TSTP Solution File: LCL457+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL457+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 04:56:23 EDT 2022
% Result : Theorem 46.31s 30.04s
% Output : Proof 46.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL457+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 21:32:34 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 46.31/30.04 % SZS status Theorem
% 46.31/30.04 % SZS output start Proof
% 46.31/30.04 tff(is_a_theorem_type, type, (
% 46.31/30.04 is_a_theorem: $i > $o)).
% 46.31/30.04 tff(implies_type, type, (
% 46.31/30.04 implies: ( $i * $i ) > $i)).
% 46.31/30.04 tff(or_type, type, (
% 46.31/30.04 or: ( $i * $i ) > $i)).
% 46.31/30.04 tff(not_type, type, (
% 46.31/30.04 not: $i > $i)).
% 46.31/30.04 tff(tptp_fun_R_0_type, type, (
% 46.31/30.04 tptp_fun_R_0: $i)).
% 46.31/30.04 tff(tptp_fun_P_2_type, type, (
% 46.31/30.04 tptp_fun_P_2: $i)).
% 46.31/30.04 tff(tptp_fun_Q_1_type, type, (
% 46.31/30.04 tptp_fun_Q_1: $i)).
% 46.31/30.04 tff(and_type, type, (
% 46.31/30.04 and: ( $i * $i ) > $i)).
% 46.31/30.04 tff(op_implies_or_type, type, (
% 46.31/30.04 op_implies_or: $o)).
% 46.31/30.04 tff(op_or_type, type, (
% 46.31/30.04 op_or: $o)).
% 46.31/30.04 tff(or_3_type, type, (
% 46.31/30.04 or_3: $o)).
% 46.31/30.04 tff(op_and_type, type, (
% 46.31/30.04 op_and: $o)).
% 46.31/30.04 tff(modus_tollens_type, type, (
% 46.31/30.04 modus_tollens: $o)).
% 46.31/30.04 tff(op_implies_and_type, type, (
% 46.31/30.04 op_implies_and: $o)).
% 46.31/30.04 tff(or_2_type, type, (
% 46.31/30.04 or_2: $o)).
% 46.31/30.04 tff(modus_ponens_type, type, (
% 46.31/30.04 modus_ponens: $o)).
% 46.31/30.04 tff(and_2_type, type, (
% 46.31/30.04 and_2: $o)).
% 46.31/30.04 tff(implies_3_type, type, (
% 46.31/30.04 implies_3: $o)).
% 46.31/30.04 tff(or_1_type, type, (
% 46.31/30.04 or_1: $o)).
% 46.31/30.04 tff(r4_type, type, (
% 46.31/30.04 r4: $o)).
% 46.31/30.04 tff(1,plain,
% 46.31/30.04 (^[X: $i, Y: $i] : refl((implies(X, Y) = or(not(X), Y)) <=> (implies(X, Y) = or(not(X), Y)))),
% 46.31/30.04 inference(bind,[status(th)],[])).
% 46.31/30.04 tff(2,plain,
% 46.31/30.04 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 46.31/30.04 inference(quant_intro,[status(thm)],[1])).
% 46.31/30.04 tff(3,plain,
% 46.31/30.04 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 46.31/30.04 inference(rewrite,[status(thm)],[])).
% 46.31/30.04 tff(4,plain,
% 46.31/30.04 (($false | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 46.31/30.04 inference(rewrite,[status(thm)],[])).
% 46.31/30.04 tff(5,plain,
% 46.31/30.04 ((~$true) <=> $false),
% 46.31/30.04 inference(rewrite,[status(thm)],[])).
% 46.31/30.04 tff(6,axiom,(op_implies_or), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','principia_op_implies_or')).
% 46.31/30.04 tff(7,plain,
% 46.31/30.04 (op_implies_or <=> $true),
% 46.31/30.04 inference(iff_true,[status(thm)],[6])).
% 46.31/30.04 tff(8,plain,
% 46.31/30.04 ((~op_implies_or) <=> (~$true)),
% 46.31/30.04 inference(monotonicity,[status(thm)],[7])).
% 46.31/30.04 tff(9,plain,
% 46.31/30.04 ((~op_implies_or) <=> $false),
% 46.31/30.04 inference(transitivity,[status(thm)],[8, 5])).
% 46.31/30.04 tff(10,plain,
% 46.31/30.04 (((~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)))),
% 46.31/30.04 inference(monotonicity,[status(thm)],[9])).
% 46.31/30.04 tff(11,plain,
% 46.31/30.04 (((~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))),
% 46.31/30.04 inference(transitivity,[status(thm)],[10, 4])).
% 46.31/30.04 tff(12,plain,
% 46.31/30.04 (((~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)))),
% 46.31/30.04 inference(rewrite,[status(thm)],[])).
% 46.31/30.04 tff(13,plain,
% 46.31/30.04 ((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)))),
% 46.31/30.04 inference(rewrite,[status(thm)],[])).
% 46.31/30.04 tff(14,axiom,(op_implies_or => ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_implies_or')).
% 46.31/30.04 tff(15,plain,
% 46.31/30.04 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 46.31/30.04 inference(modus_ponens,[status(thm)],[14, 13])).
% 46.31/30.04 tff(16,plain,
% 46.31/30.04 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 46.31/30.04 inference(modus_ponens,[status(thm)],[15, 12])).
% 46.31/30.04 tff(17,plain,
% 46.31/30.04 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 46.31/30.04 inference(modus_ponens,[status(thm)],[16, 11])).
% 46.31/30.04 tff(18,plain,
% 46.31/30.04 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 46.31/30.04 inference(modus_ponens,[status(thm)],[17, 3])).
% 46.31/30.04 tff(19,plain,(
% 46.31/30.04 ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 46.31/30.04 inference(skolemize,[status(sab)],[18])).
% 46.31/30.04 tff(20,plain,
% 46.31/30.04 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 46.31/30.04 inference(modus_ponens,[status(thm)],[19, 2])).
% 46.31/30.04 tff(21,plain,
% 46.31/30.04 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(P!2), not(or(Q!1, R!0)))), not(not(or(Q!1, or(P!2, R!0))))) = or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.31/30.04 inference(quant_inst,[status(thm)],[])).
% 46.31/30.04 tff(22,plain,
% 46.31/30.04 (implies(not(and(not(P!2), not(or(Q!1, R!0)))), not(not(or(Q!1, or(P!2, R!0))))) = or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0)))))),
% 46.31/30.04 inference(unit_resolution,[status(thm)],[21, 20])).
% 46.31/30.04 tff(23,plain,
% 46.31/30.04 (^[X: $i, Y: $i] : refl((or(X, Y) = not(and(not(X), not(Y)))) <=> (or(X, Y) = not(and(not(X), not(Y)))))),
% 46.31/30.04 inference(bind,[status(th)],[])).
% 46.31/30.04 tff(24,plain,
% 46.31/30.04 (![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))))),
% 46.31/30.04 inference(quant_intro,[status(thm)],[23])).
% 46.31/30.04 tff(25,plain,
% 46.31/30.04 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 46.31/30.04 inference(rewrite,[status(thm)],[])).
% 46.31/30.04 tff(26,plain,
% 46.31/30.04 (($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))))),
% 46.31/30.04 inference(rewrite,[status(thm)],[])).
% 46.31/30.04 tff(27,axiom,(op_or), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_op_or')).
% 46.31/30.04 tff(28,plain,
% 46.31/30.04 (op_or <=> $true),
% 46.31/30.04 inference(iff_true,[status(thm)],[27])).
% 46.31/30.04 tff(29,plain,
% 46.31/30.04 ((~op_or) <=> (~$true)),
% 46.31/30.04 inference(monotonicity,[status(thm)],[28])).
% 46.31/30.04 tff(30,plain,
% 46.31/30.04 ((~op_or) <=> $false),
% 46.31/30.04 inference(transitivity,[status(thm)],[29, 5])).
% 46.31/30.04 tff(31,plain,
% 46.31/30.04 (((~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)))))),
% 46.31/30.04 inference(monotonicity,[status(thm)],[30])).
% 46.31/30.04 tff(32,plain,
% 46.31/30.04 (((~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))))),
% 46.31/30.04 inference(transitivity,[status(thm)],[31, 26])).
% 46.31/30.04 tff(33,plain,
% 46.31/30.04 (((~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)))))),
% 46.31/30.04 inference(rewrite,[status(thm)],[])).
% 46.31/30.04 tff(34,plain,
% 46.31/30.04 ((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)))))),
% 46.31/30.04 inference(rewrite,[status(thm)],[])).
% 46.31/30.04 tff(35,axiom,(op_or => ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_or')).
% 46.31/30.04 tff(36,plain,
% 46.31/30.04 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 46.31/30.04 inference(modus_ponens,[status(thm)],[35, 34])).
% 46.31/30.04 tff(37,plain,
% 46.31/30.04 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 46.31/30.04 inference(modus_ponens,[status(thm)],[36, 33])).
% 46.31/30.04 tff(38,plain,
% 46.31/30.04 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 46.31/30.04 inference(modus_ponens,[status(thm)],[37, 32])).
% 46.31/30.04 tff(39,plain,
% 46.31/30.04 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 46.31/30.04 inference(modus_ponens,[status(thm)],[38, 25])).
% 46.31/30.04 tff(40,plain,(
% 46.31/30.04 ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 46.31/30.04 inference(skolemize,[status(sab)],[39])).
% 46.31/30.04 tff(41,plain,
% 46.31/30.04 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 46.31/30.04 inference(modus_ponens,[status(thm)],[40, 24])).
% 46.31/30.04 tff(42,plain,
% 46.31/30.04 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(P!2, or(Q!1, R!0)) = not(and(not(P!2), not(or(Q!1, R!0)))))),
% 46.31/30.04 inference(quant_inst,[status(thm)],[])).
% 46.31/30.04 tff(43,plain,
% 46.31/30.04 (or(P!2, or(Q!1, R!0)) = not(and(not(P!2), not(or(Q!1, R!0))))),
% 46.31/30.04 inference(unit_resolution,[status(thm)],[42, 41])).
% 46.31/30.04 tff(44,plain,
% 46.31/30.04 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(Q!1, R!0) = not(and(not(Q!1), not(R!0))))),
% 46.31/30.04 inference(quant_inst,[status(thm)],[])).
% 46.31/30.04 tff(45,plain,
% 46.31/30.04 (or(Q!1, R!0) = not(and(not(Q!1), not(R!0)))),
% 46.31/30.04 inference(unit_resolution,[status(thm)],[44, 41])).
% 46.31/30.04 tff(46,plain,
% 46.31/30.04 (not(and(not(Q!1), not(R!0))) = or(Q!1, R!0)),
% 46.31/30.04 inference(symmetry,[status(thm)],[45])).
% 46.31/30.04 tff(47,plain,
% 46.31/30.04 (or(P!2, not(and(not(Q!1), not(R!0)))) = or(P!2, or(Q!1, R!0))),
% 46.31/30.04 inference(monotonicity,[status(thm)],[46])).
% 46.31/30.04 tff(48,plain,
% 46.31/30.04 (or(P!2, not(and(not(Q!1), not(R!0)))) = not(and(not(P!2), not(or(Q!1, R!0))))),
% 46.31/30.04 inference(transitivity,[status(thm)],[47, 43])).
% 46.31/30.04 tff(49,plain,
% 46.31/30.04 (implies(or(P!2, not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))) = implies(not(and(not(P!2), not(or(Q!1, R!0)))), not(not(or(Q!1, or(P!2, R!0)))))),
% 46.31/30.04 inference(monotonicity,[status(thm)],[48])).
% 46.31/30.04 tff(50,plain,
% 46.31/30.04 (implies(or(P!2, not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))) = or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0)))))),
% 46.31/30.04 inference(transitivity,[status(thm)],[49, 22])).
% 46.31/30.04 tff(51,plain,
% 46.31/30.04 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(Q!1), not(R!0))), not(not(or(Q!1, or(P!2, R!0))))) = or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.31/30.04 inference(quant_inst,[status(thm)],[])).
% 46.31/30.04 tff(52,plain,
% 46.31/30.04 (implies(not(and(not(Q!1), not(R!0))), not(not(or(Q!1, or(P!2, R!0))))) = or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))),
% 46.31/30.04 inference(unit_resolution,[status(thm)],[51, 20])).
% 46.31/30.04 tff(53,plain,
% 46.31/30.04 (implies(implies(not(and(not(Q!1), not(R!0))), not(not(or(Q!1, or(P!2, R!0))))), implies(or(P!2, not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) = implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.31/30.04 inference(monotonicity,[status(thm)],[52, 50])).
% 46.31/30.04 tff(54,plain,
% 46.31/30.04 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(P!2, not(not(or(Q!1, or(P!2, R!0))))) = or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.31/30.04 inference(quant_inst,[status(thm)],[])).
% 46.31/30.04 tff(55,plain,
% 46.31/30.04 (implies(P!2, not(not(or(Q!1, or(P!2, R!0))))) = or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))),
% 46.31/30.04 inference(unit_resolution,[status(thm)],[54, 20])).
% 46.31/30.04 tff(56,plain,
% 46.31/30.04 (implies(implies(P!2, not(not(or(Q!1, or(P!2, R!0))))), implies(implies(not(and(not(Q!1), not(R!0))), not(not(or(Q!1, or(P!2, R!0))))), implies(or(P!2, not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) = implies(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))), implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.31/30.04 inference(monotonicity,[status(thm)],[55, 53])).
% 46.31/30.04 tff(57,plain,
% 46.31/30.04 (is_a_theorem(implies(implies(P!2, not(not(or(Q!1, or(P!2, R!0))))), implies(implies(not(and(not(Q!1), not(R!0))), not(not(or(Q!1, or(P!2, R!0))))), implies(or(P!2, not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))) <=> is_a_theorem(implies(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))), implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.31/30.04 inference(monotonicity,[status(thm)],[56])).
% 46.31/30.04 tff(58,plain,
% 46.31/30.04 (^[X: $i, Y: $i, Z: $i] : refl(is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z)))) <=> is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z)))))),
% 46.31/30.04 inference(bind,[status(th)],[])).
% 46.31/30.04 tff(59,plain,
% 46.31/30.04 (![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z)))) <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 46.31/30.04 inference(quant_intro,[status(thm)],[58])).
% 46.31/30.04 tff(60,plain,
% 46.31/30.04 (![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z)))) <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 46.31/30.04 inference(rewrite,[status(thm)],[])).
% 46.31/30.04 tff(61,plain,
% 46.31/30.04 (($true <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))) <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 46.31/30.04 inference(rewrite,[status(thm)],[])).
% 46.31/30.04 tff(62,axiom,(or_3), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_or_3')).
% 46.31/30.05 tff(63,plain,
% 46.31/30.05 (or_3 <=> $true),
% 46.31/30.05 inference(iff_true,[status(thm)],[62])).
% 46.31/30.05 tff(64,plain,
% 46.31/30.05 ((or_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))) <=> ($true <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z)))))),
% 46.31/30.05 inference(monotonicity,[status(thm)],[63])).
% 46.31/30.05 tff(65,plain,
% 46.31/30.05 ((or_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))) <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 46.31/30.05 inference(transitivity,[status(thm)],[64, 61])).
% 46.31/30.05 tff(66,plain,
% 46.31/30.05 ((or_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))) <=> (or_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z)))))),
% 46.31/30.05 inference(rewrite,[status(thm)],[])).
% 46.31/30.05 tff(67,axiom,(or_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','or_3')).
% 46.31/30.05 tff(68,plain,
% 46.31/30.05 (or_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 46.31/30.05 inference(modus_ponens,[status(thm)],[67, 66])).
% 46.31/30.05 tff(69,plain,
% 46.31/30.05 (or_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 46.31/30.05 inference(modus_ponens,[status(thm)],[68, 66])).
% 46.31/30.05 tff(70,plain,
% 46.31/30.05 (![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 46.31/30.05 inference(modus_ponens,[status(thm)],[69, 65])).
% 46.31/30.05 tff(71,plain,
% 46.31/30.05 (![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 46.31/30.05 inference(modus_ponens,[status(thm)],[70, 60])).
% 46.31/30.05 tff(72,plain,(
% 46.31/30.05 ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 46.31/30.05 inference(skolemize,[status(sab)],[71])).
% 46.31/30.05 tff(73,plain,
% 46.31/30.05 (![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 46.31/30.05 inference(modus_ponens,[status(thm)],[72, 59])).
% 46.31/30.05 tff(74,plain,
% 46.31/30.05 ((~![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))) | is_a_theorem(implies(implies(P!2, not(not(or(Q!1, or(P!2, R!0))))), implies(implies(not(and(not(Q!1), not(R!0))), not(not(or(Q!1, or(P!2, R!0))))), implies(or(P!2, not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.31/30.05 inference(quant_inst,[status(thm)],[])).
% 46.31/30.05 tff(75,plain,
% 46.31/30.05 (is_a_theorem(implies(implies(P!2, not(not(or(Q!1, or(P!2, R!0))))), implies(implies(not(and(not(Q!1), not(R!0))), not(not(or(Q!1, or(P!2, R!0))))), implies(or(P!2, not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.31/30.05 inference(unit_resolution,[status(thm)],[74, 73])).
% 46.31/30.05 tff(76,plain,
% 46.31/30.05 (is_a_theorem(implies(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))), implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.31/30.05 inference(modus_ponens,[status(thm)],[75, 57])).
% 46.31/30.05 tff(77,plain,
% 46.31/30.05 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))) = or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))))),
% 46.31/30.05 inference(quant_inst,[status(thm)],[])).
% 46.31/30.05 tff(78,plain,
% 46.31/30.05 (implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))) = or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0)))))))),
% 46.31/30.05 inference(unit_resolution,[status(thm)],[77, 20])).
% 46.31/30.05 tff(79,plain,
% 46.31/30.05 (^[X: $i, Y: $i] : refl((and(X, Y) = not(or(not(X), not(Y)))) <=> (and(X, Y) = not(or(not(X), not(Y)))))),
% 46.31/30.05 inference(bind,[status(th)],[])).
% 46.31/30.05 tff(80,plain,
% 46.31/30.05 (![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))))),
% 46.31/30.05 inference(quant_intro,[status(thm)],[79])).
% 46.31/30.05 tff(81,plain,
% 46.31/30.05 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 46.31/30.05 inference(rewrite,[status(thm)],[])).
% 46.31/30.05 tff(82,plain,
% 46.31/30.05 (($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))))),
% 46.31/30.05 inference(rewrite,[status(thm)],[])).
% 46.31/30.05 tff(83,axiom,(op_and), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','principia_op_and')).
% 46.31/30.05 tff(84,plain,
% 46.31/30.05 (op_and <=> $true),
% 46.31/30.05 inference(iff_true,[status(thm)],[83])).
% 46.31/30.05 tff(85,plain,
% 46.31/30.05 ((~op_and) <=> (~$true)),
% 46.31/30.05 inference(monotonicity,[status(thm)],[84])).
% 46.31/30.05 tff(86,plain,
% 46.31/30.05 ((~op_and) <=> $false),
% 46.31/30.05 inference(transitivity,[status(thm)],[85, 5])).
% 46.31/30.05 tff(87,plain,
% 46.31/30.05 (((~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)))))),
% 46.31/30.05 inference(monotonicity,[status(thm)],[86])).
% 46.31/30.05 tff(88,plain,
% 46.31/30.05 (((~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))))),
% 46.31/30.05 inference(transitivity,[status(thm)],[87, 82])).
% 46.31/30.05 tff(89,plain,
% 46.31/30.05 (((~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)))))),
% 46.31/30.05 inference(rewrite,[status(thm)],[])).
% 46.31/30.05 tff(90,plain,
% 46.31/30.05 ((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)))))),
% 46.31/30.05 inference(rewrite,[status(thm)],[])).
% 46.31/30.05 tff(91,axiom,(op_and => ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_and')).
% 46.31/30.05 tff(92,plain,
% 46.31/30.05 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 46.31/30.05 inference(modus_ponens,[status(thm)],[91, 90])).
% 46.31/30.05 tff(93,plain,
% 46.31/30.05 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 46.31/30.05 inference(modus_ponens,[status(thm)],[92, 89])).
% 46.31/30.05 tff(94,plain,
% 46.31/30.05 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 46.31/30.05 inference(modus_ponens,[status(thm)],[93, 88])).
% 46.31/30.05 tff(95,plain,
% 46.31/30.05 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 46.31/30.05 inference(modus_ponens,[status(thm)],[94, 81])).
% 46.31/30.05 tff(96,plain,(
% 46.31/30.05 ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 46.31/30.05 inference(skolemize,[status(sab)],[95])).
% 46.31/30.05 tff(97,plain,
% 46.31/30.05 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 46.31/30.05 inference(modus_ponens,[status(thm)],[96, 80])).
% 46.31/30.05 tff(98,plain,
% 46.31/30.05 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(and(not(P!2), not(R!0)))) = not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0)))))))),
% 46.31/30.05 inference(quant_inst,[status(thm)],[])).
% 46.31/30.05 tff(99,plain,
% 46.31/30.05 (and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(and(not(P!2), not(R!0)))) = not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))),
% 46.31/30.05 inference(unit_resolution,[status(thm)],[98, 97])).
% 46.31/30.05 tff(100,plain,
% 46.31/30.05 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(P!2), not(R!0)) = not(or(not(not(P!2)), not(not(R!0)))))),
% 46.31/30.05 inference(quant_inst,[status(thm)],[])).
% 46.31/30.05 tff(101,plain,
% 46.31/30.05 (and(not(P!2), not(R!0)) = not(or(not(not(P!2)), not(not(R!0))))),
% 46.31/30.05 inference(unit_resolution,[status(thm)],[100, 97])).
% 46.31/30.05 tff(102,plain,
% 46.31/30.05 (not(or(not(not(P!2)), not(not(R!0)))) = and(not(P!2), not(R!0))),
% 46.31/30.05 inference(symmetry,[status(thm)],[101])).
% 46.31/30.05 tff(103,plain,
% 46.31/30.05 (not(not(or(not(not(P!2)), not(not(R!0))))) = not(and(not(P!2), not(R!0)))),
% 46.31/30.05 inference(monotonicity,[status(thm)],[102])).
% 46.31/30.05 tff(104,plain,
% 46.31/30.05 (and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))) = and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(and(not(P!2), not(R!0))))),
% 46.31/30.05 inference(monotonicity,[status(thm)],[103])).
% 46.31/30.05 tff(105,plain,
% 46.31/30.05 (and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))) = not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))),
% 46.31/30.05 inference(transitivity,[status(thm)],[104, 99])).
% 46.31/30.05 tff(106,plain,
% 46.31/30.05 (implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))) = implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0)))))))),
% 46.31/30.05 inference(monotonicity,[status(thm)],[105])).
% 46.31/30.05 tff(107,plain,
% 46.31/30.05 (and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(and(not(P!2), not(R!0)))) = and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))),
% 46.31/30.05 inference(symmetry,[status(thm)],[104])).
% 46.31/30.05 tff(108,plain,
% 46.31/30.05 (not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0)))))) = and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(and(not(P!2), not(R!0))))),
% 46.31/30.05 inference(symmetry,[status(thm)],[99])).
% 46.31/30.05 tff(109,plain,
% 46.31/30.05 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(P!2, R!0) = not(and(not(P!2), not(R!0))))),
% 46.31/30.05 inference(quant_inst,[status(thm)],[])).
% 46.31/30.05 tff(110,plain,
% 46.31/30.05 (or(P!2, R!0) = not(and(not(P!2), not(R!0)))),
% 46.31/30.05 inference(unit_resolution,[status(thm)],[109, 41])).
% 46.31/30.05 tff(111,plain,
% 46.31/30.05 (not(and(not(P!2), not(R!0))) = or(P!2, R!0)),
% 46.31/30.05 inference(symmetry,[status(thm)],[110])).
% 46.31/30.05 tff(112,plain,
% 46.31/30.05 (not(not(and(not(P!2), not(R!0)))) = not(or(P!2, R!0))),
% 46.31/30.05 inference(monotonicity,[status(thm)],[111])).
% 46.31/30.05 tff(113,plain,
% 46.31/30.05 (or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))) = or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0)))),
% 46.31/30.05 inference(monotonicity,[status(thm)],[112])).
% 46.31/30.05 tff(114,plain,
% 46.31/30.05 (or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))) = or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0)))))),
% 46.31/30.05 inference(symmetry,[status(thm)],[113])).
% 46.31/30.05 tff(115,plain,
% 46.31/30.05 (not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0)))) = not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))),
% 46.31/30.05 inference(monotonicity,[status(thm)],[114])).
% 46.31/30.05 tff(116,plain,
% 46.31/30.05 (not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0)))) = and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))),
% 46.31/30.05 inference(transitivity,[status(thm)],[115, 108, 107])).
% 46.31/30.05 tff(117,plain,
% 46.31/30.05 (implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))))) = implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))),
% 46.31/30.05 inference(monotonicity,[status(thm)],[116])).
% 46.31/30.05 tff(118,plain,
% 46.31/30.05 (implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))))) = or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0)))))))),
% 46.31/30.05 inference(transitivity,[status(thm)],[117, 106, 78])).
% 46.31/30.05 tff(119,plain,
% 46.31/30.05 (implies(implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))))), implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) = implies(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))), implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.31/30.05 inference(monotonicity,[status(thm)],[118])).
% 46.31/30.05 tff(120,plain,
% 46.31/30.05 (implies(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))), implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) = implies(implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))))), implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.31/30.05 inference(symmetry,[status(thm)],[119])).
% 46.31/30.05 tff(121,plain,
% 46.31/30.05 (is_a_theorem(implies(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))), implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))) <=> is_a_theorem(implies(implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))))), implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.31/30.05 inference(monotonicity,[status(thm)],[120])).
% 46.31/30.05 tff(122,plain,
% 46.31/30.05 (is_a_theorem(implies(implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))))), implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))) <=> is_a_theorem(implies(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))), implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.31/30.05 inference(symmetry,[status(thm)],[121])).
% 46.31/30.05 tff(123,plain,
% 46.31/30.05 (^[X: $i, Y: $i] : refl(is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y))) <=> is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y))))),
% 46.31/30.05 inference(bind,[status(th)],[])).
% 46.31/30.05 tff(124,plain,
% 46.31/30.05 (![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 46.31/30.05 inference(quant_intro,[status(thm)],[123])).
% 46.31/30.05 tff(125,plain,
% 46.31/30.05 (![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 46.31/30.05 inference(rewrite,[status(thm)],[])).
% 46.31/30.05 tff(126,plain,
% 46.31/30.05 (($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 46.31/30.05 inference(rewrite,[status(thm)],[])).
% 46.31/30.05 tff(127,axiom,(modus_tollens), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_modus_tollens')).
% 46.31/30.05 tff(128,plain,
% 46.31/30.05 (modus_tollens <=> $true),
% 46.31/30.05 inference(iff_true,[status(thm)],[127])).
% 46.31/30.05 tff(129,plain,
% 46.31/30.05 ((modus_tollens <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) <=> ($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y))))),
% 46.31/30.05 inference(monotonicity,[status(thm)],[128])).
% 46.31/30.05 tff(130,plain,
% 46.31/30.05 ((modus_tollens <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 46.31/30.05 inference(transitivity,[status(thm)],[129, 126])).
% 46.31/30.05 tff(131,plain,
% 46.31/30.05 ((modus_tollens <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) <=> (modus_tollens <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y))))),
% 46.31/30.05 inference(rewrite,[status(thm)],[])).
% 46.31/30.05 tff(132,axiom,(modus_tollens <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','modus_tollens')).
% 46.31/30.05 tff(133,plain,
% 46.31/30.05 (modus_tollens <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 46.31/30.05 inference(modus_ponens,[status(thm)],[132, 131])).
% 46.31/30.05 tff(134,plain,
% 46.31/30.05 (modus_tollens <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 46.31/30.05 inference(modus_ponens,[status(thm)],[133, 131])).
% 46.31/30.05 tff(135,plain,
% 46.31/30.05 (![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 46.31/30.05 inference(modus_ponens,[status(thm)],[134, 130])).
% 46.31/30.05 tff(136,plain,
% 46.31/30.05 (![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 46.31/30.05 inference(modus_ponens,[status(thm)],[135, 125])).
% 46.31/30.05 tff(137,plain,(
% 46.31/30.05 ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 46.31/30.05 inference(skolemize,[status(sab)],[136])).
% 46.31/30.05 tff(138,plain,
% 46.31/30.05 (![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 46.31/30.05 inference(modus_ponens,[status(thm)],[137, 124])).
% 46.31/30.05 tff(139,plain,
% 46.31/30.05 ((~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) | is_a_theorem(implies(implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))))), implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.31/30.05 inference(quant_inst,[status(thm)],[])).
% 46.31/30.05 tff(140,plain,
% 46.31/30.05 (is_a_theorem(implies(implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))))), implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.31/30.05 inference(unit_resolution,[status(thm)],[139, 138])).
% 46.31/30.05 tff(141,plain,
% 46.31/30.05 (is_a_theorem(implies(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))), implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.31/30.05 inference(modus_ponens,[status(thm)],[140, 122])).
% 46.31/30.05 tff(142,plain,
% 46.31/30.05 (or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))) = implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0)))))))),
% 46.31/30.05 inference(symmetry,[status(thm)],[78])).
% 46.31/30.05 tff(143,plain,
% 46.31/30.05 (is_a_theorem(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0)))))))) <=> is_a_theorem(implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))))),
% 46.31/30.05 inference(monotonicity,[status(thm)],[142])).
% 46.31/30.05 tff(144,plain,
% 46.31/30.05 (is_a_theorem(implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0)))))))) <=> is_a_theorem(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))))),
% 46.31/30.05 inference(symmetry,[status(thm)],[143])).
% 46.31/30.05 tff(145,plain,
% 46.31/30.05 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(Q!1, or(P!2, R!0)) = not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.31/30.05 inference(quant_inst,[status(thm)],[])).
% 46.31/30.05 tff(146,plain,
% 46.31/30.05 (or(Q!1, or(P!2, R!0)) = not(and(not(Q!1), not(or(P!2, R!0))))),
% 46.31/30.05 inference(unit_resolution,[status(thm)],[145, 41])).
% 46.31/30.05 tff(147,plain,
% 46.31/30.05 (not(and(not(Q!1), not(or(P!2, R!0)))) = or(Q!1, or(P!2, R!0))),
% 46.31/30.05 inference(symmetry,[status(thm)],[146])).
% 46.31/30.05 tff(148,plain,
% 46.31/30.05 (not(not(and(not(Q!1), not(or(P!2, R!0))))) = not(or(Q!1, or(P!2, R!0)))),
% 46.31/30.05 inference(monotonicity,[status(thm)],[147])).
% 46.31/30.05 tff(149,plain,
% 46.31/30.05 (and(not(and(not(P!2), not(R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))) = and(not(and(not(P!2), not(R!0))), not(or(Q!1, or(P!2, R!0))))),
% 46.31/30.05 inference(monotonicity,[status(thm)],[148])).
% 46.31/30.05 tff(150,plain,
% 46.31/30.05 (and(not(and(not(P!2), not(R!0))), not(or(Q!1, or(P!2, R!0)))) = and(not(and(not(P!2), not(R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.31/30.05 inference(symmetry,[status(thm)],[149])).
% 46.31/30.05 tff(151,plain,
% 46.31/30.05 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(P!2), not(R!0))), not(or(Q!1, or(P!2, R!0)))) = not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.31/30.05 inference(quant_inst,[status(thm)],[])).
% 46.31/30.05 tff(152,plain,
% 46.31/30.05 (and(not(and(not(P!2), not(R!0))), not(or(Q!1, or(P!2, R!0)))) = not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.31/30.05 inference(unit_resolution,[status(thm)],[151, 97])).
% 46.31/30.05 tff(153,plain,
% 46.31/30.05 (not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) = and(not(and(not(P!2), not(R!0))), not(or(Q!1, or(P!2, R!0))))),
% 46.31/30.05 inference(symmetry,[status(thm)],[152])).
% 46.31/30.05 tff(154,plain,
% 46.31/30.05 (not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) = and(not(and(not(P!2), not(R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.31/30.05 inference(transitivity,[status(thm)],[153, 150])).
% 46.31/30.05 tff(155,plain,
% 46.31/30.05 (not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) = not(and(not(and(not(P!2), not(R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.31/30.05 inference(monotonicity,[status(thm)],[154])).
% 46.31/30.05 tff(156,plain,
% 46.31/30.05 (not(and(not(and(not(P!2), not(R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))) = not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.31/30.05 inference(symmetry,[status(thm)],[155])).
% 46.31/30.05 tff(157,plain,
% 46.31/30.05 (^[X: $i, Y: $i] : refl((implies(X, Y) = not(and(X, not(Y)))) <=> (implies(X, Y) = not(and(X, not(Y)))))),
% 46.31/30.05 inference(bind,[status(th)],[])).
% 46.31/30.05 tff(158,plain,
% 46.31/30.05 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 46.31/30.05 inference(quant_intro,[status(thm)],[157])).
% 46.31/30.05 tff(159,plain,
% 46.31/30.05 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 46.31/30.05 inference(rewrite,[status(thm)],[])).
% 46.31/30.05 tff(160,plain,
% 46.31/30.05 (($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))))),
% 46.31/30.05 inference(rewrite,[status(thm)],[])).
% 46.31/30.05 tff(161,axiom,(op_implies_and), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_op_implies_and')).
% 46.31/30.05 tff(162,plain,
% 46.31/30.05 (op_implies_and <=> $true),
% 46.31/30.05 inference(iff_true,[status(thm)],[161])).
% 46.31/30.05 tff(163,plain,
% 46.31/30.05 ((~op_implies_and) <=> (~$true)),
% 46.31/30.05 inference(monotonicity,[status(thm)],[162])).
% 46.31/30.05 tff(164,plain,
% 46.31/30.05 ((~op_implies_and) <=> $false),
% 46.31/30.06 inference(transitivity,[status(thm)],[163, 5])).
% 46.31/30.06 tff(165,plain,
% 46.31/30.06 (((~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)))))),
% 46.31/30.06 inference(monotonicity,[status(thm)],[164])).
% 46.31/30.06 tff(166,plain,
% 46.31/30.06 (((~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))))),
% 46.31/30.06 inference(transitivity,[status(thm)],[165, 160])).
% 46.31/30.06 tff(167,plain,
% 46.31/30.06 (((~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)))))),
% 46.31/30.06 inference(rewrite,[status(thm)],[])).
% 46.31/30.06 tff(168,plain,
% 46.31/30.06 ((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)))))),
% 46.31/30.06 inference(rewrite,[status(thm)],[])).
% 46.31/30.06 tff(169,axiom,(op_implies_and => ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_implies_and')).
% 46.31/30.06 tff(170,plain,
% 46.31/30.06 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 46.31/30.06 inference(modus_ponens,[status(thm)],[169, 168])).
% 46.31/30.06 tff(171,plain,
% 46.31/30.06 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 46.31/30.06 inference(modus_ponens,[status(thm)],[170, 167])).
% 46.31/30.06 tff(172,plain,
% 46.31/30.06 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 46.31/30.06 inference(modus_ponens,[status(thm)],[171, 166])).
% 46.31/30.06 tff(173,plain,
% 46.31/30.06 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 46.31/30.06 inference(modus_ponens,[status(thm)],[172, 159])).
% 46.31/30.06 tff(174,plain,(
% 46.31/30.06 ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 46.31/30.06 inference(skolemize,[status(sab)],[173])).
% 46.31/30.06 tff(175,plain,
% 46.31/30.06 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 46.31/30.06 inference(modus_ponens,[status(thm)],[174, 158])).
% 46.31/30.06 tff(176,plain,
% 46.31/30.06 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(and(not(P!2), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(not(and(not(P!2), not(R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.31/30.06 inference(quant_inst,[status(thm)],[])).
% 46.31/30.06 tff(177,plain,
% 46.31/30.06 (implies(not(and(not(P!2), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(not(and(not(P!2), not(R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.31/30.06 inference(unit_resolution,[status(thm)],[176, 175])).
% 46.31/30.06 tff(178,plain,
% 46.31/30.06 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(P!2), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.31/30.06 inference(quant_inst,[status(thm)],[])).
% 46.31/30.06 tff(179,plain,
% 46.31/30.06 (implies(not(and(not(P!2), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.31/30.06 inference(unit_resolution,[status(thm)],[178, 20])).
% 46.31/30.06 tff(180,plain,
% 46.31/30.06 (or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))) = implies(not(and(not(P!2), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.31/30.06 inference(symmetry,[status(thm)],[179])).
% 46.31/30.06 tff(181,plain,
% 46.31/30.06 (not(or(P!2, R!0)) = not(not(and(not(P!2), not(R!0))))),
% 46.31/30.06 inference(symmetry,[status(thm)],[112])).
% 46.31/30.06 tff(182,plain,
% 46.31/30.06 (or(not(or(P!2, R!0)), not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.31/30.06 inference(monotonicity,[status(thm)],[181])).
% 46.31/30.06 tff(183,plain,
% 46.31/30.06 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(P!2, R!0)), not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.31/30.06 inference(quant_inst,[status(thm)],[])).
% 46.31/30.06 tff(184,plain,
% 46.31/30.06 (or(not(or(P!2, R!0)), not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.31/30.06 inference(unit_resolution,[status(thm)],[183, 41])).
% 46.31/30.06 tff(185,plain,
% 46.31/30.06 (not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))) = or(not(or(P!2, R!0)), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.31/30.06 inference(symmetry,[status(thm)],[184])).
% 46.31/30.06 tff(186,plain,
% 46.31/30.06 (and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))) = and(not(not(or(P!2, R!0))), not(or(Q!1, or(P!2, R!0))))),
% 46.31/30.06 inference(monotonicity,[status(thm)],[148])).
% 46.31/30.06 tff(187,plain,
% 46.31/30.06 (and(not(not(or(P!2, R!0))), not(or(Q!1, or(P!2, R!0)))) = and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.31/30.06 inference(symmetry,[status(thm)],[186])).
% 46.31/30.06 tff(188,plain,
% 46.31/30.06 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(not(or(P!2, R!0))), not(or(Q!1, or(P!2, R!0)))) = not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.31/30.06 inference(quant_inst,[status(thm)],[])).
% 46.31/30.06 tff(189,plain,
% 46.31/30.06 (and(not(not(or(P!2, R!0))), not(or(Q!1, or(P!2, R!0)))) = not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.31/30.06 inference(unit_resolution,[status(thm)],[188, 97])).
% 46.31/30.06 tff(190,plain,
% 46.31/30.06 (not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) = and(not(not(or(P!2, R!0))), not(or(Q!1, or(P!2, R!0))))),
% 46.31/30.06 inference(symmetry,[status(thm)],[189])).
% 46.31/30.06 tff(191,plain,
% 46.31/30.06 (not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) = and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.31/30.06 inference(transitivity,[status(thm)],[190, 187])).
% 46.31/30.06 tff(192,plain,
% 46.31/30.06 (not(not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) = not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.31/30.06 inference(monotonicity,[status(thm)],[191])).
% 46.31/30.06 tff(193,plain,
% 46.31/30.06 (not(not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) = not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.31/30.06 inference(transitivity,[status(thm)],[192, 185, 182, 180, 177, 156])).
% 46.31/30.06 tff(194,plain,
% 46.31/30.06 (or(not(not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))) = or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0)))))))),
% 46.31/30.06 inference(monotonicity,[status(thm)],[193])).
% 46.31/30.06 tff(195,plain,
% 46.31/30.06 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))) = or(not(not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))))),
% 46.31/30.06 inference(quant_inst,[status(thm)],[])).
% 46.31/30.06 tff(196,plain,
% 46.31/30.06 (implies(not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))) = or(not(not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0)))))))),
% 46.31/30.06 inference(unit_resolution,[status(thm)],[195, 20])).
% 46.31/30.06 tff(197,plain,
% 46.31/30.06 (implies(not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))) = implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0)))))))),
% 46.31/30.06 inference(transitivity,[status(thm)],[196, 194, 142])).
% 46.31/30.06 tff(198,plain,
% 46.31/30.06 (is_a_theorem(implies(not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0)))))))) <=> is_a_theorem(implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))))),
% 46.31/30.06 inference(monotonicity,[status(thm)],[197])).
% 46.31/30.06 tff(199,plain,
% 46.31/30.06 (and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))) = not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.31/30.06 inference(transitivity,[status(thm)],[186, 189])).
% 46.31/30.06 tff(200,plain,
% 46.31/30.06 (implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))) = implies(not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0)))))))),
% 46.31/30.06 inference(monotonicity,[status(thm)],[199, 105])).
% 46.31/30.06 tff(201,plain,
% 46.31/30.06 (is_a_theorem(implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))) <=> is_a_theorem(implies(not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))))),
% 46.31/30.06 inference(monotonicity,[status(thm)],[200])).
% 46.31/30.06 tff(202,plain,
% 46.31/30.06 (is_a_theorem(implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))) <=> is_a_theorem(implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))))),
% 46.31/30.06 inference(transitivity,[status(thm)],[201, 198])).
% 46.31/30.06 tff(203,plain,
% 46.31/30.06 (not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))) = or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.31/30.06 inference(transitivity,[status(thm)],[185, 182])).
% 46.31/30.06 tff(204,plain,
% 46.31/30.06 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(Q!1), not(or(P!2, R!0))) = not(or(not(not(Q!1)), not(not(or(P!2, R!0))))))),
% 46.31/30.06 inference(quant_inst,[status(thm)],[])).
% 46.31/30.06 tff(205,plain,
% 46.31/30.06 (and(not(Q!1), not(or(P!2, R!0))) = not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))),
% 46.31/30.06 inference(unit_resolution,[status(thm)],[204, 97])).
% 46.31/30.06 tff(206,plain,
% 46.31/30.06 (implies(and(not(Q!1), not(or(P!2, R!0))), and(not(P!2), not(R!0))) = implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(R!0)))))),
% 46.31/30.06 inference(monotonicity,[status(thm)],[205, 101])).
% 46.31/30.06 tff(207,plain,
% 46.31/30.06 (implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(R!0))))) = implies(and(not(Q!1), not(or(P!2, R!0))), and(not(P!2), not(R!0)))),
% 46.31/30.06 inference(symmetry,[status(thm)],[206])).
% 46.31/30.06 tff(208,plain,
% 46.31/30.06 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(R!0))))) = not(and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))))),
% 46.31/30.06 inference(quant_inst,[status(thm)],[])).
% 46.31/30.06 tff(209,plain,
% 46.31/30.06 (implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(R!0))))) = not(and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))),
% 46.31/30.06 inference(unit_resolution,[status(thm)],[208, 175])).
% 46.31/30.06 tff(210,plain,
% 46.31/30.06 (not(and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))) = implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(R!0)))))),
% 46.31/30.06 inference(symmetry,[status(thm)],[209])).
% 46.31/30.06 tff(211,plain,
% 46.31/30.06 (not(and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))) = implies(and(not(Q!1), not(or(P!2, R!0))), and(not(P!2), not(R!0)))),
% 46.31/30.06 inference(transitivity,[status(thm)],[210, 207])).
% 46.31/30.06 tff(212,plain,
% 46.31/30.06 (implies(not(and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))), not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))) = implies(implies(and(not(Q!1), not(or(P!2, R!0))), and(not(P!2), not(R!0))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.31/30.06 inference(monotonicity,[status(thm)],[211, 203])).
% 46.31/30.06 tff(213,plain,
% 46.31/30.06 (implies(implies(and(not(Q!1), not(or(P!2, R!0))), and(not(P!2), not(R!0))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(not(and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))), not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.31/30.06 inference(symmetry,[status(thm)],[212])).
% 46.31/30.06 tff(214,plain,
% 46.31/30.06 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(R!0))))) = or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0))))))),
% 46.31/30.06 inference(quant_inst,[status(thm)],[])).
% 46.31/30.06 tff(215,plain,
% 46.31/30.06 (implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(R!0))))) = or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))),
% 46.31/30.06 inference(unit_resolution,[status(thm)],[214, 20])).
% 46.31/30.06 tff(216,plain,
% 46.31/30.06 (implies(and(not(Q!1), not(or(P!2, R!0))), and(not(P!2), not(R!0))) = or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))),
% 46.31/30.06 inference(transitivity,[status(thm)],[206, 215])).
% 46.31/30.06 tff(217,plain,
% 46.31/30.06 (implies(implies(and(not(Q!1), not(or(P!2, R!0))), and(not(P!2), not(R!0))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.31/30.06 inference(monotonicity,[status(thm)],[216])).
% 46.31/30.06 tff(218,plain,
% 46.31/30.06 (implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(implies(and(not(Q!1), not(or(P!2, R!0))), and(not(P!2), not(R!0))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.31/30.06 inference(symmetry,[status(thm)],[217])).
% 46.31/30.06 tff(219,plain,
% 46.31/30.06 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))) = or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.31/30.06 inference(quant_inst,[status(thm)],[])).
% 46.31/30.06 tff(220,plain,
% 46.31/30.06 (implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))) = or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.31/30.06 inference(unit_resolution,[status(thm)],[219, 20])).
% 46.31/30.06 tff(221,plain,
% 46.31/30.06 (or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.31/30.06 inference(symmetry,[status(thm)],[220])).
% 46.31/30.06 tff(222,plain,
% 46.31/30.06 (or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(not(and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))), not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.31/30.06 inference(transitivity,[status(thm)],[221, 218, 213])).
% 46.31/30.06 tff(223,plain,
% 46.31/30.06 (implies(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))) = implies(implies(not(and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))), not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))), implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))))),
% 46.31/30.06 inference(monotonicity,[status(thm)],[222])).
% 46.31/30.06 tff(224,plain,
% 46.31/30.06 (implies(implies(not(and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))), not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))), implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))) = implies(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))))),
% 46.31/30.06 inference(symmetry,[status(thm)],[223])).
% 46.31/30.06 tff(225,plain,
% 46.31/30.06 (is_a_theorem(implies(implies(not(and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))), not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))), implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))))) <=> is_a_theorem(implies(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))))),
% 46.31/30.06 inference(monotonicity,[status(thm)],[224])).
% 46.31/30.06 tff(226,plain,
% 46.31/30.06 ((~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) | is_a_theorem(implies(implies(not(and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))), not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))), implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))))),
% 46.31/30.06 inference(quant_inst,[status(thm)],[])).
% 46.31/30.06 tff(227,plain,
% 46.31/30.06 (is_a_theorem(implies(implies(not(and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))), not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))), implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))))),
% 46.31/30.06 inference(unit_resolution,[status(thm)],[226, 138])).
% 46.31/30.06 tff(228,plain,
% 46.31/30.06 (is_a_theorem(implies(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))))),
% 46.31/30.06 inference(modus_ponens,[status(thm)],[227, 225])).
% 46.31/30.06 tff(229,plain,
% 46.31/30.06 (^[X: $i, Y: $i] : refl(is_a_theorem(implies(Y, or(X, Y))) <=> is_a_theorem(implies(Y, or(X, Y))))),
% 46.31/30.06 inference(bind,[status(th)],[])).
% 46.31/30.06 tff(230,plain,
% 46.31/30.07 (![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 46.31/30.07 inference(quant_intro,[status(thm)],[229])).
% 46.31/30.07 tff(231,plain,
% 46.31/30.07 (![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 46.31/30.07 inference(rewrite,[status(thm)],[])).
% 46.31/30.07 tff(232,plain,
% 46.31/30.07 (($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 46.31/30.07 inference(rewrite,[status(thm)],[])).
% 46.31/30.07 tff(233,axiom,(or_2), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_or_2')).
% 46.31/30.07 tff(234,plain,
% 46.31/30.07 (or_2 <=> $true),
% 46.31/30.07 inference(iff_true,[status(thm)],[233])).
% 46.31/30.07 tff(235,plain,
% 46.31/30.07 ((or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) <=> ($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y))))),
% 46.31/30.07 inference(monotonicity,[status(thm)],[234])).
% 46.31/30.07 tff(236,plain,
% 46.31/30.07 ((or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 46.31/30.07 inference(transitivity,[status(thm)],[235, 232])).
% 46.31/30.07 tff(237,plain,
% 46.31/30.07 ((or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) <=> (or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y))))),
% 46.31/30.07 inference(rewrite,[status(thm)],[])).
% 46.31/30.07 tff(238,axiom,(or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','or_2')).
% 46.31/30.07 tff(239,plain,
% 46.31/30.07 (or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 46.31/30.07 inference(modus_ponens,[status(thm)],[238, 237])).
% 46.31/30.07 tff(240,plain,
% 46.31/30.07 (or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 46.31/30.07 inference(modus_ponens,[status(thm)],[239, 237])).
% 46.31/30.07 tff(241,plain,
% 46.31/30.07 (![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 46.31/30.07 inference(modus_ponens,[status(thm)],[240, 236])).
% 46.31/30.07 tff(242,plain,
% 46.31/30.07 (![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 46.31/30.07 inference(modus_ponens,[status(thm)],[241, 231])).
% 46.31/30.07 tff(243,plain,(
% 46.31/30.07 ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 46.31/30.07 inference(skolemize,[status(sab)],[242])).
% 46.31/30.07 tff(244,plain,
% 46.31/30.07 (![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 46.31/30.07 inference(modus_ponens,[status(thm)],[243, 230])).
% 46.31/30.07 tff(245,plain,
% 46.31/30.07 ((~![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) | is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.31/30.07 inference(quant_inst,[status(thm)],[])).
% 46.31/30.07 tff(246,plain,
% 46.31/30.07 (is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.31/30.07 inference(unit_resolution,[status(thm)],[245, 244])).
% 46.31/30.07 tff(247,plain,
% 46.31/30.07 (is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))) <=> is_a_theorem(implies(not(and(not(P!2), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.31/30.07 inference(monotonicity,[status(thm)],[180])).
% 46.31/30.07 tff(248,plain,
% 46.31/30.07 (is_a_theorem(implies(not(and(not(P!2), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0)))))) <=> is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.31/30.07 inference(symmetry,[status(thm)],[247])).
% 46.31/30.07 tff(249,plain,
% 46.31/30.07 (implies(or(P!2, R!0), or(Q!1, or(P!2, R!0))) = implies(not(and(not(P!2), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.31/30.07 inference(monotonicity,[status(thm)],[110, 146])).
% 46.31/30.07 tff(250,plain,
% 46.31/30.07 (is_a_theorem(implies(or(P!2, R!0), or(Q!1, or(P!2, R!0)))) <=> is_a_theorem(implies(not(and(not(P!2), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.31/30.07 inference(monotonicity,[status(thm)],[249])).
% 46.31/30.07 tff(251,plain,
% 46.31/30.07 ((~![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) | is_a_theorem(implies(or(P!2, R!0), or(Q!1, or(P!2, R!0))))),
% 46.31/30.07 inference(quant_inst,[status(thm)],[])).
% 46.31/30.07 tff(252,plain,
% 46.31/30.07 (is_a_theorem(implies(or(P!2, R!0), or(Q!1, or(P!2, R!0))))),
% 46.31/30.07 inference(unit_resolution,[status(thm)],[251, 244])).
% 46.31/30.07 tff(253,plain,
% 46.31/30.07 (is_a_theorem(implies(not(and(not(P!2), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.31/30.07 inference(modus_ponens,[status(thm)],[252, 250])).
% 46.31/30.07 tff(254,plain,
% 46.31/30.07 (is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.31/30.07 inference(modus_ponens,[status(thm)],[253, 248])).
% 46.31/30.07 tff(255,plain,
% 46.31/30.07 (^[X: $i, Y: $i] : refl((is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))) <=> (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))),
% 46.31/30.07 inference(bind,[status(th)],[])).
% 46.31/30.07 tff(256,plain,
% 46.31/30.07 (![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))))),
% 46.31/30.07 inference(quant_intro,[status(thm)],[255])).
% 46.31/30.07 tff(257,plain,
% 46.31/30.07 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((is_a_theorem(X) & is_a_theorem(implies(X, Y))) <=> (~((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))), ((~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))) <=> (~(~((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))))), rewrite((~(~((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))) <=> ((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))), ((~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))) <=> ((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))), ((is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> (is_a_theorem(Y) | ((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))))), rewrite((is_a_theorem(Y) | ((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) <=> (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))), ((is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))))),
% 46.31/30.07 inference(bind,[status(th)],[])).
% 46.31/30.07 tff(258,plain,
% 46.31/30.07 (![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))))),
% 46.31/30.07 inference(quant_intro,[status(thm)],[257])).
% 46.31/30.07 tff(259,plain,
% 46.31/30.07 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 46.31/30.07 inference(rewrite,[status(thm)],[])).
% 46.31/30.07 tff(260,plain,
% 46.31/30.07 (($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)))))),
% 46.31/30.07 inference(rewrite,[status(thm)],[])).
% 46.31/30.07 tff(261,axiom,(modus_ponens), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_modus_ponens')).
% 46.31/30.07 tff(262,plain,
% 46.31/30.07 (modus_ponens <=> $true),
% 46.31/30.07 inference(iff_true,[status(thm)],[261])).
% 46.31/30.07 tff(263,plain,
% 46.31/30.07 ((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))))))),
% 46.31/30.07 inference(monotonicity,[status(thm)],[262])).
% 46.31/30.07 tff(264,plain,
% 46.31/30.07 ((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)))))),
% 46.31/30.07 inference(transitivity,[status(thm)],[263, 260])).
% 46.31/30.07 tff(265,plain,
% 46.31/30.07 ((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))))))),
% 46.31/30.07 inference(rewrite,[status(thm)],[])).
% 46.31/30.07 tff(266,plain,
% 46.31/30.07 ((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))))))),
% 46.31/30.07 inference(rewrite,[status(thm)],[])).
% 46.31/30.07 tff(267,axiom,(modus_ponens <=> ![X: $i, Y: $i] : ((is_a_theorem(X) & is_a_theorem(implies(X, Y))) => is_a_theorem(Y))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','modus_ponens')).
% 46.31/30.07 tff(268,plain,
% 46.31/30.07 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 46.31/30.07 inference(modus_ponens,[status(thm)],[267, 266])).
% 46.31/30.07 tff(269,plain,
% 46.31/30.07 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 46.31/30.07 inference(modus_ponens,[status(thm)],[268, 265])).
% 46.31/30.07 tff(270,plain,
% 46.31/30.07 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 46.31/30.07 inference(modus_ponens,[status(thm)],[269, 264])).
% 46.31/30.07 tff(271,plain,
% 46.31/30.07 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 46.31/30.07 inference(modus_ponens,[status(thm)],[270, 259])).
% 46.31/30.07 tff(272,plain,(
% 46.31/30.07 ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 46.31/30.07 inference(skolemize,[status(sab)],[271])).
% 46.31/30.07 tff(273,plain,
% 46.31/30.07 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 46.31/30.07 inference(modus_ponens,[status(thm)],[272, 258])).
% 46.31/30.07 tff(274,plain,
% 46.31/30.07 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 46.31/30.07 inference(modus_ponens,[status(thm)],[273, 256])).
% 46.31/30.07 tff(275,plain,
% 46.31/30.07 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | is_a_theorem(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | is_a_theorem(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.31/30.07 inference(rewrite,[status(thm)],[])).
% 46.31/30.07 tff(276,plain,
% 46.31/30.07 ((is_a_theorem(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))))) <=> ((~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | is_a_theorem(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.31/30.07 inference(rewrite,[status(thm)],[])).
% 46.31/30.07 tff(277,plain,
% 46.31/30.07 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | is_a_theorem(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))))))),
% 46.31/30.07 inference(monotonicity,[status(thm)],[276])).
% 46.31/30.07 tff(278,plain,
% 46.31/30.07 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | is_a_theorem(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.31/30.07 inference(transitivity,[status(thm)],[277, 275])).
% 46.31/30.07 tff(279,plain,
% 46.31/30.07 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.31/30.07 inference(quant_inst,[status(thm)],[])).
% 46.31/30.07 tff(280,plain,
% 46.31/30.07 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | is_a_theorem(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))))),
% 46.31/30.07 inference(modus_ponens,[status(thm)],[279, 278])).
% 46.31/30.07 tff(281,plain,
% 46.31/30.07 (is_a_theorem(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.31/30.07 inference(unit_resolution,[status(thm)],[280, 274, 254, 246])).
% 46.31/30.07 tff(282,plain,
% 46.31/30.07 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))) | (~is_a_theorem(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))) | (~is_a_theorem(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))))))),
% 46.31/30.07 inference(rewrite,[status(thm)],[])).
% 46.31/30.07 tff(283,plain,
% 46.31/30.07 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))) | (~is_a_theorem(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))))))),
% 46.31/30.07 inference(quant_inst,[status(thm)],[])).
% 46.31/30.07 tff(284,plain,
% 46.31/30.07 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))) | (~is_a_theorem(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))))))),
% 46.31/30.07 inference(modus_ponens,[status(thm)],[283, 282])).
% 46.31/30.07 tff(285,plain,
% 46.31/30.07 (is_a_theorem(implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0)))))))) | (~is_a_theorem(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(R!0)))))), or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))))))),
% 46.31/30.07 inference(unit_resolution,[status(thm)],[284, 274])).
% 46.31/30.07 tff(286,plain,
% 46.31/30.07 (is_a_theorem(implies(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(R!0))))))))),
% 46.31/30.07 inference(unit_resolution,[status(thm)],[285, 281, 228])).
% 46.31/30.07 tff(287,plain,
% 46.31/30.07 (is_a_theorem(implies(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))))),
% 46.31/30.07 inference(modus_ponens,[status(thm)],[286, 202])).
% 46.31/30.07 tff(288,plain,
% 46.31/30.07 (is_a_theorem(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))))),
% 46.31/30.07 inference(modus_ponens,[status(thm)],[287, 144])).
% 46.31/30.07 tff(289,plain,
% 46.31/30.07 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))))) | (~is_a_theorem(implies(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))), implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))))) | (~is_a_theorem(implies(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))), implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))))),
% 46.31/30.07 inference(rewrite,[status(thm)],[])).
% 46.31/30.07 tff(290,plain,
% 46.31/30.07 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))))) | (~is_a_theorem(implies(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))), implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))))),
% 46.31/30.08 inference(quant_inst,[status(thm)],[])).
% 46.31/30.08 tff(291,plain,
% 46.31/30.08 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))))) | (~is_a_theorem(implies(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))), implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.31/30.08 inference(modus_ponens,[status(thm)],[290, 289])).
% 46.31/30.08 tff(292,plain,
% 46.31/30.08 (is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))))) | (~is_a_theorem(implies(or(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(not(and(not(P!2), not(R!0))))))), implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.31/30.08 inference(unit_resolution,[status(thm)],[291, 274])).
% 46.31/30.08 tff(293,plain,
% 46.31/30.08 (is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.31/30.08 inference(unit_resolution,[status(thm)],[292, 288, 141])).
% 46.31/30.08 tff(294,plain,
% 46.31/30.08 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(P!2, R!0))) = or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))))),
% 46.31/30.08 inference(quant_inst,[status(thm)],[])).
% 46.31/30.08 tff(295,plain,
% 46.31/30.08 (implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(P!2, R!0))) = or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0)))),
% 46.31/30.08 inference(unit_resolution,[status(thm)],[294, 20])).
% 46.31/30.08 tff(296,plain,
% 46.31/30.08 (or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))) = implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(P!2, R!0)))),
% 46.31/30.08 inference(symmetry,[status(thm)],[295])).
% 46.31/30.08 tff(297,plain,
% 46.31/30.08 (is_a_theorem(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0)))) <=> is_a_theorem(implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(P!2, R!0))))),
% 46.31/30.08 inference(monotonicity,[status(thm)],[296])).
% 46.31/30.08 tff(298,plain,
% 46.31/30.08 (is_a_theorem(implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(P!2, R!0)))) <=> is_a_theorem(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))))),
% 46.31/30.08 inference(symmetry,[status(thm)],[297])).
% 46.31/30.08 tff(299,plain,
% 46.31/30.08 (implies(and(not(Q!1), not(or(P!2, R!0))), not(or(P!2, R!0))) = implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(P!2, R!0)))),
% 46.31/30.08 inference(monotonicity,[status(thm)],[205])).
% 46.31/30.08 tff(300,plain,
% 46.31/30.08 (is_a_theorem(implies(and(not(Q!1), not(or(P!2, R!0))), not(or(P!2, R!0)))) <=> is_a_theorem(implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(P!2, R!0))))),
% 46.31/30.08 inference(monotonicity,[status(thm)],[299])).
% 46.31/30.08 tff(301,plain,
% 46.31/30.08 (^[X: $i, Y: $i] : refl(is_a_theorem(implies(and(X, Y), Y)) <=> is_a_theorem(implies(and(X, Y), Y)))),
% 46.31/30.08 inference(bind,[status(th)],[])).
% 46.31/30.08 tff(302,plain,
% 46.31/30.08 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y)) <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 46.31/30.08 inference(quant_intro,[status(thm)],[301])).
% 46.31/30.08 tff(303,plain,
% 46.31/30.08 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y)) <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 46.31/30.08 inference(rewrite,[status(thm)],[])).
% 46.31/30.08 tff(304,plain,
% 46.31/30.08 (($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 46.31/30.08 inference(rewrite,[status(thm)],[])).
% 46.31/30.08 tff(305,axiom,(and_2), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_and_2')).
% 46.31/30.08 tff(306,plain,
% 46.31/30.08 (and_2 <=> $true),
% 46.31/30.08 inference(iff_true,[status(thm)],[305])).
% 46.31/30.08 tff(307,plain,
% 46.31/30.08 ((and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))) <=> ($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y)))),
% 46.31/30.08 inference(monotonicity,[status(thm)],[306])).
% 46.31/30.08 tff(308,plain,
% 46.31/30.08 ((and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 46.31/30.08 inference(transitivity,[status(thm)],[307, 304])).
% 46.31/30.08 tff(309,plain,
% 46.31/30.08 ((and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))) <=> (and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y)))),
% 46.31/30.08 inference(rewrite,[status(thm)],[])).
% 46.31/30.08 tff(310,axiom,(and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','and_2')).
% 46.31/30.08 tff(311,plain,
% 46.31/30.08 (and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 46.31/30.08 inference(modus_ponens,[status(thm)],[310, 309])).
% 46.31/30.08 tff(312,plain,
% 46.31/30.08 (and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 46.31/30.08 inference(modus_ponens,[status(thm)],[311, 309])).
% 46.31/30.08 tff(313,plain,
% 46.31/30.08 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 46.31/30.08 inference(modus_ponens,[status(thm)],[312, 308])).
% 46.37/30.08 tff(314,plain,
% 46.37/30.08 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 46.37/30.08 inference(modus_ponens,[status(thm)],[313, 303])).
% 46.37/30.08 tff(315,plain,(
% 46.37/30.08 ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 46.37/30.08 inference(skolemize,[status(sab)],[314])).
% 46.37/30.08 tff(316,plain,
% 46.37/30.08 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 46.37/30.08 inference(modus_ponens,[status(thm)],[315, 302])).
% 46.37/30.08 tff(317,plain,
% 46.37/30.08 ((~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))) | is_a_theorem(implies(and(not(Q!1), not(or(P!2, R!0))), not(or(P!2, R!0))))),
% 46.37/30.08 inference(quant_inst,[status(thm)],[])).
% 46.37/30.08 tff(318,plain,
% 46.37/30.08 (is_a_theorem(implies(and(not(Q!1), not(or(P!2, R!0))), not(or(P!2, R!0))))),
% 46.37/30.08 inference(unit_resolution,[status(thm)],[317, 316])).
% 46.37/30.08 tff(319,plain,
% 46.37/30.08 (is_a_theorem(implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(P!2, R!0))))),
% 46.37/30.08 inference(modus_ponens,[status(thm)],[318, 300])).
% 46.37/30.08 tff(320,plain,
% 46.37/30.08 (is_a_theorem(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))))),
% 46.37/30.08 inference(modus_ponens,[status(thm)],[319, 298])).
% 46.37/30.08 tff(321,plain,
% 46.37/30.08 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))))) | (~is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))))) | (~is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.08 inference(rewrite,[status(thm)],[])).
% 46.37/30.08 tff(322,plain,
% 46.37/30.08 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))))) | (~is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.08 inference(quant_inst,[status(thm)],[])).
% 46.37/30.08 tff(323,plain,
% 46.37/30.08 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))))) | (~is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.08 inference(modus_ponens,[status(thm)],[322, 321])).
% 46.37/30.08 tff(324,plain,
% 46.37/30.08 (is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(P!2, R!0))), or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.08 inference(unit_resolution,[status(thm)],[323, 274, 320])).
% 46.37/30.08 tff(325,plain,
% 46.37/30.08 (is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.37/30.08 inference(unit_resolution,[status(thm)],[324, 293])).
% 46.37/30.08 tff(326,plain,
% 46.37/30.08 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(P!2, not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.08 inference(quant_inst,[status(thm)],[])).
% 46.37/30.08 tff(327,plain,
% 46.37/30.08 (implies(P!2, not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.08 inference(unit_resolution,[status(thm)],[326, 20])).
% 46.37/30.08 tff(328,plain,
% 46.37/30.08 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(P!2, not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(P!2, not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.08 inference(quant_inst,[status(thm)],[])).
% 46.37/30.08 tff(329,plain,
% 46.37/30.08 (implies(P!2, not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(P!2, not(not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.08 inference(unit_resolution,[status(thm)],[328, 175])).
% 46.37/30.08 tff(330,plain,
% 46.37/30.08 (not(and(P!2, not(not(and(not(Q!1), not(or(P!2, R!0))))))) = implies(P!2, not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.08 inference(symmetry,[status(thm)],[329])).
% 46.37/30.08 tff(331,plain,
% 46.37/30.08 (and(P!2, not(not(and(not(Q!1), not(or(P!2, R!0)))))) = and(P!2, not(or(Q!1, or(P!2, R!0))))),
% 46.37/30.08 inference(monotonicity,[status(thm)],[148])).
% 46.37/30.08 tff(332,plain,
% 46.37/30.08 (and(P!2, not(or(Q!1, or(P!2, R!0)))) = and(P!2, not(not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.08 inference(symmetry,[status(thm)],[331])).
% 46.37/30.08 tff(333,plain,
% 46.37/30.08 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(P!2, not(or(Q!1, or(P!2, R!0)))) = not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.08 inference(quant_inst,[status(thm)],[])).
% 46.37/30.08 tff(334,plain,
% 46.37/30.08 (and(P!2, not(or(Q!1, or(P!2, R!0)))) = not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.37/30.08 inference(unit_resolution,[status(thm)],[333, 97])).
% 46.37/30.08 tff(335,plain,
% 46.37/30.08 (not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))) = and(P!2, not(or(Q!1, or(P!2, R!0))))),
% 46.37/30.08 inference(symmetry,[status(thm)],[334])).
% 46.37/30.08 tff(336,plain,
% 46.37/30.08 (not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))) = and(P!2, not(not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.08 inference(transitivity,[status(thm)],[335, 332])).
% 46.37/30.08 tff(337,plain,
% 46.37/30.08 (not(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) = not(and(P!2, not(not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.08 inference(monotonicity,[status(thm)],[336])).
% 46.37/30.08 tff(338,plain,
% 46.37/30.08 (not(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) = or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.08 inference(transitivity,[status(thm)],[337, 330, 327])).
% 46.37/30.08 tff(339,plain,
% 46.37/30.08 (not(and(not(and(not(P!2), not(R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))) = implies(not(and(not(P!2), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.08 inference(symmetry,[status(thm)],[177])).
% 46.37/30.08 tff(340,plain,
% 46.37/30.08 (not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) = or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.08 inference(transitivity,[status(thm)],[155, 339, 179])).
% 46.37/30.08 tff(341,plain,
% 46.37/30.08 (implies(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))))) = implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.08 inference(monotonicity,[status(thm)],[340, 338])).
% 46.37/30.08 tff(342,plain,
% 46.37/30.08 (implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.08 inference(symmetry,[status(thm)],[341])).
% 46.37/30.08 tff(343,plain,
% 46.37/30.08 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))) = or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.08 inference(quant_inst,[status(thm)],[])).
% 46.37/30.08 tff(344,plain,
% 46.37/30.08 (implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))) = or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.08 inference(unit_resolution,[status(thm)],[343, 20])).
% 46.37/30.08 tff(345,plain,
% 46.37/30.08 (or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.08 inference(symmetry,[status(thm)],[344])).
% 46.37/30.08 tff(346,plain,
% 46.37/30.08 (or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.08 inference(transitivity,[status(thm)],[345, 342])).
% 46.37/30.08 tff(347,plain,
% 46.37/30.08 (implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))) = implies(implies(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))))), implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.08 inference(monotonicity,[status(thm)],[346])).
% 46.37/30.08 tff(348,plain,
% 46.37/30.08 (is_a_theorem(implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))) <=> is_a_theorem(implies(implies(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))))), implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.08 inference(monotonicity,[status(thm)],[347])).
% 46.37/30.08 tff(349,plain,
% 46.37/30.08 (is_a_theorem(implies(implies(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))))), implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))) <=> is_a_theorem(implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.08 inference(symmetry,[status(thm)],[348])).
% 46.37/30.08 tff(350,plain,
% 46.37/30.08 ((~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) | is_a_theorem(implies(implies(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))))), implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.08 inference(quant_inst,[status(thm)],[])).
% 46.37/30.08 tff(351,plain,
% 46.37/30.08 (is_a_theorem(implies(implies(not(not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))))), implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.08 inference(unit_resolution,[status(thm)],[350, 138])).
% 46.37/30.08 tff(352,plain,
% 46.37/30.08 (is_a_theorem(implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.08 inference(modus_ponens,[status(thm)],[351, 349])).
% 46.37/30.08 tff(353,plain,
% 46.37/30.08 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(not(not(P!2)), not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.08 inference(quant_inst,[status(thm)],[])).
% 46.37/30.08 tff(354,plain,
% 46.37/30.08 (or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(not(not(P!2)), not(not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.08 inference(unit_resolution,[status(thm)],[353, 41])).
% 46.37/30.08 tff(355,plain,
% 46.37/30.08 (not(and(not(not(P!2)), not(not(and(not(Q!1), not(or(P!2, R!0))))))) = or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.08 inference(symmetry,[status(thm)],[354])).
% 46.37/30.08 tff(356,plain,
% 46.37/30.08 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(P!2)), not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(not(not(P!2)), not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.08 inference(quant_inst,[status(thm)],[])).
% 46.37/30.08 tff(357,plain,
% 46.37/30.08 (implies(not(not(P!2)), not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(not(not(P!2)), not(not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.08 inference(unit_resolution,[status(thm)],[356, 175])).
% 46.37/30.08 tff(358,plain,
% 46.37/30.08 (implies(not(not(P!2)), not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.08 inference(transitivity,[status(thm)],[357, 355])).
% 46.37/30.08 tff(359,plain,
% 46.37/30.08 (and(not(not(or(not(not(P!2)), not(not(R!0))))), not(not(and(not(Q!1), not(or(P!2, R!0)))))) = and(not(and(not(P!2), not(R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.08 inference(monotonicity,[status(thm)],[103])).
% 46.37/30.08 tff(360,plain,
% 46.37/30.08 (not(and(not(not(or(not(not(P!2)), not(not(R!0))))), not(not(and(not(Q!1), not(or(P!2, R!0))))))) = not(and(not(and(not(P!2), not(R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.08 inference(monotonicity,[status(thm)],[359])).
% 46.37/30.08 tff(361,plain,
% 46.37/30.08 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(not(P!2)), not(not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(not(not(or(not(not(P!2)), not(not(R!0))))), not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.08 inference(quant_inst,[status(thm)],[])).
% 46.37/30.08 tff(362,plain,
% 46.37/30.08 (or(not(or(not(not(P!2)), not(not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(not(not(or(not(not(P!2)), not(not(R!0))))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.08 inference(unit_resolution,[status(thm)],[361, 41])).
% 46.37/30.08 tff(363,plain,
% 46.37/30.08 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(P!2)), not(not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(or(not(not(P!2)), not(not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.08 inference(quant_inst,[status(thm)],[])).
% 46.37/30.08 tff(364,plain,
% 46.37/30.08 (implies(or(not(not(P!2)), not(not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(or(not(not(P!2)), not(not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.08 inference(unit_resolution,[status(thm)],[363, 20])).
% 46.37/30.08 tff(365,plain,
% 46.37/30.08 (implies(or(not(not(P!2)), not(not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.08 inference(transitivity,[status(thm)],[364, 362, 360, 339, 179])).
% 46.37/30.08 tff(366,plain,
% 46.37/30.08 (implies(implies(or(not(not(P!2)), not(not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(not(not(P!2)), not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.08 inference(monotonicity,[status(thm)],[365, 358])).
% 46.37/30.08 tff(367,plain,
% 46.37/30.08 (implies(implies(or(not(not(P!2)), not(not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(not(not(P!2)), not(and(not(Q!1), not(or(P!2, R!0)))))) = or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.08 inference(transitivity,[status(thm)],[366, 344])).
% 46.37/30.08 tff(368,plain,
% 46.37/30.08 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(not(P!2)), or(not(not(P!2)), not(not(R!0)))) = or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))))),
% 46.37/30.08 inference(quant_inst,[status(thm)],[])).
% 46.37/30.08 tff(369,plain,
% 46.37/30.08 (implies(not(not(P!2)), or(not(not(P!2)), not(not(R!0)))) = or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0))))),
% 46.37/30.08 inference(unit_resolution,[status(thm)],[368, 20])).
% 46.37/30.08 tff(370,plain,
% 46.37/30.08 (implies(implies(not(not(P!2)), or(not(not(P!2)), not(not(R!0)))), implies(implies(or(not(not(P!2)), not(not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(not(not(P!2)), not(and(not(Q!1), not(or(P!2, R!0))))))) = implies(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.08 inference(monotonicity,[status(thm)],[369, 367])).
% 46.37/30.08 tff(371,plain,
% 46.37/30.08 (implies(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))) = implies(implies(not(not(P!2)), or(not(not(P!2)), not(not(R!0)))), implies(implies(or(not(not(P!2)), not(not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(not(not(P!2)), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.08 inference(symmetry,[status(thm)],[370])).
% 46.37/30.08 tff(372,plain,
% 46.37/30.08 (is_a_theorem(implies(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))))) <=> is_a_theorem(implies(implies(not(not(P!2)), or(not(not(P!2)), not(not(R!0)))), implies(implies(or(not(not(P!2)), not(not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(not(not(P!2)), not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.08 inference(monotonicity,[status(thm)],[371])).
% 46.37/30.08 tff(373,plain,
% 46.37/30.08 (is_a_theorem(implies(implies(not(not(P!2)), or(not(not(P!2)), not(not(R!0)))), implies(implies(or(not(not(P!2)), not(not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(not(not(P!2)), not(and(not(Q!1), not(or(P!2, R!0)))))))) <=> is_a_theorem(implies(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.08 inference(symmetry,[status(thm)],[372])).
% 46.37/30.08 tff(374,plain,
% 46.37/30.08 (^[X: $i, Y: $i, Z: $i] : refl(is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) <=> is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))))),
% 46.37/30.09 inference(bind,[status(th)],[])).
% 46.37/30.09 tff(375,plain,
% 46.37/30.09 (![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 46.37/30.09 inference(quant_intro,[status(thm)],[374])).
% 46.37/30.09 tff(376,plain,
% 46.37/30.09 (![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 46.37/30.09 inference(rewrite,[status(thm)],[])).
% 46.37/30.09 tff(377,plain,
% 46.37/30.09 (($true <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 46.37/30.09 inference(rewrite,[status(thm)],[])).
% 46.37/30.09 tff(378,axiom,(implies_3), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_implies_3')).
% 46.37/30.09 tff(379,plain,
% 46.37/30.09 (implies_3 <=> $true),
% 46.37/30.09 inference(iff_true,[status(thm)],[378])).
% 46.37/30.09 tff(380,plain,
% 46.37/30.09 ((implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) <=> ($true <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))))),
% 46.37/30.09 inference(monotonicity,[status(thm)],[379])).
% 46.37/30.09 tff(381,plain,
% 46.37/30.09 ((implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 46.37/30.09 inference(transitivity,[status(thm)],[380, 377])).
% 46.37/30.09 tff(382,plain,
% 46.37/30.09 ((implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) <=> (implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))))),
% 46.37/30.09 inference(rewrite,[status(thm)],[])).
% 46.37/30.09 tff(383,axiom,(implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','implies_3')).
% 46.37/30.09 tff(384,plain,
% 46.37/30.09 (implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 46.37/30.09 inference(modus_ponens,[status(thm)],[383, 382])).
% 46.37/30.09 tff(385,plain,
% 46.37/30.09 (implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 46.37/30.09 inference(modus_ponens,[status(thm)],[384, 382])).
% 46.37/30.09 tff(386,plain,
% 46.37/30.09 (![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 46.37/30.09 inference(modus_ponens,[status(thm)],[385, 381])).
% 46.37/30.09 tff(387,plain,
% 46.37/30.09 (![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 46.37/30.09 inference(modus_ponens,[status(thm)],[386, 376])).
% 46.37/30.09 tff(388,plain,(
% 46.37/30.09 ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 46.37/30.09 inference(skolemize,[status(sab)],[387])).
% 46.37/30.09 tff(389,plain,
% 46.37/30.09 (![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 46.37/30.09 inference(modus_ponens,[status(thm)],[388, 375])).
% 46.37/30.09 tff(390,plain,
% 46.37/30.09 ((~![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) | is_a_theorem(implies(implies(not(not(P!2)), or(not(not(P!2)), not(not(R!0)))), implies(implies(or(not(not(P!2)), not(not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(not(not(P!2)), not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.09 inference(quant_inst,[status(thm)],[])).
% 46.37/30.09 tff(391,plain,
% 46.37/30.09 (is_a_theorem(implies(implies(not(not(P!2)), or(not(not(P!2)), not(not(R!0)))), implies(implies(or(not(not(P!2)), not(not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(not(not(P!2)), not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.09 inference(unit_resolution,[status(thm)],[390, 389])).
% 46.37/30.09 tff(392,plain,
% 46.37/30.09 (is_a_theorem(implies(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.09 inference(modus_ponens,[status(thm)],[391, 373])).
% 46.37/30.09 tff(393,plain,
% 46.37/30.09 (or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))) = implies(not(not(P!2)), or(not(not(P!2)), not(not(R!0))))),
% 46.37/30.09 inference(symmetry,[status(thm)],[369])).
% 46.37/30.09 tff(394,plain,
% 46.37/30.09 (is_a_theorem(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0))))) <=> is_a_theorem(implies(not(not(P!2)), or(not(not(P!2)), not(not(R!0)))))),
% 46.37/30.09 inference(monotonicity,[status(thm)],[393])).
% 46.37/30.09 tff(395,plain,
% 46.37/30.09 (is_a_theorem(implies(not(not(P!2)), or(not(not(P!2)), not(not(R!0))))) <=> is_a_theorem(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))))),
% 46.37/30.09 inference(symmetry,[status(thm)],[394])).
% 46.37/30.09 tff(396,plain,
% 46.37/30.09 (^[X: $i, Y: $i] : refl(is_a_theorem(implies(X, or(X, Y))) <=> is_a_theorem(implies(X, or(X, Y))))),
% 46.37/30.09 inference(bind,[status(th)],[])).
% 46.37/30.09 tff(397,plain,
% 46.37/30.09 (![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 46.37/30.09 inference(quant_intro,[status(thm)],[396])).
% 46.37/30.09 tff(398,plain,
% 46.37/30.09 (![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 46.37/30.09 inference(rewrite,[status(thm)],[])).
% 46.37/30.09 tff(399,plain,
% 46.37/30.09 (($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 46.37/30.09 inference(rewrite,[status(thm)],[])).
% 46.37/30.09 tff(400,axiom,(or_1), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_or_1')).
% 46.37/30.09 tff(401,plain,
% 46.37/30.09 (or_1 <=> $true),
% 46.37/30.09 inference(iff_true,[status(thm)],[400])).
% 46.37/30.09 tff(402,plain,
% 46.37/30.09 ((or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))) <=> ($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y))))),
% 46.37/30.09 inference(monotonicity,[status(thm)],[401])).
% 46.37/30.09 tff(403,plain,
% 46.37/30.09 ((or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 46.37/30.09 inference(transitivity,[status(thm)],[402, 399])).
% 46.37/30.09 tff(404,plain,
% 46.37/30.09 ((or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))) <=> (or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y))))),
% 46.37/30.09 inference(rewrite,[status(thm)],[])).
% 46.37/30.09 tff(405,axiom,(or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','or_1')).
% 46.37/30.09 tff(406,plain,
% 46.37/30.09 (or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 46.37/30.09 inference(modus_ponens,[status(thm)],[405, 404])).
% 46.37/30.09 tff(407,plain,
% 46.37/30.09 (or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 46.37/30.09 inference(modus_ponens,[status(thm)],[406, 404])).
% 46.37/30.09 tff(408,plain,
% 46.37/30.09 (![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 46.37/30.09 inference(modus_ponens,[status(thm)],[407, 403])).
% 46.37/30.09 tff(409,plain,
% 46.37/30.09 (![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 46.37/30.09 inference(modus_ponens,[status(thm)],[408, 398])).
% 46.37/30.09 tff(410,plain,(
% 46.37/30.09 ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 46.37/30.09 inference(skolemize,[status(sab)],[409])).
% 46.37/30.09 tff(411,plain,
% 46.37/30.09 (![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 46.37/30.09 inference(modus_ponens,[status(thm)],[410, 397])).
% 46.37/30.09 tff(412,plain,
% 46.37/30.09 ((~![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))) | is_a_theorem(implies(not(not(P!2)), or(not(not(P!2)), not(not(R!0)))))),
% 46.37/30.09 inference(quant_inst,[status(thm)],[])).
% 46.37/30.09 tff(413,plain,
% 46.37/30.09 (is_a_theorem(implies(not(not(P!2)), or(not(not(P!2)), not(not(R!0)))))),
% 46.37/30.09 inference(unit_resolution,[status(thm)],[412, 411])).
% 46.37/30.09 tff(414,plain,
% 46.37/30.09 (is_a_theorem(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))))),
% 46.37/30.09 inference(modus_ponens,[status(thm)],[413, 395])).
% 46.37/30.09 tff(415,plain,
% 46.37/30.09 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))))) | is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))))) | is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.37/30.09 inference(rewrite,[status(thm)],[])).
% 46.37/30.09 tff(416,plain,
% 46.37/30.09 ((is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))))) | (~is_a_theorem(implies(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))))))) <=> ((~is_a_theorem(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))))) | is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.37/30.09 inference(rewrite,[status(thm)],[])).
% 46.37/30.09 tff(417,plain,
% 46.37/30.09 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))))) | (~is_a_theorem(implies(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))))) | is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))))))))),
% 46.37/30.09 inference(monotonicity,[status(thm)],[416])).
% 46.37/30.09 tff(418,plain,
% 46.37/30.09 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))))) | (~is_a_theorem(implies(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))))) | is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.37/30.09 inference(transitivity,[status(thm)],[417, 415])).
% 46.37/30.09 tff(419,plain,
% 46.37/30.09 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))))) | (~is_a_theorem(implies(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.37/30.09 inference(quant_inst,[status(thm)],[])).
% 46.37/30.09 tff(420,plain,
% 46.37/30.09 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))))) | is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))))))),
% 46.37/30.09 inference(modus_ponens,[status(thm)],[419, 418])).
% 46.37/30.09 tff(421,plain,
% 46.37/30.09 (is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(not(P!2))), or(not(not(P!2)), not(not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))))))),
% 46.37/30.09 inference(unit_resolution,[status(thm)],[420, 274, 414])).
% 46.37/30.09 tff(422,plain,
% 46.37/30.09 (is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.09 inference(unit_resolution,[status(thm)],[421, 392])).
% 46.37/30.09 tff(423,plain,
% 46.37/30.09 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))) | (~is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))) | (~is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))))),
% 46.37/30.09 inference(rewrite,[status(thm)],[])).
% 46.37/30.09 tff(424,plain,
% 46.37/30.09 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))) | (~is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))))),
% 46.37/30.09 inference(quant_inst,[status(thm)],[])).
% 46.37/30.09 tff(425,plain,
% 46.37/30.09 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))) | (~is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))))),
% 46.37/30.09 inference(modus_ponens,[status(thm)],[424, 423])).
% 46.37/30.09 tff(426,plain,
% 46.37/30.09 (is_a_theorem(implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))) | (~is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(P!2), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))))),
% 46.37/30.09 inference(unit_resolution,[status(thm)],[425, 274])).
% 46.37/30.09 tff(427,plain,
% 46.37/30.09 (is_a_theorem(implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.09 inference(unit_resolution,[status(thm)],[426, 422, 352])).
% 46.37/30.09 tff(428,plain,
% 46.37/30.09 ((~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) | is_a_theorem(implies(implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.09 inference(quant_inst,[status(thm)],[])).
% 46.37/30.09 tff(429,plain,
% 46.37/30.09 (is_a_theorem(implies(implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.09 inference(unit_resolution,[status(thm)],[428, 138])).
% 46.37/30.09 tff(430,plain,
% 46.37/30.09 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))) | (~is_a_theorem(implies(implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))) | (~is_a_theorem(implies(implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))))))),
% 46.37/30.09 inference(rewrite,[status(thm)],[])).
% 46.37/30.09 tff(431,plain,
% 46.37/30.09 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))) | (~is_a_theorem(implies(implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))))))),
% 46.37/30.09 inference(quant_inst,[status(thm)],[])).
% 46.37/30.09 tff(432,plain,
% 46.37/30.09 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))) | (~is_a_theorem(implies(implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.09 inference(modus_ponens,[status(thm)],[431, 430])).
% 46.37/30.09 tff(433,plain,
% 46.37/30.09 (is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(not(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.09 inference(unit_resolution,[status(thm)],[432, 274, 429])).
% 46.37/30.09 tff(434,plain,
% 46.37/30.09 (is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.09 inference(unit_resolution,[status(thm)],[433, 427])).
% 46.37/30.09 tff(435,plain,
% 46.37/30.09 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.09 inference(rewrite,[status(thm)],[])).
% 46.37/30.09 tff(436,plain,
% 46.37/30.09 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.09 inference(quant_inst,[status(thm)],[])).
% 46.37/30.09 tff(437,plain,
% 46.37/30.09 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.09 inference(modus_ponens,[status(thm)],[436, 435])).
% 46.37/30.10 tff(438,plain,
% 46.37/30.10 (is_a_theorem(or(not(P!2), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.10 inference(unit_resolution,[status(thm)],[437, 274])).
% 46.37/30.10 tff(439,plain,
% 46.37/30.10 (is_a_theorem(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.37/30.10 inference(unit_resolution,[status(thm)],[438, 434, 325])).
% 46.37/30.10 tff(440,plain,
% 46.37/30.10 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(P!2), not(or(Q!1, R!0))) = not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))),
% 46.37/30.10 inference(quant_inst,[status(thm)],[])).
% 46.37/30.10 tff(441,plain,
% 46.37/30.10 (and(not(P!2), not(or(Q!1, R!0))) = not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))),
% 46.37/30.10 inference(unit_resolution,[status(thm)],[440, 97])).
% 46.37/30.10 tff(442,plain,
% 46.37/30.10 (not(or(not(not(P!2)), not(not(or(Q!1, R!0))))) = and(not(P!2), not(or(Q!1, R!0)))),
% 46.37/30.10 inference(symmetry,[status(thm)],[441])).
% 46.37/30.10 tff(443,plain,
% 46.37/30.10 (not(not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))) = not(and(not(P!2), not(or(Q!1, R!0))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[442])).
% 46.37/30.10 tff(444,plain,
% 46.37/30.10 (implies(not(not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), not(not(or(Q!1, or(P!2, R!0))))) = implies(not(and(not(P!2), not(or(Q!1, R!0)))), not(not(or(Q!1, or(P!2, R!0)))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[443])).
% 46.37/30.10 tff(445,plain,
% 46.37/30.10 (implies(not(and(not(P!2), not(or(Q!1, R!0)))), not(not(or(Q!1, or(P!2, R!0))))) = implies(not(not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), not(not(or(Q!1, or(P!2, R!0)))))),
% 46.37/30.10 inference(symmetry,[status(thm)],[444])).
% 46.37/30.10 tff(446,plain,
% 46.37/30.10 (or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))) = implies(not(and(not(P!2), not(or(Q!1, R!0)))), not(not(or(Q!1, or(P!2, R!0)))))),
% 46.37/30.10 inference(symmetry,[status(thm)],[22])).
% 46.37/30.10 tff(447,plain,
% 46.37/30.10 (or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))) = implies(not(not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), not(not(or(Q!1, or(P!2, R!0)))))),
% 46.37/30.10 inference(transitivity,[status(thm)],[446, 445])).
% 46.37/30.10 tff(448,plain,
% 46.37/30.10 (implies(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))), implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))) = implies(implies(not(not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), not(not(or(Q!1, or(P!2, R!0))))), implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[447])).
% 46.37/30.10 tff(449,plain,
% 46.37/30.10 (implies(implies(not(not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), not(not(or(Q!1, or(P!2, R!0))))), implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))) = implies(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))), implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))),
% 46.37/30.10 inference(symmetry,[status(thm)],[448])).
% 46.37/30.10 tff(450,plain,
% 46.37/30.10 (is_a_theorem(implies(implies(not(not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), not(not(or(Q!1, or(P!2, R!0))))), implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))) <=> is_a_theorem(implies(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))), implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[449])).
% 46.37/30.10 tff(451,plain,
% 46.37/30.10 ((~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) | is_a_theorem(implies(implies(not(not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), not(not(or(Q!1, or(P!2, R!0))))), implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))))),
% 46.37/30.10 inference(quant_inst,[status(thm)],[])).
% 46.37/30.10 tff(452,plain,
% 46.37/30.10 (is_a_theorem(implies(implies(not(not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), not(not(or(Q!1, or(P!2, R!0))))), implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))))),
% 46.37/30.10 inference(unit_resolution,[status(thm)],[451, 138])).
% 46.37/30.10 tff(453,plain,
% 46.37/30.10 (is_a_theorem(implies(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))), implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))))),
% 46.37/30.10 inference(modus_ponens,[status(thm)],[452, 450])).
% 46.37/30.10 tff(454,plain,
% 46.37/30.10 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))) = or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))),
% 46.37/30.10 inference(quant_inst,[status(thm)],[])).
% 46.37/30.10 tff(455,plain,
% 46.37/30.10 (implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))) = or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))),
% 46.37/30.10 inference(unit_resolution,[status(thm)],[454, 20])).
% 46.37/30.10 tff(456,plain,
% 46.37/30.10 (or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))) = implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))),
% 46.37/30.10 inference(symmetry,[status(thm)],[455])).
% 46.37/30.10 tff(457,plain,
% 46.37/30.10 (not(or(not(not(Q!1)), not(not(or(P!2, R!0))))) = and(not(Q!1), not(or(P!2, R!0)))),
% 46.37/30.10 inference(symmetry,[status(thm)],[205])).
% 46.37/30.10 tff(458,plain,
% 46.37/30.10 (not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))) = not(and(not(Q!1), not(or(P!2, R!0))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[457])).
% 46.37/30.10 tff(459,plain,
% 46.37/30.10 (not(and(not(Q!1), not(or(P!2, R!0)))) = not(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))))),
% 46.37/30.10 inference(symmetry,[status(thm)],[458])).
% 46.37/30.10 tff(460,plain,
% 46.37/30.10 (or(not(and(not(Q!1), not(or(P!2, R!0)))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))) = or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[459])).
% 46.37/30.10 tff(461,plain,
% 46.37/30.10 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(and(not(Q!1), not(or(P!2, R!0)))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))) = not(and(not(not(and(not(Q!1), not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))))),
% 46.37/30.10 inference(quant_inst,[status(thm)],[])).
% 46.37/30.10 tff(462,plain,
% 46.37/30.10 (or(not(and(not(Q!1), not(or(P!2, R!0)))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))) = not(and(not(not(and(not(Q!1), not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))))),
% 46.37/30.10 inference(unit_resolution,[status(thm)],[461, 41])).
% 46.37/30.10 tff(463,plain,
% 46.37/30.10 (not(and(not(not(and(not(Q!1), not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))) = or(not(and(not(Q!1), not(or(P!2, R!0)))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))),
% 46.37/30.10 inference(symmetry,[status(thm)],[462])).
% 46.37/30.10 tff(464,plain,
% 46.37/30.10 (not(or(Q!1, or(P!2, R!0))) = not(not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.10 inference(symmetry,[status(thm)],[148])).
% 46.37/30.10 tff(465,plain,
% 46.37/30.10 (and(not(or(Q!1, or(P!2, R!0))), not(not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))) = and(not(not(and(not(Q!1), not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[464])).
% 46.37/30.10 tff(466,plain,
% 46.37/30.10 (not(and(not(or(Q!1, or(P!2, R!0))), not(not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))) = not(and(not(not(and(not(Q!1), not(or(P!2, R!0))))), not(not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[465])).
% 46.37/30.10 tff(467,plain,
% 46.37/30.10 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))) = not(and(not(or(Q!1, or(P!2, R!0))), not(not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))))),
% 46.37/30.10 inference(quant_inst,[status(thm)],[])).
% 46.37/30.10 tff(468,plain,
% 46.37/30.10 (implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))) = not(and(not(or(Q!1, or(P!2, R!0))), not(not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))))),
% 46.37/30.10 inference(unit_resolution,[status(thm)],[467, 175])).
% 46.37/30.10 tff(469,plain,
% 46.37/30.10 (implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))) = implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))),
% 46.37/30.10 inference(transitivity,[status(thm)],[468, 466, 463, 460, 456])).
% 46.37/30.10 tff(470,plain,
% 46.37/30.10 (is_a_theorem(implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))) <=> is_a_theorem(implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[469])).
% 46.37/30.10 tff(471,plain,
% 46.37/30.10 (is_a_theorem(implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))) <=> is_a_theorem(implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))),
% 46.37/30.10 inference(symmetry,[status(thm)],[470])).
% 46.37/30.10 tff(472,plain,
% 46.37/30.10 (is_a_theorem(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))) <=> is_a_theorem(implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[456])).
% 46.37/30.10 tff(473,plain,
% 46.37/30.10 (is_a_theorem(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))) <=> is_a_theorem(implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))),
% 46.37/30.10 inference(transitivity,[status(thm)],[472, 471])).
% 46.37/30.10 tff(474,plain,
% 46.37/30.10 ((~is_a_theorem(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))) <=> (~is_a_theorem(implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[473])).
% 46.37/30.10 tff(475,plain,
% 46.37/30.10 (implies(and(not(Q!1), not(or(P!2, R!0))), and(not(P!2), not(or(Q!1, R!0)))) = implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[205, 441])).
% 46.37/30.10 tff(476,plain,
% 46.37/30.10 (implies(and(not(Q!1), not(or(P!2, R!0))), and(not(P!2), not(or(Q!1, R!0)))) = or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))),
% 46.37/30.10 inference(transitivity,[status(thm)],[475, 455])).
% 46.37/30.10 tff(477,plain,
% 46.37/30.10 (implies(implies(and(not(Q!1), not(or(P!2, R!0))), and(not(P!2), not(or(Q!1, R!0)))), or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0)))) = implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[476])).
% 46.37/30.10 tff(478,plain,
% 46.37/30.10 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(P!2, or(Q!1, R!0)), or(Q!1, or(P!2, R!0))) = or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0))))),
% 46.37/30.10 inference(quant_inst,[status(thm)],[])).
% 46.37/30.10 tff(479,plain,
% 46.37/30.10 (implies(or(P!2, or(Q!1, R!0)), or(Q!1, or(P!2, R!0))) = or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0)))),
% 46.37/30.10 inference(unit_resolution,[status(thm)],[478, 20])).
% 46.37/30.10 tff(480,plain,
% 46.37/30.10 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(P!2, or(Q!1, R!0)), or(Q!1, or(P!2, R!0))) = not(and(or(P!2, or(Q!1, R!0)), not(or(Q!1, or(P!2, R!0))))))),
% 46.37/30.10 inference(quant_inst,[status(thm)],[])).
% 46.37/30.10 tff(481,plain,
% 46.37/30.10 (implies(or(P!2, or(Q!1, R!0)), or(Q!1, or(P!2, R!0))) = not(and(or(P!2, or(Q!1, R!0)), not(or(Q!1, or(P!2, R!0)))))),
% 46.37/30.10 inference(unit_resolution,[status(thm)],[480, 175])).
% 46.37/30.10 tff(482,plain,
% 46.37/30.10 (not(and(or(P!2, or(Q!1, R!0)), not(or(Q!1, or(P!2, R!0))))) = implies(or(P!2, or(Q!1, R!0)), or(Q!1, or(P!2, R!0)))),
% 46.37/30.10 inference(symmetry,[status(thm)],[481])).
% 46.37/30.10 tff(483,plain,
% 46.37/30.10 (not(and(not(P!2), not(or(Q!1, R!0)))) = or(P!2, or(Q!1, R!0))),
% 46.37/30.10 inference(symmetry,[status(thm)],[43])).
% 46.37/30.10 tff(484,plain,
% 46.37/30.10 (and(not(and(not(P!2), not(or(Q!1, R!0)))), not(not(and(not(Q!1), not(or(P!2, R!0)))))) = and(or(P!2, or(Q!1, R!0)), not(or(Q!1, or(P!2, R!0))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[483, 148])).
% 46.37/30.10 tff(485,plain,
% 46.37/30.10 (not(and(not(and(not(P!2), not(or(Q!1, R!0)))), not(not(and(not(Q!1), not(or(P!2, R!0))))))) = not(and(or(P!2, or(Q!1, R!0)), not(or(Q!1, or(P!2, R!0)))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[484])).
% 46.37/30.10 tff(486,plain,
% 46.37/30.10 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(not(P!2), not(or(Q!1, R!0))), not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(not(and(not(P!2), not(or(Q!1, R!0)))), not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.10 inference(quant_inst,[status(thm)],[])).
% 46.37/30.10 tff(487,plain,
% 46.37/30.10 (or(and(not(P!2), not(or(Q!1, R!0))), not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(not(and(not(P!2), not(or(Q!1, R!0)))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.10 inference(unit_resolution,[status(thm)],[486, 41])).
% 46.37/30.10 tff(488,plain,
% 46.37/30.10 (or(not(or(not(not(P!2)), not(not(or(Q!1, R!0))))), not(and(not(Q!1), not(or(P!2, R!0))))) = or(and(not(P!2), not(or(Q!1, R!0))), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[442])).
% 46.37/30.10 tff(489,plain,
% 46.37/30.10 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(P!2)), not(not(or(Q!1, R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(or(not(not(P!2)), not(not(or(Q!1, R!0))))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.10 inference(quant_inst,[status(thm)],[])).
% 46.37/30.10 tff(490,plain,
% 46.37/30.10 (implies(or(not(not(P!2)), not(not(or(Q!1, R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(or(not(not(P!2)), not(not(or(Q!1, R!0))))), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.10 inference(unit_resolution,[status(thm)],[489, 20])).
% 46.37/30.10 tff(491,plain,
% 46.37/30.10 (implies(or(not(not(P!2)), not(not(or(Q!1, R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0)))),
% 46.37/30.10 inference(transitivity,[status(thm)],[490, 488, 487, 485, 482, 479])).
% 46.37/30.10 tff(492,plain,
% 46.37/30.10 (implies(not(or(not(not(Q!1)), not(not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))) = implies(and(not(Q!1), not(or(P!2, R!0))), and(not(P!2), not(or(Q!1, R!0))))),
% 46.37/30.10 inference(symmetry,[status(thm)],[475])).
% 46.37/30.10 tff(493,plain,
% 46.37/30.10 (implies(not(not(and(not(Q!1), not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))) = implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[148])).
% 46.37/30.10 tff(494,plain,
% 46.37/30.10 (implies(not(not(and(not(Q!1), not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))) = implies(and(not(Q!1), not(or(P!2, R!0))), and(not(P!2), not(or(Q!1, R!0))))),
% 46.37/30.10 inference(transitivity,[status(thm)],[493, 468, 466, 463, 460, 456, 492])).
% 46.37/30.10 tff(495,plain,
% 46.37/30.10 (implies(implies(not(not(and(not(Q!1), not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), implies(or(not(not(P!2)), not(not(or(Q!1, R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(implies(and(not(Q!1), not(or(P!2, R!0))), and(not(P!2), not(or(Q!1, R!0)))), or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[494, 491])).
% 46.37/30.10 tff(496,plain,
% 46.37/30.10 (implies(implies(not(not(and(not(Q!1), not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), implies(or(not(not(P!2)), not(not(or(Q!1, R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0))))),
% 46.37/30.10 inference(transitivity,[status(thm)],[495, 477])).
% 46.37/30.10 tff(497,plain,
% 46.37/30.10 (is_a_theorem(implies(implies(not(not(and(not(Q!1), not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), implies(or(not(not(P!2)), not(not(or(Q!1, R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) <=> is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0)))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[496])).
% 46.37/30.10 tff(498,plain,
% 46.37/30.10 ((~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) | is_a_theorem(implies(implies(not(not(and(not(Q!1), not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), implies(or(not(not(P!2)), not(not(or(Q!1, R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.10 inference(quant_inst,[status(thm)],[])).
% 46.37/30.10 tff(499,plain,
% 46.37/30.10 (is_a_theorem(implies(implies(not(not(and(not(Q!1), not(or(P!2, R!0))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), implies(or(not(not(P!2)), not(not(or(Q!1, R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.10 inference(unit_resolution,[status(thm)],[498, 138])).
% 46.37/30.10 tff(500,plain,
% 46.37/30.10 (is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0)))))),
% 46.37/30.10 inference(modus_ponens,[status(thm)],[499, 497])).
% 46.37/30.10 tff(501,plain,
% 46.37/30.10 (or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0))) = implies(or(P!2, or(Q!1, R!0)), or(Q!1, or(P!2, R!0)))),
% 46.37/30.10 inference(symmetry,[status(thm)],[479])).
% 46.37/30.10 tff(502,plain,
% 46.37/30.10 (is_a_theorem(or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0)))) <=> is_a_theorem(implies(or(P!2, or(Q!1, R!0)), or(Q!1, or(P!2, R!0))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[501])).
% 46.37/30.10 tff(503,plain,
% 46.37/30.10 (is_a_theorem(implies(or(P!2, or(Q!1, R!0)), or(Q!1, or(P!2, R!0)))) <=> is_a_theorem(or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0))))),
% 46.37/30.10 inference(symmetry,[status(thm)],[502])).
% 46.37/30.10 tff(504,plain,
% 46.37/30.10 ((~is_a_theorem(implies(or(P!2, or(Q!1, R!0)), or(Q!1, or(P!2, R!0))))) <=> (~is_a_theorem(or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0)))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[503])).
% 46.37/30.10 tff(505,plain,
% 46.37/30.10 ((~![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: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R)))))),
% 46.37/30.10 inference(rewrite,[status(thm)],[])).
% 46.37/30.10 tff(506,plain,
% 46.37/30.10 (($false <=> ![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)))))),
% 46.37/30.10 inference(rewrite,[status(thm)],[])).
% 46.37/30.10 tff(507,axiom,(~r4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','principia_r4')).
% 46.37/30.10 tff(508,plain,
% 46.37/30.10 (r4 <=> $false),
% 46.37/30.10 inference(iff_false,[status(thm)],[507])).
% 46.37/30.10 tff(509,plain,
% 46.37/30.10 ((r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) <=> ($false <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R)))))),
% 46.37/30.10 inference(monotonicity,[status(thm)],[508])).
% 46.37/30.10 tff(510,plain,
% 46.37/30.10 ((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)))))),
% 46.37/30.10 inference(transitivity,[status(thm)],[509, 506])).
% 46.37/30.10 tff(511,plain,
% 46.37/30.10 ((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)))))),
% 46.37/30.10 inference(rewrite,[status(thm)],[])).
% 46.37/30.10 tff(512,axiom,(r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','r4')).
% 46.37/30.10 tff(513,plain,
% 46.37/30.10 (r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 46.37/30.10 inference(modus_ponens,[status(thm)],[512, 511])).
% 46.37/30.10 tff(514,plain,
% 46.37/30.10 (r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 46.37/30.10 inference(modus_ponens,[status(thm)],[513, 511])).
% 46.37/30.10 tff(515,plain,
% 46.37/30.10 (~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 46.37/30.10 inference(modus_ponens,[status(thm)],[514, 510])).
% 46.37/30.10 tff(516,plain,
% 46.37/30.10 (~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 46.37/30.10 inference(modus_ponens,[status(thm)],[515, 505])).
% 46.37/30.10 tff(517,plain,
% 46.37/30.10 (~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 46.37/30.10 inference(modus_ponens,[status(thm)],[516, 505])).
% 46.37/30.10 tff(518,plain,
% 46.37/30.10 (~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 46.37/30.10 inference(modus_ponens,[status(thm)],[517, 505])).
% 46.37/30.11 tff(519,plain,
% 46.37/30.11 (~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 46.37/30.11 inference(modus_ponens,[status(thm)],[518, 505])).
% 46.37/30.11 tff(520,plain,
% 46.37/30.11 (~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 46.37/30.11 inference(modus_ponens,[status(thm)],[519, 505])).
% 46.37/30.11 tff(521,plain,
% 46.37/30.11 (~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 46.37/30.11 inference(modus_ponens,[status(thm)],[520, 505])).
% 46.37/30.11 tff(522,plain,(
% 46.37/30.11 ~is_a_theorem(implies(or(P!2, or(Q!1, R!0)), or(Q!1, or(P!2, R!0))))),
% 46.37/30.11 inference(skolemize,[status(sab)],[521])).
% 46.37/30.11 tff(523,plain,
% 46.37/30.11 (~is_a_theorem(or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0))))),
% 46.37/30.11 inference(modus_ponens,[status(thm)],[522, 504])).
% 46.37/30.11 tff(524,plain,
% 46.37/30.11 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0)))) | (~is_a_theorem(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))) | (~is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0)))) | (~is_a_theorem(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))) | (~is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.11 inference(rewrite,[status(thm)],[])).
% 46.37/30.11 tff(525,plain,
% 46.37/30.11 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0)))) | (~is_a_theorem(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))) | (~is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.11 inference(quant_inst,[status(thm)],[])).
% 46.37/30.11 tff(526,plain,
% 46.37/30.11 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0)))) | (~is_a_theorem(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))) | (~is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0))))))),
% 46.37/30.11 inference(modus_ponens,[status(thm)],[525, 524])).
% 46.37/30.11 tff(527,plain,
% 46.37/30.11 ((~is_a_theorem(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))) | (~is_a_theorem(implies(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))), or(not(or(P!2, or(Q!1, R!0))), or(Q!1, or(P!2, R!0))))))),
% 46.37/30.11 inference(unit_resolution,[status(thm)],[526, 274, 523])).
% 46.37/30.11 tff(528,plain,
% 46.37/30.11 (~is_a_theorem(or(not(not(or(not(not(Q!1)), not(not(or(P!2, R!0)))))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))),
% 46.37/30.11 inference(unit_resolution,[status(thm)],[527, 500])).
% 46.37/30.11 tff(529,plain,
% 46.37/30.11 (~is_a_theorem(implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))),
% 46.37/30.11 inference(modus_ponens,[status(thm)],[528, 474])).
% 46.37/30.11 tff(530,plain,
% 46.37/30.11 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))), implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))), implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))))))),
% 46.37/30.11 inference(rewrite,[status(thm)],[])).
% 46.37/30.11 tff(531,plain,
% 46.37/30.11 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))), implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))))))),
% 46.37/30.11 inference(quant_inst,[status(thm)],[])).
% 46.37/30.11 tff(532,plain,
% 46.37/30.11 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))), implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))))),
% 46.37/30.11 inference(modus_ponens,[status(thm)],[531, 530])).
% 46.37/30.11 tff(533,plain,
% 46.37/30.11 (is_a_theorem(implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0))))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))), implies(not(or(Q!1, or(P!2, R!0))), not(or(not(not(P!2)), not(not(or(Q!1, R!0)))))))))),
% 46.37/30.11 inference(unit_resolution,[status(thm)],[532, 274])).
% 46.37/30.11 tff(534,plain,
% 46.37/30.11 (~is_a_theorem(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.37/30.11 inference(unit_resolution,[status(thm)],[533, 529, 453])).
% 46.37/30.11 tff(535,plain,
% 46.37/30.11 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))) = or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.11 inference(quant_inst,[status(thm)],[])).
% 46.37/30.11 tff(536,plain,
% 46.37/30.11 (implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))) = or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.11 inference(unit_resolution,[status(thm)],[535, 20])).
% 46.37/30.11 tff(537,plain,
% 46.37/30.11 (implies(implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) = implies(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.11 inference(monotonicity,[status(thm)],[536])).
% 46.37/30.11 tff(538,plain,
% 46.37/30.11 (implies(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) = implies(implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.11 inference(symmetry,[status(thm)],[537])).
% 46.37/30.11 tff(539,plain,
% 46.37/30.11 (is_a_theorem(implies(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))) <=> is_a_theorem(implies(implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.11 inference(monotonicity,[status(thm)],[538])).
% 46.37/30.11 tff(540,plain,
% 46.37/30.11 (is_a_theorem(implies(implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))) <=> is_a_theorem(implies(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.11 inference(symmetry,[status(thm)],[539])).
% 46.37/30.11 tff(541,plain,
% 46.37/30.11 ((~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) | is_a_theorem(implies(implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.11 inference(quant_inst,[status(thm)],[])).
% 46.37/30.11 tff(542,plain,
% 46.37/30.11 (is_a_theorem(implies(implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.11 inference(unit_resolution,[status(thm)],[541, 138])).
% 46.37/30.11 tff(543,plain,
% 46.37/30.11 (is_a_theorem(implies(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.11 inference(modus_ponens,[status(thm)],[542, 540])).
% 46.37/30.11 tff(544,plain,
% 46.37/30.11 (or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))) = implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.11 inference(symmetry,[status(thm)],[536])).
% 46.37/30.11 tff(545,plain,
% 46.37/30.11 (is_a_theorem(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))))) <=> is_a_theorem(implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.11 inference(monotonicity,[status(thm)],[544])).
% 46.37/30.11 tff(546,plain,
% 46.37/30.11 (is_a_theorem(implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))))) <=> is_a_theorem(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.11 inference(symmetry,[status(thm)],[545])).
% 46.37/30.11 tff(547,plain,
% 46.37/30.11 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(R!0, not(or(Q!1, or(P!2, R!0)))) = not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.11 inference(quant_inst,[status(thm)],[])).
% 46.37/30.11 tff(548,plain,
% 46.37/30.11 (and(R!0, not(or(Q!1, or(P!2, R!0)))) = not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.37/30.11 inference(unit_resolution,[status(thm)],[547, 97])).
% 46.37/30.11 tff(549,plain,
% 46.37/30.11 (and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))) = and(R!0, not(or(Q!1, or(P!2, R!0))))),
% 46.37/30.11 inference(monotonicity,[status(thm)],[148])).
% 46.37/30.11 tff(550,plain,
% 46.37/30.11 (and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))) = not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.37/30.11 inference(transitivity,[status(thm)],[549, 548])).
% 46.37/30.11 tff(551,plain,
% 46.37/30.11 (implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))) = implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.11 inference(monotonicity,[status(thm)],[550])).
% 46.37/30.11 tff(552,plain,
% 46.37/30.11 (is_a_theorem(implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))) <=> is_a_theorem(implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.11 inference(monotonicity,[status(thm)],[551])).
% 46.37/30.11 tff(553,plain,
% 46.37/30.11 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))) = or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.11 inference(quant_inst,[status(thm)],[])).
% 46.37/30.11 tff(554,plain,
% 46.37/30.11 (implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))) = or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.11 inference(unit_resolution,[status(thm)],[553, 20])).
% 46.37/30.11 tff(555,plain,
% 46.37/30.11 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(Q!1), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.11 inference(quant_inst,[status(thm)],[])).
% 46.37/30.11 tff(556,plain,
% 46.37/30.11 (implies(not(and(not(Q!1), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.11 inference(unit_resolution,[status(thm)],[555, 20])).
% 46.37/30.11 tff(557,plain,
% 46.37/30.11 (implies(or(Q!1, R!0), or(Q!1, or(P!2, R!0))) = implies(not(and(not(Q!1), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.11 inference(monotonicity,[status(thm)],[45, 146])).
% 46.37/30.11 tff(558,plain,
% 46.37/30.11 (implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0))))) = implies(or(Q!1, R!0), or(Q!1, or(P!2, R!0)))),
% 46.37/30.11 inference(monotonicity,[status(thm)],[147])).
% 46.37/30.11 tff(559,plain,
% 46.37/30.11 (implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.11 inference(transitivity,[status(thm)],[558, 557, 556])).
% 46.37/30.11 tff(560,plain,
% 46.37/30.11 (implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.11 inference(monotonicity,[status(thm)],[559])).
% 46.37/30.11 tff(561,plain,
% 46.37/30.11 (implies(or(Q!1, R!0), or(Q!1, or(P!2, R!0))) = implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.11 inference(symmetry,[status(thm)],[558])).
% 46.37/30.11 tff(562,plain,
% 46.37/30.11 (implies(not(and(not(Q!1), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))) = implies(or(Q!1, R!0), or(Q!1, or(P!2, R!0)))),
% 46.37/30.11 inference(symmetry,[status(thm)],[557])).
% 46.37/30.11 tff(563,plain,
% 46.37/30.11 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(and(not(Q!1), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(not(and(not(Q!1), not(R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.11 inference(quant_inst,[status(thm)],[])).
% 46.37/30.11 tff(564,plain,
% 46.37/30.11 (implies(not(and(not(Q!1), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(not(and(not(Q!1), not(R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.11 inference(unit_resolution,[status(thm)],[563, 175])).
% 46.37/30.11 tff(565,plain,
% 46.37/30.11 (not(and(not(and(not(Q!1), not(R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))) = implies(not(and(not(Q!1), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.11 inference(symmetry,[status(thm)],[564])).
% 46.37/30.11 tff(566,plain,
% 46.37/30.11 (and(not(and(not(Q!1), not(R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))) = and(not(and(not(Q!1), not(R!0))), not(or(Q!1, or(P!2, R!0))))),
% 46.37/30.11 inference(monotonicity,[status(thm)],[148])).
% 46.37/30.11 tff(567,plain,
% 46.37/30.11 (and(not(and(not(Q!1), not(R!0))), not(or(Q!1, or(P!2, R!0)))) = and(not(and(not(Q!1), not(R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.11 inference(symmetry,[status(thm)],[566])).
% 46.37/30.11 tff(568,plain,
% 46.37/30.11 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(Q!1), not(R!0))), not(or(Q!1, or(P!2, R!0)))) = not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.11 inference(quant_inst,[status(thm)],[])).
% 46.37/30.11 tff(569,plain,
% 46.37/30.11 (and(not(and(not(Q!1), not(R!0))), not(or(Q!1, or(P!2, R!0)))) = not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.37/30.11 inference(unit_resolution,[status(thm)],[568, 97])).
% 46.37/30.11 tff(570,plain,
% 46.37/30.11 (not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) = and(not(and(not(Q!1), not(R!0))), not(or(Q!1, or(P!2, R!0))))),
% 46.37/30.11 inference(symmetry,[status(thm)],[569])).
% 46.37/30.11 tff(571,plain,
% 46.37/30.11 (not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) = and(not(and(not(Q!1), not(R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.11 inference(transitivity,[status(thm)],[570, 567])).
% 46.37/30.11 tff(572,plain,
% 46.37/30.11 (not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) = not(and(not(and(not(Q!1), not(R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.11 inference(monotonicity,[status(thm)],[571])).
% 46.37/30.11 tff(573,plain,
% 46.37/30.11 (not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) = implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.11 inference(transitivity,[status(thm)],[572, 565, 562, 561])).
% 46.37/30.11 tff(574,plain,
% 46.37/30.11 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.11 inference(quant_inst,[status(thm)],[])).
% 46.37/30.11 tff(575,plain,
% 46.37/30.11 (implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))) = not(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.11 inference(unit_resolution,[status(thm)],[574, 175])).
% 46.37/30.11 tff(576,plain,
% 46.37/30.11 (not(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))) = implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.11 inference(symmetry,[status(thm)],[575])).
% 46.37/30.11 tff(577,plain,
% 46.37/30.11 (implies(not(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))), not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))) = implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.11 inference(monotonicity,[status(thm)],[576, 573])).
% 46.37/30.11 tff(578,plain,
% 46.37/30.11 (implies(not(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))), not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))) = or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.11 inference(transitivity,[status(thm)],[577, 560, 554])).
% 46.37/30.11 tff(579,plain,
% 46.37/30.11 (implies(implies(not(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))), not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))), implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))) = implies(or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.12 inference(monotonicity,[status(thm)],[578])).
% 46.37/30.12 tff(580,plain,
% 46.37/30.12 (is_a_theorem(implies(implies(not(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))), not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))), implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))))) <=> is_a_theorem(implies(or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))))),
% 46.37/30.12 inference(monotonicity,[status(thm)],[579])).
% 46.37/30.12 tff(581,plain,
% 46.37/30.12 ((~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) | is_a_theorem(implies(implies(not(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))), not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))), implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))))),
% 46.37/30.12 inference(quant_inst,[status(thm)],[])).
% 46.37/30.12 tff(582,plain,
% 46.37/30.12 (is_a_theorem(implies(implies(not(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))), not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))), implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))))),
% 46.37/30.12 inference(unit_resolution,[status(thm)],[581, 138])).
% 46.37/30.12 tff(583,plain,
% 46.37/30.12 (is_a_theorem(implies(or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))))),
% 46.37/30.12 inference(modus_ponens,[status(thm)],[582, 580])).
% 46.37/30.12 tff(584,plain,
% 46.37/30.12 (or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.12 inference(symmetry,[status(thm)],[554])).
% 46.37/30.12 tff(585,plain,
% 46.37/30.12 (is_a_theorem(or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) <=> is_a_theorem(implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.12 inference(monotonicity,[status(thm)],[584])).
% 46.37/30.12 tff(586,plain,
% 46.37/30.12 (is_a_theorem(implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))))) <=> is_a_theorem(or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.12 inference(symmetry,[status(thm)],[585])).
% 46.37/30.12 tff(587,plain,
% 46.37/30.12 (is_a_theorem(implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) <=> is_a_theorem(implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.12 inference(monotonicity,[status(thm)],[560])).
% 46.37/30.12 tff(588,plain,
% 46.37/30.12 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(Q!1, not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.12 inference(quant_inst,[status(thm)],[])).
% 46.37/30.12 tff(589,plain,
% 46.37/30.12 (implies(Q!1, not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.12 inference(unit_resolution,[status(thm)],[588, 20])).
% 46.37/30.12 tff(590,plain,
% 46.37/30.12 (implies(implies(Q!1, not(and(not(Q!1), not(or(P!2, R!0))))), implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) = implies(or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0))))), implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.12 inference(monotonicity,[status(thm)],[589])).
% 46.37/30.12 tff(591,plain,
% 46.37/30.12 (is_a_theorem(implies(implies(Q!1, not(and(not(Q!1), not(or(P!2, R!0))))), implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0)))))))) <=> is_a_theorem(implies(or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0))))), implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.12 inference(monotonicity,[status(thm)],[590])).
% 46.37/30.12 tff(592,plain,
% 46.37/30.12 ((~![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))) | is_a_theorem(implies(implies(Q!1, not(and(not(Q!1), not(or(P!2, R!0))))), implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.12 inference(quant_inst,[status(thm)],[])).
% 46.37/30.12 tff(593,plain,
% 46.37/30.12 (is_a_theorem(implies(implies(Q!1, not(and(not(Q!1), not(or(P!2, R!0))))), implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.12 inference(unit_resolution,[status(thm)],[592, 73])).
% 46.37/30.12 tff(594,plain,
% 46.37/30.12 (is_a_theorem(implies(or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0))))), implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.12 inference(modus_ponens,[status(thm)],[593, 591])).
% 46.37/30.12 tff(595,plain,
% 46.37/30.12 (or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0))))) = implies(Q!1, not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.12 inference(symmetry,[status(thm)],[589])).
% 46.37/30.12 tff(596,plain,
% 46.37/30.12 (is_a_theorem(or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0)))))) <=> is_a_theorem(implies(Q!1, not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.12 inference(monotonicity,[status(thm)],[595])).
% 46.37/30.12 tff(597,plain,
% 46.37/30.12 (is_a_theorem(implies(Q!1, not(and(not(Q!1), not(or(P!2, R!0)))))) <=> is_a_theorem(or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.12 inference(symmetry,[status(thm)],[596])).
% 46.37/30.12 tff(598,plain,
% 46.37/30.12 (implies(Q!1, or(Q!1, or(P!2, R!0))) = implies(Q!1, not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.12 inference(monotonicity,[status(thm)],[146])).
% 46.37/30.12 tff(599,plain,
% 46.37/30.12 (is_a_theorem(implies(Q!1, or(Q!1, or(P!2, R!0)))) <=> is_a_theorem(implies(Q!1, not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.12 inference(monotonicity,[status(thm)],[598])).
% 46.37/30.12 tff(600,plain,
% 46.37/30.12 ((~![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))) | is_a_theorem(implies(Q!1, or(Q!1, or(P!2, R!0))))),
% 46.37/30.12 inference(quant_inst,[status(thm)],[])).
% 46.37/30.12 tff(601,plain,
% 46.37/30.12 (is_a_theorem(implies(Q!1, or(Q!1, or(P!2, R!0))))),
% 46.37/30.12 inference(unit_resolution,[status(thm)],[600, 411])).
% 46.37/30.12 tff(602,plain,
% 46.37/30.12 (is_a_theorem(implies(Q!1, not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.12 inference(modus_ponens,[status(thm)],[601, 599])).
% 46.37/30.12 tff(603,plain,
% 46.37/30.12 (is_a_theorem(or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.12 inference(modus_ponens,[status(thm)],[602, 597])).
% 46.37/30.12 tff(604,plain,
% 46.37/30.12 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0))))), implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0))))), implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.37/30.12 inference(rewrite,[status(thm)],[])).
% 46.37/30.12 tff(605,plain,
% 46.37/30.12 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0))))), implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.37/30.12 inference(quant_inst,[status(thm)],[])).
% 46.37/30.12 tff(606,plain,
% 46.37/30.12 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0))))), implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0)))))))))),
% 46.37/30.12 inference(modus_ponens,[status(thm)],[605, 604])).
% 46.37/30.12 tff(607,plain,
% 46.37/30.12 (is_a_theorem(implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(Q!1), not(and(not(Q!1), not(or(P!2, R!0))))), implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0)))))))))),
% 46.37/30.12 inference(unit_resolution,[status(thm)],[606, 274])).
% 46.37/30.12 tff(608,plain,
% 46.37/30.12 (is_a_theorem(implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), implies(or(Q!1, R!0), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.12 inference(unit_resolution,[status(thm)],[607, 603, 594])).
% 46.37/30.12 tff(609,plain,
% 46.37/30.12 (is_a_theorem(implies(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.12 inference(modus_ponens,[status(thm)],[608, 587])).
% 46.37/30.12 tff(610,plain,
% 46.37/30.12 (is_a_theorem(or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.12 inference(modus_ponens,[status(thm)],[609, 586])).
% 46.37/30.12 tff(611,plain,
% 46.37/30.12 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))))))),
% 46.37/30.12 inference(rewrite,[status(thm)],[])).
% 46.37/30.12 tff(612,plain,
% 46.37/30.12 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))))))),
% 46.37/30.12 inference(quant_inst,[status(thm)],[])).
% 46.37/30.12 tff(613,plain,
% 46.37/30.12 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.37/30.12 inference(modus_ponens,[status(thm)],[612, 611])).
% 46.37/30.12 tff(614,plain,
% 46.37/30.12 (is_a_theorem(implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(not(and(not(Q!1), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.37/30.12 inference(unit_resolution,[status(thm)],[613, 274, 610])).
% 46.37/30.12 tff(615,plain,
% 46.37/30.12 (is_a_theorem(implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.12 inference(unit_resolution,[status(thm)],[614, 583])).
% 46.37/30.12 tff(616,plain,
% 46.37/30.12 (is_a_theorem(implies(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.12 inference(modus_ponens,[status(thm)],[615, 552])).
% 46.37/30.12 tff(617,plain,
% 46.37/30.12 (is_a_theorem(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.12 inference(modus_ponens,[status(thm)],[616, 546])).
% 46.37/30.12 tff(618,plain,
% 46.37/30.12 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))) | (~is_a_theorem(implies(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))) | (~is_a_theorem(implies(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))))),
% 46.37/30.12 inference(rewrite,[status(thm)],[])).
% 46.37/30.12 tff(619,plain,
% 46.37/30.12 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))) | (~is_a_theorem(implies(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))))),
% 46.37/30.12 inference(quant_inst,[status(thm)],[])).
% 46.37/30.12 tff(620,plain,
% 46.37/30.12 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))) | (~is_a_theorem(implies(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.12 inference(modus_ponens,[status(thm)],[619, 618])).
% 46.37/30.12 tff(621,plain,
% 46.37/30.12 (is_a_theorem(implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))) | (~is_a_theorem(implies(or(not(not(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.12 inference(unit_resolution,[status(thm)],[620, 274])).
% 46.37/30.12 tff(622,plain,
% 46.37/30.12 (is_a_theorem(implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.12 inference(unit_resolution,[status(thm)],[621, 617, 543])).
% 46.37/30.12 tff(623,plain,
% 46.37/30.12 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) = or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.12 inference(quant_inst,[status(thm)],[])).
% 46.37/30.12 tff(624,plain,
% 46.37/30.12 (implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) = or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.12 inference(unit_resolution,[status(thm)],[623, 20])).
% 46.37/30.12 tff(625,plain,
% 46.37/30.12 (implies(implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))) = implies(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.12 inference(monotonicity,[status(thm)],[624])).
% 46.37/30.12 tff(626,plain,
% 46.37/30.12 (implies(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))) = implies(implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.13 inference(symmetry,[status(thm)],[625])).
% 46.37/30.13 tff(627,plain,
% 46.37/30.13 (is_a_theorem(implies(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))))) <=> is_a_theorem(implies(implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[626])).
% 46.37/30.13 tff(628,plain,
% 46.37/30.13 (is_a_theorem(implies(implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))))) <=> is_a_theorem(implies(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.13 inference(symmetry,[status(thm)],[627])).
% 46.37/30.13 tff(629,plain,
% 46.37/30.13 ((~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) | is_a_theorem(implies(implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.13 inference(quant_inst,[status(thm)],[])).
% 46.37/30.13 tff(630,plain,
% 46.37/30.13 (is_a_theorem(implies(implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.13 inference(unit_resolution,[status(thm)],[629, 138])).
% 46.37/30.13 tff(631,plain,
% 46.37/30.13 (is_a_theorem(implies(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.13 inference(modus_ponens,[status(thm)],[630, 628])).
% 46.37/30.13 tff(632,plain,
% 46.37/30.13 (or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) = implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.13 inference(symmetry,[status(thm)],[624])).
% 46.37/30.13 tff(633,plain,
% 46.37/30.13 (is_a_theorem(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))) <=> is_a_theorem(implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[632])).
% 46.37/30.13 tff(634,plain,
% 46.37/30.13 (is_a_theorem(implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))) <=> is_a_theorem(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.13 inference(symmetry,[status(thm)],[633])).
% 46.37/30.13 tff(635,plain,
% 46.37/30.13 (implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) = implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[550])).
% 46.37/30.13 tff(636,plain,
% 46.37/30.13 (or(not(or(P!2, R!0)), not(not(or(Q!1, or(P!2, R!0))))) = or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[181])).
% 46.37/30.13 tff(637,plain,
% 46.37/30.13 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(P!2, R!0)), not(not(or(Q!1, or(P!2, R!0))))) = not(and(not(not(or(P!2, R!0))), not(not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.13 inference(quant_inst,[status(thm)],[])).
% 46.37/30.13 tff(638,plain,
% 46.37/30.13 (or(not(or(P!2, R!0)), not(not(or(Q!1, or(P!2, R!0))))) = not(and(not(not(or(P!2, R!0))), not(not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.13 inference(unit_resolution,[status(thm)],[637, 41])).
% 46.37/30.13 tff(639,plain,
% 46.37/30.13 (not(and(not(not(or(P!2, R!0))), not(not(not(or(Q!1, or(P!2, R!0))))))) = or(not(or(P!2, R!0)), not(not(or(Q!1, or(P!2, R!0)))))),
% 46.37/30.13 inference(symmetry,[status(thm)],[638])).
% 46.37/30.13 tff(640,plain,
% 46.37/30.13 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(or(P!2, R!0))), not(not(or(Q!1, or(P!2, R!0))))) = not(and(not(not(or(P!2, R!0))), not(not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.13 inference(quant_inst,[status(thm)],[])).
% 46.37/30.13 tff(641,plain,
% 46.37/30.13 (implies(not(not(or(P!2, R!0))), not(not(or(Q!1, or(P!2, R!0))))) = not(and(not(not(or(P!2, R!0))), not(not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.13 inference(unit_resolution,[status(thm)],[640, 175])).
% 46.37/30.13 tff(642,plain,
% 46.37/30.13 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(not(or(P!2, R!0))), not(not(or(Q!1, or(P!2, R!0))))) = or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.37/30.13 inference(quant_inst,[status(thm)],[])).
% 46.37/30.13 tff(643,plain,
% 46.37/30.13 (implies(not(not(or(P!2, R!0))), not(not(or(Q!1, or(P!2, R!0))))) = or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0)))))),
% 46.37/30.13 inference(unit_resolution,[status(thm)],[642, 20])).
% 46.37/30.13 tff(644,plain,
% 46.37/30.13 (or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0))))) = implies(not(not(or(P!2, R!0))), not(not(or(Q!1, or(P!2, R!0)))))),
% 46.37/30.13 inference(symmetry,[status(thm)],[643])).
% 46.37/30.13 tff(645,plain,
% 46.37/30.13 (or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0))))) = or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))),
% 46.37/30.13 inference(transitivity,[status(thm)],[644, 641, 639, 636])).
% 46.37/30.13 tff(646,plain,
% 46.37/30.13 (not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) = not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[645])).
% 46.37/30.13 tff(647,plain,
% 46.37/30.13 (and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))) = not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.37/30.13 inference(transitivity,[status(thm)],[186, 189, 646])).
% 46.37/30.13 tff(648,plain,
% 46.37/30.13 (implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))) = implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[647])).
% 46.37/30.13 tff(649,plain,
% 46.37/30.13 (and(R!0, not(or(Q!1, or(P!2, R!0)))) = and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.13 inference(symmetry,[status(thm)],[549])).
% 46.37/30.13 tff(650,plain,
% 46.37/30.13 (not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))) = and(R!0, not(or(Q!1, or(P!2, R!0))))),
% 46.37/30.13 inference(symmetry,[status(thm)],[548])).
% 46.37/30.13 tff(651,plain,
% 46.37/30.13 (not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))) = and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.13 inference(transitivity,[status(thm)],[650, 649])).
% 46.37/30.13 tff(652,plain,
% 46.37/30.13 (implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) = implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[651, 191])).
% 46.37/30.13 tff(653,plain,
% 46.37/30.13 (implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) = implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.13 inference(transitivity,[status(thm)],[652, 648, 635])).
% 46.37/30.13 tff(654,plain,
% 46.37/30.13 (is_a_theorem(implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))) <=> is_a_theorem(implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[653])).
% 46.37/30.13 tff(655,plain,
% 46.37/30.13 (implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))) = implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.13 inference(symmetry,[status(thm)],[652])).
% 46.37/30.13 tff(656,plain,
% 46.37/30.13 (is_a_theorem(implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))) <=> is_a_theorem(implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(not(or(P!2, R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[655])).
% 46.37/30.13 tff(657,plain,
% 46.37/30.13 (is_a_theorem(implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))) <=> is_a_theorem(implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.13 inference(transitivity,[status(thm)],[656, 654])).
% 46.37/30.13 tff(658,plain,
% 46.37/30.13 (implies(not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))), not(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))) = implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[203, 576])).
% 46.37/30.13 tff(659,plain,
% 46.37/30.13 (implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))), not(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.13 inference(symmetry,[status(thm)],[658])).
% 46.37/30.13 tff(660,plain,
% 46.37/30.13 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.13 inference(quant_inst,[status(thm)],[])).
% 46.37/30.13 tff(661,plain,
% 46.37/30.13 (implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))) = or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))),
% 46.37/30.13 inference(unit_resolution,[status(thm)],[660, 20])).
% 46.37/30.13 tff(662,plain,
% 46.37/30.13 (implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[661])).
% 46.37/30.13 tff(663,plain,
% 46.37/30.13 (implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.13 inference(symmetry,[status(thm)],[662])).
% 46.37/30.13 tff(664,plain,
% 46.37/30.13 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))) = or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.13 inference(quant_inst,[status(thm)],[])).
% 46.37/30.13 tff(665,plain,
% 46.37/30.13 (implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))) = or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.13 inference(unit_resolution,[status(thm)],[664, 20])).
% 46.37/30.13 tff(666,plain,
% 46.37/30.13 (or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.13 inference(symmetry,[status(thm)],[665])).
% 46.37/30.13 tff(667,plain,
% 46.37/30.13 (or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))), not(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.13 inference(transitivity,[status(thm)],[666, 663, 659])).
% 46.37/30.13 tff(668,plain,
% 46.37/30.13 (implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))) = implies(implies(not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))), not(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))), implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[667])).
% 46.37/30.13 tff(669,plain,
% 46.37/30.13 (implies(implies(not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))), not(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))), implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))) = implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.13 inference(symmetry,[status(thm)],[668])).
% 46.37/30.13 tff(670,plain,
% 46.37/30.13 (is_a_theorem(implies(implies(not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))), not(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))), implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))))) <=> is_a_theorem(implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[669])).
% 46.37/30.13 tff(671,plain,
% 46.37/30.13 ((~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) | is_a_theorem(implies(implies(not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))), not(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))), implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))))),
% 46.37/30.13 inference(quant_inst,[status(thm)],[])).
% 46.37/30.13 tff(672,plain,
% 46.37/30.13 (is_a_theorem(implies(implies(not(and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))), not(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))))), implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))))),
% 46.37/30.13 inference(unit_resolution,[status(thm)],[671, 138])).
% 46.37/30.13 tff(673,plain,
% 46.37/30.13 (is_a_theorem(implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))))),
% 46.37/30.13 inference(modus_ponens,[status(thm)],[672, 670])).
% 46.37/30.13 tff(674,plain,
% 46.37/30.13 (implies(implies(not(and(not(P!2), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))) = implies(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[179])).
% 46.37/30.13 tff(675,plain,
% 46.37/30.13 (implies(implies(not(and(not(P!2), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))) = or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))),
% 46.37/30.13 inference(transitivity,[status(thm)],[674, 662, 665])).
% 46.37/30.13 tff(676,plain,
% 46.37/30.13 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(R!0, not(and(not(P!2), not(R!0)))) = or(not(R!0), not(and(not(P!2), not(R!0)))))),
% 46.37/30.13 inference(quant_inst,[status(thm)],[])).
% 46.37/30.13 tff(677,plain,
% 46.37/30.13 (implies(R!0, not(and(not(P!2), not(R!0)))) = or(not(R!0), not(and(not(P!2), not(R!0))))),
% 46.37/30.13 inference(unit_resolution,[status(thm)],[676, 20])).
% 46.37/30.13 tff(678,plain,
% 46.37/30.13 (implies(implies(R!0, not(and(not(P!2), not(R!0)))), implies(implies(not(and(not(P!2), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))))) = implies(or(not(R!0), not(and(not(P!2), not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[677, 675])).
% 46.37/30.13 tff(679,plain,
% 46.37/30.13 (is_a_theorem(implies(implies(R!0, not(and(not(P!2), not(R!0)))), implies(implies(not(and(not(P!2), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(R!0, not(and(not(Q!1), not(or(P!2, R!0)))))))) <=> is_a_theorem(implies(or(not(R!0), not(and(not(P!2), not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[678])).
% 46.37/30.13 tff(680,plain,
% 46.37/30.13 ((~![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) | is_a_theorem(implies(implies(R!0, not(and(not(P!2), not(R!0)))), implies(implies(not(and(not(P!2), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.13 inference(quant_inst,[status(thm)],[])).
% 46.37/30.13 tff(681,plain,
% 46.37/30.13 (is_a_theorem(implies(implies(R!0, not(and(not(P!2), not(R!0)))), implies(implies(not(and(not(P!2), not(R!0))), not(and(not(Q!1), not(or(P!2, R!0))))), implies(R!0, not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.13 inference(unit_resolution,[status(thm)],[680, 389])).
% 46.37/30.13 tff(682,plain,
% 46.37/30.13 (is_a_theorem(implies(or(not(R!0), not(and(not(P!2), not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.13 inference(modus_ponens,[status(thm)],[681, 679])).
% 46.37/30.13 tff(683,plain,
% 46.37/30.13 (or(not(R!0), not(and(not(P!2), not(R!0)))) = implies(R!0, not(and(not(P!2), not(R!0))))),
% 46.37/30.13 inference(symmetry,[status(thm)],[677])).
% 46.37/30.13 tff(684,plain,
% 46.37/30.13 (is_a_theorem(or(not(R!0), not(and(not(P!2), not(R!0))))) <=> is_a_theorem(implies(R!0, not(and(not(P!2), not(R!0)))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[683])).
% 46.37/30.13 tff(685,plain,
% 46.37/30.13 (is_a_theorem(implies(R!0, not(and(not(P!2), not(R!0))))) <=> is_a_theorem(or(not(R!0), not(and(not(P!2), not(R!0)))))),
% 46.37/30.13 inference(symmetry,[status(thm)],[684])).
% 46.37/30.13 tff(686,plain,
% 46.37/30.13 (implies(R!0, or(P!2, R!0)) = implies(R!0, not(and(not(P!2), not(R!0))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[110])).
% 46.37/30.13 tff(687,plain,
% 46.37/30.13 (is_a_theorem(implies(R!0, or(P!2, R!0))) <=> is_a_theorem(implies(R!0, not(and(not(P!2), not(R!0)))))),
% 46.37/30.13 inference(monotonicity,[status(thm)],[686])).
% 46.37/30.13 tff(688,plain,
% 46.37/30.13 ((~![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) | is_a_theorem(implies(R!0, or(P!2, R!0)))),
% 46.37/30.14 inference(quant_inst,[status(thm)],[])).
% 46.37/30.14 tff(689,plain,
% 46.37/30.14 (is_a_theorem(implies(R!0, or(P!2, R!0)))),
% 46.37/30.14 inference(unit_resolution,[status(thm)],[688, 244])).
% 46.37/30.14 tff(690,plain,
% 46.37/30.14 (is_a_theorem(implies(R!0, not(and(not(P!2), not(R!0)))))),
% 46.37/30.14 inference(modus_ponens,[status(thm)],[689, 687])).
% 46.37/30.14 tff(691,plain,
% 46.37/30.14 (is_a_theorem(or(not(R!0), not(and(not(P!2), not(R!0)))))),
% 46.37/30.14 inference(modus_ponens,[status(thm)],[690, 685])).
% 46.37/30.14 tff(692,plain,
% 46.37/30.14 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(R!0), not(and(not(P!2), not(R!0)))))) | is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(R!0), not(and(not(P!2), not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(R!0), not(and(not(P!2), not(R!0)))))) | is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(R!0), not(and(not(P!2), not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.37/30.14 inference(rewrite,[status(thm)],[])).
% 46.37/30.14 tff(693,plain,
% 46.37/30.14 ((is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(or(not(R!0), not(and(not(P!2), not(R!0)))))) | (~is_a_theorem(implies(or(not(R!0), not(and(not(P!2), not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))))))) <=> ((~is_a_theorem(or(not(R!0), not(and(not(P!2), not(R!0)))))) | is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(R!0), not(and(not(P!2), not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.37/30.14 inference(rewrite,[status(thm)],[])).
% 46.37/30.14 tff(694,plain,
% 46.37/30.14 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(or(not(R!0), not(and(not(P!2), not(R!0)))))) | (~is_a_theorem(implies(or(not(R!0), not(and(not(P!2), not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(R!0), not(and(not(P!2), not(R!0)))))) | is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(R!0), not(and(not(P!2), not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))))))))),
% 46.37/30.14 inference(monotonicity,[status(thm)],[693])).
% 46.37/30.14 tff(695,plain,
% 46.37/30.14 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(or(not(R!0), not(and(not(P!2), not(R!0)))))) | (~is_a_theorem(implies(or(not(R!0), not(and(not(P!2), not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(R!0), not(and(not(P!2), not(R!0)))))) | is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(R!0), not(and(not(P!2), not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.37/30.14 inference(transitivity,[status(thm)],[694, 692])).
% 46.37/30.14 tff(696,plain,
% 46.37/30.14 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(or(not(R!0), not(and(not(P!2), not(R!0)))))) | (~is_a_theorem(implies(or(not(R!0), not(and(not(P!2), not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.37/30.14 inference(quant_inst,[status(thm)],[])).
% 46.37/30.14 tff(697,plain,
% 46.37/30.14 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(R!0), not(and(not(P!2), not(R!0)))))) | is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(R!0), not(and(not(P!2), not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))))))),
% 46.37/30.14 inference(modus_ponens,[status(thm)],[696, 695])).
% 46.37/30.14 tff(698,plain,
% 46.37/30.14 (is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(R!0), not(and(not(P!2), not(R!0)))), or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))))))),
% 46.37/30.14 inference(unit_resolution,[status(thm)],[697, 274, 691])).
% 46.37/30.14 tff(699,plain,
% 46.37/30.14 (is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))))),
% 46.37/30.14 inference(unit_resolution,[status(thm)],[698, 682])).
% 46.37/30.14 tff(700,plain,
% 46.37/30.14 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))))))),
% 46.37/30.14 inference(rewrite,[status(thm)],[])).
% 46.37/30.14 tff(701,plain,
% 46.37/30.14 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))))))),
% 46.37/30.14 inference(quant_inst,[status(thm)],[])).
% 46.37/30.14 tff(702,plain,
% 46.37/30.14 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.37/30.14 inference(modus_ponens,[status(thm)],[701, 700])).
% 46.37/30.14 tff(703,plain,
% 46.37/30.14 (is_a_theorem(implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(not(P!2), not(R!0)))), not(and(not(Q!1), not(or(P!2, R!0)))))), or(not(R!0), not(and(not(Q!1), not(or(P!2, R!0)))))), implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))))))),
% 46.37/30.14 inference(unit_resolution,[status(thm)],[702, 274])).
% 46.37/30.14 tff(704,plain,
% 46.37/30.14 (is_a_theorem(implies(and(R!0, not(not(and(not(Q!1), not(or(P!2, R!0)))))), and(not(not(or(P!2, R!0))), not(not(and(not(Q!1), not(or(P!2, R!0))))))))),
% 46.37/30.14 inference(unit_resolution,[status(thm)],[703, 699, 673])).
% 46.37/30.14 tff(705,plain,
% 46.37/30.14 (is_a_theorem(implies(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.14 inference(modus_ponens,[status(thm)],[704, 657])).
% 46.37/30.14 tff(706,plain,
% 46.37/30.14 (is_a_theorem(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.14 inference(modus_ponens,[status(thm)],[705, 634])).
% 46.37/30.14 tff(707,plain,
% 46.37/30.14 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))) | (~is_a_theorem(implies(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))) | (~is_a_theorem(implies(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))))),
% 46.37/30.14 inference(rewrite,[status(thm)],[])).
% 46.37/30.14 tff(708,plain,
% 46.37/30.14 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))) | (~is_a_theorem(implies(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))))),
% 46.37/30.14 inference(quant_inst,[status(thm)],[])).
% 46.37/30.14 tff(709,plain,
% 46.37/30.14 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))) | (~is_a_theorem(implies(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.14 inference(modus_ponens,[status(thm)],[708, 707])).
% 46.37/30.14 tff(710,plain,
% 46.37/30.14 (is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))) | (~is_a_theorem(implies(or(not(not(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))), not(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))), implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.14 inference(unit_resolution,[status(thm)],[709, 274])).
% 46.37/30.14 tff(711,plain,
% 46.37/30.14 (is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.14 inference(unit_resolution,[status(thm)],[710, 706, 631])).
% 46.37/30.14 tff(712,plain,
% 46.37/30.14 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.14 inference(rewrite,[status(thm)],[])).
% 46.37/30.14 tff(713,plain,
% 46.37/30.14 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.14 inference(quant_inst,[status(thm)],[])).
% 46.37/30.14 tff(714,plain,
% 46.37/30.14 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.14 inference(modus_ponens,[status(thm)],[713, 712])).
% 46.37/30.14 tff(715,plain,
% 46.37/30.14 (is_a_theorem(or(not(R!0), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(P!2), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.14 inference(unit_resolution,[status(thm)],[714, 274])).
% 46.37/30.14 tff(716,plain,
% 46.37/30.14 (is_a_theorem(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.37/30.14 inference(unit_resolution,[status(thm)],[715, 325, 711])).
% 46.37/30.14 tff(717,plain,
% 46.37/30.14 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.14 inference(rewrite,[status(thm)],[])).
% 46.37/30.14 tff(718,plain,
% 46.37/30.14 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.14 inference(quant_inst,[status(thm)],[])).
% 46.37/30.14 tff(719,plain,
% 46.37/30.14 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.14 inference(modus_ponens,[status(thm)],[718, 717])).
% 46.37/30.14 tff(720,plain,
% 46.37/30.14 (is_a_theorem(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(R!0), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.14 inference(unit_resolution,[status(thm)],[719, 274])).
% 46.37/30.14 tff(721,plain,
% 46.37/30.14 (is_a_theorem(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))),
% 46.37/30.14 inference(unit_resolution,[status(thm)],[720, 716, 622])).
% 46.37/30.14 tff(722,plain,
% 46.37/30.14 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0)))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.15 inference(rewrite,[status(thm)],[])).
% 46.37/30.15 tff(723,plain,
% 46.37/30.15 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.15 inference(quant_inst,[status(thm)],[])).
% 46.37/30.15 tff(724,plain,
% 46.37/30.15 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.15 inference(modus_ponens,[status(thm)],[723, 722])).
% 46.37/30.15 tff(725,plain,
% 46.37/30.15 (is_a_theorem(or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0)))))) | (~is_a_theorem(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))))),
% 46.37/30.15 inference(unit_resolution,[status(thm)],[724, 274])).
% 46.37/30.15 tff(726,plain,
% 46.37/30.15 (~is_a_theorem(implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0)))))))),
% 46.37/30.15 inference(unit_resolution,[status(thm)],[725, 721, 534])).
% 46.37/30.15 tff(727,plain,
% 46.37/30.15 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) | is_a_theorem(implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))), implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) | is_a_theorem(implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))), implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))))))),
% 46.37/30.15 inference(rewrite,[status(thm)],[])).
% 46.37/30.15 tff(728,plain,
% 46.37/30.15 ((is_a_theorem(implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))), implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0)))))))))) <=> ((~is_a_theorem(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) | is_a_theorem(implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))), implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))))))),
% 46.37/30.15 inference(rewrite,[status(thm)],[])).
% 46.37/30.15 tff(729,plain,
% 46.37/30.15 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))), implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) | is_a_theorem(implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))), implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0)))))))))))),
% 46.37/30.15 inference(monotonicity,[status(thm)],[728])).
% 46.37/30.15 tff(730,plain,
% 46.37/30.15 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))), implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) | is_a_theorem(implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))), implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))))))),
% 46.37/30.15 inference(transitivity,[status(thm)],[729, 727])).
% 46.37/30.15 tff(731,plain,
% 46.37/30.15 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))), implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))))))),
% 46.37/30.15 inference(quant_inst,[status(thm)],[])).
% 46.37/30.15 tff(732,plain,
% 46.37/30.15 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) | is_a_theorem(implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))), implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.37/30.15 inference(modus_ponens,[status(thm)],[731, 730])).
% 46.37/30.15 tff(733,plain,
% 46.37/30.15 ((~is_a_theorem(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))))) | is_a_theorem(implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(or(Q!1, or(P!2, R!0))))), implies(or(not(not(and(not(Q!1), not(R!0)))), not(not(or(Q!1, or(P!2, R!0))))), or(not(not(and(not(P!2), not(or(Q!1, R!0))))), not(not(or(Q!1, or(P!2, R!0)))))))))),
% 46.53/30.23 inference(unit_resolution,[status(thm)],[732, 274])).
% 46.53/30.23 tff(734,plain,
% 46.53/30.23 ($false),
% 46.53/30.23 inference(unit_resolution,[status(thm)],[733, 726, 439, 76])).
% 46.53/30.23 % SZS output end Proof
%------------------------------------------------------------------------------