is_a_theorem(or(not(and(P!1, Q!0)), P!1)) <=> is_a_theorem(implies(and(P!1, Q!0), P!1))),
% 64.76/41.72 inference(monotonicity,[status(thm)],[735])).
% 64.76/41.72 tff(1022,plain,
% 64.76/41.72 (is_a_theorem(implies(and(P!1, Q!0), P!1)) <=> is_a_theorem(or(not(and(P!1, Q!0)), P!1))),
% 64.76/41.72 inference(symmetry,[status(thm)],[1021])).
% 64.76/41.72 tff(1023,plain,
% 64.76/41.72 ((~is_a_theorem(implies(and(P!1, Q!0), P!1))) <=> (~is_a_theorem(or(not(and(P!1, Q!0)), P!1)))),
% 64.76/41.72 inference(monotonicity,[status(thm)],[1022])).
% 64.76/41.72 tff(1024,plain,
% 64.76/41.72 ((~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) <=> (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P)))),
% 64.76/41.72 inference(rewrite,[status(thm)],[])).
% 64.76/41.72 tff(1025,plain,
% 64.76/41.72 (($false <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) <=> (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P)))),
% 64.76/41.72 inference(rewrite,[status(thm)],[])).
% 64.76/41.72 tff(1026,axiom,(~kn2), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rosser_kn2')).
% 64.76/41.72 tff(1027,plain,
% 64.76/41.72 (kn2 <=> $false),
% 64.76/41.72 inference(iff_false,[status(thm)],[1026])).
% 64.76/41.72 tff(1028,plain,
% 64.76/41.72 ((kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) <=> ($false <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P)))),
% 64.76/41.72 inference(monotonicity,[status(thm)],[1027])).
% 64.76/41.72 tff(1029,plain,
% 64.76/41.72 ((kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) <=> (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P)))),
% 64.76/41.72 inference(transitivity,[status(thm)],[1028, 1025])).
% 64.76/41.72 tff(1030,plain,
% 64.76/41.72 ((kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) <=> (kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P)))),
% 64.76/41.72 inference(rewrite,[status(thm)],[])).
% 64.76/41.72 tff(1031,axiom,(kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','kn2')).
% 64.76/41.72 tff(1032,plain,
% 64.76/41.72 (kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 64.76/41.72 tff(1033,plain,
% 64.76/41.72 (kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1032, 1030])).
% 64.76/41.72 tff(1034,plain,
% 64.76/41.72 (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1033, 1029])).
% 64.76/41.72 tff(1035,plain,
% 64.76/41.72 (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1034, 1024])).
% 64.76/41.72 tff(1036,plain,
% 64.76/41.72 (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1035, 1024])).
% 64.76/41.72 tff(1037,plain,
% 64.76/41.72 (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1036, 1024])).
% 64.76/41.72 tff(1038,plain,
% 64.76/41.72 (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1037, 1024])).
% 64.76/41.72 tff(1039,plain,
% 64.76/41.72 (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1038, 1024])).
% 64.76/41.72 tff(1040,plain,
% 64.76/41.72 (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1039, 1024])).
% 64.76/41.72 tff(1041,plain,(
% 64.76/41.72 ~is_a_theorem(implies(and(P!1, Q!0), P!1))),
% 64.76/41.72 inference(skolemize,[status(sab)],[1040])).
% 64.76/41.72 tff(1042,plain,
% 64.76/41.72 (~is_a_theorem(or(not(and(P!1, Q!0)), P!1))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1041, 1023])).
% 64.76/41.72 tff(1043,plain,
% 64.76/41.72 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(and(P!1, Q!0)), P!1)) | (~is_a_theorem(implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)))) | (~is_a_theorem(or(P!1, not(and(P!1, Q!0))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | is_a_theorem(or(not(and(P!1, Q!0)), P!1)) | (~is_a_theorem(implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)))) | (~is_a_theorem(or(P!1, not(and(P!1, Q!0))))))),
% 64.76/41.72 inference(rewrite,[status(thm)],[])).
% 64.76/41.72 tff(1044,plain,
% 64.76/41.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(and(P!1, Q!0)), P!1)) | (~is_a_theorem(implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)))) | (~is_a_theorem(or(P!1, not(and(P!1, Q!0))))))),
% 64.76/41.72 inference(quant_inst,[status(thm)],[])).
% 64.76/41.72 tff(1045,plain,
% 64.76/41.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | is_a_theorem(or(not(and(P!1, Q!0)), P!1)) | (~is_a_theorem(implies(or(P!1, not(and(P!1, Q!0))), or(not(and(P!1, Q!0)), P!1)))) | (~is_a_theorem(or(P!1, not(and(P!1, Q!0)))))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 64.76/41.72 tff(1046,plain,
% 64.76/41.72 (is_a_theorem(or(not(and(P!1, Q!0)), P!1)) | (~is_a_theorem(or(P!1, not(and(P!1, Q!0)))))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[1045, 429, 493])).
% 64.76/41.72 tff(1047,plain,
% 64.76/41.72 (~is_a_theorem(or(P!1, not(and(P!1, Q!0))))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[1046, 1042])).
% 64.76/41.72 tff(1048,plain,
% 64.76/41.72 (~is_a_theorem(or(not(not(P!1)), not(and(P!1, Q!0))))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1047, 1020])).
% 64.76/41.72 tff(1049,plain,
% 64.76/41.72 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(not(P!1)), not(and(P!1, Q!0)))) | (~is_a_theorem(implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), or(not(not(P!1)), not(and(P!1, Q!0)))))) | (~is_a_theorem(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | is_a_theorem(or(not(not(P!1)), not(and(P!1, Q!0)))) | (~is_a_theorem(implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), or(not(not(P!1)), not(and(P!1, Q!0)))))) | (~is_a_theorem(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))),
% 64.76/41.72 inference(rewrite,[status(thm)],[])).
% 64.76/41.72 tff(1050,plain,
% 64.76/41.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(not(P!1)), not(and(P!1, Q!0)))) | (~is_a_theorem(implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), or(not(not(P!1)), not(and(P!1, Q!0)))))) | (~is_a_theorem(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))))),
% 64.76/41.72 inference(quant_inst,[status(thm)],[])).
% 64.76/41.72 tff(1051,plain,
% 64.76/41.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | is_a_theorem(or(not(not(P!1)), not(and(P!1, Q!0)))) | (~is_a_theorem(implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), or(not(not(P!1)), not(and(P!1, Q!0)))))) | (~is_a_theorem(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 64.76/41.72 tff(1052,plain,
% 64.76/41.72 (is_a_theorem(or(not(not(P!1)), not(and(P!1, Q!0)))) | (~is_a_theorem(implies(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))), or(not(not(P!1)), not(and(P!1, Q!0)))))) | (~is_a_theorem(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1)))))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[1051, 429])).
% 64.76/41.72 tff(1053,plain,
% 64.76/41.72 (~is_a_theorem(or(not(not(or(not(P!1), not(Q!0)))), not(not(P!1))))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[1052, 1048, 450])).
% 64.76/41.72 tff(1054,plain,
% 64.76/41.72 (~is_a_theorem(implies(not(or(not(P!1), not(Q!0))), not(not(P!1))))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1053, 1017])).
% 64.76/41.72 tff(1055,plain,
% 64.76/41.72 (~is_a_theorem(or(not(not(P!1)), not(not(or(not(Q!0), not(P!1))))))),
% 64.76/41.72 inference(modus_ponens,[status(thm)],[1054, 1015])).
% 64.76/41.72 tff(1056,plain,
% 64.76/41.72 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(or(not(Q!0), not(P!1)), not(not(P!1))) = not(and(not(or(not(Q!0), not(P!1))), not(not(not(P!1))))))),
% 64.76/41.72 inference(quant_inst,[status(thm)],[])).
% 64.76/41.72 tff(1057,plain,
% 64.76/41.72 (or(or(not(Q!0), not(P!1)), not(not(P!1))) = not(and(not(or(not(Q!0), not(P!1))), not(not(not(P!1)))))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[1056, 42])).
% 64.76/41.72 tff(1058,plain,
% 64.76/41.72 (not(and(not(or(not(Q!0), not(P!1))), not(not(not(P!1))))) = or(or(not(Q!0), not(P!1)), not(not(P!1)))),
% 64.76/41.72 inference(symmetry,[status(thm)],[1057])).
% 64.76/41.72 tff(1059,plain,
% 64.76/41.72 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(or(not(Q!0), not(P!1))), not(not(P!1))) = not(and(not(or(not(Q!0), not(P!1))), not(not(not(P!1))))))),
% 64.76/41.72 inference(quant_inst,[status(thm)],[])).
% 64.76/41.72 tff(1060,plain,
% 64.76/41.72 (implies(not(or(not(Q!0), not(P!1))), not(not(P!1))) = not(and(not(or(not(Q!0), not(P!1))), not(not(not(P!1)))))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[1059, 91])).
% 64.76/41.72 tff(1061,plain,
% 64.76/41.72 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(not(Q!0), not(P!1))), not(not(P!1))) = or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1))))),
% 64.76/41.72 inference(quant_inst,[status(thm)],[])).
% 64.76/41.72 tff(1062,plain,
% 64.76/41.72 (implies(not(or(not(Q!0), not(P!1))), not(not(P!1))) = or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1)))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[1061, 20])).
% 64.76/41.72 tff(1063,plain,
% 64.76/41.72 (or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1))) = implies(not(or(not(Q!0), not(P!1))), not(not(P!1)))),
% 64.76/41.72 inference(symmetry,[status(thm)],[1062])).
% 64.76/41.72 tff(1064,plain,
% 64.76/41.72 (or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1))) = or(or(not(Q!0), not(P!1)), not(not(P!1)))),
% 64.76/41.72 inference(transitivity,[status(thm)],[1063, 1060, 1058])).
% 64.76/41.72 tff(1065,plain,
% 64.76/41.72 (is_a_theorem(or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1)))) <=> is_a_theorem(or(or(not(Q!0), not(P!1)), not(not(P!1))))),
% 64.76/41.72 inference(monotonicity,[status(thm)],[1064])).
% 64.76/41.72 tff(1066,plain,
% 64.76/41.72 (is_a_theorem(or(or(not(Q!0), not(P!1)), not(not(P!1)))) <=> is_a_theorem(or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1))))),
% 64.76/41.72 inference(symmetry,[status(thm)],[1065])).
% 64.76/41.72 tff(1067,plain,
% 64.76/41.72 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(P!1), or(not(Q!0), not(P!1))) = or(not(not(P!1)), or(not(Q!0), not(P!1))))),
% 64.76/41.72 inference(quant_inst,[status(thm)],[])).
% 64.76/41.72 tff(1068,plain,
% 64.76/41.72 (implies(not(P!1), or(not(Q!0), not(P!1))) = or(not(not(P!1)), or(not(Q!0), not(P!1)))),
% 64.76/41.72 inference(unit_resolution,[status(thm)],[1067, 20])).
% 64.76/41.72 tff(1069,plain,
% 64.76/41.72 (or(not(not(P!1)), or(not(Q!0), not(P!1))) = implies(not(P!1), or(not(Q!0), not(P!1)))),
% 64.76/41.72 inference(symmetry,[status(thm)],[1068])).
% 64.76/41.72 tff(1070,plain,
% 64.76/41.72 (is_a_theorem(or(not(not(P!1)), or(not(Q!0), not(P!1)))) <=> is_a_theorem(implies(not(P!1), or(not(Q!0), not(P!1))))),
% 64.76/41.72 inference(monotonicity,[status(thm)],[1069])).
% 64.76/41.72 tff(1071,plain,
% 64.76/41.72 (is_a_theorem(implies(not(P!1), or(not(Q!0), not(P!1)))) <=> is_a_theorem(or(not(not(P!1)), or(not(Q!0), not(P!1))))),
% 64.76/41.72 inference(symmetry,[status(thm)],[1070])).
% 64.76/41.72 tff(1072,plain,
% 64.76/41.72 (^[P: $i, Q: $i] : refl(is_a_theorem(implies(Q, or(P, Q))) <=> is_a_theorem(implies(Q, or(P, Q))))),
% 64.76/41.72 inference(bind,[status(th)],[])).
% 64.76/41.73 tff(1073,plain,
% 64.76/41.73 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 64.76/41.73 inference(quant_intro,[status(thm)],[1072])).
% 64.76/41.73 tff(1074,plain,
% 64.76/41.73 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 64.76/41.73 inference(rewrite,[status(thm)],[])).
% 64.76/41.73 tff(1075,plain,
% 64.76/41.73 (($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)))),
% 64.76/41.73 inference(rewrite,[status(thm)],[])).
% 64.76/41.73 tff(1076,axiom,(r2), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_r2')).
% 64.76/41.73 tff(1077,plain,
% 64.76/41.73 (r2 <=> $true),
% 64.76/41.73 inference(iff_true,[status(thm)],[1076])).
% 64.76/41.73 tff(1078,plain,
% 64.76/41.73 ((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))))),
% 64.76/41.73 inference(monotonicity,[status(thm)],[1077])).
% 64.76/41.73 tff(1079,plain,
% 64.76/41.73 ((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)))),
% 64.76/41.73 inference(transitivity,[status(thm)],[1078, 1075])).
% 64.76/41.73 tff(1080,plain,
% 64.76/41.73 ((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))))),
% 64.76/41.73 inference(rewrite,[status(thm)],[])).
% 64.76/41.73 tff(1081,axiom,(r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','r2')).
% 64.76/41.73 tff(1082,plain,
% 64.76/41.73 (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 64.76/41.73 inference(modus_ponens,[status(thm)],[1081, 1080])).
% 64.76/41.73 tff(1083,plain,
% 64.76/41.73 (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 64.76/41.73 inference(modus_ponens,[status(thm)],[1082, 1080])).
% 64.76/41.73 tff(1084,plain,
% 64.76/41.73 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 64.76/41.73 inference(modus_ponens,[status(thm)],[1083, 1079])).
% 64.76/41.73 tff(1085,plain,
% 64.76/41.73 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 64.76/41.73 inference(modus_ponens,[status(thm)],[1084, 1074])).
% 64.76/41.73 tff(1086,plain,(
% 64.76/41.73 ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 64.76/41.73 inference(skolemize,[status(sab)],[1085])).
% 64.76/41.73 tff(1087,plain,
% 64.76/41.73 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 64.76/41.73 inference(modus_ponens,[status(thm)],[1086, 1073])).
% 64.76/41.73 tff(1088,plain,
% 64.76/41.73 ((~![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) | is_a_theorem(implies(not(P!1), or(not(Q!0), not(P!1))))),
% 64.76/41.73 inference(quant_inst,[status(thm)],[])).
% 64.76/41.73 tff(1089,plain,
% 64.76/41.73 (is_a_theorem(implies(not(P!1), or(not(Q!0), not(P!1))))),
% 64.76/41.73 inference(unit_resolution,[status(thm)],[1088, 1087])).
% 64.76/41.73 tff(1090,plain,
% 64.76/41.73 (is_a_theorem(or(not(not(P!1)), or(not(Q!0), not(P!1))))),
% 64.76/41.73 inference(modus_ponens,[status(thm)],[1089, 1071])).
% 64.76/41.73 tff(1091,plain,
% 64.76/41.73 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(not(P!1)), or(not(Q!0), not(P!1))), or(or(not(Q!0), not(P!1)), not(not(P!1)))))),
% 64.76/41.73 inference(quant_inst,[status(thm)],[])).
% 64.76/41.73 tff(1092,plain,
% 64.76/41.73 (is_a_theorem(implies(or(not(not(P!1)), or(not(Q!0), not(P!1))), or(or(not(Q!0), not(P!1)), not(not(P!1)))))),
% 64.76/41.73 inference(unit_resolution,[status(thm)],[1091, 405])).
% 64.76/41.73 tff(1093,plain,
% 64.76/41.73 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(not(P!1)), or(not(Q!0), not(P!1))))) | is_a_theorem(or(or(not(Q!0), not(P!1)), not(not(P!1)))) | (~is_a_theorem(implies(or(not(not(P!1)), or(not(Q!0), not(P!1))), or(or(not(Q!0), not(P!1)), not(not(P!1)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(not(P!1)), or(not(Q!0), not(P!1))))) | is_a_theorem(or(or(not(Q!0), not(P!1)), not(not(P!1)))) | (~is_a_theorem(implies(or(not(not(P!1)), or(not(Q!0), not(P!1))), or(or(not(Q!0), not(P!1)), not(not(P!1)))))))),
% 64.76/41.73 inference(rewrite,[status(thm)],[])).
% 64.76/41.73 tff(1094,plain,
% 64.76/41.73 ((is_a_theorem(or(or(not(Q!0), not(P!1)), not(not(P!1)))) | (~is_a_theorem(implies(or(not(not(P!1)), or(not(Q!0), not(P!1))), or(or(not(Q!0), not(P!1)), not(not(P!1)))))) | (~is_a_theorem(or(not(not(P!1)), or(not(Q!0), not(P!1)))))) <=> ((~is_a_theorem(or(not(not(P!1)), or(not(Q!0), not(P!1))))) | is_a_theorem(or(or(not(Q!0), not(P!1)), not(not(P!1)))) | (~is_a_theorem(implies(or(not(not(P!1)), or(not(Q!0), not(P!1))), or(or(not(Q!0), not(P!1)), not(not(P!1)))))))),
% 64.76/41.73 inference(rewrite,[status(thm)],[])).
% 64.76/41.73 tff(1095,plain,
% 64.76/41.73 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(or(not(Q!0), not(P!1)), not(not(P!1)))) | (~is_a_theorem(implies(or(not(not(P!1)), or(not(Q!0), not(P!1))), or(or(not(Q!0), not(P!1)), not(not(P!1)))))) | (~is_a_theorem(or(not(not(P!1)), or(not(Q!0), not(P!1))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(or(not(not(P!1)), or(not(Q!0), not(P!1))))) | is_a_theorem(or(or(not(Q!0), not(P!1)), not(not(P!1)))) | (~is_a_theorem(implies(or(not(not(P!1)), or(not(Q!0), not(P!1))), or(or(not(Q!0), not(P!1)), not(not(P!1))))))))),
% 64.76/41.73 inference(monotonicity,[status(thm)],[1094])).
% 64.76/41.73 tff(1096,plain,
% 64.76/41.73 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(or(not(Q!0), not(P!1)), not(not(P!1)))) | (~is_a_theorem(implies(or(not(not(P!1)), or(not(Q!0), not(P!1))), or(or(not(Q!0), not(P!1)), not(not(P!1)))))) | (~is_a_theorem(or(not(not(P!1)), or(not(Q!0), not(P!1))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(not(P!1)), or(not(Q!0), not(P!1))))) | is_a_theorem(or(or(not(Q!0), not(P!1)), not(not(P!1)))) | (~is_a_theorem(implies(or(not(not(P!1)), or(not(Q!0), not(P!1))), or(or(not(Q!0), not(P!1)), not(not(P!1)))))))),
% 64.76/41.73 inference(transitivity,[status(thm)],[1095, 1093])).
% 64.76/41.73 tff(1097,plain,
% 64.76/41.73 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(or(not(Q!0), not(P!1)), not(not(P!1)))) | (~is_a_theorem(implies(or(not(not(P!1)), or(not(Q!0), not(P!1))), or(or(not(Q!0), not(P!1)), not(not(P!1)))))) | (~is_a_theorem(or(not(not(P!1)), or(not(Q!0), not(P!1))))))),
% 64.76/41.73 inference(quant_inst,[status(thm)],[])).
% 64.76/41.73 tff(1098,plain,
% 64.76/41.73 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(or(not(not(P!1)), or(not(Q!0), not(P!1))))) | is_a_theorem(or(or(not(Q!0), not(P!1)), not(not(P!1)))) | (~is_a_theorem(implies(or(not(not(P!1)), or(not(Q!0), not(P!1))), or(or(not(Q!0), not(P!1)), not(not(P!1))))))),
% 64.76/41.73 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 64.76/41.73 tff(1099,plain,
% 64.76/41.73 ((~is_a_theorem(or(not(not(P!1)), or(not(Q!0), not(P!1))))) | is_a_theorem(or(or(not(Q!0), not(P!1)), not(not(P!1))))),
% 64.76/41.73 inference(unit_resolution,[status(thm)],[1098, 429, 1092])).
% 64.76/41.73 tff(1100,plain,
% 64.76/41.73 (is_a_theorem(or(or(not(Q!0), not(P!1)), not(not(P!1))))),
% 64.76/41.73 inference(unit_resolution,[status(thm)],[1099, 1090])).
% 64.76/41.73 tff(1101,plain,
% 64.76/41.73 (is_a_theorem(or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1))))),
% 64.76/41.73 inference(modus_ponens,[status(thm)],[1100, 1066])).
% 64.76/41.73 tff(1102,plain,
% 64.76/41.73 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1))), or(not(not(P!1)), not(not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.73 inference(quant_inst,[status(thm)],[])).
% 64.76/41.73 tff(1103,plain,
% 64.76/41.73 (is_a_theorem(implies(or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1))), or(not(not(P!1)), not(not(or(not(Q!0), not(P!1)))))))),
% 64.76/41.73 inference(unit_resolution,[status(thm)],[1102, 405])).
% 64.76/41.73 tff(1104,plain,
% 64.76/41.73 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(not(P!1)), not(not(or(not(Q!0), not(P!1)))))) | (~is_a_theorem(implies(or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1))), or(not(not(P!1)), not(not(or(not(Q!0), not(P!1)))))))) | (~is_a_theorem(or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | is_a_theorem(or(not(not(P!1)), not(not(or(not(Q!0), not(P!1)))))) | (~is_a_theorem(implies(or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1))), or(not(not(P!1)), not(not(or(not(Q!0), not(P!1)))))))) | (~is_a_theorem(or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1))))))),
% 64.88/41.80 inference(rewrite,[status(thm)],[])).
% 64.88/41.80 tff(1105,plain,
% 64.88/41.80 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(or(not(not(P!1)), not(not(or(not(Q!0), not(P!1)))))) | (~is_a_theorem(implies(or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1))), or(not(not(P!1)), not(not(or(not(Q!0), not(P!1)))))))) | (~is_a_theorem(or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1))))))),
% 64.88/41.80 inference(quant_inst,[status(thm)],[])).
% 64.88/41.80 tff(1106,plain,
% 64.88/41.80 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | is_a_theorem(or(not(not(P!1)), not(not(or(not(Q!0), not(P!1)))))) | (~is_a_theorem(implies(or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1))), or(not(not(P!1)), not(not(or(not(Q!0), not(P!1)))))))) | (~is_a_theorem(or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1)))))),
% 64.88/41.80 inference(modus_ponens,[status(thm)],[1105, 1104])).
% 64.88/41.80 tff(1107,plain,
% 64.88/41.80 (is_a_theorem(or(not(not(P!1)), not(not(or(not(Q!0), not(P!1)))))) | (~is_a_theorem(or(not(not(or(not(Q!0), not(P!1)))), not(not(P!1)))))),
% 64.88/41.80 inference(unit_resolution,[status(thm)],[1106, 429, 1103])).
% 64.88/41.80 tff(1108,plain,
% 64.88/41.80 (is_a_theorem(or(not(not(P!1)), not(not(or(not(Q!0), not(P!1))))))),
% 64.88/41.80 inference(unit_resolution,[status(thm)],[1107, 1101])).
% 64.88/41.80 tff(1109,plain,
% 64.88/41.80 ($false),
% 64.88/41.80 inference(unit_resolution,[status(thm)],[1108, 1055])).
% 64.88/41.80 % SZS output end Proof
%------------------------------------------------------------------------------